History of scientific ideas

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Title: History of scientific ideas
Author: Whewell, William
Language: English
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*** Start of this LibraryBlog Digital Book "History of scientific ideas" ***
IDEAS ***

HISTORY
OF
SCIENTIFIC IDEAS.

VOLUME I.

Cambridge;
PRINTED BY C. J. CLAY, M.A.
AT THE UNIVERSITY PRESS.

HISTORY
OF
SCIENTIFIC IDEAS.

BY WILLIAM WHEWELL, D.D.,
MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.

BEING THE FIRST PART OF THE PHILOSOPHY
OF THE INDUCTIVE SCIENCES.

_THE THIRD EDITION._

IN TWO VOLUMES.

ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ

VOLUME I.

LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1858.

{{v}}
PREFACE TO THIS EDITION.

THE Chapters now offered to the Reader were formerly
published as a portion of _The Philosophy of the Inductive
Sciences, founded upon their History_: but the nature and
subject of these Chapters are more exactly described by the
present title, _The History of Scientific Ideas_. For this
part of the work is mainly historical, and was, in fact,
collected from the body of scientific literature, at the
same time that the _History of the Inductive Sciences_ was
so collected. The present work contains the history of
Science so far as it depends on _Ideas_; the former work
contains the same history so far as it is derived from
_Observation_. The leading features in _that_ were Theories
inferred from Facts; the leading features of _this_ are
Discussions of Theories tending to make them consistent with
the conditions of human thought.

The Ideas of which the History is here given are mainly the
following:
_Space_, _Time_, _Number_, _Motion_, _Cause_, _Force_,
_Matter_, _Medium_, _Intensity_, _Scale_, _Polarity_,
_Element_, _Affinity_, _Substance_, _Atom_, _Symmetry_,
_Likeness_, _Natural Classes_, _Species_, _Life_,
_Function_, _Vital Forces_, _Final_ {vi} _Causes_,
_Historical Causation_, _Catastrophe and Uniformity_, _First
Cause_.

The controversies to which the exact fixation of these Ideas
and their properties have given occasion form a large and
essential part of the History of Science: but they also form
an important part of the Philosophy of Science, for no
Philosophy of Science can be complete which does not solve
the difficulties, antitheses, and paradoxes on which such
controversies have turned. I have given a survey of such
controversies, generally carried from their earliest origin
to their latest aspect; and have stated what appeared to me
the best solution of each problem. This has necessarily
involved me in much thorny metaphysics; but such metaphysics
is a necessary part of the progress of Science. The human
mind deriving its knowledge of Truth from the observation of
nature, cannot evade the task of determining at every step
how Truth is consistent with itself. This is the Metaphysics
of Progressive Knowledge, and this is the matter of this
present History.

Of the remaining part of what was formerly published as the
Philosophy of the Inductive Sciences, an additional part,
described in the Introduction to the present work, will
shortly be published.

TRINITY LODGE,
_May_ 24, 1858.

ERRATUM, p. 157, l. 11 from top, _for_ sciences
_read_ science.

CONTENTS
OF
THE FIRST VOLUME.

PAGE
PREFACE v

PART I.
OF IDEAS.

INTRODUCTION 3

BOOK I.

OF IDEAS IN GENERAL.

CHAP. I. OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY 23

_Sect._ 1. _Thoughts and Things_ --
2. _Necessary and Experiential Truths_ 25
3. _Deduction and Induction_ 27
4. _Theories and Facts_ 29
5. _Ideas and Sensations_ 30
6. _Reflexion and Sensation_ 33
7. _Subjective and Objective_ 35
8. _Matter and Form_ 38
9. _Man the Interpreter of Nature_ 41
10. _The Fundamental Antithesis is inseparable_ 43
11. _Successive Generalization_ 49
{viii}

CHAP. II. OF TECHNICAL TERMS 54

_Art._ 1. Examples.
2. Use of Terms.

CHAP. III. OF NECESSARY TRUTHS 57

_Art._ 1. The two Elements of Knowledge,
2. Shown by necessary Truths.
3. Examples of necessary Truths in numbers.
4. The opposite cannot be distinctly conceived.
5. Other Examples.
6. Universal Truths.

CHAP. IV. OF EXPERIENCE 65

_Art._ 1. Experience cannot prove necessary Truths,
2. Except when aided by Ideas.

CHAP. V. OF THE GROUNDS OF NECESSARY TRUTHS 69

_Art._ 1. These Grounds are Fundamental Ideas.
2. These are to be reviewed.
3. Definitions and Axioms.
4. Syllogism,
5. Produces no new Truths.
6. Axioms needed.
7. Axioms depend on Ideas:
8. So do Definitions.
9. Idea not completely expressed.

CHAP. VI. THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE 76

_Art._ 1. No connexion observed.
2. Faculties implied in observation.
3. We are to examine our Faculties.

CHAP. VII. OF THE PHILOSOPHY OF THE SCIENCES 81

Sciences arranged according to Ideas.
{ix}

BOOK II.

THE PHILOSOPHY OF THE PURE SCIENCES.

CHAP. I. OF THE PURE SCIENCES 88

_Art._ 1. Geometry, Arithmetic, Algebra,
2. Are not Inductive Sciences:
3. Are Mathematical Sciences.
4. Mixed Mathematics.
5. Space, Time, Number.

CHAP. II. OF THE IDEA OF SPACE 91

_Art._ 1. Space is an Idea,
2. Not derived from Experience,
3. As Geometrical Truth shows.
4. Space is a Form of Experience.
5. The phrase not essential.

CHAP. III. OF SOME PECULIARITIES OF THE IDEA OF SPACE 95

_Art._ 1. Space is not an Abstract Notion.
2. Space is infinite.
3. Space is real.
4. Space is a Form of Intuition.
5. Figure.
6. Three Dimensions.

CHAP. IV. OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE 98

_Art._ 1. Geometry.
2. Definitions.
3. Axioms.
4. Not Hypotheses.
5. Axioms necessary.
6. Straight Lines.
7. Planes.
8. Elementary Geometry.

CHAP. V. OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE
DOCTRINES STATED IN THE PREVIOUS CHAPTER 107

_Art._ 1. How is Geometry hypothetical?
2. What was Stewart's view?
{x}
3. 'Legitimate filiations' of Definitions.
4. Is a Definition a complete explanation?
5. Are some Axioms Definitions?
6. Axiom concerning Circles.
7. Can Axioms become truisms?
8. Use of such.

CHAP. VI. OF THE PERCEPTION OF SPACE 117

_Art._ 1. Which Senses apprehend Space?
2. Perception of solid figure.
3. Is an interpretation.
4. May be analysed.
5. Outline.
6. Reversed convexity.
7. Do we perceive Space by Touch?
8. Brown's Opinion.
9. The Muscular Sense.
10. Bell's Opinion.
11. Perception includes Activity.
12. Perception of the Skyey Dome.
13. Reid's Idomenians.
14. Motion of the Eye.
15. Searching Motion.
16. Sensible Spot.
17. Expressions implying Motion.

CHAP. VII. OF THE IDEA OF TIME 131

_Art._ 1. Time an Idea not derived from Experience.
2. Time is a Form of Experience.
3. Number.
4. Is Time derived from Motion?

CHAP. VIII. OF SOME PECULIARITIES IN THE IDEA OF TIME 134

_Art._ 1. Time is not an Abstract Notion.
2. Time is infinite.
3. Time is a Form of Intuition.
4. Time is of one Dimension,
5. And no more.
6. Rhythm.
7. Alternation.
8. Arithmetic.
{xi}

CHAP. IX. OF THE AXIOMS WHICH RELATE TO NUMBER 138

_Art._ 1. Grounds of Arithmetic.
2. Intuition.
3. Arithmetical Axioms,
4. Are Conditions of Numerical Reasoning
5. In all Arithmetical Operations.
6. Higher Numbers.

CHAP. X. OF THE PERCEPTION OF TIME AND NUMBER 141

_Art._ 1. Memory.
2. Sense of Successiveness
3. Implies Activity.
4. Number also does so.
5. And apprehension of Rhythm.
Note to Chapter X. 145

CHAP. XI. OF MATHEMATICAL REASONING 147

_Art._ 1. Discursive Reasoning.
2. Technical Terms of Reasoning.
3. Geometrical Analysis and Synthesis.

CHAP. XII. OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS 151

_Art._ 1. The Idea of a Limit.
2. The use of General Symbols.
3. Connexion of Symbols and Analysis.

CHAP. XIII. THE DOCTRINE OF MOTION 156

_Art._ 1. Pure Mechanism.
2. Formal Astronomy.

CHAP. XIV. OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE
SCIENCES 159

_Art._ 1. The Ideas of Space and Number are clear from
the first.
2. Their application in Astronomy.
3. Conic Sections, &c.
4. Arabian Numerals.
5. Newton's Lemmas.
6. Tides.
7. Mechanics.
8. Optics.
9. Conclusion.
{xii}

BOOK III.

THE PHILOSOPHY OF THE MECHANICAL SCIENCES.

CHAP. I. OF THE MECHANICAL SCIENCES 171

CHAP. II. OF THE IDEA OF CAUSE 173

_Art._ 1. Not derived from Observation,
2. As appears by its use.
3. Cause cannot be observed.
4. Is Cause only constant succession?
5. Other reasons.

CHAP. III. MODERN OPINIONS RESPECTING THE IDEA OF CAUSE 178

_Art._ 1. Hume's Doctrine.
2. Stewart and Brown.
3. Kant.
4. Relation of Kant and Brown.
5. Axioms flow from the Idea.
6. The Idea implies activity in the Mind.

CHAP. IV. OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE 184

_Art._ 1. Causes are Abstract Conceptions.
2. First Axiom.
3. Second Axiom.
4. Limitation of the Second Axiom.
5. Third Axiom.
6. Extent of the Third Axiom.

CHAP. V. OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER 205

_Art._ 1. Force.
2. Matter.
3. Solidity.
4. Inertia.
5. Application.
{xiii}

CHAP. VI. OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS 212

_Art._ 1. Object of the Chapter.
2. Statics and Dynamics.
3. Equilibrium.
4. Measure of Statical Forces.
5. The Center of Gravity.
6. Oblique Forces.
7. Force acts at any point of its Direction.
8. The Parallelogram of Forces
9. Is a necessary Truth.
10. Center of Gravity descends.
11. Stevinus's Proof.
12. Principle of Virtual Velocities.
13. Fluids press equally.
14. Foundation of this Axiom.

CHAP. VII. OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS 235

_Art._ 1. History.
2. The First Law of Motion.
3. Gravity is a Uniform Force.
4. The Second Law of Motion.
5. The Third Law of Motion.
6. Action and Reaction in Moving Bodies.
7. D'Alembert's Principle.
8. Connexion of Statics and Dynamics.
9. Mechanical Principles grow more evident.
10. Controversy of the Measure of Force.

CHAP. VIII. OF THE PARADOX OF UNIVERSAL PROPOSITIONS
OBTAINED FROM EXPERIENCE 263

_Art._ 1. Experience cannot establish necessary Truths;
2. But can interpret Axioms.
3. Gives us the Matter of Truths.
4. Exemplifies Truths.
5. Cannot shake Axioms.
6. Is this applicable in other cases?

CHAP. IX. OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL
GRAVITATION 272

_Art._ 1. General course of the History.
{xiv}
2. Particulars as to the Law.
3. As to the Gravity of Matter.
4. Universality of the Law.
5. Is Gravity an essential quality?
6. Newton's Rule of Philosophizing.
7. Hypotheses respecting Gravity.
8. Do Bodies act at a distance?

CHAP. X. OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS 279

_Art._ 1. Nature of the Process
2. Among the Ancients.
3. Kepler, &c.
4. Lord Monboddo, &c.
5. Schelling, &c.
6. Common usage.
7. Effect of Phrases.
8. Contempt of Predecessors.
9. Less detail hereafter.
10. Mechanico-Chemical Sciences.
11. Secondary Mechanical Sciences.

BOOK IV.

THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.

CHAP. I. OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED 293

_Art._ 1. Of Primary and Secondary Qualities.
2. The Idea of Externality.
3. Sensation by a Medium.
4. Process of Perception of Secondary Qualities.

CHAP. II. ON PECULIARITIES IN THE PERCEPTIONS OF THE
DIFFERENT SENSES 302

_Art._ 1. Difference of Senses.

_Sect._ I. _Prerogatives of Sight._
_Art._ 2. Position.
3. Distance.
{xv}
_Sect._ II. _Prerogatives of Hearing._
_Art._ 4. Musical Intervals.
5. Chords.
6. Rhythm.

_Sect._ III. _The Paradoxes of Vision._
_Art._ 7. First Paradox.
8. Second Paradox.
9. The same for near Objects.
10. Objections answered.

_Sect._ IV. _The Perception of Visible Figures._
_Art._ 11. Brown's Opinion.

CHAP. III. SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC
APPLICATION OF THE IDEA OF A MEDIUM 322

_Art._ 1. Introduction.
2. Sound.
3. Light.
4. Heat.

CHAP. IV. OF THE MEASURE OF SECONDARY QUALITIES 333

_Sect._ I. _Scales of Qualities in General._
_Art._ 1. Intensity.
2. Quantity and Quality.

_Sect._ II. _The Musical Scale._
_Art._ 3. Musical Relations.
4. Musical Standard.

_Sect._ III. _Scales of Colour._
_Art._ 5. The Prismatic Scale.
6. Newton's Scale.
7. Scales of Impure Colours.
8. Chromatometer.

_Sect._ IV. _Scales of Light._
_Art._ 9. Photometer.
10. Cyanometer.

_Sect._ V. _Scales of Heat._
_Art._ 11. Thermometers.
12. Their progress.
13. Fixed Points.
14. Concordance of Thermometers.
15. Natural Measure.
16. Law of Cooling.
{xvi}
17. Theory of Exchanges.
18. Air Thermometer.
19. Theory of Heat.
20. Other Instruments.

_Sect._ VI. _Scales of other Quantities._
_Art._ 21. Tastes and Smells.
22. Quality of Sounds.
23. Articulate Sounds.
24. Transition.

BOOK V.

OF THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.

CHAP. I. ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA
OF POLARITY 359

_Art._ 1. Introduction of the Idea.
2. Magnetism.
3. Electricity.
4. Voltaic Electricity.
5. Light.
6. Crystallization.
7. Chemical Affinity.
8. General Remarks.
9. Like _repels_ like.

CHAP. II. OF THE CONNEXION OF POLARITIES 371

_Art._ 1. Different Polar Phenomena from one Cause.
2. Connexion of Magnetic and Electric Polarity.
3. Ampère's Theory.
4. Faraday's views.
5. Connexion of Electrical and Chemical Polarity.
6. Davy's and Faraday's views
7. Depend upon Ideas as well as Experiments.
8. Faraday's Anticipations.
9. Connexion of Chemical and Crystalline Polarities.
10. Connexion of Crystalline and Optical Polarities.
11. Connexion of Polarities in general.
12. Schelling's Speculations.
13. Hegel's vague notions.
14. Ideas must guide Experiment.

{{1}}
THE
PHILOSOPHY
OF THE
INDUCTIVE SCIENCES.

INTRODUCTION.

{{3}}
INTRODUCTION.

THE PHILOSOPHY OF SCIENCE, if the phrase were to be
understood in the comprehensive sense which most naturally
offers itself to our thoughts, would imply nothing less than
a complete insight into the essence and conditions of all
real knowledge, and an exposition of the best methods for
the discovery of new truths. We must narrow and lower this
conception, in order to mould it into a form in which we may
make it the immediate object of our labours with a good hope
of success; yet still it may be a rational and useful
undertaking, to endeavour to make some advance towards such
a Philosophy, even according to the most ample conception of
it which we can form. The present work has been written with
a view of contributing, in some measure, however small it
may be, towards such an undertaking.

But in this, as in every attempt to advance beyond the
position which we at present occupy, our hope of success
must depend mainly upon our being able to profit, to the
fullest extent, by the progress already made. We may best
hope to understand the nature and conditions of real
knowledge, by studying the nature and conditions of the most
certain and stable portions of knowledge which we already
possess: and we are most likely to learn the best methods of
discovering truth, by examining how truths, now universally
recognized, have really been discovered. Now there do exist
among us doctrines of solid and acknowledged certainty, and
truths of which the discovery has been received with
universal applause. These constitute what we commonly term
_Sciences_; and of these bodies of exact and enduring
knowledge, we have within our {4} reach so large and varied
a collection, that we may examine them, and the history of
their formation, with a good prospect of deriving from the
study such instruction as we seek. We may best hope to make
some progress towards the Philosophy of Science, by
employing ourselves upon THE PHILOSOPHY OF THE SCIENCES.

The _Sciences_ to which the name is most commonly and
unhesitatingly given, are those which are concerned about
the material world; whether they deal with the celestial
bodies, as the sun and stars, or the earth and its products,
or the elements; whether they consider the differences which
prevail among such objects, or their origin, or their mutual
operation. And in all these Sciences it is familiarly
understood and assumed, that their doctrines are obtained by
a common process of collecting general truths from
particular observed facts, which process is termed
_Induction_. It is further assumed that both in these and in
other provinces of knowledge, so long as this process is
duly and legitimately performed, the results will be real
substantial truth. And although this process, with the
conditions under which it is legitimate, and the general
laws of the formation of Sciences, will hereafter be
subjects of discussion in this work, I shall at present so
far adopt the assumption of which I speak, as to give to the
Sciences from which our lessons are to be collected the name
of _Inductive Sciences_. And thus it is that I am led to
designate my work as THE PHILOSOPHY OF THE INDUCTIVE
SCIENCES.

The views respecting the nature and progress of knowledge,
towards which we shall be directed by such a course of
inquiry as I have pointed out, though derived from those
portions of human knowledge which are more peculiarly and
technically termed _Sciences_, will by no means be confined,
in their bearing, to the domain of such Sciences as deal
with the material world, nor even to the whole range of
Sciences now existing. On the contrary, we shall be led to
believe that the nature of truth is in all subjects the
same, and that its discovery involves, in all cases, the
like {5} conditions. On one subject of human speculation
after another, man's knowledge assumes that exact and
substantial character which leads us to term it _Science_;
and in all these cases, whether inert matter or living
bodies, whether permanent relations or successive
occurrences, be the subject of our attention, we can point
out certain universal characters which belong to truth,
certain general laws which have regulated its progress among
men. And we naturally expect that, even when we extend our
range of speculation wider still, when we contemplate the
world within us as well as the world without us, when we
consider the thoughts and actions of men as well as the
motions and operations of unintelligent bodies, we shall
still find some general analogies which belong to the
essence of truth, and run through the whole intellectual
universe. Hence we have reason to trust that a just
Philosophy of the Sciences may throw light upon the nature
and extent of our knowledge in every department of human
speculation. By considering what is the real import of our
acquisitions, where they are certain and definite, we may
learn something respecting the difference between true
knowledge and its precarious or illusory semblances; by
examining the steps by which such acquisitions have been
made, we may discover the conditions under which truth is to
be obtained; by tracing the boundary-line between our
knowledge and our ignorance, we may ascertain in some
measure the extent of the powers of man's understanding.

But it may be said, in such a design there is nothing new;
these are objects at which inquiring men have often before
aimed. To determine the difference between real and
imaginary knowledge, the conditions under which we arrive at
truth, the range of the powers of the human mind, has been a
favourite employment of speculative men from the earliest to
the most recent times. To inquire into the original,
certainty, and compass of man's knowledge, the limits of his
capacity, the strength and weakness of his reason, has been
the professed purpose of many of the most conspicuous and
valued labours of the philosophers of {6} all periods up to
our own day. It may appear, therefore, that there is little
necessity to add one more to these numerous essays; and
little hope that any new attempt will make any very
important addition to the stores of thought upon such
questions, which have been accumulated by the profoundest
and acutest thinkers of all ages.

To this I reply, that without at all disparaging the value
or importance of the labours of those who have previously
written respecting the foundations and conditions of human
knowledge, it may still be possible to add something to what
they have done. The writings of all great philosophers, up
to our own time, form a series which is not yet terminated.
The books and systems of philosophy which have, each in its
own time, won the admiration of men, and exercised a
powerful influence upon their thoughts, have had each its
own part and functions in the intellectual history of the
world; and other labours which shall succeed these may also
have their proper office and useful effect. We may not be
able to do much, and yet still it may be in our power to
effect something. Perhaps the very advances made by former
inquirers may have made it possible for us, at present, to
advance still further. In the discovery of truth, in the
development of man's mental powers and privileges, each
generation has its assigned part; and it is for us to
endeavour to perform our portion of this perpetual task of
our species. Although the terms which describe our
undertaking may be the same which have often been employed
by previous writers to express their purpose, yet our
position is different from theirs, and thus the result may
be different too. We have, as they had, to run our
appropriate course of speculation with the exertion of our
best powers; but our course lies in a more advanced part of
the great line along which Philosophy travels from age to
age. However familiar and old, therefore, be the design of
such a work as this, the execution may have, and if it be
performed in a manner suitable to the time, will have,
something that is new and not unimportant. {7}

Indeed, it appears to be absolutely necessary, in order to
check the prevalence of grave and pernicious errour, that
the doctrines which are taught concerning the foundations of
human knowledge and the powers of the human mind, should be
from time to time revised and corrected or extended.
Erroneous and partial views are promulgated and accepted;
one portion of the truth is insisted upon to the undue
exclusion of another; or principles true in themselves are
exaggerated till they produce on men's minds the effect of
falsehood. When evils of this kind have grown to a serious
height, a _Reform_ is requisite. The faults of the existing
systems must be remedied by correcting what is wrong, and
supplying what is wanting. In such cases, all the merits and
excellencies of the labours of the preceding times do not
supersede the necessity of putting forth new views suited to
the emergency which has arrived. The new form which errour
has assumed makes it proper to endeavour to give a new and
corresponding form to truth. Thus the mere progress of time,
and the natural growth of opinion from one stage to another,
leads to the production of new systems and forms of
philosophy. It will be found, I think, that some of the
doctrines now most widely prevalent respecting the
foundations and nature of truth are of such a kind that a
Reform is needed. The present age seems, by many
indications, to be called upon to seek a sounder Philosophy
of Knowledge than is now current among us. To contribute
towards such a Philosophy is the object of the present work.
The work is, therefore, like all works which take into
account the most recent forms of speculative doctrine,
invested with a certain degree of novelty in its aspect and
import, by the mere time and circumstances of its
appearance.

But, moreover, we can point out a very important peculiarity
by which this work is, in its design, distinguished from
preceding essays on like subjects; and this difference
appears to be of such a kind as may well entitle us to
expect some substantial addition to our knowledge as the
result of our labours. The peculiarity {8} of which I speak
has already been announced;--it is this: that we purpose to
collect our doctrines concerning the nature of knowledge,
and the best mode of acquiring it, from a contemplation of
the Structure and History of those Sciences (the Material
Sciences), which are universally recognized as the clearest
and surest examples of knowledge and of discovery. It is by
surveying and studying the whole mass of such Sciences, and
the various steps of their progress, that we now hope to
approach to the true Philosophy of Science.

Now this, I venture to say, is a new method of pursuing the
philosophy of human knowledge. Those who have hitherto
endeavoured to explain the nature of knowledge, and the
process of discovery, have, it is true, often illustrated
their views by adducing special examples of truths which
they conceived to be established, and by referring to the
mode of their establishment. But these examples have, for
the most part, been taken at random, not selected according
to any principle or system. Often they have involved
doctrines so precarious or so vague that they confused
rather than elucidated the subject; and instead of a single
difficulty,--What is the nature of Knowledge? these attempts
at illustration introduced two,--What was the true analysis
of the Doctrines thus adduced? and,--Whether they might
safely be taken as types of real Knowledge?

This has usually been the case when there have been adduced,
as standard examples of the formation of human knowledge,
doctrines belonging to supposed sciences other than the
material sciences; doctrines, for example, of Political
Economy, or Philology, or Morals, or the Philosophy of the
Fine Arts. I am very far from thinking that, in regard to
such subjects, there are no important truths hitherto
established: but it would seem that those truths which have
been obtained in these provinces of knowledge, have not yet
been fixed by means of distinct and permanent phraseology,
and sanctioned by universal reception, and formed into a
connected system, and traced through the steps of their
gradual discovery and establishment, so as to make {9} them
instructive examples of the nature and progress of truth in
general. Hereafter we trust to be able to show that the
progress of moral, and political, and philological, and
other knowledge, is governed by the same laws as that of
physical science. But since, at present, the former class of
subjects are full of controversy, doubt, and obscurity,
while the latter consist of undisputed truths clearly
understood and expressed, it may be considered a wise
procedure to make the latter class of doctrines the basis of
our speculations. And on the having taken this course, is,
in a great measure, my hope founded, of obtaining valuable
truths which have escaped preceding inquirers.

But it may be said that many preceding writers on the nature
and progress of knowledge have taken their examples
abundantly from the Physical Sciences. It would be easy to
point out admirable works, which have appeared during the
present and former generations, in which instances of
discovery, borrowed from the Physical Sciences, are
introduced in a manner most happily instructive. And to the
works in which this has been done, I gladly give my most
cordial admiration. But at the same time I may venture to
remark that there still remains a difference between my
design and theirs: and that I use the Physical Sciences as
exemplifications of the general progress of knowledge in a
manner very materially different from the course which is
followed in works such as are now referred to. For the
conclusions stated in the present work, respecting knowledge
and discovery, are drawn from _a connected and systematic
survey of the whole range of Physical Science and its
History_; whereas, hitherto, philosophers have contented
themselves with adducing detached examples of scientific
doctrines, drawn from one or two departments of science. So
long as we select our examples in this arbitrary and limited
manner, we lose the best part of that philosophical
instruction, which the sciences are fitted to afford when we
consider them as all members of one series, and as governed
by rules which are the same for all. Mathematical and
chemical truths, physical and physiological doctrines, the
sciences of {10} classification and of causation, must alike
be taken into our account, in order that we may learn what
are the general characters of real knowledge. When our
conclusions assume so comprehensive a shape that they apply
to a range of subjects so vast and varied as these, we may
feel some confidence that they represent the genuine form of
universal and permanent truth. But if our exemplification is
of a narrower kind, it may easily cramp and disturb our
philosophy. We may, for instance, render our views of truth
and its evidence so rigid and confined as to be quite
worthless, by founding them too much on the contemplation of
mathematical truth. We may overlook some of the most
important steps in the general course of discovery, by
fixing our attention too exclusively upon some one
conspicuous group of discoveries, as, for instance, those of
Newton. We may misunderstand the nature of physiological
discoveries, by attempting to force an analogy between them
and discoveries of mechanical laws, and by not attending to
the intermediate sciences which fill up the vast interval
between these extreme terms in the series of material
sciences. In these and in many other ways, a partial and
arbitrary reference to the material sciences in our inquiry
into human knowledge may mislead us; or at least may fail to
give us those wider views, and that deeper insight, which
should result from a systematic study of the whole range of
sciences with this particular object.

The design of the following work, then, is to form a
Philosophy of Science, by analyzing the substance and
examining the progress of the existing body of the sciences.
As a preliminary to this undertaking, a survey of the
history of the sciences was necessary. This, accordingly, I
have already performed; and the result of the labour thus
undertaken has been laid before the public as a _History of
the Inductive Sciences_.

In that work I have endeavoured to trace the steps by which
men acquired each main portion of that knowledge on which
they now look with so much confidence and satisfaction. The
events which that History relates, the speculations and
controversies {11} which are there described, and
discussions of the same kind, far more extensive, which are
there omitted, must all be taken into our account at
present, as the prominent and standard examples of the
circumstances which attend the progress of knowledge. With
so much of real historical fact before us, we may hope to
avoid such views of the processes of the human mind as are
too partial and limited, or too vague and loose, or too
abstract and unsubstantial, to represent fitly the real
forms of discovery and of truth.

Of former attempts, made with the same view of tracing the
conditions of the progress of knowledge, that of Bacon is
perhaps the most conspicuous: and his labours on this
subject were opened by his book on the _Advancement of
Learning_, which contains, among other matter, a survey of
the then existing state of knowledge. But this review was
undertaken rather with the object of ascertaining in what
quarters future advances were to be hoped for, than of
learning by what means they were to be made. His examination
of the domain of human knowledge was conducted rather with
the view of discovering what remained undone, than of
finding out how so much had been done. Bacon's survey was
made for the purpose of tracing the boundaries, rather than
of detecting the principles of knowledge. 'I will now
attempt,' he says[1\I], 'to make a general and faithful
perambulation of learning, with an inquiry what parts
thereof lie fresh and waste, and not improved and converted
by the industry of man; to the end that such a plot made and
recorded to memory, may both minister light to any public
designation, and also serve to excite voluntary endeavours.'
Nor will it be foreign to our scheme also hereafter to
examine with a like purpose the frontier-line of man's
intellectual estate. But the object of our perambulation in
the first place, is not so much to determine the extent of
the field, as the sources of its fertility. We would learn
by what plan and rules {12} of culture, conspiring with the
native forces of the bounteous soil, those rich harvests
have been produced which fill our garners. Bacon's maxims,
on the other hand, respecting the mode in which he conceived
that knowledge was thenceforth to be cultivated, have little
reference to the failures, still less to the successes,
which are recorded in his Review of the learning of his
time. His precepts are connected with his historical views
in a slight and unessential manner. His Philosophy of the
Sciences is not collected from the Sciences which are
noticed in his survey. Nor, in truth, could this, at the
time when he wrote, have easily been otherwise. At that
period, scarce any branch of physics existed as a science,
except Astronomy. The rules which Bacon gives for the
conduct of scientific researches are obtained, as it were,
by divination, from the contemplation of subjects with
regard to which no sciences as yet were. His instances of
steps rightly or wrongly made in this path, are in a great
measure cases of his own devising. He could not have
exemplified his Aphorisms by references to treatises then
extant, on the laws of nature; for the constant burden of
his exhortation is, that men up to his time had almost
universally followed an erroneous course. And however we may
admire the sagacity with which he pointed the way along a
better path, we have this great advantage over him;--that we
can interrogate the many travellers who since his time have
journeyed on this road. At the present day, when we have
under our notice so many sciences, of such wide extent, so
well established; a Philosophy of the Sciences ought, it
must seem, to be founded, not upon conjecture, but upon an
examination of many instances;--should not consist of a few
vague and unconnected maxims, difficult and doubtful in
their application, but should form a system of which every
part has been repeatedly confirmed and verified.

[Note 1\I: _Advancement of Learning_, b. i. p. 74.]

This accordingly it is the purpose of the present work to
attempt. But I may further observe, that as my hope of
making any progress in this undertaking is {13} founded upon
the design of keeping constantly in view the whole result of
the past history and present condition of science, I have
also been led to draw my lessons from my examples in a
manner more systematic and regular, as appears to me, than
has been done by preceding writers. Bacon, as I have just
said, was led to his maxims for the promotion of knowledge
by the sagacity of his own mind, with little or no aid from
previous examples. Succeeding philosophers may often have
gathered useful instruction from the instances of scientific
truths and discoveries which they adduced, but their
conclusions were drawn from their instances casually and
arbitrarily. They took for their moral any which the story
might suggest. But such a proceeding as this cannot suffice
for us, whose aim is to obtain a consistent body of
philosophy from a contemplation of the whole of Science and
its History. For our purpose it is necessary to resolve
scientific truths into their conditions and ingredients, in
order that we may see in what manner each of these has been
and is to be provided, in the cases which we may have to
consider. This accordingly is necessarily the first part of
our task:--_to analyse Scientific Truth into its Elements_.
This attempt will occupy the earlier portion of the present
work; and will necessarily be somewhat long, and perhaps, in
many parts, abstruse and uninviting. The risk of such an
inconvenience is inevitable; for the inquiry brings before
us many of the most dark and entangled questions in which
men have at any time busied themselves. And even if these
can now be made clearer and plainer than of yore, still they
can be made so only by means of mental discipline and mental
effort. Moreover this analysis of scientific truth into its
elements contains much, both in its principles and in its
results, different from the doctrines most generally
prevalent among us in recent times: but on that very account
this analysis is an essential part of the doctrines which I
have now to lay before the reader: and I must therefore
crave his indulgence towards any portion of it which may
appear to him obscure or repulsive. {14}

There is another circumstance which may tend to make the
present work less pleasing than others on the same subject,
in the nature of the examples of human knowledge to which I
confine myself; all my instances being, as I have said,
taken from the material sciences. For the truths belonging
to these sciences are, for the most part, neither so
familiar nor so interesting to the bulk of readers as those
doctrines which belong to some other subjects. Every general
proposition concerning politics or morals at once stirs up
an interest in men's bosoms, which makes them listen with
curiosity to the attempts to trace it to its origin and
foundation. Every rule of art or language brings before the
mind of cultivated men subjects of familiar and agreeable
thought, and is dwelt upon with pleasure for its own sake,
as well as on account of the philosophical lessons which it
may convey. But the curiosity which regards the truths of
physics or chemistry, or even of physiology or astronomy, is
of a more limited and less animated kind. Hence, in the mode
of inquiry which I have prescribed to myself, the examples
which I have to adduce will not amuse and relieve the
reader's mind as much as they might do, if I could allow
myself to collect them from the whole field of human
knowledge. They will have in them nothing to engage his
fancy, or to warm his heart. I am compelled to detain the
listener in the chilly air of the external world, in order
that we may have the advantage of full daylight.

But although I cannot avoid this inconvenience, so far as it
is one, I hope it will be recollected how great are the
advantages which we obtain by this restriction. We are thus
enabled to draw all our conclusions from doctrines which are
universally allowed to be eminently certain, clear, and
definite. The portions of knowledge to which I refer are
well known, and well established among men. Their names are
familiar, their assertions uncontested. Astronomy and
Geology, Mechanics and Chemistry, Optics and Acoustics,
Botany and Physiology, are each recognized as large and
substantial collections of undoubted truths. Men are {15}
wont to dwell with pride and triumph on the acquisitions of
knowledge which have been made in each of these provinces;
and to speak with confidence of the certainty of their
results. And all can easily learn in what repositories these
treasures of human knowledge are to be found. When,
therefore, we begin our inquiry from such examples, we
proceed upon a solid foundation. With such a clear ground of
confidence, we shall not be met with general assertions of
the vagueness and uncertainty of human knowledge; with the
question, What truth is, and How we are to recognize it;
with complaints concerning the hopelessness and
unprofitableness of such researches. We have, at least, a
definite problem before us. We have to examine the structure
and scheme, not of a shapeless mass of incoherent materials,
of which we doubt whether it be a ruin or a natural
wilderness, but of a fair and lofty palace, still erect and
tenanted, where hundreds of different apartments belong to a
common plan, where every generation adds something to the
extent and magnificence of the pile. The certainty and the
constant progress of science are things so unquestioned,
that we are at least engaged in an intelligible inquiry,
when we are examining the grounds and nature of that
certainty, the causes and laws of that progress.

To this inquiry, then, we now proceed. And in entering upon
this task, however our plan or our principles may differ
from those of the eminent philosophers who have endeavoured,
in our own or in former times, to illustrate or enforce the
philosophy of science, we most willingly acknowledge them as
in many things our leaders and teachers. Each reform must
involve its own peculiar principles, and the result of our
attempts, so far as they lead to a result, must be, in some
respects, different from those of former works. But we may
still share with the great writers who have treated this
subject before us, their spirit of hope and trust, their
reverence for the dignity of the subject, their belief in
the vast powers and boundless destiny of man. And we may
once more venture to use the {16} words of hopeful
exhortation, with which the greatest of those who have
trodden this path encouraged himself and his followers when
he set out upon his way.

'Concerning ourselves we speak not; but as touching the
matter which we have in hand, this we ask;--that men deem it
not to be the setting up an Opinion, but the performing of a
Work: and that they receive this as a certainty; that we are
not laying the foundations of any sect or doctrine, but of
the profit and dignity of mankind. Furthermore, that being
well disposed to what shall advantage themselves, and
putting off factions and prejudices, they take common
counsel with us, to the end that being by these our aids and
appliances freed and defended from wanderings and
impediments, they may lend their hands also to the labours
which remain to be performed: and yet further, that they be
of good hope; neither imagine to themselves this our Reform
as something of infinite dimension, and beyond the grasp of
mortal man, when in truth it is the end and true limit of
infinite errour; and is by no means unmindful of the
condition of mortality and humanity, not confiding that such
a thing can be carried to its perfect close in the space of
one single age, but assigning it as a task to a succession
of generations.'

[The Philosophy of the Inductive Sciences, according to our
view, must be founded upon the History of such Sciences;
which history we have attempted in a former work. The events
of that history may be described generally as the rise of
Theories out of Facts. But besides this, which we may term
the _external_ history of Theories, there is an internal
history of Theories, namely, the series of steps by which
the human mind becomes capable of forming each Theory. Hence
to complete the History of the Sciences as derived from
Facts, we require a history of the Ideas by which such
derivation has been made possible: and thus, the _First
Part_ of our Philosophy must be a _History of Scientific
Ideas_;--a labour no less historical than our former work,
and concerned with the same events; but which has been
purposely kept separate during the {17} composition, in
order that it might be afterwards presented in a more
systematic form, which I have here attempted to do.

Scientific Ideas are the Conditions of the derivation of
Sciences from Facts: but can any method or methods be given
by which such a Derivation can be ensured, or at least,
aided? Many such methods have been proposed; of which the
most celebrated is the _Novum Organon_ of Bacon, of which
the title was intended to imply that its scope goes much
beyond the _Organon_ of Aristotle. With the experience of
the formation of Science which the world has had since
Bacon's time, it does not appear presumptuous to suppose
that we can now improve or correct his methods; nor to term
such an attempt _Novum Organon Renovatum_.

The Philosophy of the Inductive Sciences, then, contains
these two parts, _The History of Scientific Ideas_, and the
_Novum Organon Renovatum_.]

{{19}}
THE
PHILOSOPHY
OF THE
INDUCTIVE SCIENCES.

PART I.

HISTORY OF SCIENTIFIC IDEAS.

[We have just spoken of _Theories_ and _Facts_, of _Ideas_
and _Facts_, and of _Inductive_ Sciences, which imply the
opposition of _Induction_ and _Deduction_. The explanation
of these antitheses must be the starting point of our
Philosophy.]

[Knowledge grows, and] through the ages one increasing purpose runs,
And the thoughts of men are widen'd with the process of the Suns.

BOOK I.

OF IDEAS IN GENERAL.

Quæ adhuc inventa sunt in Scientiis, ea hujusmodi sunt ut
Notionibus Vulgaribus fere subjaceant: ut vero ad interiora
et remotiora Naturæ penetretur, necesse est ut tam NOTIONES
quam AXIOMATA magis certâ et munitâ viâ a particularibus
abstrahantur; atque omnino melior et certior intellectûs
adoperatio in usum veniat.

BACON, _Nov. Org._, Lib. 1. Aphor. xviii.

{{23}}
BOOK I.

OF IDEAS IN GENERAL.

CHAPTER I.

OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY.

_Sect._ 1.--_Thoughts and Things._

IN order that we may do something towards determining the
nature and conditions of human knowledge, (which I have
already stated as the purpose of this work,) I shall have to
refer to an antithesis or opposition, which is familiar and
generally recognized, and in which the distinction of the
things opposed to each other is commonly considered very
clear and plain. I shall have to attempt to make this
opposition sharper and stronger than it is usually
conceived, and yet to shew that the distinction is far from
being so clear and definite as it is usually assumed to be:
I shall have to point the contrast, yet shew that the things
which are contrasted cannot be separated:--I must explain
that the antithesis is constant and essential, but yet that
there is no fixed and permanent line dividing its members. I
may thus appear, in different parts of my discussion, to be
proceeding in opposite directions, but I hope that the
reader who gives me a patient attention will see that both
steps lead to the point of view to which I wish to lead him.

The antithesis or opposition of which I speak is denoted,
with various modifications, by various pairs of terms: I
shall endeavour to shew the connexion of these different
modes of expression, and I will begin with that form which
is the simplest and most idiomatic. {24}

The simplest and most idiomatic expression of the antithesis
to which I refer is that in which we oppose to each other
THINGS and THOUGHTS. The opposition is familiar and plain.
Our thoughts are something which belongs to ourselves;
something which takes place within us; they are what we
think; they are actions of our minds. Things, on the
contrary, are something different from ourselves and
independent of us; something which is without us; they
_are_; we see them, touch them, and thus know that they
exist; but we do not make them by seeing or touching them,
as we make our _Thoughts_ by thinking them; we are passive,
and _Things_ act upon our organs of perception.

Now what I wish especially to remark is this: that in all
human KNOWLEDGE both Thoughts and Things are concerned. In
every part of my knowledge there must be some _thing_ about
which I know, and an internal act of _me_ who know. Thus, to
take simple yet definite parts of our knowledge, if I know
that a solar year consists of 365 days, or a lunar month of
30 days, I know something about the sun or the moon; namely,
that those objects perform certain revolutions and go
through certain changes, in those numbers of days; but I
count such numbers and conceive such revolutions and changes
by acts of my own thoughts. And both these elements of my
knowledge are indispensable. If there were not such external
Things as the sun and the moon I could not have any
knowledge of the progress of time as marked by them. And
however regular were the motions of the sun and moon, if I
could not count their appearances and combine their changes
into a cycle, or if I could not understand this when done by
other men, I could not know anything about a year or a
month. In the former case I might be conceived as a human
being, possessing the human powers of thinking and
reckoning, but kept in a dark world with nothing to mark the
progress of existence. The latter is the case of brute
animals, which see the sun and moon, but do not know how
many days make a month or a year, because they have not
human powers of thinking and reckoning. {25}

The two elements which are essential to our knowledge in the
above cases, are necessary to human knowledge in all cases.
In all cases, Knowledge implies a combination of Thoughts
and Things. Without this combination, it would not be
Knowledge. Without Thoughts, there could be no connexion;
without Things, there could be no reality. Thoughts and
Things are so intimately combined in our Knowledge, that we
do not look upon them as distinct. One single act of the
mind involves them both; and their contrast disappears in
their union.

But though Knowledge requires the union of these two
elements, Philosophy requires the separation of them, in
order that the nature and structure of Knowledge may be
seen. Therefore I begin by considering this separation. And
I now proceed to speak of another way of looking at the
antithesis of which I have spoken; and which I may, for the
reasons which I have just mentioned, call the FUNDAMENTAL
ANTITHESIS OF PHILOSOPHY.

_Sect._ 2.--_Necessary and Experiential Truths._

MOST persons are familiar with the distinction of
_necessary_ and _contingent_ truths. The former kind are
Truths which cannot but be true; as that 19 and 11 make
30;--that parallelograms upon the same base and between the
same parallels are equal;--that all the angles in the same
segment of a circle are equal. The latter are Truths which
_it happens_ (_contingit_) are true; but which, for anything
which we can see, might have been otherwise; as that a lunar
month contains 30 days, or that the stars revolve in circles
round the pole. The latter kind of Truths are learnt by
experience, and hence we may call them _Truths of
Experience_, or, for the sake of convenience, _Experiential_
Truths, in contrast with Necessary Truths.

Geometrical propositions are the most manifest examples of
Necessary Truths. All persons who have read and understood
the elements of geometry, know that the propositions above
stated (that parallelograms {26} upon the same base and
between the same parallels are equal; that all the angles in
the same segment of a circle are equal,) are necessarily
true; not only they are true, but they _must be_ true. The
meaning of the terms being understood, and the proof being
gone through, the truth of the propositions must be assented
to. We learn these propositions to be true by demonstrations
deduced from definitions and axioms; and when we have thus
learnt them, we see that they could not be otherwise. In the
same manner, the truths which concern numbers are necessary
truths: 19 and 11 not only _do_ make 30, but _must_ make
that number, and cannot make anything else. In the same
manner, it is a necessary truth that half the sum of two
numbers added to half their difference is equal to the
greater number.

It is easy to find examples of Experiential Truths;--
propositions which we know to be true, but know by
experience only. We know, in this way, that salt will
dissolve in water; that plants cannot live without light;--
in short, we know in this way all that we do know in
chemistry, physiology, and the material sciences in general.
I take the _Sciences_ as my examples of human knowledge,
rather than the common truths of daily life, or moral or
political truths; because, though the latter are more
generally interesting, the former are much more definite and
certain, and therefore better starting-points for our
speculations, as I have already said. And we may take
elementary astronomical truths as the most familiar examples
of Experiential Truths in the domain of science.

With these examples, the distinction of Necessary and
Experiential Truths is, I hope, clear. The former kind, we
see to be true by thinking about them, and see that they
could not be otherwise. The latter kind, men could never
have discovered to be true without looking at them; and
having so discovered them, still no one will pretend to say
they might not have been otherwise. For aught we can see,
the astronomical truths which express the motions and
periods of the sun, moon and stars, might have been
otherwise. If we had been placed in another part of the
solar system, our {27} experiential truths respecting days,
years, and the motions of the heavenly bodies, would have
been other than they are, as we know from astronomy itself.

It is evident that this distinction of Necessary and
Experiential Truths involves the same antithesis which we
have already considered;--the antithesis of Thoughts and
Things. Necessary Truths are derived from our own Thoughts:
Experiential truths are derived from our observation of
Things about us. The opposition of Necessary and
Experiential Truths is another aspect of the Fundamental
Antithesis of Philosophy.

_Sect._ 3.--_Deduction and Induction._

I HAVE already stated that geometrical truths are
established by demonstrations _deduced_ from definitions and
axioms. The term _Deduction_ is specially applied to such a
course of demonstration of truths from definitions and
axioms. In the case of the parallelograms upon the same base
and between the same parallels, we prove certain triangles
to be equal, by supposing them placed so that their two
bases have the same extremities; and hence, referring to an
Axiom respecting straight lines, we infer that the bases
coincide. We combine these equal triangles with other equal
spaces, and in this way make up both the one and the other
of the parallelograms, in such a manner as to shew that they
are equal. In this manner, going on step by step, deducing
the equality of the triangles from the axiom, and the
equality of the parallelograms from that of the triangles,
we travel to the conclusion. And this process of successive
deduction is the scheme of all geometrical proof. We begin
with Definitions of the notions which we reason about, and
with Axioms, or self-evident truths, respecting these
notions; and we get, by reasoning from these, other truths
which are demonstratively evident; and from these truths
again, others of the same kind, and so on. We begin with our
own Thoughts, which supply us with Axioms to start from; and
we reason from these, till we come to propositions {28}
which are applicable to the Things about us; as for
instance, the propositions respecting circles and spheres
applicable to the motions of the heavenly bodies. This is
_Deduction_, or _Deductive Reasoning_.

Experiential truths are acquired in a very different way. In
order to obtain such truths, we begin with Things. In order
to learn how many days there are in a year, or in a lunar
month, we must begin by observing the sun and the moon. We
must observe their changes day by day, and try to make the
cycle of change fit into some notion of number which we
supply from our own Thoughts. We shall find that a cycle of
30 days nearly will fit the changes of phase of the
moon;--that a cycle of 365 days nearly will fit the changes
of daily motion of the sun. Or, to go on to experiential
truths of which the discovery comes within the limits of the
history of science--we shall find (as Hipparchus found) that
the unequal motion of the sun among the stars, such as
observation shews it to be, may be fitly represented by the
notion of an _eccentric_;--a circle in which the sun has an
equable annual motion, the spectator not being in the center
of the circle. Again, in the same manner, at a later period,
Kepler started from more exact observations of the sun, and
compared them with a supposed motion in a certain ellipse;
and was able to shew that, not a circle about an eccentric
point, but an ellipse, supplied the mode of conception which
truly agreed with the motion of the sun about the earth; or
rather, as Copernicus had already shewn, of the earth about
the sun. In such cases, in which truths are obtained by
beginning from observation of external things and by finding
some notion with which the Things, as observed, agree, the
truths are said to be obtained by _Induction_. The process
is an _Inductive Process_.

The contrast of the Deductive and Inductive process is
obvious. In the former, we proceed at each step from general
truths to particular applications of them; in the latter,
from particular observations to a general truth which
includes them. In the former case we may be said to reason
_downwards_, in the latter case, {29} _upwards_; for general
notions are conceived as standing above particulars.
Necessary truths are proved, like arithmetical sums, by
adding together the portions of which they consist. An
inductive truth is proved, like the guess which answers a
riddle, by its agreeing with the facts described.
Demonstration is irresistible in its effect on the belief,
but does not produce surprize, because all the steps to the
conclusion are exhibited, before we arrive at the
conclusion. Inductive inference is not demonstrative, but it
is often more striking than demonstrative reasoning, because
the intermediate links between the particulars and the
inference are not shewn. Deductive truths are the results of
relations among our own Thoughts. Inductive truths are
relations which we discern among existing Things; and thus,
this opposition of Deduction and Induction is again an
aspect of the Fundamental Antithesis already spoken of.

_Sect._ 4.--_Theories and Facts._

GENERAL experiential Truths, such as we have just spoken of,
are called _Theories_, and the particular observations from
which they are collected, and which they include and
explain, are called _Facts_. Thus Hipparchus's doctrine,
that the sun moves in an eccentric about the earth, is _his
Theory_ of the Sun, or the _Eccentric Theory_. The doctrine
of Kepler, that the Earth moves in an Ellipse about the Sun,
is _Kepler's Theory_ of the Earth, the Elliptical Theory.
Newton's doctrine that this elliptical motion of the Earth
about the Sun is produced and governed by the Sun's
attraction upon the Earth, is the _Newtonian_ theory, the
_Theory of Attraction_. Each of these Theories was accepted,
because it included, connected and explained the _Facts_;
the Facts being, in the two former cases, the motions of the
Sun as observed; and in the other case, the elliptical
motion of the Earth as known by Kepler's Theory. This
antithesis of _Theory_ and _Fact_ is included in what has
just been said of Inductive Propositions. A Theory is an
Inductive Proposition, and the Facts {30} are the particular
observations from which, as I have said, such Propositions
are inferred by Induction. The Antithesis of Theory and Fact
implies the fundamental Antithesis of Thoughts and Things;
for a Theory (that is, a true Theory) may be described as a
Thought which is contemplated distinct from Things and seen
to agree with them; while a Fact is a combination of our
Thoughts with Things in so complete agreement that we do not
regard them as separate.

Thus the antithesis of Theory and Fact involves the
antithesis of Thoughts and Things, but is not identical with
it. Facts involve Thoughts, for we know Facts only by
thinking about them. The Fact that the year consists of 365
days; the Fact that the month consists of 30 days, cannot be
known to us, except we have the Thoughts of Time, Number and
Recurrence. But these Thoughts are so familiar, that we have
the fact in our mind as a simple Thing without attending to
the Thought which it involves. When we mould our Thoughts
into a Theory, we consider the thought as distinct from the
Facts; but yet, though distinct, not independent of them;
for it is a true Theory, only by including and agreeing with
the Facts.

_Sect._ 5.--_Ideas and Sensations._

WE have just seen that the antithesis of Theory and Fact,
although it involves the antithesis of Thoughts and Things,
is not identical with it. There are other modes of
expression also, which involve the same Fundamental
Antithesis, more or less modified. Of these, the pair of
words which in their relations appear to separate the
members of the antithesis most distinctly are _Ideas_ and
_Sensations_. We see and hear and touch external things, and
thus perceive them by our senses; but in perceiving them, we
connect the impressions of sense according to relations of
space, time, number, likeness, cause, &c. Now some at least
of these kinds of connexion, as space, time, number, may be
contemplated distinct from the things to which they are
applied; and so contemplated, I term them _Ideas_. And {31}
the other element, the impressions upon our senses which
they connect, are called _Sensations_.

I term space, time, cause, &c., _Ideas_, because they are
general relations among our sensations, apprehended by an
act of the mind, not by the senses simply. These relations
involve something beyond what the senses alone could
furnish. By the sense of sight we see various shades and
colours and shapes before us, but the _outlines_ by which
they are separated into distinct objects of definite forms,
are the work of the mind itself. And again, when we conceive
visible things, not only as surfaces of a certain form, but
as _solid bodies_, placed at various distances in space, we
again exert an act of the mind upon them. When we see a body
move, we see it move in a path or _orbit_, but this orbit is
not itself seen; it is constructed by the mind. In like
manner when we see the motions of a needle towards a magnet,
we do not _see_ the attraction or force which produces the
effects; but we infer the force, by having in our minds the
Idea of Cause. Such acts of thought, such _Ideas_, enter
into our perceptions of external things.

But though our perceptions of external things involve some
act of the mind, they must involve something else besides an
act of the mind. If we must exercise an act of thought in
order to see force exerted, or orbits described by bodies in
motion, or even in order to see bodies existing in space,
and to distinguish one kind of object from another, still
the act of thought alone does not make the Bodies. There
must be something besides, _on which_ the thought is
exerted. A colour, a form, a sound, are not produced by the
mind, however they may be moulded, combined, and interpreted
by our mental acts. A philosophical poet has spoken of
All the world
Of eye and ear, both what they half create,
And what perceive.
But it is clear, that though they _half_ create, they do not
wholly create: there must be an external world of colour and
sound to give impressions to the eye and ear, as well as internal
powers by which we perceive {32} what is offered to our organs.
The mind is in some way passive as well as active: there are
objects without as well as faculties within;--Sensations,
as well as acts of Thought.

Indeed this is so far generally acknowledged, that according
to common apprehension, the mind is passive _rather_ than
active in acquiring the knowledge which it receives
concerning the material world. Its sensations are generally
considered more distinct than its operations. The world
without is held to be more clearly real than the faculties
within. That there is something different from ourselves,
something external to us, something independent of us,
something which no act of our minds can make or can destroy,
is held by all men to be at least as evident, as that our
minds can exert any effectual process in modifying and
appreciating the impressions made upon them. Most persons
are more likely to doubt whether the mind be always actively
applying Ideas to the objects which it perceives, than
whether it perceive them passively by means of Sensations.

But yet a little consideration will show us that an activity
of the mind, and an activity according to certain Ideas, is
requisite in all our knowledge of external objects. We see
objects, of various solid forms, and at various distances
from us. But we do not thus perceive them by sensation
alone. Our visual impressions cannot, of themselves, convey
to us a knowledge of solid form, or of distance from us.
Such knowledge is inferred from what we see:--inferred by
conceiving the objects as existing in space, and by applying
to them the Idea of Space. Again:--day after day passes,
till they make up a year: but we do not know that the days
are 365, except we count them; and thus apply to them our
Idea of Number. Again:--we see a needle drawn to a magnet:
but, in truth, the _drawing_ is what we cannot see. We see
the needle move, and infer the attraction, by applying to
the fact our Idea of Force, as the cause of motion.
Again:--we see two trees of different kinds; but we cannot
know that they are so, except by applying to them our Idea
of the resemblance {33} and difference which makes kinds.
And thus Ideas, as well as Sensations, necessarily enter
into all our knowledge of objects: and these two words
express, perhaps more exactly than any of the pairs before
mentioned, that Fundamental Antithesis, in the union of
which, as I have said, all knowledge consists.

_Sect._ 6.--_Reflexion and Sensation._

IT will hereafter be my business to show what the Ideas are,
which thus enter into our knowledge; and how each Idea has
been, as a matter of historical fact, introduced into the
Science to which it especially belongs. But before I proceed
to do this, I will notice some other terms, besides the
phrases already noticed, which have a reference, more or
less direct, to the Fundamental Antithesis of Ideas and
Sensations. I will mention some of these, in order that if
they should come under the reader's notice, he may not be
perplexed as to their bearing upon the view here presented
to him.

The celebrated doctrine of Locke, that all our 'Ideas,'
(that is, in his use of the word, all our objects of
thinking,) come from Sensation or Reflexion, will naturally
occur to the reader as connected with the antithesis of
which I have been speaking. But there is a great difference
between Locke's account of Sensation and Reflexion, and our
view of Sensation and Ideas. He is speaking of the origin of
our knowledge;--we, of its nature and composition. He is
content to say that all the knowledge which we do not
receive directly by Sensation, we obtain by Reflex Acts of
the mind, which make up his Reflexion. But we hold that
there is no Sensation without an act of the mind, and that
the mind's activity is not only reflexly exerted upon
itself, but directly upon objects, so as to perceive in them
connexions and relations which are not Sensations. He is
content to put together, under the name of Reflexion,
everything in our knowledge which is not Sensation: we are
to attempt to analyze all that is not Sensation; not only to
say it consists of Ideas, but {34} to point out what those
Ideas are, and to show the mode in which each of them enters
into our knowledge. His purpose was, to prove that there are
no Ideas, except the reflex acts of the mind: our endeavour
will be to show that the acts of the mind, both direct and
reflex, are governed by certain Laws, which may be
conveniently termed Ideas. His procedure was, to deny that
any knowledge could be derived from the mind alone: our
course will be, to show that in every part of our most
certain and exact knowledge, those who have added to our
knowledge in every age have referred to principles which the
mind itself supplies. I do not say that my view is contrary
to his: but it is altogether different from his. If I grant
that all our knowledge comes from Sensation and Reflexion,
still my task then is only begun; for I want further to
determine, in each science, what portion comes, not from
mere Sensation, but from those Ideas by the aid of which
either Sensation or Reflexion can lead to Science.

Locke's use of the word 'idea' is, as the reader will
perceive, different from ours. He uses the word, as he says,
which 'serves best to stand for whatsoever is the object of
the understanding when a man thinks.' 'I have used it,' he
adds, 'to express whatever is meant by _phantasm_, _notion_,
_species_, or whatever it is to which the mind can be
employed about in thinking.' It might be shown that this
separation of the _mind itself_ from the ideal _objects_
about which it is employed in thinking, may lead to very
erroneous results. But it may suffice to observe that we use
the word _Ideas_, in the manner already explained, to
express that element, supplied by the mind itself, which
must be combined with Sensation in order to produce
knowledge. For us, Ideas are not Objects of Thought, but
rather Laws of Thought. Ideas are not synonymous with
Notions; they are Principles which give to our Notions
whatever they contain of truth. But our use of the term
_Idea_ will be more fully explained hereafter. {35}

_Sect._ 7.--_Subjective and Objective._

THE Fundamental Antithesis of Philosophy of which I have to
speak has been brought into great prominence in the writings
of modern German philosophers, and has conspicuously formed
the basis of their systems. They have indicated this
antithesis by the terms _subjective_ and _objective_.
According to the technical language of old writers, a thing
and its qualities are described as _subject_ and
_attributes_; and thus a man's faculties and acts are
attributes of which he is the _subject_. The mind is the
_subject_ in which ideas inhere. Moreover, the man's
faculties and acts are employed upon external _objects_; and
from objects all his sensations arise. Hence the part of a
man's knowledge which belongs to his own mind, is
_subjective_: that which flows in upon him from the world
external to him, is _objective_. And as in man's
contemplation of nature, there is always some act of thought
which depends upon himself, and some matter of thought which
is independent of him, there is, in every part of his
knowledge, a subjective and an objective element. The
combination of the two elements, the subjective or ideal,
and the objective or observed, is necessary, in order to
give us any insight into the laws of nature. But different
persons, according to their mental habits and constitution,
may be inclined to dwell by preference upon the one or the
other of these two elements. It may perhaps interest the
reader to see this difference of intellectual character
illustrated in two eminent men of genius of modern times,
Göthe and Schiller.

Göthe himself gives us the account to which I refer, in his
history of the progress of his speculations concerning the
Metamorphosis of Plants; a mode of viewing their structure
by which he explained, in a very striking and beautiful
manner, the relations of the different parts of a plant to
each other; as has been narrated in the _History of the
Inductive Sciences_. Göthe felt a delight in the passive
contemplation of nature, unmingled with the desire of
reasoning and theorizing; a delight such as naturally
belongs to those poets who {36} merely embody the images
which a fertile genius suggests, and do not mix with these
pictures, judgments and reflexions of their own. Schiller,
on the other hand, both by his own strong feeling of the
value of a moral purpose in poetry, and by his adoption of a
system of metaphysics in which the subjective element was
made very prominent, was well disposed to recognize fully
the authority of ideas over external impressions.

Göthe for a time felt a degree of estrangement towards
Schiller, arising from this contrariety in their views and
characters. But on one occasion they fell into discussion on
the study of natural history; and Göthe endeavoured to
impress upon his companion his persuasion that nature was to
be considered, not as composed of detached and incoherent
parts, but as active and alive, and unfolding herself in
each portion, in virtue of principles which pervade the
whole. Schiller objected that no such view of the objects of
natural history had been pointed out by observation, the
only guide which the natural historians recommended; and was
disposed on this account to think the whole of their study
narrow and shallow. 'Upon this,' says Göthe, 'I expounded to
him, in as lively a way as I could, the metamorphosis of
plants, drawing on paper for him, as I proceeded, a diagram
to represent that general form of a plant which shows itself
in so many and so various transformations. Schiller attended
and understood; and, accepting the explanation, he said,
"This is not observation, but an idea." I replied,' adds
Göthe, 'with some degree of irritation; for the point which
separated us was most luminously marked by this expression:
but I smothered my vexation, and merely said, "I was happy
to find that I had got ideas without knowing it; nay, that I
saw them before my eyes."' Göthe then goes on to say, that
he had been grieved to the very soul by maxims promulgated
by Schiller, that no observed fact ever could correspond
with an idea. Since he himself loved best to wander in the
domain of external observation, he had been led to look with
repugnance and hostility upon anything which professed to
depend upon ideas. 'Yet,' he {37} observes, 'it occurred to
me that if my Observation was identical with his Idea, there
must be some common ground on which we might meet.' They
went on with their mutual explanations, and became intimate
and lasting friends. 'And thus,' adds the poet, by means of
that mighty and interminable controversy between _object_
and _subject_, we two concluded an alliance which remained
unbroken, and produced much benefit to ourselves and others.'

The general diagram of a plant, of which Göthe here speaks,
must have been a combination of lines and marks expressing
the relations of position and equivalence among the elements
of vegetable forms, by which so many of their resemblances
and differences may be explained. Such a symbol is not an
Idea in that general sense in which we propose to use the
term, but is a particular modification of the general Ideas
of symmetry, developement, and the like; and we shall
hereafter see, according to the phraseology which we shall
explain in the next chapter, how such a diagram might
express the _ideal conception_ of a plant.

The antithesis of _subjective_ and _objective_ is very
familiar in the philosophical literature of Germany and
France; nor is it uncommon in any age of our own literature.
But though efforts have recently been made to give currency
among us to this phraseology, it has not been cordially
received, and has been much complained of as not of obvious
meaning. Nor is the complaint without ground: for when we
regard the mind as the _subject_ in which ideas inhere, it
becomes for us an _object_, and the antithesis vanishes. We
are not so much accustomed to use _subject_ in this sense,
as to make it a proper contrast to _object_. The combination
'_ideal_ and _objective_,' would more readily convey to a
modern reader the opposition which is intended between the
ideas of the mind itself, and the objects which it
contemplates around it.

To the antitheses already noticed--Thoughts and Things;
Necessary and Experiential Truths; Deduction and Induction;
Theory and Fact; Ideas and Sensations; Reflexion and
Sensation; Subjective and {38} Objective; we may add others,
by which distinctions depending more or less upon the
fundamental antithesis have been denoted. Thus we speak of
the _internal_ and _external_ sources of our knowledge; of
the world _within_ and the world _without_ us; of _Man_ and
_Nature_. Some of the more recent metaphysical writers of
Germany have divided the universe into the _Me_ and _Not-me_
(Ich and Nicht-ich). Upon such phraseology we may observe,
that to have the fundamental antithesis of which we speak
really understood, is of the highest consequence to
philosophy, but that little appears to be gained by
expressing it in any novel manner. The most weighty part of
the philosopher's task is to analyze the operations of the
mind; and in this task, it can aid us but little to call it,
instead of the _mind_, the _subject_, or the _me_.

_Sect._ 8.--_Matter and Form._

THERE are some other ways of expressing, or rather of
illustrating, the fundamental antithesis, which I may
briefly notice. The antithesis has been at different times
presented by means of various images. One of the most
ancient of these, and one which is still very instructive,
is that which speaks of Sensations as the _Matter_, and
Ideas as the _Form_, of our knowledge; just as ivory is the
matter, and a cube the form, of a die. This comparison has
the advantage of showing that two elements of an antithesis
which cannot be separated in fact, may yet be advantageously
separated in our reasonings. For Matter and Form cannot by
any means be detached from each other. All matter must have
some form; all form must be the form of some material thing.
If the ivory be not a cube, it must have a spherical or some
other form. And the cube, in order to be a cube, must be of
some material;--if not of ivory, of wood, or stone, for
instance, A figure without matter is merely a geometrical
conception;--a modification of the idea of space. Matter
without figure is a mere abstract term;--a supposed union of
certain sensible qualities which, so insulated {39} from
others, cannot exist. Yet the distinction of Matter and Form
is real; and, as a subject of contemplation, clear and
plain. Nor is the distinction by any means useless. The
speculations which treat of the two subjects, Matter and
Figure, are very different. Matter is the subject of the
sciences of Mechanics and Chemistry; Figure, of Geometry.
These two classes of Sciences have quite different sets of
principles. If we refuse to consider the Matter and the Form
of bodies separately, because we cannot exhibit Matter and
Form separately, we shut the door to all philosophy on such
subjects. In like manner, though Sensations and Ideas are
necessarily united in all our knowledge, they can be
considered as distinct; and this distinction is the basis of
all philosophy concerning knowledge.

This illustration of the relation of Ideas and Sensations
may enable us to estimate a doctrine which has been put
forwards at various times. In a certain school of
speculators there has existed a disposition to derive all
our Ideas from our Sensations, the term _Idea_, being, in
this school, used in its wider sense, so as to include all
modifications and limitations of our Fundamental Ideas. The
doctrines of this school have been summarily expressed by
saying that 'Every Idea is a transformed Sensation.' Now,
even supposing this assertion to be exactly true, we easily
see, from what has been said, how little we are likely to
answer the ends of philosophy by putting forward such a
maxim as one of primary importance. For we might say, in
like manner, that every statue is but a transformed block of
marble, or every edifice but a collection of transformed
stones. But what would these assertions avail us, if our
object were to trace the rules of art by which beautiful
statues were formed, or great works of architecture erected?
The question naturally occurs, What is the nature, the
principle, the law of this Transformation? In what faculty
resides the transforming power? What train of ideas of
beauty, and symmetry, and stability, in the mind of the
statuary or the architect, has produced those great works
which {40} mankind look upon as among their most valuable
possessions;--the Apollo of the Belvidere, the Parthenon,
the Cathedral of Cologne? When this is what we want to know,
how are we helped by learning that the Apollo is of Parian
marble, or the Cathedral of basaltic stone? We must know
much more than this, in order to acquire any insight into
the principles of statuary or of architecture. In like
manner, in order that we may make any progress in the
philosophy of knowledge, which is our purpose, we must
endeavour to learn something further respecting ideas than
that they are transformed sensations, even if they were this.

But, in reality, the assertion that our ideas are
transformed sensations, is erroneous as well as frivolous.
For it conveys, and is intended to convey, the opinion that
our sensations have one form which properly belongs to them;
and that, in order to become ideas, they are converted into
some other form. But the truth is, that our sensations, of
themselves, without some act of the mind, such as involves
what we have termed an Idea, have no form. We cannot see one
object without the idea of space; we cannot see two without
the idea of resemblance or difference; and space and
difference are not sensations. Thus, if we are to employ the
metaphor of Matter and Form, which is implied in the
expression to which I have referred, our sensations, from
their first reception, have their Form not _changed_, but
_given_ by our Ideas. Without the relations of thought which
we here term _Ideas_, the sensations are matter without
form. Matter without form cannot exist: and in like manner
sensations cannot become perceptions of objects, without
some formative power of the mind. By the very act of being
received as perceptions, they have a formative power
exercised upon them, the operation of which might be
expressed, by speaking of them, not as _transformed_, but
simply as _formed_;--as invested with form, instead of being
the mere formless material of perception. The word _inform_,
according to its Latin etymology, at first implied this
process by which matter is {41} invested with form. Thus
Virgil[1\1] speaks of the thunderbolt as _informed_ by the
hands of Brontes, and Steropes, and Pyracmon. And Dryden
introduces the word in another place:--
Let others better mould the running mass
Of metals, or _inform_ the breathing brass.
Even in this use of the word, the form is something superior
to the brute manner, and gives it a new significance and
purpose. And hence the term is again used to denote the
effect produced by an intelligent principle of a still
higher kind:--
. . . . He _informed_
This ill-shaped body with a daring soul.
And finally even the soul itself, in its original condition,
is looked upon as matter, when viewed with reference to
education and knowledge, by which it is afterwards moulded;
and hence these are, in our language, termed _information_.
If we confine ourselves to the first of these three uses of
the term, we may correct the erroneous opinion of which we
have just been speaking, and retain the metaphor by which it
is expressed, by saying, that ideas are not _transformed_,
but _informed_ sensations.

[Note 1\1: Ferrum exercebant vasto Cyclopes in Antro
Brontesque Steropesque et nudus membra Pyracmon;
His informatum manibus, jam parte polita
Fulmen erat.--_Æn._ viii. 424.]

_Sect._ 9.--_Man the Interpreter of Nature._

THERE is another image by which writers have represented the
acts of thought through which knowledge is obtained from the
observation of the external world. Nature is the Book, and
Man is the _Interpreter_. The facts of the external world
are marks, in which man discovers a meaning, and so reads
them. Man is the Interpreter of Nature, and Science is the
right Interpretation. And this image also is, in many
respects, {42} instructive. It exhibits to us the necessity
of both elements;--the marks which man has to look at, and
the knowledge of the alphabet and language which he must
possess and apply before he can find any meaning in what he
sees. Moreover this image presents to us, as the ideal
element, an activity of the mind of that very kind which we
wish to point out. Indeed the illustration is rather an
example than a comparison of the composition of our
knowledge. The letters and symbols which are presented to
the Interpreter are really objects of sensation: the notion
of letters as signs of words, the notion of connexions among
words by which they have meaning, really are among our
Ideas;--_Signs_ and _Meaning_ are Ideas, supplied by the
mind, and added to all that sensation can disclose in any
collection of visible marks. The Sciences are not
figuratively, but really, Interpretations of Nature. But
this image, whether taken as example or comparison, may
serve to show both the opposite character of the two
elements of knowledge, and their necessary combination, in
order that there may be knowledge.

This illustration may also serve to explain another point in
the conditions of human knowledge which we shall have to
notice:--namely, the very different degrees in which, in
different cases, we are conscious of the mental act by which
our sensations are converted into knowledge. For the same
difference occurs in reading an inscription. If the
inscription were entire and plain, in a language with which
we were familiar, we should be unconscious of any mental act
in reading it. We should seem to collect its meaning by the
sight alone. But if we had to decipher an ancient
inscription, of which only imperfect marks remained, with a
few entire letters among them, we should probably make
several suppositions as to the mode of reading it, before we
found any mode which was quite successful; and thus, our
guesses, being separate from the observed facts, and at
first not fully in agreement with them, we should be clearly
aware that the conjectured meaning, on the one hand, and the
observed marks on the other, were distinct things, though
these {43} two things would become united as elements of one
act of knowledge when we had hit upon the right conjecture.

_Sect._ 10.--_The Fundamental Antithesis inseparable._

THE illustration just referred to, as well as other ways of
considering the subject, may help us to get over a
difficulty which at first sight appears perplexing. We have
spoken of the common opposition of _Theory_ and _Fact_ as
important, and as involving what we have called the
Fundamental Antithesis of Philosophy. But after all, it may
be asked, Is this distinction of Theory and Fact really
tenable? Is it not often difficult to say whether a special
part of our knowledge is a Fact or a Theory? Is it a Fact or
a Theory that the stars revolve round the pole? Is it a Fact
or a Theory that the earth is a globe revolving on its axis?
Is it a Fact or a Theory that the earth travels in an
ellipse round the sun? Is it a Fact or a Theory that the sun
attracts the earth? Is it a Fact or a Theory that the
loadstone attracts the needle? In all these cases, probably
some persons would answer one way, and some persons the
other. There are many persons by whom the doctrine of the
globular form of the earth, the doctrine of the earth's
elliptical orbit, the doctrine of the sun's attraction on
the earth, would be called _theories_, even if they allowed
them to be true theories. But yet if each of these
propositions be true, is it not a _fact_? And even with
regard to the simpler facts, as the motion of the stars
round the pole, although this may be a Fact to one who has
watched and measured the motions of the stars, one who has
not done this, and who has only carelessly looked at these
stars from time to time, may naturally speak of the circles
which the astronomer makes them describe as Theories. It
would seem, then, that we cannot in such cases expect
general assent, if we say, _This is a Fact and not a
Theory_, or _This is a Theory and not a Fact_. And the same
is true in a vast range of cases. It would seem, therefore,
that we cannot rest any reasoning upon this distinction of
Theory {44} and Fact; and we cannot avoid asking whether
there is any real distinction in this antithesis, and if so,
what it is.

To this I reply: the distinction between Theory (that is,
true Theory) and Fact, is this: that in Theory the Ideas are
considered as distinct from the Facts: in Facts, though
Ideas may be involved, they are not, in our apprehension,
separated from the sensations. In a Fact, the Ideas are
applied so readily and familiarly, and incorporated with the
sensations so entirely, that we do not see _them_, we see
_through them_. A person who carefully notes the motion of a
star all night, sees the circle which it describes, as he
sees the star, though the circle is, really, a result of his
own Ideas. A person who has in his mind the measures of
different lines and countries on the earth's surface, and
who can put them, together into one conception, finds that
they can make no figure but a globular one: to him, the
earth's globular form is a Fact, as much as the square form
of his chamber. A person to whom the grounds of believing
the earth to travel round the sun are as familiar as the
grounds for believing the movements of the mail-coaches in
this country, looks upon the former event as a Fact, just as
he looks upon the latter events as Facts. And a person who,
knowing the Fact of the earth's annual motion, refers it
distinctly to its mechanical cause, conceives the sun's
attraction as a Fact, just as he conceives as a Fact, the
action of the wind which turns the sails of a mill. He
cannot _see_ the force in either case; he supplies it out of
his own Ideas. And thus, a true Theory is a Fact; a Fact is
a familiar Theory. That which is a Fact under one aspect, is
a Theory under another. The most recondite Theories when
firmly established are Facts: the simplest Facts involve
something of the nature of Theory. Theory and Fact
correspond, in a certain degree, with Ideas and Sensations,
as to the nature of their opposition. But the Facts are
Facts, so far as the Ideas have been combined with the
Sensations and absorbed in them: the Theories are Theories,
so far as the Ideas are kept distinct from the Sensations,
and so far as it is {45} considered still a question whether
those can be made to agree with these.

We may, as I have said, illustrate this matter by
considering man as _interpreting_ the phenomena which he
sees. He often interprets without being aware that he does
so. Thus when we see the needle move towards the magnet, we
assert that the magnet exercises an attractive force on the
needle. But it is only by an interpretative act of our own
minds that we ascribe this motion to attraction. That, in
this case, a force is exerted--something of the nature of
the pull which we could apply by our own volition--is our
interpretation of the phenomena; although we may be
conscious of the act of interpretation, and may then regard
the attraction as a Fact.

Nor is it in such cases only that we interpret phenomena in
our own way, without being conscious of what we do. We see a
tree at a distance, and judge it to be a chestnut or a lime;
yet this is only an inference from the colour or form of the
mass according to preconceived classifications of our own.
Our lives are full of such unconscious interpretations. The
farmer recognizes a good or a bad soil; the artist a picture
of a favourite master; the geologist a rock of a known
locality, as we recognize the faces and voices of our
friends; that is, by judgments formed on what we see and
hear; but judgments in which we do not analyze the steps, or
distinguish the inference from the appearance. And in these
mixtures of observation and inference, we speak of the
judgment thus formed, as a Fact directly observed.

Even in the case in which our perceptions appear to be most
direct, and least to involve any interpretations of our
own,--in the simple process of seeing,--who does not know
how much we, by an act of the mind, add to that which our
senses receive? Does any one fancy that he sees a solid
cube? It is easy to show that the solidity of the figure,
the relative position of its faces and edges to each other,
are inferences of the spectator; no more conveyed to his
conviction by the eye alone, than they would be if he were
looking at {46} a painted representation of a cube. The
scene of nature is a picture without depth of substance, no
less than the scene of art; and in the one case as in the
other, it is the mind which, by an act of its own, discovers
that colour and shape denote distance and solidity. Most men
are unconscious of this perpetual habit of reading the
language of the external world, and translating as they
read. The draughtsman, indeed, is compelled, for his
purposes, to return back in thought from the solid bodies
which he has inferred, to the shapes of surface which he
really sees. He knows that there is a mask of theory over
the whole face of nature, if it be _theory_ to infer more
than we _see_. But other men, unaware of this masquerade,
hold it to be a fact that they see cubes and spheres,
spacious apartments and winding avenues. And these things
are facts to them, because they are unconscious of the
mental operation by which they have penetrated nature's
disguise.

And thus, we still have an intelligible distinction of Fact
and Theory, if we consider Theory as a conscious, and Fact
as an unconscious inference, from the phenomena which are
presented to our senses.

But still, Theory and Fact, Inference and Perception,
Reasoning and Observation, are antitheses in none of which
can we separate the two members by any fixed and definite line.

Even the simplest terms by which the antithesis is expressed
cannot be separated. Ideas and Sensations, Thoughts and
Things, Subject and Object, cannot in any case be applied
absolutely and exclusively. Our Sensations require Ideas to
bind them together, namely, Ideas of space, time, number,
and the like. If not so bound together, Sensations do not
give us any apprehension of Things or Objects. All Things,
all Objects, must exist in space and in time--must be one or
many. Now space, time, number, are not Sensations or Things.
They are something different from, and opposed to Sensations
and Things. We have termed them Ideas. It may be said they
are _Relations_ of Things, or of Sensations. But granting
this form of expression, still a _Relation_ is not a Thing
or a {47} Sensation; and therefore we must still have
another and opposite element, along with our Sensations. And
yet, though we have thus these two elements in every act of
perception, we cannot designate any portion of the act as
absolutely and exclusively belonging to one of the elements.
Perception involves Sensation, along with Ideas of time,
space, and the like; or, if any one prefers the expression,
we may say, Perception involves Sensations along with the
apprehension of Relations. Perception is Sensation, along
with such Ideas as make Sensation into an apprehension of
Things or Objects.

And as Perception of Objects implies Ideas,--as Observation
implies Reasoning;--so, on the other hand, Ideas cannot
exist where Sensation has not been; Reasoning cannot go on
when there has not been previous Observation. This is
evident from the necessary order of developement of the
human faculties. Sensation necessarily exists from the first
moments of our existence, and is constantly at work.
Observation begins before we can suppose the existence of
any Reasoning which is not involved in Observation. Hence,
at whatever period we consider our Ideas, we must consider
them as having been already engaged in connecting our
Sensations, and as having been modified by this employment.
By being so employed, our Ideas are unfolded and defined;
and such developement and definition cannot be separated
from the Ideas themselves. We cannot conceive space, without
boundaries or forms; now Forms involve Sensations. We cannot
conceive time, without events which mark the course of time;
but events involve Sensations. We cannot conceive number,
without conceiving things which are numbered; and Things
imply sensations. And the forms, things, events, which are
thus implied in our Ideas, having been the objects of
Sensation constantly in every part of our life, have
modified, unfolded, and fixed our Ideas, to an extent which
we cannot estimate, but which we must suppose to be
essential to the processes which at present go on in our
minds. We cannot say that Objects create Ideas; for to
perceive Objects we must already have Ideas. But we may {48}
say, that Objects and the constant Perception of Objects
have so far modified our Ideas, that we cannot, even in
thought, separate our Ideas from the perception of Objects.

We cannot say of any Ideas, as of the Idea of space, or
time, or number, that they are absolutely and exclusively
Ideas. We cannot conceive what space, or time, or number,
would be in our minds, if we had never perceived any Thing
or Things in space or time. We cannot conceive ourselves in
such a condition as never to have perceived any Thing or
Things in space or time. But, on the other hand, just as
little can we conceive ourselves becoming acquainted with
space and time or numbers as objects of Sensation. We cannot
reason without having the operations of our minds affected
by previous Sensations; but we cannot conceive Reasoning to
be merely a series of Sensations. In order to be used in
Reasoning, Sensation must become Observation; and, as we
have seen, Observation already involves Reasoning. In order
to be connected by our Ideas, Sensations must be Things or
Objects, and Things or Objects already include Ideas. And
thus, none of the terms by which the fundamental antithesis
is expressed can be absolutely and exclusively applied.

I will make a remark suggested by the views which have thus
been presented. Since, as we have just seen, none of the
terms which express the fundamental antithesis can be
applied absolutely and exclusively, the absolute application
of the antithesis in any particular case can never be a
conclusive or immoveable principle. This remark is the more
necessary to be borne in mind, as the terms of this
antithesis are often used in a vehement and peremptory
manner. Thus we are often told that such a thing is _a
Fact_; A FACT and not a Theory, with all the emphasis which,
in speaking or writing, tone or italics or capitals can
give. We see from what has been said, that when this is
urged, before we can estimate the truth, or the value of the
assertion, we must ask to whom is it a Fact? what habits of
thought, what previous information, what Ideas does it
imply, to conceive the Fact as a Fact? {49} Does not the
apprehension of the Fact imply assumptions which may with
equal justice be called Theory, and which are perhaps false
Theory? in which case, the Fact is no Fact. Did not the
ancients assert it as a Fact, that the earth stood still,
and the stars moved? and can any Fact have stronger apparent
evidence to justify persons in asserting it emphatically
than this had?

These remarks are by no means urged in order to show that no
Fact can be certainly known to be true; but only, to show
that no Fact can be certainly shown to be a Fact, merely by
calling it a Fact, however emphatically. There is by no
means any ground of general skepticism with regard to truth,
involved in the doctrine of the necessary combination of two
elements in all our knowledge. On the contrary, Ideas are
requisite to the essence, and Things to the reality of our
knowledge in every case. The proportions of Geometry and
Arithmetic are examples of knowledge respecting our Ideas of
space and number, with regard to which there is no room for
doubt. The doctrines of Astronomy are examples of truths not
less certain respecting the Facts of the external world.

_Sect._ 11.--_Successive Generalization._

IN the preceding pages we have been led to the doctrine,
that though, in the Antithesis of Theory and Fact, there is
involved an essential opposition; namely the opposition of
the thoughts within us and the phenomena without us; yet
that we cannot distinguish and define the members of this
antithesis separately. Theories become Facts, by becoming
certain and familiar: and thus, as our knowledge becomes
more sure and more extensive, we are constantly transferring
to the class of facts, opinions which were at first regarded
as theories.

Now we have further to remark, that in the progress of human
knowledge respecting any branch of speculation, there may be
several such steps in succession, each depending upon and
including the preceding. {50} The theoretical views which
one generation of discoverers establishes, become the facts
from which the next generation advances to new theories. As
men rise from the particular to the general, so, in the same
manner, they rise from what is general to what is more
general. Each induction supplies the materials of fresh
inductions; each generalization, with all that it embraces
in its circle, may be found to be but one of many circles,
comprehended within the circuit of some wider
generalization.

This remark has already been made, and illustrated, in the
_History of the Inductive Sciences_[2\1]; and, in truth, the
whole of the history of science is full of suggestions and
exemplifications of this course of things. It may be
convenient, however, to select a few instances which may
further explain and confirm this view of the progress of
scientific knowledge.

[Note 2\1: _Hist. Inductive Sciences_, b. vii. c. ii. sect. 5.]

The most conspicuous instance of this succession is to be
found in that science which has been progressive from the
beginning of the world to our own times, and which exhibits
by far the richest collection of successive discoveries: I
mean Astronomy. It is easy to see that each of these
successive discoveries depended on those antecedently made,
and that in each, the truths which were the highest point of
the knowledge of one age were the fundamental basis of the
efforts of the age which came next. Thus we find, in the
days of Greek discovery, Hipparchus and Ptolemy combining
and explaining the particular _facts_ of the motion of the
sun, moon, and planets, by means of the _theory_ of
epicycles and eccentrics;--a highly important step, which
gave an intelligible connexion and rule to the motions of
each of these luminaries. When these cycles and epicycles,
thus truly representing the apparent motions of the heavenly
bodies, had accumulated to an inconvenient amount, by the
discovery of many inequalities in the observed motions,
Copernicus showed that their effects might all be more
simply included, by making the sun the center of motion of
the planets, instead of {51} the earth. But in this new
view, he still retained the epicycles and eccentrics which
governed the motion of each body. Tycho Brahe's
observations, and Kepler's calculations, showed that,
besides the vast number of facts which the epicyclical
theory could account for, there were some which it would not
exactly include, and Kepler was led to the persuasion that
the planets move in ellipses. But this view of motion was at
first conceived by Kepler as a modification of the
conception of epicycles. On one occasion he blames himself
for not sooner seeing that such a modification was possible.
'What an absurdity on my part!' he cries[3\1]; 'as if
libration in the diameter of the epicycle might not come to
the same thing as motion in the ellipse.' But again;
Kepler's _laws_ of the elliptical motion of the planets were
established; and these laws immediately became the _facts_
on which the mathematicians had to found their mechanical
theories. From these facts, Newton, as we have related,
proved that the central force of the sun retains the planets
in their orbits, according to the law of the inverse square
of the distance. The same _law_ was shown to prevail in the
gravitation of the earth. It was shown, too, by induction
from the motions of Jupiter and Saturn, that the planets
attract each other; by calculations from the figure of the
earth, that the parts of the earth attract each other; and,
by considering the course of the tides, that the sun and
moon attract the waters of the ocean. And all these curious
discoveries being established as _facts_, the subject was
ready for another step of generalization. By an unparalleled
rapidity in the progress of discovery in this case, not only
were all the inductions which we have first mentioned made
by one individual, but the new advance, the higher flight,
the closing victory, fell to the lot of the same
extraordinary person.

[Note 3\1: _Hist. Inductive Sciences_, b. v. c. iv. sect. 3.]

The attraction of the sun upon the planets, of the moon upon
the earth, of the planets on each other, of the parts of the
earth on themselves, of the sun and {52} moon upon the
ocean;--all these truths, each of itself a great discovery,
were included by Newton in the higher _generalization_, of
the universal gravitation of matter, by which each particle
is drawn to every other according to the law of the inverse
square: and thus this long advance from discovery to
discovery, from truths to truths, each justly admired when
new, and then rightly used as old, was closed in a worthy
and consistent manner, by a truth which is the most worthy
admiration, because it includes all the researches of
preceding ages of Astronomy.

We may take another example of a succession of this kind
from the history of a science, which, though it has made
wonderful advances, has not yet reached its goal, as
physical astronomy appears to have done, but seems to have
before it a long prospect of future progress. I now refer to
Chemistry, in which I shall try to point out how the
preceding discoveries afforded the materials of the
succeeding; although this subordination and connexion is, in
this case, less familiar to men's minds than in Astronomy,
and is, perhaps, more difficult to present in a clear and
definite shape. Sylvius saw, in the facts which occur, when
an acid and an alkali are brought together, the evidence
that they neutralize each other. But cases of
neutralization, and acidification, and many other effects of
mixture of the ingredients of bodies, being thus viewed as
_facts_, had an aspect of unity and law given them by
Geoffroy and Bergman[4\1], who introduced the _conception_
of the Chemical Affinity or Elective Attraction, by which
certain elements select other elements, as if by preference.
That combustion, whether a chemical union or a chemical
separation of ingredients, is of the same nature with
acidification, was the doctrine of Beccher and Stahl, and
was soon established as a truth which must form a part of
every succeeding physical theory. That the rules of affinity
and chemical composition may include gaseous elements, was
established by Black and Cavendish. And all these truths,
thus brought to light by {53} chemical
discoverers,--affinity, the identity of acidification and
combustion, the importance of gaseous elements,--along with
all the facts respecting the weight of ingredients and
compounds which the balance disclosed,--were taken up,
connected, and included as _particulars_ in the oxygen
_theory_ of Lavoisier. Again, the results of this theory,
and the quantity of the several ingredients which entered
into each compound--(such results, for the most part, being
now no longer mere theoretical speculations, but recognized
facts)--were the _particulars_ from which Dalton derived
that wide law of chemical combination which we term the
Atomic _Theory_. And this law, soon generally accepted among
chemists, is already in its turn become one of the _facts_
included in Faraday's _Theory_ of the identity of Chemical
Affinity and Electric Attraction.

[Note 4\1: _Hist. Inductive Sciences_, b. xiv. c. iii.]

It is unnecessary to give further exemplifications of this
constant ascent from one step to a higher; this perpetual
conversion of true theories into the materials of other and
wider theories. It will hereafter be our business to
exhibit, in a more full and formal manner, the mode in which
this principle determines the whole scheme and structure of
all the most exact sciences. And thus, beginning with the
facts of sense, we gradually climb to the highest forms of
human knowledge, and obtain from experience and observation
a vast collection of the most wide and elevated truths.

There are, however, truths of a very different kind, to
which we must turn our attention, in order to pursue our
researches respecting the nature and grounds of our
knowledge. But before we do this, we must notice one more
feature in that progress of science which we have already in
part described.

{{54}}
CHAPTER II.

OF TECHNICAL TERMS.

1. IT has already been stated that we gather knowledge from
the external world, when we are able to apply, to the facts
which we observe, some ideal conception, which gives unity
and connexion to multiplied and separate perceptions. We
have also shown that our conceptions, thus verified by
facts, may themselves be united and connected by a new bond
of the same nature; and that man may thus have to pursue his
way from truth to truth through a long progression of
discoveries, each resting on the preceding, and rising above it.

Each of these steps, in succession, is recorded, fixed, and
made available, by some peculiar form of words; and such
words, thus rendered precise in their meaning, and
appropriated to the service of science, we may call
_Technical Terms_. It is in a great measure by inventing
such Terms that men not only best express the discoveries
they have made, but also enable their followers to become so
familiar with these discoveries, and to possess them so
thoroughly, that they can readily use them in advancing to
ulterior generalizations.

Most of our ideal conceptions are described by exact and
constant words or phrases, such as those of which we here
speak. We have already had occasion to employ many of these.
Thus we have had instances of technical Terms expressing
geometrical conceptions, as _Ellipsis_, _Radius Vector_,
_Axis_, _Plane_, the Proportion of the _Inverse Square_, and
the like. Other Terms have described mechanical conceptions,
as _Accelerating Force_ and _Attraction_. Again, chemistry
exhibits (as do all sciences) a series of Terms which mark
the steps of our {55} progress. The views of the first real
founders of the science are recorded by the Terms which are
still in use, _Neutral Salts_, _Affinity_, and the like. The
establishment of Dalton's theory has produced the use of the
word _Atom_ in a peculiar sense, or of some other word, as
_Proportion_, in a sense equally technical. And Mr. Faraday
has found it necessary, in order to expound his
electro-chemical theory, to introduce such terms as _Anode_
and _Cathode_, _Anïon_ and _Cathïon_.

2. I need not adduce any further examples, for my object at
present is only to point out the use and influence of such
language: its rules and principles I shall hereafter try, in
some measure, to fix. But what we have here to remark is,
the extraordinary degree in which the progress of science is
facilitated, by thus investing each new discovery with a
compendious and steady form of expression. These terms soon
become part of the current language of all who take an
interest in speculation. However strange they may sound at
first, they soon grow familiar in our ears, and are used
without any effort, or any recollection of the difficulty
they once involved. They become as common as the phrases
which express our most frequent feelings and interests,
while yet they have incomparably more precision than belongs
to any terms which express feelings; and they carry with
them, in their import, the results of deep and laborious
trains of research. They convey the mental treasures of one
period to the generations that follow; and laden with this,
their precious freight, they sail safely across gulfs of
time in which empires have suffered shipwreck, and the
languages of common life have sunk into oblivion. We have
still in constant circulation among us the Terms which
belong to the geometry, the astronomy, the zoology, the
medicine of the Greeks, and the algebra and chemistry of the
Arabians. And we can in an instant, by means of a few words,
call to our own recollection, or convey to the apprehension
of another person, phenomena and relations of phenomena in
optics, mineralogy, chemistry, which are so complex and
abstruse, that it might seem to require the utmost subtlety
of the human mind to {56} grasp them, even if that were made
the sole object of its efforts. By this remarkable effect of
Technical Language, we have the results of all the labours
of past times not only always accessible, but so prepared
that we may (provided we are careful in the use of our
instrument) employ what is really useful and efficacious for
the purpose of further success, without being in any way
impeded or perplexed by the length and weight of the chain
of past connexions which we drag along with us.

By such means,--by the use of the Inductive Process, and by
the aid of Technical Terms,--man has been constantly
advancing in the path of scientific truth. In a succeeding
part of this work we shall endeavour to trace the general
rules of this advance, and to lay down the maxims by which
it may be most successfully guided and forwarded. But in
order that we may do this to the best advantage, we must
pursue still further the analysis of knowledge into its
elements; and this will be our employment in the first part
of the work.

{{57}}
CHAPTER III.

OF NECESSARY TRUTHS.

1. EVERY advance in human knowledge consists, as we have
seen, in adapting new ideal conceptions to ascertained
facts, and thus in superinducing the Form upon the Matter,
the active upon the passive processes of our minds. Every
such step introduces into our knowledge an additional
portion of the ideal element, and of those relations which
flow from the nature of Ideas. It is, therefore, important
for our purpose to examine more closely this element, and to
learn what the relations are which may thus come to form
part of our knowledge. An inquiry into those Ideas which
form the foundations of our sciences;--into the reality,
independence, extent, and principal heads of the knowledge
which we thus acquire; is a task on which we must now enter,
and which will employ us for several of the succeeding Books.

In this inquiry our object will be to pass in review all the
most important Fundamental Ideas which our sciences involve;
and to prove more distinctly in reference to each, what we
have already asserted with regard to all, that there are
everywhere involved in our knowledge acts of the mind as
well as impressions of sense; and that our knowledge
derives, from these acts, a generality, certainty, and
evidence which the senses could in no degree have supplied.
But before I proceed to do this in particular cases, I will
give some account of the argument in its general form.

We have already considered the separation of our knowledge
into its two elements,--Impressions of Sense and Ideas,--as
evidently indicated by this; that all knowledge possesses
characters which neither of these {58} elements alone could
bestow. Without our ideas, our sensations could have no
connexion; without external impressions, our ideas would
have no reality; and thus both ingredients of our knowledge
must exist.

2. There is another mode in which the distinction of the two
elements of knowledge appears, as I have already said (c. i.
sect. 2): namely in the distinction of _necessary_, and
_contingent_ or _experiential_, truths. For of these two
classes of truths, the difference arises from this;--that
the one class derives its nature from the one, and the other
from the other, of the two elements of knowledge. I have
already stated briefly the difference of these two kinds of
truths:--namely, that the former are truths which, we see,
must be true:--the latter are true, but so far as we can
see, might be otherwise. The former are true necessarily and
universally: the latter are learnt from experience and
limited by experience. Now with regard to the former kind of
truths, I wish to show that the universality and necessity
which distinguish them can by no means be derived from
experience; that these characters do in reality flow from
the ideas which these truths involve; and that when the
necessity of the truth is exhibited in the way of logical
demonstration, it is found to depend upon certain
fundamental principles, (Definitions and Axioms,) which may
thus be considered as expressing, in some measure, the
essential characters of our ideas. These fundamental
principles I shall afterwards proceed to discuss and to
exhibit in each of the principal departments of science.

I shall begin by considering Necessary Truths more fully
than I have yet done. As I have already said, necessary
truths are those in which we not only learn, that the
proposition _is_ true, but see that it _must be_ true; in
which the negation of the truth is not only false, but
impossible; in which we cannot, even by an effort of
imagination, or in a supposition, conceive the reverse of
that which is asserted.

3. That there are such truths cannot be doubted. We may
take, for example, all relations of number. Three and Two
added together make Five. We cannot {59} conceive it to be
otherwise. We cannot, by any freak of thought, imagine Three
and Two to make Seven.

It may be said that this assertion merely expresses what we
mean by our words; that it is a matter of definition; that
the proposition is an identical one.

But this is by no means so. The definition of Five is not
Three and Two, but Four and One. How does it appear that
Three and Two is the same number as Four and One? It is
evident that it is so; but _why_ is it evident?--not because
the proposition is identical; for if that were the reason,
all numerical propositions must be evident for the same
reason. If it be a matter of definition that 3 and 2 make 5,
it must be a matter of definition that 39 and 27 make 66.
But who will say that the definition of 66 is 39 and 27? Yet
the magnitude of the numbers can make no difference in the
ground of the truth. How do we know that the product of 13
and 17 is 4 less than the product of 15 and 15? We see that
it is so, if we perform certain operations by the rules of
arithmetic; but how do we know the truth of the rules of
arithmetic? If we divide 123375 by 987 according to the
process taught us at school, how are we assured that the
result is correct, and that the number 125 thus obtained is
really the number of times one number is contained in the
other?

The correctness of the rule, it may be replied, can be
rigorously demonstrated. It can be shown that the process
must inevitably give the true quotient.

Certainly this can be shown to be the case. And precisely
because it _can_ be shown that the result must be true, we
have here an example of a necessary truth; and this truth,
it appears, is not _therefore_ necessary because it is
itself evidently identical, however it may be possible to
prove it by reducing it to evidently identical propositions.
And the same is the case with all other numerical
propositions; for, as we have said, the nature of all of
them is the same.

Here, then, we have instances of truths which are not only
true, but demonstrably and necessarily true. Now such truths
are, in this respect at least, altogether {60} different
from truths, which, however certain they may be, are learnt
to be so only by the evidence of observation, interpreted,
as observation must be interpreted, by our own mental
faculties. There is no difficulty in finding examples of
these merely observed truths. We find that sugar dissolves
in water, and forms a transparent fluid, but no one will say
that we can see any reason beforehand why the result _must_
be so. We find that all animals which chew the cud have also
the divided hoof; but could any one have predicted that this
would be universally the case? or supposing the truth of the
rule to be known, can any one say that he cannot conceive
the facts as occurring otherwise? Water expands when it
crystallizes, some other substances contract in the same
circumstances; but can any one know that this will be so
otherwise than by observation? We have here propositions
_rigorously_ true, (we will assume,) but can any one say
they are _necessarily_ true? These, and the great mass of
the doctrines established by induction, are actual, but so
far as we can see, accidental laws; results determined by
some unknown selection, not demonstrable consequences of the
essence of things, inevitable and perceived to be
inevitable. According to the phraseology which has been
frequently used by philosophical writers, they are
_contingent_, not necessary truths.

It is requisite to insist upon this opposition, because no
insight can be obtained into the true nature of knowledge,
and the mode of arriving at it, by any one who does not
clearly appreciate the distinction. The separation of truths
which are learnt by observation, and truths which can be
seen to be true by a pure act of thought, is one of the
first and most essential steps in our examination of the
nature of truth, and the mode of its discovery. If any one
does not clearly comprehend this distinction of necessary
and contingent truths, he will not be able to go along with
us in our researches into the foundations of human
knowledge; nor, indeed, to pursue with success any
speculation on the subject. But, in fact, this distinction
is one that can hardly fail to be at once understood. It
{61} is insisted upon by almost all the best modern, as well
as ancient, metaphysicians[5\1], as of primary importance.
And if any person does not fully apprehend, at first, the
different kinds of truth thus pointed out, let him study, to
some extent, those sciences which have necessary truth for
their subject, as geometry, or the properties of numbers, so
as to obtain a familiar acquaintance with such truth; and he
will then hardly fail to see how different the evidence of
the propositions which occur in these sciences, is from the
evidence of the facts which are merely learnt from
experience. That the year goes through its course in 365
days, can only be known by observation of the sun or stars:
that 365 days is 52 weeks and a day, it requires no
experience, but only a little thought to perceive. That bees
build their cells in the form of hexagons, we cannot know
without looking at them; that regular hexagons may be
arranged so as to fill space, may be proved with the utmost
rigour, even if there were not in existence such a thing as
a material hexagon.

[Note 5\1: Aristotle, Dr Whately, Dugald Stewart, &c.]

4. As I have already said, one mode in which we may express
the difference of necessary truths and truths of experience,
is, that necessary truths are those of which we cannot
distinctly conceive the contrary. We can very readily
conceive the contrary of experiential truths. We can
conceive the stars moving about the pole or across the sky
in any kind of curves with any velocities; we can conceive
the moon always appearing during the whole month as a
luminous disk, as she might do if her light were inherent
and not borrowed. But we cannot conceive one of the
parallelograms on the same base and between the same
parallels larger than the other; for we find that, if we
attempt to do this, when we separate the parallelograms into
parts, we have to conceive one triangle larger than another,
both having all their parts equal; which we cannot conceive
at all, if we conceive the triangles distinctly. We make
this impossibility more clear by conceiving {62} the
triangles to be placed so that two sides of the one coincide
with two sides of the other; and it is then seen, that in
order to conceive the triangles unequal, we must conceive
the two bases which have the same extremities both ways, to
be different lines, though both straight lines. This it is
impossible to conceive: we assent to the impossibility as an
axiom, when it is expressed by saying, that two straight
lines cannot inclose a space; and thus we cannot distinctly
conceive the contrary of the proposition just mentioned
respecting parallelograms.

But it is necessary, in applying this distinction, to bear
in mind the terms of it;--that we cannot _distinctly_
conceive the contrary of a necessary truth. For in a certain
loose, indistinct way, persons conceive the contrary of
necessary geometrical truths, when they erroneously conceive
false propositions to be true. Thus, Hobbes erroneously held
that he had discovered a means of geometrically 'doubling
the cube,' as it is called, that is, finding two mean
proportionals between two given lines; a problem which
cannot be solved by plane geometry. Hobbes not only proposed
a construction for this purpose, but obstinately maintained
that it was right, when it had been proved to be wrong. But
then, the discussion showed how indistinct the geometrical
conceptions of Hobbes were; for when his critics had proved
that one of the lines in his diagram would not meet the
other in the point which his reasoning supposed, but in
another point near to it; he maintained, in reply, that one
of these points was large enough to include the other, so
that they might be considered as the same point. Such a mode
of conceiving the opposite of a geometrical truth, forms no
exception to the assertion, that this opposite cannot be
distinctly conceived.

In like manner, the indistinct conceptions of children and
of rude savages do not invalidate the distinction of
necessary and experiential truths. Children and savages make
mistakes even with regard to numbers; and might easily
happen to assert that 27 and 38 are equal to 63 or 64. But
such mistakes cannot {63} make arithmetical truths cease to
be necessary truths. When any person conceives these numbers
and their addition distinctly, by resolving them into parts,
or in any other way, he sees that their sum is necessarily
65. If, on the ground of the possibility of children and
savages conceiving something different, it be held that this
is not a necessary truth, it must be held on the same
ground, that it is not a necessary truth that 7 and 4 are
equal to 11; for children and savages might be found so
unfamiliar with numbers as not to reject the assertion that
7 and 4 are 10, or even that 4 and 3 are 6, or 8. But I
suppose that no persons would on such grounds hold that
these arithmetical truths are truths known only by
experience.

5. I have taken examples of necessary truths from the
properties of number and space; but such truths exist no
less in other subjects, although the discipline of thought
which is requisite to perceive them distinctly, may not be
so usual among men with regard to the sciences of mechanics
and hydrostatics, as it is with regard to the sciences of
geometry and arithmetic. Yet every one may perceive that
there are such truths in mechanics. If I press the table
with my hand, the table presses my hand with an equal force:
here is a self-evident and necessary truth. In any machine,
constructed in whatever manner to increase the force which I
can exert, it is certain that what I gain in force I must
lose in the velocity which I communicate. This is not a
contingent truth, borrowed from and limited by observation;
for a man of sound mechanical views applies it with like
confidence, however novel be the construction of the
machine. When I come to speak of the ideas which are
involved in our mechanical knowledge, I may, perhaps, be
able to bring more clearly into view the necessary truth of
general propositions on such subjects. That reaction is
equal and opposite to action, is as necessarily true as that
two straight lines cannot inclose a space; it is as
impossible theoretically to make a perpetual motion by mere
mechanism as to make the diagonal of a square commensurable
with the side. {64}

6. Necessary truths must be _universal_ truths. If any
property belong to a right-angled triangle _necessarily_, it
must belong to _all_ right-angled triangles. And it shall be
proved in the following Chapter, that truths possessing
these two characters, of Necessity and Universality, cannot
possibly be the mere results of experience.

[Necessary truths are not considered as a portion of the
_Inductive_ Sciences. They are Deductions from our Ideas.
Thus the necessary truths which constitute the Science of
Geometry are Deductions from our Idea of Space: the
necessary truths which constitute the Science of Arithmetic
are Deductions from our notions of Number; which perhaps
involves necessarily the Idea of Time. But though we do not
call those Sciences _Inductive_ which involve properties of
Space, Number and Time alone, the properties of Space, Time
and Number enter in many very important ways into the
Inductive Sciences; and therefore the Ideas of Space, Time
and Number require to be considered in the first place. And
moreover the examination of these Ideas is an essential step
towards the examination of other Ideas: and the conditions
of the possibility and certainty of truth, which are
exemplified in Geometry and Arithmetic, open to us important
views respecting the conditions of the possibility and
certainty of all Scientific Truth. We shall therefore in the
next Book examine the Ideas on which the Pure Sciences,
Geometry and Arithmetic, are founded. But we must first say
a little more of Ideas in general.]

{{65}}
CHAPTER IV.

OF EXPERIENCE.

1. I HERE employ the term Experience in a more definite and
limited sense than that which it possesses in common usage;
for I restrict it to matters belonging to the domain of
science. In such cases, the knowledge which we acquire, by
means of experience, is of a clear and precise nature; and
the passions and feelings and interests, which make the
lessons of experience in practical matters so difficult to
read aright, no longer disturb and confuse us. We may,
therefore, hope, by attending to such cases, to learn what
efficacy experience really has, in the discovery of truth.

That from _experience_ (including intentional experience, or
_observation_,) we obtain much knowledge which is highly
important, and which could not be procured from any other
source, is abundantly clear. We have already taken several
examples of such knowledge. We know by experience that
animals which ruminate are cloven-hoofed; and we know this
in no other manner. We know, in like manner, that all the
planets and their satellites revolve round the sun from west
to east. It has been found by experience that all meteoric
stones contain chrome. Many similar portions of our
knowledge might be mentioned.

Now what we have here to remark is this;--that in no case
can experience prove a proposition to be _necessarily_ or
_universally_ true. However many instances we may have
observed of the truth of a proposition, yet if it be known
merely by observation, there is nothing to assure us that
the next case shall not be an exception to the rule. If it
be strictly true that every ruminant animal yet known has
cloven hoofs, we {66} still cannot be sure that some
creature will not hereafter be discovered which has the
first of these attributes without having the other. When the
planets and their satellites, as far as Saturn, had been all
found to move round the sun in one direction, it was still
possible that there might be other such bodies not obeying
this rule; and, accordingly, when the satellites of Uranus
were detected, they appeared to offer an exception of this
kind. Even in the mathematical sciences, we have examples of
such rules suggested by experience, and also of their
precariousness. However far they may have been tested, we
cannot depend upon their correctness, except we see some
reason for the rule. For instance, various rules have been
given, for the purpose of pointing out _prime numbers_; that
is, those which cannot be divided by any other number. We
may try, as an example of such a rule, this one--any odd
power of the number two, diminished by one. Thus the third
power of two, diminished by one, is seven; the fifth power,
diminished by one, is thirty-one; the seventh power so
diminished is one hundred and twenty-seven. All these are
prime numbers: and we might be led to suppose that the rule
is universal. But the next example shows us the
fallaciousness of such a belief. The ninth power of two,
diminished by one, is five hundred and eleven, which is not
a prime, being divisible by seven.

Experience must always consist of a limited number of
observations. And, however numerous these may be, they can
show nothing with regard to the infinite number of cases in
which the experiment has not been made. Experience being
thus unable to prove a fact to be universal, is, as will
readily be seen, still more incapable of proving a truth to
be necessary. Experience cannot, indeed, offer the smallest
ground for the necessity of a proposition. She can observe
and record what has happened; but she cannot find, in any
case, or in any accumulation of cases, any reason for what
must happen. She may see objects side by side; but she
cannot see a reason why they must ever be side by side. She
finds certain events to occur in succession; but the
succession supplies, in its occurrence, no {67} reason for
its recurrence. She contemplates external objects; but she
cannot detect any internal bond, which indissolubly connects
the future with the past, the possible with the real. To
learn a proposition by experience, and to see it to be
necessarily true, are two altogether different processes of
thought.

2. But it may be said, that we do learn by means of
observation and experience many universal truths; indeed,
all the general truths of which science consists. Is not the
doctrine of universal gravitation learnt by experience? Are
not the laws of motion, the properties of light, the general
principles of chemistry, so learnt? How, with these examples
before us, can we say that experience teaches no universal
truths?

To this we reply, that these truths can only be known to be
general, not universal, if they depend upon experience
alone. Experience cannot bestow that universality which she
herself cannot have, and that necessity of which she has no
comprehension. If these doctrines _are_ universally true,
this universality flows from the _ideas_ which we apply to
our experience, and which are, as we have seen, the real
sources of necessary truth. How far these ideas can
communicate their universality and necessity to the results
of experience, it will hereafter be our business to
consider. It will then appear, that when the mind collects
from observation truths of a wide and comprehensive kind,
which approach to the simplicity and universality of the
truths of pure science; she gives them this character by
throwing upon them the light of her own Fundamental Ideas.

But the truths which we discover by observation of the
external world, even when most strikingly simple and
universal, are not necessary truths. Is the doctrine of
universal gravitation necessarily true? It was doubted by
Clairaut (so far as it refers to the moon), when the
progression of the apogee in fact appeared to be twice as
great as the theory admitted. It has been doubted, even more
recently, with respect to the planets, their mutual
perturbations appearing to indicate a deviation from the
law. It is doubted still, by some {68} persons, with respect
to the double stars. But suppose all these doubts to be
banished, and the law to be universal; is it then proved to
be necessary? Manifestly not: the very existence of these
doubts proves that it is not so. For the doubts were
dissipated by reference to observation and calculation, not
by reasoning on the nature of the law. Clairaut's difficulty
was removed by a more exact calculation of the effect of the
sun's force on the motion of the apogee. The suggestion of
Bessel, that the intensity of gravitation might be different
for different planets, was found to be unnecessary, when
Professor Airy gave a more accurate determination of the
mass of Jupiter. And the question whether the extension of
the law of the inverse square to the double stars be true,
(one of the most remarkable questions now before the
scientific world,) must be answered, not by any speculations
concerning what the laws of attraction must necessarily be,
but by carefully determining the actual laws of the motion
of these curious objects, by means of the observations such
as those which Sir John Herschel has collected for that
purpose, by his unexampled survey of both hemispheres of the
sky. And since the extent of this truth is thus to be
determined by reference to observed facts, it is clear that
no mere accumulation of them can make its universality
certain, or its necessity apparent.

Thus no knowledge of the necessity of any truths can result
from the observation of what really happens. This being
clearly understood, we are led to an important inquiry.

The characters of universality and necessity in the truths
which form part of our knowledge, can never be derived from
experience, by which so large a part of our knowledge is
obtained. But since, as we have seen, we really do possess a
large body of truths which are necessary, and because
necessary, therefore universal, the question still recurs,
from what source these characters of universality and
necessity are derived.

The answer to this question we will attempt to give in the
next chapter.

{{69}}
CHAPTER V.

OF THE GROUNDS OF NECESSARY TRUTHS.

1. TO the question just stated, I reply, that the necessity
and universality of the truths which form a part of our
knowledge, are derived from the _Fundamental Ideas_ which
those truths involve. These ideas entirely shape and
circumscribe our knowledge; they regulate the active
operations of our minds, without which our passive
sensations do not become knowledge. They govern these
operations, according to rules which are not only fixed and
permanent, but which may be expressed in plain and definite
terms; and these rules, when thus expressed, may be made the
basis of demonstrations by which the necessary relations
imparted to our knowledge by our Ideas may be traced to
their consequences in the most remote ramifications of
scientific truth.

These enunciations of the necessary and evident conditions
imposed upon our knowledge by the Fundamental Ideas which it
involves, are termed _Axioms_. Thus the Axioms of Geometry
express the necessary conditions which result from the Idea
of Space; the Axioms of Mechanics express the necessary
conditions which flow from the Ideas of Force and Motion;
and so on.

2. It will be the office of several of the succeeding Books
of this work to establish and illustrate in detail what I
have thus stated in general terms. I shall there pass in
review many of the most important fundamental ideas on which
the existing body of our science depends; and I shall
endeavour to show, for each such idea in succession, that
knowledge involves an active as well as a passive element;
that it is not possible without an act of the mind,
regulated by certain {70} laws. I shall further attempt to
enumerate some of the principal fundamental relations which
each idea thus introduces into our thoughts, and to express
them by means of definitions and axioms, and other suitable
forms.

I will only add a remark or two to illustrate further this
view of the ideal grounds of our knowledge.

3. To persons familiar with any of the demonstrative
sciences, it will be apparent that if we state all the
Definitions and Axioms which are employed in the
demonstrations, we state the whole basis on which those
reasonings rest. For the whole process of demonstrative or
deductive reasoning in any science, (as in geometry, for
instance,) consists entirely in combining some of these
first principles so as to obtain the simplest propositions
of the science; then combining these so as to obtain other
propositions of greater complexity; and so on, till we
advance to the most recondite demonstrable truths; these
last, however intricate and unexpected, still involving no
principles except the original definitions and axioms. Thus,
by combining the Definition of a triangle, and the
Definitions of equal lines and equal angles, namely, that
they are such as when applied to each other, coincide, with
the Axiom respecting straight lines (that two such lines
cannot inclose a space,) we demonstrate the equality of
triangles, under certain assumed conditions. Again, by
combining this result with the Definition of parallelograms,
and with the Axiom that if equals be taken from equals the
wholes are equal, we prove the equality of parallelograms
between the same parallels and upon the same base. From this
proposition, again, we prove the equality of the square on
the hypotenuse of a triangle to the squares on the two sides
containing the right angle. But in all this there is nothing
contained which is not rigorously the result of our
geometrical Definitions and Axioms. All the rest of our
treatises of geometry consists only of terms and phrases of
reasoning, the object of which is to connect those first
principles, and to exhibit the effects of their combination
in the shape of demonstration. {71}

4. This combination of first principles takes place
according to the forms and rules of _Logic_. All the steps
of the demonstration may be stated in the shape in which
logicians are accustomed to exhibit processes of reasoning
in order to show their conclusiveness, that is, in
_Syllogisms_. Thus our geometrical reasonings might be
resolved into such steps as the following:--
All straight lines drawn from the centre of a circle to its
circumference are equal:
But the straight lines AB, AC, are drawn from the centre of
a circle to its circumference:
Therefore the straight lines AB, AC, are equal.

Each step of geometrical, and all other demonstrative
reasoning, may be resolved into three such clauses as these;
and these three clauses are termed respectively, the _major
premiss_, the _minor premiss_, and the _conclusion_; or,
more briefly, the _major_, the _minor_, and the
_**conclusion_.

The principle which justifies the reasoning when exhibited
in this syllogistic form, is this:--that a truth which can
be asserted as generally, or rather as universally true, can
be asserted as true also in each particular case. The
_minor_ only asserts a certain particular case to be an
example of such conditions as are spoken of in the _major_;
and hence the conclusion, which is true of the major by
supposition, is true of the minor by consequence; and thus
we proceed from syllogism to syllogism, in each one
employing some general truth in some particular instance.
Any proof which occurs in geometry, or any other science of
demonstration, may thus be reduced to a series of processes,
in each of which we pass from some general proposition to
the narrower and more special propositions which it
includes. And this process of deriving truths by the mere
combination of general principles, applied in particular
hypothetical cases, is called _deduction_; being opposed to
_induction_, in which, as we have seen (chap. i. sect. 3), a
new general principle is introduced at every step.

5. Now we have to remark that, this being so, however far we
follow such deductive reasoning, we can {72} never have, in
our conclusion any truth which is not virtually included in
the original principles from which the reasoning started.
For since at any step we merely take out of a general
proposition something included in it, while at the preceding
step we have taken this general proposition out of one more
general, and so on perpetually, it is manifest that our last
result was really included in the principle or principles
with which we began. I say _principles_, because, although
our logical conclusion can only exhibit the legitimate issue
of our first principles, it may, nevertheless, contain the
result of the combination of several such principles, and
may thus assume a great degree of complexity, and may appear
so far removed from the parent truths, as to betray at first
sight hardly any relationship with them. Thus the
proposition which has already been quoted respecting the
squares on the sides of a right-angled triangle, contains
the results of many elementary principles; as, the
definitions of parallels, triangle, and square; the axioms
respecting straight lines, and respecting parallels; and,
perhaps, others. The conclusion is complicated by containing
the effects of the combination of all these elements; but it
contains nothing, and can contain nothing, but such elements
and their combinations.

This doctrine, that logical reasoning produces no new
truths, but only unfolds and brings into view those truths
which were, in effect, contained in the first principles of
the reasoning, is assented to by almost all who, in modern
times, have attended to the science of logic. Such a view is
admitted both by those who defend, and by those who
depreciate the value of logic. 'Whatever is established by
reasoning, must have been contained and virtually asserted
in the premises[6\1].' 'The only truth which such
propositions can possess consists in conformity to the
original principles.'

[Note 6\1: Whately's _Logic_, pp. 237, 238.]

In this manner the whole substance of our geometry is
reduced to the Definitions and Axioms which we employ in our
elementary reasonings; and in like {73} manner we reduce the
demonstrative truths of any other science to the definitions
and axioms which we there employ.

6. But in reference to this subject, it has sometimes been
said that demonstrative sciences do in reality depend upon
Definitions only; and that no additional kind of principle,
such as we have supposed Axioms to be, is absolutely
required. It has been asserted that in geometry, for
example, the source of the necessary truth of our
propositions is this, that they depend upon definitions
alone, and consequently merely state the identity of the
same thing under different aspects.

That in the sciences which admit of demonstration, as
geometry, mechanics, and the like, Axioms as well as
Definitions are needed, in order to express the grounds of
our necessary convictions, must be shown hereafter by an
examination of each of these sciences in particular. But
that the propositions of these sciences, those of geometry
for example, do not merely assert the identity of the same
thing, will, I think, be generally allowed, if we consider
the assertions which we are enabled to make. When we declare
that 'a straight line is the shortest distance between two
points,' is this merely an identical proposition? the
definition of a straight line in another form? Not so: the
definition of a straight line involves the notion of form
only, and does not contain anything about magnitude;
consequently, it cannot contain anything equivalent to
'shortest.' Thus the propositions of geometry are not merely
identical propositions; nor have we in their general
character anything to countenance the assertion, that they
are the results of definitions alone. And when we come to
examine this and other sciences more closely, we shall find
that axioms, such as are usually in our treatises made the
fundamental principles of our demonstrations, neither have
ever been, nor can be, dispensed with. Axioms, as well as
Definitions, are in all cases requisite, in order properly
to exhibit the grounds of necessary truth.

7. Thus the real logical basis of every body of demonstrated
truths are the Definitions and Axioms {74} which are the
first principles of the reasonings. But when we are arrived
at this point, the question further occurs, what is the
ground of the truth of these Axioms? It is not the logical,
but the philosophical, not the formal, but the real
foundation of necessary truth, which we are seeking. Hence
this inquiry necessarily comes before us, What is the ground
of the Axioms of Geometry, of Mechanics, and of any other
demonstrable science?

The answer which we are led to give, by the view which we
have taken of the nature of knowledge, has already been
stated. The ground of the axioms belonging to each science
is the _Idea_ which the axiom involves. The ground of the
Axioms of Geometry is the _Idea of Space_: the ground of the
Axioms of Mechanics is the _Idea of Force_, of _Action_ and
_Reaction_, and the like. And hence these Ideas are
Fundamental Ideas; and since they are thus the foundations,
not only of demonstration but of truth, an examination into
their real import and nature is of the greatest consequence
to our purpose.

8. Not only the Axioms, but the definitions which form the
basis of our reasonings, depend upon our Fundamental Ideas.
And the Definitions are not arbitrary definitions, but are
determined by a necessity no less rigorous than the Axioms
themselves. We could not think of geometrical truths without
conceiving a circle; and we could not reason concerning such
truths without defining a circle in some mode equivalent to
that which is commonly adopted. The Definitions of
parallels, of right angles, and the like, are quite as
necessarily prescribed by the nature of the case, as the
Axioms which these Definitions bring with them. Indeed we
may substitute one of these kinds of principles for another.
We cannot always put a Definition in the place of an Axiom;
but we may always find an Axiom which shall take the place
of a Definition. If we assume a proper Axiom respecting
straight lines, we need no Definition of a straight line.
But in whatever shape the principle appear, as Definition or
as Axiom, it has about it nothing casual or {75} arbitrary,
but is determined to be what it is, as to its import, by the
most rigorous necessity, growing out of the Idea of Space.

9. These principles,--Definitions, and Axioms,--thus
exhibiting the primary developments of a fundamental idea,
do in fact express the idea, so far as its expression in
words forms part of our science. They are different views of
the same body of truth; and though each principle, by
itself, exhibits only one aspect of this body, taken
together they convey a sufficient conception of it for our
purposes. The Idea itself cannot be fixed in words; but
these various lines of truth proceeding from it, suggest
sufficiently to a fitly-prepared mind, the place where the
idea resides, its nature, and its efficacy.

It is true that these principles,--our elementary
Definitions and Axioms,--even taken all together, express
the Idea incompletely. Thus the Definitions and Axioms of
Geometry, as they are stated in our elementary works, do not
fully express the Idea of Space as it exists in our minds.
For, in addition to these, other Axioms, independent of
these, and no less evident, can be stated; and are in fact
stated when we come to the Higher Geometry. Such, for
instance, is the Axiom of Archimedes--that a curve line
which joins two points is less than a broken line which
joins the same points and includes the curve. And thus the
Idea is disclosed but not fully revealed, imparted but not
transfused, by the use we make of it in science. When we
have taken from the fountain so much as serves our purpose,
there still remains behind a deep well of truth, which we
have not exhausted, and which we may easily believe to be
inexhaustible.

{{76}}
CHAPTER VI.

THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE.

1. BY the course of speculation contained in the last three
Chapters, we are again led to the conclusion which we have
already stated, that our knowledge contains an ideal
element, and that this element is not derived from
experience. For we have seen that there are propositions
which are known to be necessarily true; and that such
knowledge is not, and cannot be, obtained by mere
observation of actual facts. It has been shown, also, that
these necessary truths are the results of certain
fundamental ideas, such as those of space, number, and the
like. Hence it follows inevitably that these ideas and
others of the same kind are not derived from experience. For
these ideas possess a power of infusing into their
developments that very necessity which experience can in no
way bestow. This power they do not borrow from the external
world, but possess by their own nature. Thus we unfold out
of the Idea of Space the propositions of geometry, which are
plainly truths of the most rigorous necessity and
universality. But if the idea of space were merely collected
from observation of the external world, it could never
enable or entitle us to assert such propositions: it could
never authorize us to say that not merely some lines, but
_all_ lines, not only have, but _must_ have, those
properties which geometry teaches. Geometry in every
proposition speaks a language which experience never dares
to utter; and indeed of which she but half comprehends the
meaning. Experience sees that the assertions are true, but
she sees not how profound and absolute is their truth. {77}
She unhesitatingly assents to the laws which geometry
delivers, but she does not pretend to see the origin of
their obligation. She is always ready to acknowledge the
sway of pure scientific principles as a matter of fact, but
she does not dream of offering her opinion on their
authority as a matter of right; still less can she justly
claim to be herself the source of that authority.

David Hume asserted[7\1], that we are incapable of seeing in
any of the appearances which the world presents anything of
necessary connexion; and hence he inferred that our
knowledge cannot extend to any such connexion. It will be
seen from what we have said that we assent to his remark as
to the fact, but we differ from him altogether in the
consequence to be drawn from it. Our inference from Hume's
observation is, not the truth of his conclusion, but the
falsehood of his premises;--not that, therefore, we can know
nothing of natural connexion, but that, therefore, we have
some other source of knowledge than experience:--not, that
we can have no idea of connexion or causation, because, in
his language, it cannot be the copy of an impression; but
that since we have such an idea, our ideas are not the
copies of our impressions.

[Note 7\1: _Essays_, vol. ii. p. 70.]

Since it thus appears that our fundamental ideas are not
acquired from the external world by our senses, but have
some separate and independent origin, it is important for us
to examine their nature and properties, as they exist in
themselves; and this it will be our business to do through a
portion of the following pages. But it may be proper first
to notice one or two objections which may possibly occur to
some readers.

2. It may be said that without the use of our senses, of
sight and touch, for instance, we should never have any idea
of space; that this idea, therefore, may properly be said to
be derived from those senses. And to this I reply, by
referring to a parallel instance. Without light we should
have no perception of visible {78} figure; yet the power of
perceiving visible figure cannot be said to be derived from
the light, but resides in the structure of the eye. If we
had never seen objects in the light, we should be quite
unaware that we possessed a power of vision; yet we should
not possess it the less on that account. If we had never
exercised the senses of sight and touch (if we can conceive
such a state of human existence) we know not that we should
be conscious of an idea of space. But the light reveals to
us at the same time the existence of external objects and
our own power of seeing. And in a very similar manner, the
exercise of our senses discloses to us, at the same time,
the external world, and our own ideas of space, time, and
other conditions, without which the external world can
neither be observed nor conceived. That light is necessary
to vision, does not, in any degree, supersede the importance
of a separate examination of the laws of our visual powers,
if we would understand the nature of our own bodily
faculties and the extent of the information they can give
us. In like manner, the fact that intercourse with the
external world is necessary for the conscious employment of
our ideas, does not make it the less essential for us to
examine those ideas in their most intimate structure, in
order that we may understand the grounds and limits of our
knowledge. Even before we see a single object, we have a
faculty of vision; and in like manner, if we can suppose a
man who has never contemplated an object in space or time,
we must still assume him to have the faculties of
entertaining the ideas of space and time, which faculties
are called into play on the very first occasion of the use
of the senses.

3. In answer to such remarks as the above, it has sometimes
been said that to assume separate faculties in the mind for
so many different processes of thought, is to give a mere
verbal explanation, since we learn nothing concerning our
idea of space by being told that we have a faculty of
forming such an idea. It has been said that this course of
explanation leads to an endless multiplication of elements
in man's nature, without any advantage to our knowledge of
his true {79} constitution. We may, it is said, assert man
to have a faculty of walking, of standing, of breathing, of
speaking; but what, it is asked, is gained by such
assertions? To this I reply, that we undoubtedly have such
faculties as those just named; that it is by no means
unimportant to consider them; and that the main question in
such cases is, whether they are separate and independent
faculties, or complex and derivative ones; and, if the
latter be the case, what are the simple and original
faculties by the combination of which the others are
produced. In walking, standing, breathing, for instance, a
great part of the operation can be reduced to one single
faculty; the voluntary exercise of our muscles. But in
breathing this does not appear to be the whole of the
process. The operation is, in part at least, involuntary;
and it has been held that there is a certain sympathetic
action of the nerves, in addition to the voluntary agency
which they transmit, which is essential to the function. To
determine whether or no this sympathetic faculty is real and
distinct, and if so, what are its laws and limits, is
certainly a highly philosophical inquiry, and well deserving
the attention which has been bestowed upon it by eminent
physiologists. And just of the same nature are the inquiries
with respect to man's intellectual constitution, on which we
propose to enter. For instance, man has a faculty of
apprehending time, and a faculty of reckoning numbers: are
these distinct, or is one faculty derived from the other? To
analyze the various combinations of our ideas and
observations into the original faculties which they involve;
to show that these faculties are original, and not capable
of further analysis: to point out the characters which mark
these faculties and lead to the most important features of
our knowledge;--these are the kind of researches on which we
have now to enter, and these, we trust, will be found to be
far from idle or useless parts of our plan. If we succeed in
such attempts, it will appear that it is by no means a
frivolous or superfluous step to distinguish separate
faculties in the mind. If we do not learn much by being told
that we have a faculty {80} of forming the idea of space, we
at least, by such a commencement, circumscribe a certain
portion of the field of our investigations, which, we shall
afterwards endeavour to show, requires and rewards a special
examination. And though we shall thus have to separate the
domain of our philosophy into many provinces, these are, as
we trust it will appear, neither arbitrarily assigned, nor
vague in their limits, nor infinite in number.

{{81}}
CHAPTER VII.

OF THE PHILOSOPHY OF THE SCIENCES.

WE proceed, in the ensuing Books, to the closer examination
of a considerable number of those Fundamental Ideas on which
the sciences, hitherto most successfully cultivated, are
founded. In this task, our objects will be to explain and
analyze such Ideas so as to bring into view the Definitions
and Axioms, or other forms, in which we may clothe the
conditions to which our speculative knowledge is subjected.
I shall also try to prove, for some of these Ideas in
particular, what has been already urged respecting them in
general, that they are not derived from observation, but
necessarily impose their conditions upon that knowledge of
which observation supplies the materials. I shall further,
in some cases, endeavour to trace the history of these Ideas
as they have successively come into notice in the progress
of science; the gradual development by which they have
arrived at their due purity and clearness; and, as a
necessary part of such a history, I shall give a view of
some of the principal controversies which have taken place
with regard to each portion of knowledge.

An exposition and discussion of the Fundamental Ideas of
each Science may, with great propriety, be termed the
PHILOSOPHY OF such SCIENCE. These ideas contain in
themselves the elements of those truths which the science
discovers and enunciates; and in the progress of the
sciences, both in the world at large and in the mind of each
individual student, the most important steps consist in
apprehending these ideas clearly, and in bringing them into
accordance with the observed facts. I shall, therefore, in a
series of Books, {82} treat of the _Philosophy of the Pure
Sciences_, the _Philosophy of the Mechanical Sciences_, the
_Philosophy of Chemistry_, and the like, and shall analyze
and examine the ideas which these sciences respectively
involve.

In this undertaking, inevitably somewhat long, and involving
many deep and subtle discussions, I shall take, as a chart
of the country before me, by which my course is to be
guided, the scheme of the sciences which I was led to form
by travelling over the history of each in order[8\1]. Each
of the sciences of which I then narrated the progress,
depends upon several of the Fundamental Ideas of which I
have to speak: some of these Ideas are peculiar to one field
of speculation, others are common to more. A previous
enumeration of Ideas thus collected may serve both to show
the course and limits of this part of our plan, and the
variety of interest which it offers.

[Note 8\1: _History of the Inductive Sciences._]

I shall, then, successively, have to speak Of the Ideas
which are the foundation of Geometry and Arithmetic, (and
which also regulate all sciences depending upon these, as
Astronomy and Mechanics;) namely, the Ideas of _Space_,
_Time_, and _Number_ (Book II.):

Of the Ideas on which the Mechanical Sciences (as Mechanics,
Hydrostatics, Physical Astronomy) more peculiarly rest; the
ideas of _Force_ and _Matter_, or rather the idea of
_Cause_, which is the basis of these (Book III.):

Of the Ideas which the Secondary Mechanical Sciences
(Acoustics, Optics, and Thermotics) involve; namely, the
Ideas of the _Externality_ of objects, and of the _Media_ by
which we perceive their qualities (Book IV.):

Of the Ideas which are the basis of Mechanico-chemical and
Chemical Science; _Polarity_, _Chemical Affinity_, and
_Substance_; and the Idea of _Symmetry_, a necessary part of
the Philosophy of Crystallography (Books V. VI.):

Of the Ideas on which the Classificatory Sciences proceed
(Mineralogy, Botany, and Zoology); namely, {83} the Ideas of
_Resemblance_, and of its gradations, and of _Natural
Affinity_ (Books VII. VIII.):

Finally, of those Ideas on which the Physiological Sciences
are founded; the Ideas of separate Vital Powers, such as
_Assimilation_ and _Irritability_; and the Idea of _Final
Cause_ (Book IX.):

We have, besides these, the Palætiological Sciences, which
proceed mainly on the conception of _Historical Causation_
(Book X.):

It is plain that when we have proceeded so far as this, we
have advanced to the verge of those speculations which have
to do with mind as well as body. The extension of our
philosophy to such a field, if it can be justly so extended,
will be one of the most important results of our researches;
but on that very account we must fully study the lessons
which we learn in those fields of speculation where our
doctrines are most secure, before we venture into a region
where our principles will appear to be more precarious, and
where they are inevitably less precise.

We now proceed to the examination of the above Ideas, and to
such essays towards the philosophy of each Science as this
course of investigation may suggest.

{{85}}
BOOK II.

THE
PHILOSOPHY
OF THE
PURE SCIENCES.

The way in which we are led to regard human knowledge is
like the way in which Copernicus was led to regard the
heavens. When the explanation of the celestial motions could
not be made to go right so long as he assumed that all the
host of stars turns round the spectator, he tried whether it
would not answer better if he made the spectator turn, and
left the stars at rest. We may make a similar trial in
Metaphysics, as to our way of looking at objects. If our
view of them must be governed altogether by the properties
of the objects themselves, I see not how man can know
anything about them _à priori_. But if the thing, as an
object of the senses, is regulated by the constitution of
our power of knowing, I can very readily represent to myself
this possibility.

KANT, _Kritik d. R. V. Pref._

{{87}}
BOOK II.

THE PHILOSOPHY OF THE PURE SCIENCES.

[The principal question discussed in the last Book was this
(see chaps. V. and VI.): How are _necessary_ and _universal_
truths possible? And the answer then given was: that the
necessity and universality of truths are derived from the
_Fundamental Ideas_ which they involve. And we proceed in
this Book to exemplify this doctrine in the case of the
truths of Geometry and Arithmetic, which derive their
necessity and universality from the Fundamental Ideas of
Space, and Time, or Number.

The question thus examined is that which Kant undertook to
deal with in his celebrated work, _Kritik der reinen
Vernunft_ (_Examination of the Pure Reason_): and our
solution of the Problem, so far as the Ideas of Space and
Time are concerned, agrees in the main with his. The
arguments contained in chapters II. and **VII. of this Book,
are the leading arguments respecting Space and Time, in
Kant's _Kritik_. Kant, however, instead of calling Space and
Time _Ideas_, calls them the necessary _Forms_ of our
experience, as I have stated in the text.

But though I have adopted Kant's arguments as to Space and
Time, all that follows in the succeeding Books, with regard
to other Ideas, has no resemblance to any doctrines of Kant
or his school (with the exception, perhaps, of some of the
views on the Idea of _Cause_). The nature and character of
the other Scientific Ideas which I have examined, in the
succeeding Books, have been established by an analysis of
the history of the several Sciences to which those Ideas are
essential, and an examination of the writings of the
principal discoverers in those Sciences.]

{{88}}
CHAPTER I.

OF THE PURE SCIENCES.

1. ALL external objects and events which we can contemplate
are viewed as having relations of Space, Time, and Number;
and are subject to the general conditions which these Ideas
impose, as well as to the particular laws which belong to
each class of objects and occurrences. The special laws of
nature, considered under the various aspects which
constitute the different sciences, are obtained by a mixed
reference to Experience and to the Fundamental Ideas of each
science. But besides the sciences thus formed by the aid of
special experience, the conditions which flow from those
more comprehensive ideas first mentioned, Space, Time, and
Number, constitute a body of science, applicable to objects
and changes of all kinds, and deduced without recurrence
being had to any observation in particular. These sciences,
thus unfolded out of ideas alone, unmixed with any reference
to the phenomena of matter, are hence termed _Pure_
Sciences. The principal sciences of this class are Geometry,
Theoretical Arithmetic, and Algebra considered in its most
general sense, as the investigation of the relations of
space and number by means of general symbols.

2. These Pure Sciences were not included in our survey of
the history of the sciences, because they are not
_inductive_ sciences. Their progress has not consisted in
collecting laws from phenomena, true theories from observed
facts, and more general from more limited laws; but in
tracing the consequences of the ideas themselves, and in
detecting the most general and intimate analogies and
connexions which prevail {89} among such conceptions as are
derivable from the ideas. These sciences have no principles
besides definitions and axioms, and no process of proof but
_deduction_; this process, however, assuming here a most
remarkable character; and exhibiting a combination of
simplicity and complexity, of rigour and generality, quite
unparalleled in other subjects.

3. The universality of the truths, and the rigour of the
demonstrations of these pure sciences, attracted attention
in the earliest times; and it was perceived that they
offered an exercise and a discipline of the intellectual
faculties, in a form peculiarly free from admixture of
extraneous elements. They were strenuously cultivated by the
Greeks, both with a view to such a discipline, and from the
love of speculative truth which prevailed among that people:
and the name _mathematics_, by which they are designated,
indicates this their character of _disciplinal_ studies.

4. As has already been said, the ideas which these sciences
involve extend to all the objects and changes which we
observe in the external world; and hence the consideration
of mathematical relations forms a large portion of many of
the sciences which treat of the phenomena and laws of
external nature, as Astronomy, Optics, and Mechanics. Such
sciences are hence often termed _Mixed Mathematics_, the
relations of space and number being, in these branches of
knowledge, combined with principles collected from special
observation; while Geometry, Algebra, and the like subjects,
which involve no result of experience, are called _Pure
Mathematics_.

5. Space, time, and number, may be conceived as _forms_ by
which the knowledge derived from our sensations is moulded,
and which are independent of the differences in the _matter_
of our knowledge, arising from the sensations themselves.
Hence the sciences which have these ideas for their subject
may be termed _Formal Sciences_. In this point of view, they
are distinguished from sciences in which, besides these mere
formal laws by which appearances are corrected, we endeavour
to apply to the phenomena the idea of cause, {90} or some of
the other ideas which penetrate further into the principles
of nature. We have thus, in the History, distinguished
Formal Astronomy and Formal Optics from Physical Astronomy
and Physical Optics.

We now proceed to our examination of the Ideas which
constitute the foundation of these formal or pure
mathematical sciences, beginning with the Idea of Space.

{{91}}
CHAPTER II.

OF THE IDEA OF SPACE.

1. BY speaking of space as an Idea, I intend to imply, as
has already been stated, that the apprehension of objects as
existing in space, and of the relations of position, &c.,
prevailing among them, is not a consequence of experience,
but a result of a peculiar constitution and activity of the
mind, which is independent of all experience in its origin,
though constantly combined with experience in its exercise.

That the idea of space is thus independent of experience,
has already been pointed out in speaking of ideas in
general: but it may be useful to illustrate the doctrine
further in this particular case.

I assert, then, that space is not a notion obtained by
experience. Experience gives us information concerning
things without us: but our apprehending them _as_ without
us, takes for granted their existence in space. Experience
acquaints us what are the form, position, magnitude of
particular objects: but that they have form, position,
magnitude, presupposes that they are in space. We cannot
derive from appearances, by the way of observation, the
habit of representing things to ourselves as in space; for
no single act of observation is possible any otherwise than
by beginning with such a representation, and conceiving
objects as already existing in space.

2. That our mode of representing space to ourselves is not
derived from experience, is clear also from this: that
through this mode of representation we arrive at
propositions which are rigorously universal and necessary.
Propositions of such a kind could not possibly be obtained
from experience; for experience can {92} only teach us by a
limited number of examples, and therefore can never securely
establish a universal proposition: and again, experience can
only inform us that anything is so, and can never prove that
it must be so. That two sides of a triangle are greater than
the third is a universal and necessary geometrical truth: it
is true of all triangles; it is true in such a way that the
contrary cannot be conceived. Experience could not prove
such a proposition. And experience has not proved it; for
perhaps no man ever made the trial as a means of removing
doubts: and no trial could, in fact, add in the smallest
degree to the certainty of this truth. To seek for proof of
geometrical propositions by an appeal to observation proves
nothing in reality, except that the person who has recourse
to such grounds has no due apprehension of the nature of
geometrical demonstration. We have heard of persons who
convinced themselves by measurement that the geometrical
rule respecting the squares on the sides of a right-angled
triangle was true: but these were persons whose minds had
been engrossed by practical habits, and in whom the
speculative development of the idea of space had been
stifled by other employments. The practical trial of the
rule may illustrate, but cannot prove it. The rule will of
course be confirmed by such trial, because what is true in
general is true in particular: but the rule cannot be proved
from any number of trials, for no accumulation of particular
cases makes up a universal case. To all persons who can see
the force of any proof, the geometrical rule above referred
to is as evident, and its evidence as independent of
experience, as the assertion that sixteen and nine make
twenty-five. At the same time, the truth of the geometrical
rule is quite independent of numerical truths, and results
from the relations of space alone. This could not be if our
apprehension of the relations of space were the fruit of
experience: for experience has no element from which such
truth and such proof could arise.

3. Thus the existence of necessary truths, such as those of
geometry, proves that the idea of space from {93} which they
flow is not derived from experience. Such truths are
inconceivable on the supposition of their being collected
from observation; for the impressions of sense include no
evidence of necessity. But we can readily understand the
necessary character of such truths, if we conceive that
there are certain necessary conditions under which alone the
mind receives the impressions of sense. Since these
conditions reside in the constitution of the mind, and apply
to every perception of an object to which the mind can
attain, we easily see that their rules must include, not
only all that has been, but all that can be, matter of
experience. Our sensations can each convey no information
except about itself; each can contain no trace of another
additional sensation; and thus no relation and connexion
between two sensations can be given by the sensations
themselves. But the mode in which the mind perceives these
impressions as objects, may and will introduce necessary
relations among them: and thus by conceiving the idea of
space to be a condition of perception in the mind, we can
conceive the existence of necessary truths, which apply to
all perceived objects.

4. If we consider the impressions of sense as the mere
materials of our experience, such materials may be
accumulated in any quantity and in any order. But if we
suppose that this matter has a certain form given it, in the
act of being accepted by the mind, we can understand how it
is that these materials are subject to inevitable
rules;--how nothing can be perceived exempt from the
relations which belong to such a form. And since there are
such truths applicable to our experience, and arising from
the nature of space, we may thus consider space as a _form_
which the materials given by experience necessarily assume
in the mind; as an arrangement derived from the perceiving
mind, and not from the sensations alone.

5. Thus this phrase,--that space is a _form_ belonging to
our perceptive power,--may be employed to express that we
cannot perceive objects as in space, without an operation of
the mind as well as of the senses--without active as well as
passive faculties. This phrase, however, {94} is not
necessary to the exposition of our doctrines. Whether we
call the conception of space a Condition of perception, a
Form of perception, or an Idea, or by any other term, it is
something originally inherent in the mind perceiving, and
not in the objects perceived. And it is because the
apprehension of all objects is thus subjected to certain
mental conditions, forms or ideas, that our knowledge
involves certain inviolable relations and necessary truths.
The principles of such truths, so far as they regard space,
are derived from the idea of space, and we must endeavour to
exhibit such principles in their general form. But before we
do this, we may notice some of the conditions which belong,
not to our Ideas in general, but to this Idea of Space in
particular.

{{95}}
CHAPTER III.

OF SOME PECULIARITIES OF THE IDEA OF SPACE.

1. SOME of the Ideas which we shall have to examine involve
conceptions of certain relations of objects, as the idea of
Cause and of Likeness; and may appear to be suggested by
experience, enabling us to _abstract_ this general relation
from particular cases. But it will be seen that Space is not
such a general conception of a relation. For we do not speak
of _Spaces_ as we speak of Causes and Likenesses, but of
Space. And when we speak of _spaces_, we understand by the
expression, parts of one and the same identical
everywhere-extended Space. We conceive a universal Space;
which is not made up of these partial spaces as its
component parts, for it would remain if these were taken
away; and these cannot be conceived without presupposing
absolute space. Absolute Space is essentially one; and the
complication which exists in it, and the conception of
various spaces, depends merely upon boundaries. Space must,
therefore, be, as we have said, not a general conception
abstracted from particulars, but a universal mode of
representation, altogether independent of experience.

2. Space is infinite. We represent it to ourselves as an
infinitely great magnitude. Such an idea as that of Likeness
or Cause, is, no doubt, found in an infinite number of
particular cases, and so far includes these cases. But these
ideas do not include an infinite number of cases as parts of
an infinite whole. When we say that all bodies and partial
spaces exist _in_ infinite space, we use an expression which
is not applied in the same sense to any cases except those
of Space and Time. {96}

3. What is here said may appear to be a denial of the real
existence of space. It must be observed, however, that we do
not deny, but distinctly assert, the existence of space as a
real and necessary condition of all objects perceived; and
that we not only allow that objects are seen external to us,
but we found upon the fact of their being so seen, our view
of the nature of space. If, however, it be said that we deny
the reality of space as an object or thing, this is true.
Nor does it appear easy to maintain that space exists as a
thing, when it is considered that this thing is infinite in
all its dimensions; and, moreover, that it is a thing,
which, being nothing in itself, exists only that other
things may exist in it. And those who maintain the real
existence of space, must also maintain the real existence of
time in the same sense. Now two infinite things, thus really
existing, and yet existing only as other things exist in
them, are notions so extravagant that we are driven to some
other mode of explaining the state of the matter.

4. Thus space is not an object of which we perceive the
properties, but a form of our perception; not a thing which
affects our senses, but an idea to which we conform the
impressions of sense. And its peculiarities appear to depend
upon this, that it is not only a form of sensation, but of
_intuition_; that in reference to space, we not only
perceive but _contemplate_ objects. We see objects in space,
side by side, exterior to each other; space, and objects in
so far as they occupy space, have parts exterior to other
parts; and have the whole thus made up by the juxtaposition
of parts. This mode of apprehension belongs only to the
ideas of space and time. Space and Time are made up of
parts, but Cause and Likeness are not apprehended as made up
of parts. And the term _intuition_ (in its rigorous sense)
is applicable only to that mode of contemplation in which we
thus look at objects as made up of parts, and apprehend the
relations of those parts at the same time and by the same
act by which we apprehend the objects themselves.

5. As we have said, space limited by _boundaries_ {97} gives
rise to various conceptions which we have often to consider.
Thus limited, space assumes _form_ or _figure_; and the
variety of conceptions thus brought under our notice is
infinite. We have every possible form of line, straight
line, and curve; and of curves an endless number;--circles,
parabolas, hyperbolas, spirals, helices. We have plane
surfaces of various shapes,--parallelograms, polygons,
ellipses; and we have solid figures,--cubes, cones,
cylinders, spheres, spheroids, and so on. All these have
their various properties, depending on the relations of
their boundaries; and the investigation of their properties
forms the business of the science of Geometry.

6. Space has three dimensions, or directions in which it may
be measured; it cannot have more or fewer. The simplest
measurement is that of a straight line, which has length
alone. A surface has both length and breadth: and solid
space has length, breadth, and thickness or depth. The
origin of such a difference of dimensions will be seen if we
reflect that each portion of space has a boundary, and is
extended both _in_ the direction in which its boundary
extends, and also in a direction _from_ its boundary; for
otherwise it would not be a boundary. A point has no
dimensions. A line has but one dimension,--the distance from
its boundary, or its _length_. A plane, bounded by a
straight line, has the dimension which belongs to this line,
and also has another dimension arising from the distance of
its parts from this boundary line; and this may be called
_breadth_. A solid, bounded by a plane, has the dimensions
which this plane has; and has also a third dimension, which
we may call _height_ or _depth_, as we consider the solid
extended above or below the plane; or _thickness_, if we
omit all consideration of up and down. And no space can have
any dimensions which are not resoluble into these three.

We may now proceed to consider the mode in which the idea of
space is employed in the formation of Geometry.

{{98}}
CHAPTER IV.

OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE.

1. THE relations of space have been apprehended with
peculiar distinctness and clearness from the very first
unfolding of man's speculative powers. This was a
consequence of the circumstance which we have just noticed,
that the simplest of these relations, and those on which the
others depend, are seen by intuition. Hence, as soon as men
were led to speculate concerning the relations of space,
they assumed just principles, and obtained true results. It
is said that the science of _geometry_ had its origin in
Egypt, before the dawn of the Greek philosophy: but the
knowledge of the early Egyptians (exclusive of their
mythology) appears to have been purely practical; and,
probably, their geometry consisted only in some maxims of
_land-measuring_, which is what the term implies. The Greeks
of the time of Plato, had, however, not only possessed
themselves of many of the most remarkable elementary
theorems of the science; but had, in several instances,
reached the boundary of the science in its elementary form;
as when they proposed to themselves the problems of doubling
the cube and squaring the circle.

But the deduction of these theorems by a systematic process,
and the primary exhibition of the simplest principles
involved in the idea of space, which such a deduction
requires, did not take place, so far as we are aware, till a
period somewhat later. The _Elements of Geometry_ of Euclid,
in which this task was performed, are to this day the
standard work on the subject: the author of this work taught
mathematics with great applause at Alexandria, in the reign
of Ptolemy Lagus, {99} about 280 years before Christ. The
principles which Euclid makes the basis of his system have
been very little simplified since his time; and all the
essays and controversies which bear upon these principles,
have had a reference to the form in which they are stated by him.

2. _Definitions._--The first principles of Euclid's geometry
are, as the first principles of any system of geometry must
be, definitions and axioms respecting the various ideal
conceptions which he introduces; as straight lines, parallel
lines, angles, circles, and the like. But it is to be
observed that these definitions and axioms are very far from
being arbitrary hypotheses and assumptions. They have their
origin in the idea of space, and are merely modes of
exhibiting that idea in such a manner as to make it afford
grounds of deductive reasoning. The axioms are necessary
consequences of the conceptions respecting which they are
asserted; and the definitions are no less necessary
limitations of conceptions; not requisite in order to arrive
at this or that consequence; but necessary in order that it
may be possible to draw any consequences, and to establish
any general truths.

For example, if we rest the end of one straight staff upon
the middle of another straight staff, and move the first
staff into various positions, we, by so doing, alter the
angles which the first staff makes with the other to the
right hand and to the left. But if we place the staff in
that special position in which these two angles are equal,
each of them is a right angle, according to Euclid; and this
is the _definition_ of a right angle, except that Euclid
employs the abstract conception of straight lines, instead
of speaking, as we have done, of staves. But this selection
of the case in which the two angles are equal is not a mere
act of caprice; as it might have been if he had selected a
case in which these angles are unequal in any proportion.
For the consequences which can be drawn concerning the cases
of unequal angles, do not lead to general truths, without
some reference to that peculiar case in which the angles are
equal: and thus it becomes necessary to {100} single out and
define that special case, marking it by a special phrase.
And this definition not only gives complete and distinct
knowledge what a right angle is, to any one who can form the
conception of an angle in general; but also supplies a
principle from which all the properties of right angles may
be deduced.

3. _Axioms._--With regard to other conceptions also, as
circles, squares, and the like, it is possible to lay down
definitions which are a sufficient basis for our reasoning,
so far as such figures are concerned. But, besides these
definitions, it has been found necessary to introduce
certain axioms among the fundamental principles of geometry.
These are of the simplest character; for instance, that two
straight lines cannot cut each other in more than one point,
and an axiom concerning parallel lines. Like the
definitions, these axioms flow from the Idea of Space, and
present that idea under various aspects. They are different
from the definitions; nor can the definitions be made to
take the place of the axioms in the reasoning by which
elementary geometrical properties are established. For
example, the definition of parallel straight lines is, that
they are such as, however far continued, can never meet:
but, in order to reason concerning such lines, we must
further adopt some axiom respecting them: for example, we
may very conveniently take this axiom; that two straight
lines which cut one another are not both of them parallel to
a third straight line[1\2]. The definition and the axiom are
seen to be inseparably connected by our intuition of the
properties of space; but the axiom cannot be proved from the
definition, by any rigorous deductive demonstration. And if
we were to take any other definition of two parallel
straight lines, (as that they are both perpendicular to a
third straight line,) we should still, at some point or
other of our progress, fall in with the same difficulty of
demonstratively establishing their properties without some
further assumption.

[Note 1\2: This axiom is simpler and more convenient than
that of Euclid. It is employed by the late Professor
Playfair in his _Geometry_.]

{101} 4. Thus the elementary properties of figures, which
are the basis of our geometry, are necessary results of our
Idea of Space; and are connected with each other by the
nature of that idea, and not merely by our hypotheses and
constructions. Definitions and axioms must be combined, in
order to express this idea so far as the purposes of
demonstrative reasoning require. These verbal enunciations
of the results of the idea cannot be made to depend on each
other by logical consequence; but have a mutual dependence
of a more intimate kind, which words cannot fully convey. It
is not possible to resolve these truths into certain
_hypotheses_, of which all the rest shall be the necessary
logical consequence. The necessity is not hypothetical, but
intuitive. The axioms require not to be granted, but to be
seen. If any one were to assent to them without seeing them
to be true, his assent would be of no avail for purposes of
reasoning: for he would be also unable to see in what cases
they might be applied. The clear possession of the Idea of
Space is the first requisite for all geometrical reasoning;
and this clearness of idea may be tested by examining
whether the axioms offer themselves to the mind as evident.

5. The necessity of ideas added to sensations, in order to
produce knowledge, has often been overlooked or denied in
modern times. The ground of necessary truth which ideas
supply being thus lost, it was conceived that there still
remained a ground of necessity in definitions;--that we
might have necessary truths, by asserting especially what
the definition implicitly involved in general. It was held,
also, that this was the case in geometry:--that all the
properties of a circle, for instance, were implicitly
contained in the definition of a circle. That this alone is
not the ground of the necessity of the truths which regard
the circle,--that we could not in this way unfold a
definition into proportions, without possessing an intuition
of the relations to which the definition led,--has already
been shown. But the insufficiency of the above account of
the grounds of necessary geometrical truth appeared in
another way also. It was found impossible to lay {102} down
a system of definitions out of which alone the whole of
geometrical truth could be evolved. It was found that axioms
could not be superseded. No definition of a straight line
could be given which rendered the axiom concerning straight
lines superfluous. And thus it appeared that the source of
geometrical truths was not definition alone; and we find in
this result a confirmation of the doctrine which we are here
urging, that this source of truth is to be found in the form
or conditions of our perception;--in the idea which we
unavoidably combine with the impressions of sense;--in the
activity, and not in the passivity of the mind[2\2].

[Note 2\2: I formerly stated views similar to these in some
'Remarks' appended to a work which I termed _The Mechanical
Euclid_, published in 1837. These Remarks, so far as they
bear upon the question here discussed, were noticed and
controverted in No. 135 of the _Edinburgh Review_. As an
examination of the reviewer's objections may serve further
to illustrate the subject, I shall annex to this chapter an
answer to the article to which I have referred.]

6. This will appear further when we come to consider the
mode in which we exercise our observation upon the relations
of space. But we may, in the first place, make a remark
which tends to show the connexion between our conception of
a straight line, and the axiom which is made the foundation
of our reasonings concerning space. The axiom is this;--that
two straight lines, which have both their ends joined,
cannot have the intervening parts separated so as to inclose
a space. The necessity of this axiom is of exactly the same
kind as the necessity of the definition of a right angle, of
which we have already spoken. For as the line standing on
another makes _right angles_ when it makes the angles on the
two sides of it equal; so a line is a _straight line_ when
it makes the two portions of space, on the two sides of it,
similar. And as there is only a single position of the line
first mentioned, which can make the angles equal, so there
is only a single form of a line which can make the spaces
near the line similar on one side and on the other: and
{103} therefore there cannot be two straight lines, such as
the axiom describes, which, between the same limits, give
two different boundaries to space thus separated. And thus
we see a reason for the axiom. Perhaps this view may be
further elucidated if we take a leaf of paper, double it,
and crease the folded edge. We shall thus obtain a straight
line at the folded edge; and this line divides the surface
of the paper, as it was originally spread out, into two
similar spaces. And that these spaces are similar so far as
the fold which separates them is concerned, appears from
this;--that these two parts coincide when the paper is
doubled. And thus a fold in a sheet of paper at the same
time illustrates the definition of a straight line according
to the above view, and confirms the axiom that two such
lines cannot inclose a space.

If the separation of the two parts of space were made by any
other than a straight line; if, for instance, the paper were
cut by a concave line; then, on turning one of the parts
over, it is easy to see that the edge of one part being
concave one way, and the edge of the other part concave the
other way, these two lines would enclose a space. And each
of them would divide the whole space into two portions which
were not similar; for one portion would have a concave edge,
and the other a convex edge. Between any two points, there
might be innumerable lines drawn, some, convex one way, and
some, convex the other way; but the straight line is the
line which is not convex either one way or the other; it is
the single medium standard from which the others may deviate
in opposite directions.

Such considerations as these show sufficiently that the
singleness of the straight line which connects any two
points is a result of our fundamental conceptions of space.
But yet the above conceptions of the similar form of the two
parts of space on the two sides of a line, and of the form
of a line which is intermediate among all other forms, are
of so vague a nature, that they cannot fitly be made the
basis of our elementary geometry; and they are far more
conveniently replaced, as they have been in almost all
treatises of {104} geometry, by the axiom, that two straight
lines cannot inclose a space.

7. But we may remark that, in what precedes, we have
considered space only under one of its aspects:--as a plane.
The sheet of paper which we assumed in order to illustrate
the nature of a straight line, was supposed to be perfectly
_plane_ or _flat_: for otherwise, by folding it, we might
obtain a line not straight. Now this assumption of a plane
appears to take for granted that very conception of a
straight line which the sheet was employed to illustrate;
for the definition of a plane given in the Elements of
Geometry is, that it is a surface on which lie all straight
lines drawn from one point of the surface to another. And
thus the explanation above given of the nature of a straight
line,--that it divides a plane space into similar portions
on each side,--appears to be imperfect or nugatory.

To this we reply, that the explanation must be rendered
complete and valid by deriving the conception of a plane
from considerations of the same kind as those which we
employed for a straight line. Any portion of solid space may
be divided into two portions by surfaces passing through any
given line or boundaries. And these surfaces may be convex
either on one side or on the other, and they admit of
innumerable changes from being convex on one side to being
convex on the other in any degree. So long as the surface is
convex either way, the two portions of space which it
separates are not similar, one having a convex and the other
a concave boundary. But there is a certain intermediate
position of the surface, in which position the two portions
of space which it divides have their boundaries exactly
similar. In this position, the surface is neither convex nor
concave, but plane. And thus a plane surface is determined
by this condition--of its being that single surface which is
the intermediate form among all convex and concave surfaces
by which solid space can be divided,--and of its separating
such space into two portions, of which the boundaries,
though they are the same surface in two opposite positions,
are exactly similar. {105}

Thus a plane is the simplest and most symmetrical boundary
by which a solid can be divided; and a straight line is the
simplest and most symmetrical boundary by which a plane can
be separated. These conceptions are obtained by considering
the boundaries of an interminable space, capable of
imaginary division in every direction. And as a limited
space may be separated into two parts by a plane, and a
plane again separated into two parts by a straight line, so
a line is divided into two portions by a point, which is the
common boundary of the two portions; the end of the one and
the beginning of the other portion having itself no
magnitude, form, or parts.

8. The geometrical properties of planes and solids are
deducible from the first principles of the Elements, without
any new axioms; the definition of a plane above
quoted,--that all straight lines joining its points lie in
the plane,--being a sufficient basis for all reasoning upon
these subjects. And thus, the views which we have presented
of the nature of space being verbally expressed by means of
certain definitions and axioms, become the groundwork of a
long series of deductive reasoning, by which is established
a very large and curious collection of truths, namely, the
whole science of Elementary Plane and Solid Geometry.

This science is one of indispensable use and constant
reference, for every student of the laws of nature; for the
relations of space and number are the _alphabet_ in which
those laws are written. But besides the interest and
importance of this kind which geometry possesses, it has a
great and peculiar value for all who wish to understand the
foundations of human knowledge, and the methods by which it
is acquired. For the student of geometry acquires, with a
degree of insight and clearness which the unmathematical
reader can but feebly imagine, a conviction that there are
necessary truths, many of them of a very complex and
striking character; and that a few of the most simple and
self-evident truths which it is possible for the mind of man
to apprehend, may, by systematic deduction, lead to the most
remote and unexpected results. {106}

In pursuing such philosophical researches as that in which
we are now engaged, it is of great advantage to the
speculator to have cultivated to some extent the study of
geometry; since by this study he may become fully aware of
such features in human knowledge as those which we have
mentioned. By the aid of the lesson thus learned from the
contemplation of geometrical truths, we have been
endeavouriug to establish those further doctrines;--that
these truths are but different aspects of the same
Fundamental Idea, and that the grounds of the necessity
which these truths possess reside in the Idea from which
they flow, this Idea not being a derivative result of
experience, but its primary rule. When the reader has
obtained a clear and satisfactory view of these doctrines,
so far as they are applicable to our knowledge concerning
space, he has, we may trust, overcome the main difficulty
which will occur in following the course of the speculations
now presented to him. He is then prepared to go forwards
with us; to see over how wide a field the same doctrines are
applicable: and how rich and various a harvest of knowledge
springs from these seemingly scanty principles.

But before we quit the subject now under our consideration,
we shall endeavour to answer some objections which have been
made to the views here presented; and shall attempt to
illustrate further the active powers which we have ascribed
to the mind.

{{107}}
CHAPTER V.

OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE DOCTRINES
STATED IN THE PREVIOUS CHAPTER.[3\2]

[Note 3\2: In order to render the present chapter more
intelligible, it may be proper to state briefly the
arguments which gave occasion to the review. After noticing
Stewart's assertions, that the certainty of mathematical
reasoning arises from its depending upon definitions, and
that mathematical truth is hypothetical; I urged,--that no
one has yet been able to construct a system of mathematical
truths by the aid of definitions alone; that a definition
would not be admissible or applicable except it agreed with
a distinct conception in the mind; that the definitions
which we employ in mathematics are not arbitrary or
hypothetical, but necessary definitions; that if Stewart had
taken as his examples of axioms the peculiar geometrical
axioms, his assertions would have been obviously erroneous;
and that the real foundation of the truths of mathematics is
the Idea of Space, which may be expressed (for purposes of
demonstration) partly by definitions and partly by axioms.]

THE _Edinburgh Review_, No. cxxxv., contains a critique on a
work termed _The Mechanical Euclid_, in which opinions were
delivered to nearly the same effect as some of those stated
in the last chapter, and hereafter in Chapter xi. Although I
believe that there are no arguments used by the reviewer to
which the answers will not suggest themselves in the mind of
any one who has read with attention what has been said in
the preceding chapters (except, perhaps, one or two remarks
which have reference to mechanical ideas), it may serve to
illustrate the subject if I reply to the objections
directly, taking them as the reviewer has stated them.

I. I had dissented from Stewart's assertion that
mathematical truth is hypothetical, or depends upon
arbitrary definitions; since we understand by an {108}
hypothesis a supposition, not only which we may make, but
may abstain from making, or may replace by a different
supposition; whereas the definitions and hypotheses of
geometry are necessarily such as they are, and cannot be
altered or excluded. The reviewer (p. 84) informs us that he
understands Stewart, when he speaks of hypotheses and
definitions being the foundation of geometry, to speak of
the hypothesis that real objects correspond to our
geometrical definitions. '_If_ a crystal be an exact
hexahedron, the geometrical properties of the hexahedron may
be predicated of that crystal.' To this I reply,--that such
hypotheses as this are the grounds of our applications of
geometrical truths to real objects, but can in no way be
said to be the foundation of the truths themselves;--that I
do not think that the sense which the reviewer gives was
Stewart's meaning;--but that if it was, this view of the use
of mathematics does not at all affect the question which
both he and I proposed to discuss, which was, the ground of
mathematical certainty. I may add, that whether a crystal be
an exact hexahedron, is a matter of observation and
measurement, not of definition. I think the reader can have
no difficulty in seeing how little my doctrine is affected
by the connexion on which the reviewer thus insists. I have
asserted that the proposition which affirms the square on
the diagonal of a rectangle to be equal to the squares on
two sides, does not rest upon arbitrary hypotheses; the
objector answers, that the proposition that the square on
the diagonal _of this page_ is equal to the squares on the
sides, depends upon the arbitrary hypothesis that the page
is a rectangle. Even if this fact were a matter of arbitrary
hypothesis, what could it have to do with the general
geometrical proposition? How could a single fact, observed
or hypothetical, affect a universal and necessary truth,
which would be equally true if the fact were false? If there
be nothing arbitrary or hypothetical in geometry till we
come to such steps in its application, it is plain that the
truths themselves are not hypothetical; which is the
question for us to decide. {109}

2. The reviewer then (p. 85) considers the doctrine that
axioms as well as definitions are the foundations of
geometry; and here he strangely narrows and confuses the
discussion by making himself the advocate of Stewart,
instead of arguing the question itself. I had asserted that
some axioms are necessary as the foundations of mathematical
reasoning, in addition to the definitions. If Stewart did
not intend to discuss this question, I had no concern with
what he had said about axioms. But I had every reason to
believe that this was the question which Stewart did intend
to discuss. I conceive there is no doubt that he intended to
give an opinion upon the grounds of mathematical reasoning
in general. For he begins his discussions (_Elements_, vol.
ii. p. 38) by contesting Reid's opinion on this subject,
which is stated generally; and he refers again to the same
subject, asserting in general terms, that the first
principles of mathematics are not axioms but definitions.
If, then, afterwards, he made his proof narrower than his
assertion;--if having declared that no axioms are necessary,
he afterwards limited himself to showing that seven out of
twelve of Euclid's axioms are barren truisms, it was no
concern of mine to contest this assertion, which left my
thesis untouched. I had asserted that the proper geometrical
axioms (that two straight lines cannot inclose a space, and
the axiom about parallel lines) are indispensable in
geometry. What account the reviewer gives of these axioms we
shall soon see; but if Stewart allowed them to be axioms
necessary to geometrical reasoning, he overturned his own
assertion as to the foundations of such reasoning; and if he
said nothing decisive about these axioms, which are the
points on which the battle must turn, he left his assertion
altogether unproved; nor was it necessary for me to pursue
the war into a barren and unimportant corner, when the
metropolis was surrendered. The reviewer's exultation that I
have not contested the first seven axioms is an amusing
example of the self-complacent zeal of advocacy.

3. But let us turn to the material point,--the proper
geometrical axioms. What is the reviewer's account of {110}
these? Which side of the alternative does he adopt? Do they
depend upon the definitions, and is he prepared to show the
dependence? Or are they superfluous, and can he erect the
structure of geometry without their aid? One of these two
courses, it would seem, he must take. For we both begin by
asserting the excellence of geometry as an example of
demonstrated truth. It is precisely this attribute which
gives an interest to our present inquiry. How, then, does
the reviewer explain this excellence on his views? How does
he reckon the foundation courses of the edifice which we
agree in considering as a perfect example of intellectual
building?

I presume I may take, as his answer to this question, his
hypothetical statement of what Stewart would have said (p.
87), on the supposition that there had been, among the
foundations of geometry, self-evident indemonstrable truths:
although it is certainly strange that the reviewer should
not venture to make up his mind as to the truth or falsehood
of this supposition. If there were such truths they would
be, he says, 'legitimate filiations' of the definitions.
They would be involved in the definitions. And again he
speaks of the foundation of the geometrical doctrine of
parallels as a flaw, and as a truth which requires, but has
not received demonstration. And yet again, he tells us that
each of these supposed axioms (Euclid's twelfth, for
instance) is 'merely an indication of the point at which
geometry fails to perform that which it undertakes to
perform' (p. 91); and that in reality her truths are not yet
demonstrated. The amount of this is, that the geometrical
axioms are to be held to be _legitimate filiations_ of the
definitions, because though certainly true, they cannot be
proved from the definitions; that they are involved in the
definitions, although they cannot be evolved out of them;
and that rather than admit that they have any other origin
than the definitions, we are to proclaim that geometry has
failed to perform what she undertakes to perform.

To this I reply--that I cannot understand what is meant by
'legitimate filiations' of principles, if the {111} phrase
do not mean consequences of such principles established by
rigorous and formal demonstrations;--that the reviewer, if
he claims any real signification for his phrase, must
substantiate the meaning of it by such a demonstration; he
must establish his 'legitimate filiation' by a genealogical
table in a satisfactory form. When this cannot be done, to
assert, notwithstanding, that the propositions are involved
in the definitions, is a mere begging the question; and to
excuse this defect by saying that geometry fails to perform
what she has promised, is to calumniate the character of
that science which we profess to make our standard, rather
than abandon an arbitrary and unproved assertion respecting
the real grounds of her excellence. I add, further, that if
the doctrine of parallel lines, or any other geometrical
doctrine of which we see the truth, with the most perfect
insight of its necessity, have not hitherto received
demonstration to the satisfaction of any school of
reasoners, the defect must arise from their erroneous views
of the nature of demonstrations, and the grounds of
mathematical certainty.

4. I conceive, then, that the reviewer has failed altogether
to disprove the doctrine that the axioms of geometry are
necessary as a part of the foundations of the science. I had
asserted further that these axioms supply what the
definitions leave deficient; and that they, along with
definitions, serve to present the idea of space under such
aspects that we can reason logically concerning it. To this
the reviewer opposes (p. 96) the common opinion that a
perfect definition is a complete explanation of a name, and
that the test of its perfection is, that we may substitute
the definition for the name wherever it occurs. I reply,
that my doctrine, that a definition expresses a part, but
not the whole, of the essential characters of an idea, is
certainly at variance with an opinion sometimes maintained,
that a definition merely explains a word, and should explain
it so fully that it may always replace it. The error of this
common opinion may, I think, be shown from considerations
such as these;--that if {112} we undertake to explain one
word by several, we may be called upon, on the same ground,
to explain each of these several by others, and that in this
way we can reach no limit nor resting-place;--that in point
of fact, it is not found to lead to clearness, but to
obscurity, when in the discussion of general principles, we
thus substitute definitions for single terms;--that even if
this be done, we cannot reason without conceiving what the
terms mean;--and that, in doing this, the relations of our
conceptions, and not the arbitrary equivalence of two forms
of expression, are the foundations of our reasoning.

5. The reviewer conceives that some of the so-called axioms
are really definitions. The axiom, that 'magnitudes which
coincide with each other, that is, which fill the same
space, are equal,' is a definition of geometrical
_equality_: the axiom, that 'the whole is greater than its
part,' is a definition of _whole_ and _part_. But surely
there are very serious objections to this view. It would
seem more natural to say, if the former axiom is a
definition of the word _equal_, that the latter is a
definition of the word _greater_. And how can one short
phrase define two terms? If I say, 'the heat of summer is
greater than the heat of winter,' does this assertion define
anything, though the proposition is perfectly intelligible
and distinct? I think, then, that this attempt to reduce
these axioms to definitions is quite untenable.

6. I have stated that a definition can be of no use, except
we can conceive the possibility and truth of the property
connected with it; and that if we do conceive this, we may
rightly begin our reasonings by stating the property as an
axiom; which Euclid does, in the case of straight lines and
of parallels. The reviewer inquires (p. 92), whether I am
prepared to extend this doctrine to the case of circles, for
which the reasoning is usually rested upon the
definition;--whether I would replace this definition by an
axiom, asserting the possibility of such a circle. To this I
might reply, that it is not at all incumbent upon me to
assent to such a change; for I have all along stated that it
is indifferent {113} whether the fundamental properties from
which we reason be exhibited as definitions or as axioms,
provided the necessity be clearly seen. But I am ready to
declare that I think the form of our geometry would be not
at all the worse, if, instead of the usual definition of a
circle,--'that it is a figure contained by one line, which
is called the circumference, and which is such, that all
straight lines drawn from a certain point within the
circumference are equal to one another,'--we were to
substitute an axiom and a definition, as follows:--
_Axiom_. If a line be drawn so as to be at every point
equally distant from a certain point, this line will return
into itself or will be _one_ line including a space.
_Definition_. The space is called a _circle_, the line the
_circumference_, and the point the _center_.

And this being done, it would be true, as the reviewer
remarks, that geometry cannot stir _one_ step without
resting on an axiom. And I do not at all hesitate to say,
that the above axiom, expressed or understood, is no less
necessary than the definition, and is tacitly assumed in
every proposition into which circles enter.

7. I have, I think, now disposed of the principal objections
which bear upon the proper axioms of geometry. The
principles which are stated as the first seven axioms of
Euclid's _Elements_, need not, as I have said, be here
discussed. They are principles which refer, not to Space in
particular, but to Quantity in general: such, for instance,
as these; 'If equals be added to equals the wholes are
equal;'--'If equals be taken from equals the remainders are
equal.' But I will make an observation or two upon them
before I proceed.

Both Locke and Stewart have spoken of these axioms as barren
truisms: as propositions from which it is not possible to
deduce a single inference: and the reviewer asserts that
they are not first principles, but laws of thought (p. 88).
To this last expression I am {114} willing to assent; but I
would add, that not only these, but all the principles which
express the fundamental conditions of our knowledge, may
with equal propriety be termed laws of thought; for these
principles depend upon our ideas, and regulate the active
operations of the mind, by which coherence and connexion are
given to its passive impressions. But the assertion that no
conclusions can be drawn from simple axioms, or laws of
human thought, which regard quantity, is by no means true.
The whole of arithmetic,--for instance, the rules for the
multiplication and division of large numbers, the rule for
finding a common measure, and, in short, a vast body of
theory respecting numbers,--rests upon no other foundation
than such axioms as have been just noticed, that if equals
be added to equals the wholes will be equal. And even when
Locke's assertion, that from these axioms no truths can be
deduced, is modified by Stewart and the reviewer, and
limited to _geometrical_ truths, it is hardly tenable
(although, in fact, it matters little to our argument
whether it is or no). For the greater part of the Seventh
Book of Euclid's _Elements_, (on Commensurable and
Incommensurable Quantities,) and the Fifth Book, (on
Proportion,) depend upon these axioms, with the addition
only of the definition or axiom (for it may be stated either
way) which expresses the idea of proportionality in numbers.
So that the attempt to disprove the necessity and use of
axioms, as principles of reasoning, fails even when we take
those instances which the opponents consider as the more
manifestly favourable to their doctrine.

8. But perhaps the question may have already suggested
itself to the reader's mind, of what use can it be formally
to state such principles as these, (for example, that if
equals be added to equals the wholes are equal,) since,
whether stated or no, they will be assumed in our reasoning?
And how can such principles be said to be necessary, when
our proof proceeds equally well without any reference to
them? And the answer is, that it is precisely because these
are the {115} common principles of reasoning, which we
naturally employ without specially contemplating them, that
they require to be separated from the other steps and
formally stated, when we _analyse_ the demonstrations which
we have obtained. In every mental process many principles
are combined and abbreviated, and thus in some measure
concealed and obscured. In analysing these processes, the
combination must be resolved, and the abbreviation expanded,
and thus the appearance is presented of a pedantic and
superfluous formality. But that which is superfluous for
proof, is necessary for the analysis of proof. In order to
exhibit the conditions of demonstration distinctly, they
must be exhibited formally. In the same manner, in
demonstration we do not usually express every step in the
form of a syllogism, but we see the grounds of the
conclusiveness of a demonstration, by resolving it into
syllogisms. Neither axioms nor syllogisms are necessary for
conviction; but they are necessary to display the conditions
under which conviction becomes inevitable. The application
of a single one of the axioms just spoken of is so minute a
step in the proof, that it appears pedantic to give it a
marked place; but the very essence of demonstration consists
in this, that it is composed of an indissoluble succession
of such minute steps. The admirable circumstance is, that by
the accumulation of such apparently imperceptible advances,
we can in the end make so vast and so sure a progress. The
completeness of the analysis of our knowledge appears in the
smallness of the elements into which it is thus resolved.
The minuteness of any of these elements of truth, of axioms
for instance, does not prevent their being as essential as
others which are more obvious. And any attempt to assume one
kind of element only, when the course of our analysis brings
before us two or more kinds, is altogether unphilosophical.
Axioms and definitions are the proximate constituent
principles of our demonstrations; and the intimate bond
which connects together a definition and an axiom on the
same subject is not truly expressed {116} by asserting the
latter to be derived from the former. This bond of connexion
exists in the mind of the reasoner, in his conception of
_that_ to which both definition and axiom refer, and
consequently in the general Fundamental Idea of which that
conception is a modification.

{{117}}
CHAPTER VI.

OF THE PERCEPTION OF SPACE.

1. ACCORDING to the views above explained, certain of the
impressions of our senses convey to us the perception of
objects as existing in space; inasmuch as by the
constitution of our minds we cannot receive those
impressions otherwise than in a certain form, involving such
a manner of existence. But the question deserves to be
asked, _What_ are the impressions of sense by which we thus
become acquainted with space and its relations? And as we
have seen that this idea of space implies an act of the mind
as well as an impression on the sense, what manifestations
do we find of this activity of the mind, in our observation
of the external world?

It is evident that sight and touch are the senses by which
the relations of space are perceived, principally or
entirely. It does not appear that an odour, or a feeling of
warmth or cold, would, independently of experience, suggest
to us the conception of a space surrounding us. But when we
_see_ objects, we see that they are extended and occupy
space; when we _touch_ them, we feel that they are in a
space in which we also are. We have before our eyes any
object, for instance, a board covered with geometrical
diagrams; and we distinctly perceive, by vision, those lines
of which the relations are the subjects of our mathematical
reasoning. Again, we see before us a solid object, a cubical
box for instance; we see that it is within reach; we stretch
out the hand and perceive by the touch that it has sides,
edges, corners, which we had already perceived by vision. {118}

2. Probably most persons do not generally apprehend that
there is any material difference in these two cases;--that
there are any different acts of mind concerned in perceiving
by sight a mathematical diagram upon paper, and a solid cube
lying on a table. Yet it is not difficult to show that, in
the latter case at least, the perception of the shape of the
object is not immediate. A very little attention teaches us
that there is an act of judgment as well as a mere
impression of sense requisite, in order that we may see any
solid object. For there is no visible appearance which is
inseparably connected with solidity. If a picture of a cube
be rightly drawn, in perspective and skilfully shaded, the
impression upon the sense is the same as if it were a real
cube. The picture may be mistaken for a solid object. But it
is clear that, in this case, the solidity is given to the
object by an act of mental judgment. All that is seen is
outline and shade, figures and colours on a flat board. The
solid angles and edges, the relation of the faces of the
figure by which they form a cube, are matters of inference.
This, which is evident in the case of the pictured cube, is
true in all vision whatever. We see a scene before us on
which are various figures and colours, but the eye cannot
see more. It sees length and breadth, but no third
dimension. In order to know that there are solids, we must
infer as well as see. And this we do readily and constantly;
so familiarly, indeed, that we do not perceive the
operation. Yet we may detect this latent process in many
ways; for instance, by attending to cases in which the habit
of drawing such inferences misleads us. Most persons have
experienced this delusion in looking at a scene in a
theatre, and especially that kind of scene which is called a
_diorama_, when the interior of a building is represented.
In these cases, the perspective representations of the
various members of the architecture and decoration impress
us almost irresistibly with the conviction that we have
before us a space of great extent and complex form, instead
of a flat painted canvass. Here, at least, the space is our
own creation; but yet here, it is {119} manifestly created
by the same act of thought as if we were really in the
palace or the cathedral of which the halls and aisles thus
seem to inclose us. And the act by which we thus create
space of three dimensions out of visible extent of length
and breadth, is constantly and imperceptibly going on. We
are perpetually interpreting in this manner the language of
the visible world. From the appearances of things which we
directly see, we are constantly inferring that which we
cannot directly see,--their distance from us, and the
position of their parts.

3. The characters which we thus interpret are various. They
are, for instance, the visible forms, colours, and shades of
the parts, understood according to the maxims of
perspective; (for of perspective every one has a practical
knowledge, as every one has of grammar;) the effort by which
we fix both our eyes on the same object, and adjust each eye
to distinct vision; and the like. The right interpretation
of the information which such circumstances give us
respecting the true forms and distances of things, is
gradually learned; the lesson being begun in our earliest
infancy, and inculcated upon us every hour during which we
use our eyes. The completeness with which the lesson is
mastered is truly admirable; for we forget that our
conclusion is obtained indirectly, and mistake a judgment on
evidence for an intuitive perception. We see the breadth of
the street, as clearly and readily as we see the house on
the other side of it; and we see the house to be square,
however obliquely it be presented to us. This, however, by
no means throws any doubt or difficulty on the doctrine that
in all these cases we do interpret and infer. The rapidity
of the process, and the unconsciousness of the effort, are
not more remarkable in this case than they are when we
understand the meaning of the speech which we hear, or of
the book which we read. In these latter cases we merely hear
noises or see black marks; but we make, out of these
elements, thought and feeling, without being aware of the
act by which we do so. And by an exactly similar process we
see a variously-coloured {120} expanse, and collect from it
a space occupied by solid objects. In both cases the act of
interpretation is become so habitual that we can hardly stop
short at the mere impression of sense.

4. But yet there are various ways in which we may satisfy
ourselves that these two parts of the process of seeing
objects are distinct. To separate these operations is
precisely the task which the artist has to execute, in
making a drawing of what he sees. He has to recover the
consciousness of his real and genuine sensations, and to
discern the lines of objects as they appear. This at first
he finds difficult; for he is tempted to draw what he knows
of the forms of visible objects, and not what he sees: but
as he improves in his art, he learns to put on paper what he
sees only, separated from what he infers, in order that thus
the inference, and with it a conception like that of the
reality, may be left to the spectator. And thus the natural
process of vision is the habit of seeing that which cannot
be seen; and the difficulty of the art of drawing consists
in learning not to see more than is visible.

5. But again; even in the simplest drawing we exhibit
something which we do not see. However slight is our
representation of objects, it contains something which we
create for ourselves. For we draw an _outline_. Now an
outline has no existence in nature. There are no visible
lines presented to the eye by a group of figures. We
separate each figure from the rest, and the boundary by
which we do this is the outline of the figure; and the like
may be said of each member of every figure. A painter of our
own times has made this remark in a work upon his art[4\2]:
'The effect which natural objects produce upon our sense of
vision is that of a number of parts, or distinct masses of
form and colour, and not of lines. But when we endeavour to
represent by painting the objects which are before us, or
which invention supplies to our minds, {121} the first and
the simplest means we resort to is this picture, by which we
separate the form of each object from those that surround
it, marking its boundary, the extreme extent of its
dimensions in every direction, as impressed on our vision:
and this is termed drawing its outline.'

[Note 4\2: Phillips _On Painting._]

6. Again, there are other ways in which we see clear
manifestations of the act of thought by which we assign to
the parts of objects their relations in space, the
impressions of sense being merely subservient to this act.
If we look at a medal through a glass which inverts it, we
see the figures upon it become concave depressions instead
of projecting convexities; for the light which illuminates
the nearer side of the convexity will be transferred to the
opposite side by the apparent inversion of the medal, and
will thus imply a hollow in which the side nearest the light
gathers the shade. Here our decision as to which part is
nearest to us, has reference to the side from which the
light comes. In other cases the decision is more
spontaneous. If we draw black outlines, such as represent
the edges of a cube seen in perspective, certain of the
lines will cross each other; and we may make this cube
appear to assume two different positions, by determining in
our own mind that the lines which belong to one end of the
cube shall be understood to be before or to be behind those
which they cross. Here an act of the will, operating upon
the same sensible image, gives us two cubes, occupying two
entirely different positions. Again, many persons may have
observed that when a windmill in motion at a distance from
us, (so that the outline of the sails only is seen,) stands
obliquely to the eye, we may, by an effort of thought, make
the obliquity assume one or the other of two positions; and
as we do this, the sails, which in one instance appear to
turn from right to left, in the other case turn from left to
right. A person a little familiar with this mental effort,
can invert the motion as often as he pleases, so long as the
conditions of form and light do not offer a manifest
contradiction to either position. {122}.

Thus we have these abundant and various manifestations of
the activity of the mind, in the process by which we collect
from vision the relations of solid space of three
dimensions. But we must further make some remarks on the
process by which we perceive mere visible figure; and also,
on the mode in which we perceive the relations of space by
the touch; and first, of the latter subject.

7. The opinion above illustrated, that our sight does not
give us a direct knowledge of the relations of solid space,
and that this knowledge is acquired only by an inference of
the mind, was first clearly taught by the celebrated Bishop
Berkeley[5\2], and is a doctrine now generally assented to
by metaphysical speculators.

[Note 5\2: _Theory of Vision._]

But does the sense of _touch_ give us directly a knowledge
of space? This is a question which has attracted
considerable notice in recent times; and new light has been
thrown upon it in a degree which is very remarkable, when we
consider that the philosophy of perception has been a
prominent subject of inquiry from the earliest times. Two
philosophers, advancing to this inquiry from different
sides, the one a metaphysician, the other a physiologist,
have independently arrived at the conviction that the long
current opinion, according to which we acquire a knowledge
of space by the sense of touch, is erroneous. And the
doctrine which they teach instead of the ancient errour, has
a very important bearing upon the principle which we are
endeavouring to establish,--that our knowledge of space and
its properties is derived rather from the active operations
than from the passive impressions of the percipient mind.

Undoubtedly the persuasion that we acquire a knowledge of
form by the touch is very obviously suggested by our common
habits. If we wish to know the form of any body in the dark,
or to correct the impressions conveyed by sight, when we
suspect them to be false, we have only, it seems to us, at
least at first, to stretch forth the hand and touch the
object; and we learn its {123} shape with, no chance of
errour. In these cases, form appears to be as immediate a
perception of the sense of touch, as colour is of the sense
of sight.

8. But is this perception really the result of the passive
sense of touch merely? Against such an opinion Dr. Brown,
the metaphysician of whom I speak, urges[6\2] that the
feeling of touch alone, when any object is applied to the
hand, or any other part of the body, can no more convey the
conception of form or extension, than the sensation of an
odour or a taste can do, except we have already some
knowledge of the relative position of the parts of our
bodies; that is, except we are already in possession of an
idea of space, and have, in our minds, referred our limbs to
their positions; which is to suppose the conception of form
already acquired.

[Note 6\2: _Lectures_, Vol. i. p. 459, (1824).]

9. By what faculty then do we originally acquire our
conceptions of the relations of position? Brown answers by
the _muscular sense_; that is, by the conscious exertions of
the various muscles by which we move our limbs. When we feel
out the form and position of bodies by the hand, our
knowledge is acquired, not by the mere touch of the body,
but by perceiving the course the fingers must take in order
to follow the surface of the body, or to pass from one body
to another. We are conscious of the slightest of the
volitions by which we thus feel out form and place; we know
whether we move the finger to the right or left, up or down,
to us or from us, through a large or a small space; and all
these conscious acts are bound together and regulated in our
minds by an idea of an extended space in which they are
performed. That this idea of space is not borrowed from the
sight, and transferred to the muscular feelings by habit, is
evident. For a man born blind can feel out his way with his
staff, and has his conceptions of position determined by the
conditions of space, no less than one who has the use of his
eyes. And the muscular consciousness which reveals to us the
position of objects and parts of objects, {124} when we feel
them out by means of the hand, shows itself in a thousand
other ways, and in all our limbs: for our habits of
standing, walking, and all other attitudes and motions, are
regulated by our feeling of our position and that of
surrounding objects. And thus, we cannot touch any object
without learning something respecting its position; not that
the sense of touch directly conveys such knowledge; but we
have already learnt, from the muscular sense, constantly
exercised, the position of the limb which the object thus
touches.

10. The justice of this distinction will, I think, be
assented to by all persons who attend steadily to the
process itself, and might be maintained by many forcible
reasons. Perhaps one of the most striking evidences in its
favour is that, as I have already intimated, it is the
opinion to which another distinguished philosopher, Sir
Charles Bell, has been led, reasoning entirely upon
physiological principles. From his researches it resulted
that besides the nerves which convey the impulse of the will
from the brain to the muscle, by which every motion of our
limbs is produced, there is another set of nerves which
carry back to the brain a sense of the condition of the
muscle, and thus regulate its activity; and give us the
consciousness of our position and relation to surrounding
objects. The motion of the hand and fingers, or the
consciousness of this motion, must be combined with the
sense of touch properly so called, in order to make an inlet
to the knowledge of such relations. This consciousness of
muscular exertion, which he has called a sixth sense[7\2],
is our guide, Sir C. Bell shows, in the common practical
government of our motions; and he states that having given
this explanation of perception as a physiological doctrine,
he had afterwards with satisfaction seen it confirmed by Dr.
Brown's speculations.

[Note 7\2: _Bridgewater Treatise_, p. 195. _Phil. Trans._
1826, Pt. ii. p. 167.]

11. Thus it appears that our consciousness of the relations
of space is inseparably and fundamentally connected with our
own actions in space. We perceive {125} only while we act;
our sensations require to be interpreted by our volitions.
The apprehension of extension and figure is far from being a
process in which we are inert and passive. We draw lines
with our fingers; we construct surfaces by curving our
hands; we generate spaces by the motion of our arms. When
the geometer bids us form lines, or surfaces, or solids by
motion, he intends his injunction to be taken as
hypothetical only; we need only conceive such motions. But
yet this hypothesis represents truly the origin of our
knowledge; we perceive spaces by motion at first, as we
conceive spaces by motion afterwards:--or if not always by
actual motion, at least by potential. If we perceive the
length of a staff by holding its two ends in our two hands
without running the finger along it, this is because by
habitual motion we have already acquired a measure of the
distance of our hands in any attitude of which we are
conscious. Even in the simplest case, our perceptions are
derived not from the touch, but from the sixth sense; and
this sixth sense at least, whatever may be the case with the
other five, implies an active mind along with the passive sense.

12. Upon attentive consideration, it will be clear that a
large portion of the perceptions respecting space which
appear at first to be obtained by sight alone, are, in fact,
acquired by means of this sixth sense. Thus we consider the
visible sky as a single surface surrounding us and returning
into itself, and thus forming a hemisphere. But such a mode
of conceiving an object of vision could never have occurred
to us, if we had not been able to turn our heads, to follow
this surface, to pursue it till we find it returning into
itself. And when we have done this, we necessarily present
it to ourselves as a concave inclosure within which we are.
The sense of sight alone, without the power of muscular
motion, could not have led us to view the sky as a vault or
hemisphere. Under such circumstances, we should have
perceived only what was presented to the eye in one
position; and if different appearances had been presented in
succession, we could {126} not have connected them as parts
of the same picture, for want of any perception of their
relative position. They would have been so many detached and
incoherent visual sensations. The muscular sense connects
their parts into a whole, making them to be only different
portions of one universal scene[8\2].

[Note 8\2: It has been objected to this view that we might
obtain a conception of the sky as a hemisphere, by being
ourselves turned round, (as on a music-stool, for instance,)
and thus seeing in succession all parts of the sky. But this
assertion I conceive to be erroneous. By being thus turned
round, we should see a number of pictures which we should
put together as parts of a plane picture; and when we came
round to the original point, we should have no possible
means of deciding that it was the _same_ point: it would
appear only as a _repetition_ of the picture. That sight, of
itself, can give us only a plane picture, the doctrine of
Berkeley, appears to be indisputable; and, no less so, the
doctrine that it is the consciousness of our own action in
space which puts together these pictures so that they cover
the surface of a solid body. We can see length and breadth
with our eyes, but we must thrust out our arm towards the
flat surface, in order that we may, in our thoughts, combine
a third dimension with the other two.]

13. These considerations point out the fallacy of a very
curious representation made by Dr. Reid, of the convictions
to which man would be led, if he possessed vision without
the sense of touch. To illustrate this subject, Reid uses
the fiction of a nation whom he terms the _Idomenians_, who
have no sense except that of sight. He describes their
notions of the relations of space as being entirely
different from ours. The axioms of their geometry are quite
contradictory to our axioms. For example, it is held to be
self-evident among them that two straight lines which
intersect each other once, must intersect a second time;
that the three angles of any triangle are _greater_ than two
right angles; and the like. These paradoxes are obtained by
tracing the relations of lines on the surface of a concave
sphere, which surrounds the spectator, and on which all
visible appearances may be supposed to be presented to him.
But from what is said above it appears that the notion of
such a sphere, and such a connexion of visible objects which
are seen in different {127} directions, cannot be arrived at
by sight alone. When the spectator combines in his
conception the relations of long-drawn lines and large
figures, as he sees them by turning his head to the right
and to the left, upwards and downwards, he ceases to be an
Idomenian. And thus our conceptions of the properties of
space, derived through the exercise of one mode of
perception, are not at variance with those obtained in
another way; but all such conceptions, however produced or
suggested, are in harmony with each other; being, as has
already been said, only different aspects of the same idea.

14. If our perceptions of the position of objects around us
do not depend on the sense of vision alone, but on the
muscular feeling brought into play when we turn our head, it
will obviously follow that the same is true when we turn the
eye instead of the head. And thus we may learn the form of
objects, not by looking at them with a fixed gaze, but by
following the boundary of them with the eye. While the head
is held perfectly still, the eye can rove along the outlines
of visible objects, scrutinize each point in succession, and
leap from one point to another; each such act being
accompanied by a muscular consciousness which makes us aware
of the direction in which the look is travelling. And we may
thus gather information concerning the figures and places
which we trace out with the visual ray, as the blind man
learns the forms of things which he traces out with his
staff, being conscious of the motions of his hand.

15. This view of the mode in which the eye perceives
position, which is thus supported by the analogy of other
members employed for the same purpose, is further confirmed
by Sir Charles Bell by physiological reasons. He teaches us
that[9\2] when an object is seen we employ two senses: there
is an impression on the retina; but we receive also the idea
of position or relation in space, which it is not the office
of the retina to give, by our consciousness of the efforts
of the voluntary {128} muscles of the eye: and he has traced
in detail the course of the nerves by which these muscles
convey their information. The constant _searching_ motion of
the eye, as he terms it[10\2], is the means by which we
become aware of the position of objects about us.

[Note 9\2: _Phil. Trans._ 1823. On the Motions of the Eye.]

[Note 10\2: _Bridgewater Treatise_, p. 282. I have adopted,
in writing the above, the views and expressions of Sir
Charles Bell. The essential part of the doctrine there
presented is, that the eye constantly makes efforts to turn,
so that the image of an object to which our attention is
drawn, shall fall upon a certain particular point of the
retina; and that when the image falls upon any other point,
the eye turns away from this oblique into the direct
position. Other writers have maintained that the eye thus
turns not because the point on which the image falls in
direct vision is the most _sensible_ point, but that it is
the point of _greatest distinctness_ of vision. They urge
that a small star, which disappears when the eye is turned
full upon it, may often be seen by looking a little away
from it: and hence, they infer that the parts of the retina
removed from the spot of direct vision, are more sensible
than it is. The facts are very curious, however they be
explained, but they do not disturb the doctrine delivered in
the text.]

16. It is not to our present purpose to follow the
physiology of this subject; but we may notice that Sir C.
Bell has examined the special circumstances which belong to
this operation of the eye. We learn from him that the
particular point of the eye which thus traces the forms of
visible objects is a part of the retina which has been
termed the _sensible spot_; being that part which is _most
distinctly_ sensible to the impressions of light and colour.
This part, indeed, is not a spot of definite size and form,
for it appears that proceeding from a certain point of the
retina, the distinct sensibility diminishes on every side by
degrees. And the searching motion of the eye arises from the
desire which we instinctively feel of receiving upon the
sensible spot the image of the object to which the attention
is directed. We are uneasy and impatient till the eye is
turned so that this is effected. And as our attention is
transferred from point to point of the scene before us, the
eye, and this point of the eye in particular, travel along
with the thoughts; and the muscular sense, which tells us of
these movements of the organ of {129} vision, conveys to us
a knowledge of the forms and places which we thus
successively survey.

17. How much of activity there is in the process by which we
perceive the outlines of objects appears further from the
language by which we describe their forms. We apply to them
not merely adjectives of form, but verbs of motion. An
abrupt hill _starts_ out of the plain; a beautiful figure
has a _gliding_ outline. We have
The windy summit, wild and high,
Roughly _rushing_ on the sky.
These terms express the course of the eye as it follows the
lines by which such forms are bounded and marked. In like
manner another modern poet[11\2] says of Soracte, that it
From out the plain
_Heaves_ like a long-swept wave about to break,
And on the curl _hangs pausing_.

[Note 11\2: Byron, _Ch. Har._ vi. st. 75.]

Thus the muscular sense, which is inseparably connected with
an act originating in our own mind, not only gives us all
that portion of our perceptions of space in which we use the
sense of touch, but also, at least in a great measure,
another large portion of such perceptions, in which we
employ the sense of sight. As we have before seen that our
_knowledge_ of solid space and its properties is not
conceivable in any other way than as the result of a mental
act, governed by conditions depending on its own nature; so
it now appears that our _perceptions_ of visible figure are
not obtained without an act performed under the same
conditions. The sensations of touch and sight are
subordinated to an idea which is the basis of our
speculative knowledge concerning space and its relations;
and this same idea is disclosed to our consciousness by its
practically regulating our intercourse with the external world.

By considerations such as have been adduced and referred to,
it is proved beyond doubt, that in a great {130} number of
cases our knowledge of form and position is acquired from
the muscular sense, and not from sight directly:--for
instance, in all cases in which we have before us objects so
large and prospects so extensive that we cannot see the
whole of them in one position of the eye[12\2].

[Note 12\2: The expression in the first edition was 'large
objects and extensive spaces.' In the text as now given, I
state a definite size and extent, within which the sight by
itself can judge of position and figure.

The doctrine, that we require the assistance of the muscular
sense to enable us to perceive space of three dimensions, is
not at all inconsistent with this other doctrine, that
within the space which is seen by the fixed eye, we perceive
the relative positions of points directly by vision, and
that, consequently, we have a perception of _visible
figure_.

Sir Charles Bell has said, (_Phil. Trans._ 1823, p. 181,)
'It appears to me that the utmost ingenuity will be at a
loss to devise an explanation of that power by which the eye
becomes acquainted with the position and relation of
objects, if the sense of muscular activity be excluded which
accompanies the motion of the eyeball.' But surely we should
have no difficulty in perceiving the relation of the sides
and angles of a small triangle, placed before the eye, even
if the muscles of the eyeball were severed. This subject is
resumed b. iv. c. ii. sect. 11.]

We now quit the consideration of the properties of Space,
and consider the Idea of Time.

{{131}}
CHAPTER VII.

OF THE IDEA OF TIME.

1. RESPECTING the Idea of Time, we may make several of the
same remarks which we made concerning the idea of space, in
order to show that it is not borrowed from experience, but
is a bond of connexion among the impressions of sense,
derived from a peculiar activity of the mind, and forming a
foundation both of our experience and of our speculative
knowledge.

Time is not a notion obtained by experience. Experience,
that is, the impressions of sense and our consciousness of
our thoughts, gives us various perceptions; and different
successive perceptions considered together exemplify the
notion of change. But this very connexion of different
perceptions,--this successiveness,--presupposes that the
perceptions exist _in time_. That things happen either
together, or one after the other, is intelligible only by
assuming time as the condition under which they are
presented to us.

Thus time is a necessary condition in the presentation of
all occurrences to our minds. We cannot conceive this
condition to be taken away. We can conceive time to go on
while nothing happens in it; but we cannot conceive anything
to happen while time does not go on.

It is clear from this that time is not an impression derived
from experience, in the same manner in which we derive from
experience our information concerning the objects which
exist, and the occurrences which take place in time. The
objects of experience can easily be conceived to be, or not
to be:--to be absent as well as present. Time always is, and
always is {132} present, and even in our thoughts we cannot
form the contrary supposition.

2. Thus time is something distinct from the _matter_ or
substance of our experience, and may be considered as a
necessary _form_ which that matter (the experience of
change) must assume, in order to be an object of
contemplation to the mind. Time is one of the necessary
conditions under which we apprehend the information which
our senses and consciousness give us. By considering time as
a form which belongs to our power of apprehending
occurrences and changes, and under which alone all such
experience can be accepted by the mind, we explain the
necessity, which we find to exist, of conceiving all such
changes as happening in time; and we thus see that time is
not a property perceived as existing in objects, or as
conveyed to us by our senses; but a condition impressed upon
our knowledge by the constitution of the mind itself;
involving an act of thought as well as an impression of sense.

3. We showed that space is an idea of the mind, or form of
our perceiving power, independent of experience, by pointing
out that we possess necessary and universal truths
concerning the relations of space, which could never be
given by means of experience; but of which the necessity is
readily conceivable, if we suppose them to have for their
basis the constitution of the mind. There exist also
respecting number, many truths absolutely necessary,
entirely independent of experience and anterior to it; and
so far as the conception of number depends upon the idea of
time, the same argument might be used to show that the idea
of time is not derived from experience, but is a result of
the native activity of the mind: but we shall defer all
views of this kind till we come to the consideration of Number.

4. Some persons have supposed that we obtain the notion of
time from the perception of motion. But it is clear that the
perception of motion, that is, change of place, presupposes
the conception of time, and is not capable of being
presented to the mind in any other {133} way. If we
contemplate the same body as being in different places at
different times, and connect these observations, we have the
conception of motion, which thus presupposes the necessary
conditions that existence in time implies. And thus we see
that it is possible there should be necessary truths
concerning all Motion, and consequently, concerning those
motions which are the objects of experience; but that the
source of this necessity is the Ideas of Time and Space,
which, being universal conditions of knowledge residing in
the mind, afford a foundation for necessary truths.

{{134}}
CHAPTER VIII.

OF SOME PECULIARITIES OF THE IDEA OF TIME.

1. THE Idea of Time, like the Idea of Space, offers to our
notice some characters which do not belong to our
fundamental ideas generally, but which are deserving of
remark. These characters are, in some respects, closely
similar with regard to Time and to Space, while, in other
respects, the peculiarities of these two ideas are widely
different. We shall point out some of these characters.

Time is not a general _abstract_ notion collected from
experience; as, for example, a certain general conception of
the relations of things. For we do not consider particular
_times_ as examples of Time in general, (as we consider
particular causes to be examples of Cause,) but we conceive
all particular times to be parts of a single and endless
Time. This continually-flowing and endless time is what
offers itself to us when we contemplate any series of
occurrences. All actual and possible times exist as Parts,
in this original and general Time. And since all particular
times are considered as derivable from time in general, it
is manifest that the notion of time in general cannot be
derived from the notions of particular times. The notion of
time in general is therefore not a general conception
gathered from experience.

2. Time is infinite. Since all actual and possible times
exist in the general course of time, this general time must
be infinite. All limitation merely divides, and does not
terminate, the extent of absolute time. Time has no
beginning and no end; but the beginning and the end of every
other existence takes place in it.

3. Time, like space, is not only a form of perception, but
of _intuition_. We contemplate events as {135} taking place
_in_ time. We consider its parts as added to one another,
and events as filling a larger or smaller extent of such
parts. The time which any event takes up is the sum of all
such parts, and the relation of the same to time is fully
understood when we can clearly see what portions of time it
occupies, and what it does not. Thus the relation of known
occurrences to time is perceived by intuition; and time is a
form of intuition of the external world.

4. Time is conceived as a quantity of one dimension; it has
great analogy with a line, but none at all with a surface or
solid. Time may be considered as consisting of a series of
instants, which are before and after one another; and they
have no other relation than this, of _before_ and _after_.
Just the same would be the case with a series of points
taken along a line; each would be after those on one side of
it, and before those on another. Indeed the analogy between
time, and space of one dimension, is so close, that the same
terms are applied to both ideas, and we hardly know to which
they originally belong. Times and lines are alike called
_long_ and _short_; we speak of the _beginning_ and _end_ of
a line; of a _point_ of time, and of the _limits_ of a
portion of duration.

5. But, as has been said, there is nothing in time which
corresponds to more than one dimension in space, and hence
nothing which has any obvious analogy with figure. Time
resembles a line indefinitely extended both ways; all
partial times are portions of this line; and no mode of
conceiving time suggests to us a line making any angle with
the original line, or any other combination which might give
rise to figures of any kind. The analogy between time and
space, which in many circumstances is so clear, here
disappears altogether. Spaces of two and of three
dimensions, planes and solids, have nothing to which we can
compare them in the conceptions arising out of time.

6. As figure is a conception solely appropriate to space,
there is also a conception which peculiarly belongs to time,
namely, the conception of recurrence of times similarly
marked; or, as it may be termed, {136} _rhythm_, using this
word in a general sense. The term rhythm is most commonly
used to designate the recurrence of times marked by the
syllables of a verse, or the notes of a melody: but it is
easy to see that the general conception of such a recurrence
does not depend on the mode in which it is impressed upon
the sense. The forms of such recurrence are innumerable.
Thus in such a line as
Quádrupedánte putrém sonitú quatit úngula cámpum,
we have alternately one long or forcible syllable, and two
short or light ones, recurring over and over. In like manner
in our own language, in the line
At the clóse of the dáy when the hámlet is still,
we have two light and one strong syllable repeated four
times over. Such repetition is the essence of versification.
The same kind of rhythm is one of the main elements of
music, with this difference only, that in music the forcible
syllables are made so for the purposes of rhythm by their
length only or principally; for example, if either of the
above lines were imitated by a melody in the most simple and
obvious manner, each strong syllable would occupy exactly
twice as much time as two of the weaker ones. Something very
analogous to such rhythm may be traced in other parts of
poetry and art, which we need not here dwell upon. But in
reference to our present subject, we may remark that by the
introduction of such rhythm, the flow of time, which appears
otherwise so perfectly simple and homogeneous, admits of an
infinite number of varied yet regular modes of progress. All
the kinds of versification which occur in all languages, and
the still more varied forms of recurrence of notes of
different lengths, which are heard in all the varied strains
of melodies, are only examples of such modifications, or
configurations as we may call them, of time. They involve
relations of various portions of time, as figures involve
relations of various portions of space. But yet the analogy
between rhythm and figure is by no means very close; for in
rhythm we have relations of quantity alone in the parts of
time, whereas in figure we have {137} relations not only of
quantity, but of a kind altogether different,--namely, of
position. On the other hand, a _repetition_ of similar
elements, which does not necessarily occur in figures, is
quite essential in order to impress upon us that measured
progress of time of which we here speak. And thus the ideas
of time and space have each its peculiar and exclusive
relations; position and figure belonging only to space,
while repetition and rhythm are appropriate to time.

7. One of the simplest forms of recurrence is _alternation_,
as when we have alternate strong and slight syllables. For
instance,--
Awáke, aríse, or bé for éver fáll'n.
Or without any subordination, as when we reckon numbers, and
call them in succession, _odd_, _even_, _odd_, _even_.

8. But the simplest of all forms of recurrence is that which
has no variety;--in which a series of units, each considered
as exactly similar to the rest, succeed each other; as
_one_, _one_, _one_, and so on. In this case, however, we
are led to consider each unit with reference to all that
have preceded; and thus the series _one_, _one_, _one_, and
so forth, becomes _one_, _two_, _three_, _four_, _five_, and
so on; a series with which all are familiar, and which may
be continued without limit.

We thus collect from that repetition of which time admits,
the conception of _Number_.

9. The relations of position and figure are the subject of
the science of geometry; and are, as we have already said,
traced into a very remarkable and extensive body of truths,
which rests for its foundations on axioms involved in the
Idea of Space. There is, in like manner, a science of great
complexity and extent, which has its foundation in the Idea
of Time. But this science, as it is usually pursued, applies
only to the conception of Number, which is, as we have said,
the simplest result of repetition. This science is
_Theoretical Arithmetic_, or the speculative doctrine of the
properties and relations of numbers; and we must say a few
words concerning the principles which it is requisite to
assume as the basis of this science.

{{138}}
CHAPTER IX.

OF THE AXIOMS WHICH RELATE TO NUMBER.

1. THE foundations of our speculative knowledge of the
relations and properties of Number, as well as of Space, are
contained in the mode in which we represent to ourselves the
magnitudes which are the subjects of our reasonings. To
express these foundations in axioms in the case of number,
is a matter requiring some consideration, for the same
reason as in the case of geometry; that is, because these
axioms are principles which we assume as true, without being
aware that we have made any assumption; and we cannot,
without careful scrutiny, determine when we have stated, in
the form of axioms, all that is necessary for the formation
of the science, and no more than is necessary. We will,
however, attempt to detect the principles which really must
form the basis of theoretical arithmetic.

2. Why is it that three and two are equal to four and one?
Because if we look at five things of any kind, we see that
it is so. The five are four and one; they are also three and
two. The truth of our assertion is involved in our being
able to conceive the number five at all. We perceive this
truth by _intuition_, for we cannot see, or imagine we see,
five things, without perceiving also that the assertion
above stated is true.

But how do we state in words this fundamental principle of
the doctrine of numbers? Let us consider a very simple case.
If we wish to show that seven and two are equal to four and
five, we say that seven are four and three, _therefore_
seven and two are four and three and two; and because three
and two are {139} five, this is four and five. Mathematical
reasoners justify the first inference (marked by the
conjunctive word _therefore_), by saying that "When equals
are added to equals the wholes are equal," and that thus,
since seven is equal to three and four, if we add two to
both, seven and two are equal to four and three and two.

3. Such _axioms_ as this, that when equals are added to
equals the wholes are equal, are, in fact, expressions of
the general condition of intuition, by which a whole is
contemplated as made up of parts, and as identical with the
aggregate of the parts. And a yet more general form in which
we might more adequately express this condition of intuition
would be this; that 'Two magnitudes are equal when they can
be divided into parts which are equal, each to each.' Thus
in the above example, seven and two are equal to four and
five, because each of the two sums can be divided into the
parts, four, three, and two.

4. In all these cases, a person who had never seen such
axioms enunciated in a verbal form would employ the same
reasoning as a practised mathematician, in order to satisfy
himself that the proposition was true. The steps of the
reasoning, being seen to be true by intuition, would carry
an entire conviction, whether or not the argument were made
verbally complete. Hence the axioms may appear superfluous,
and on this account such axioms have often been spoken
contemptuously of, as empty and barren assertions. In fact,
however, although they cannot supply the deficiency of the
clear intuition of number and space in the reasoner himself,
and although when he possesses such a faculty, he will
reason rightly if he have never heard of such axioms, they
still have their place properly at the beginning of our
treatises on the science of quantity; since they express, as
simply as words can express, those conditions of the
intuition of magnitudes on which all reasoning concerning
quantity must be based; and are necessary when we want, not
only to see the truth of the elementary reasonings on these
subjects, but to put such reasonings in a formal and logical
shape. {140}

5. We have considered the above-mentioned axioms as the
basis of all arithmetical operations of the nature of
_addition_. But it is easily seen that the same principle
may be carried into other cases; as for instance,
_multiplication_, which is merely a repeated addition, and
admits of the same kind of evidence. Thus five times three
are equal to three times five; why is this? If we arrange
fifteen things in five rows of three, it is seen by looking,
or by imaginary looking, which is _intuition_, that they may
also be taken as three rows of five. And thus the principle
that those wholes are equal which can be resolved into the
same partial magnitudes, is immediately applicable in this
as in the other case.

6. We may proceed to higher numbers, and may find ourselves
obliged to use artificial nomenclature and notation in order
to represent and reckon them; but the reasoning in these
cases also is still the same. And the usual artifice by
which our reasoning in such instances is assisted is, that
the number which is the root of our scale of notation (which
is _ten_ in our usual system), is alternately separated into
parts and treated as a single thing. Thus 47 and 35 are 82;
for 47 is four tens and seven; 35 is three tens and five;
whence 47 and 35 are seven tens and twelve; that is, 7 tens,
1 ten, and 2; which is 8 tens and 2, or 82. The like
reasoning is applicable in other cases. And since the most
remote and complex properties of numbers are obtained by a
prolongation of a course of reasoning exactly similar to
that by which we thus establish the most elementary
propositions, we have, in the principles just noticed, the
foundation of the whole of Theoretical Arithmetic.

{{141}}
CHAPTER X.

OF THE PERCEPTION OF TIME AND NUMBER.

1. OUR perception of the passage of time involves a series
of acts of memory. This is easily seen and assented to, when
large intervals of time and a complex train of occurrences
are concerned. But since memory is requisite in order to
apprehend time in such cases, we cannot doubt that the same
faculty must be concerned in the shortest and simplest cases
of succession; for it will hardly be maintained that the
process by which we contemplate the progress of time is
different, when small, and when large intervals are
concerned. If memory be absolutely requisite to connect two
events which begin and end a day, and to perceive a tract of
time between them, it must be equally indispensable to
connect the beginning and end of a minute, or a second;
though in this case the effort may be smaller, and
consequently more easily overlooked. In common cases, we are
unconscious of the act of thought by which we recollect the
preceding instant, though we perceive the effort when we
recollect some distant event. And this is analogous to what
happens in other instances. Thus, we walk without being
conscious of the volitions by which we move our muscles;
but, in order to leap, a distinct and manifest exertion of
the same muscles is necessary. Yet no one will doubt that we
walk as well as leap by an act of the will exerted through
the muscles; and in like manner, our consciousness of small
as well as large intervals of time involves something of the
nature of an act of memory.

2. But this constant and almost imperceptible kind of
memory, by which we connect the beginning and {142} end of
each instant as it passes, may very fitly be distinguished
in common cases from manifest acts of recollection, although
it may be difficult or impossible to separate the two
operations in general. This perpetual and latent kind of
memory may be termed a _sense of successiveness_; and must
be considered as an internal sense by which we perceive
ourselves existing in time, much in the same way as by our
external and muscular sense we perceive ourselves existing
in space. And both our internal thoughts and feelings, and
the events which take place around us, are apprehended as
objects of this internal sense, and thus as taking place in
time.

3. In the same manner in which our interpretation of the
notices of the muscular sense implies the power of moving
our limbs, and of touching at will this object or that; our
apprehension of the relations of time, by means of the
internal sense of successiveness, implies a power of
recalling what has past, and of retaining what is passing.
We are able to seize the occurrences which have just taken
place, and to hold them fast in our minds so as mentally to
measure their distance in time from occurrences now present.
And thus, this sense of successiveness, like the muscular
sense with which we have compared it, implies activity of
the mind itself, and is not a sense passively receiving
impressions.

4. The conception of _Number_ appears to require the
exercise of the same sense of succession. At first sight,
indeed, we seem to apprehend Number without any act of
memory, or any reference to time: for example, we look at a
horse, and see that his legs are four; and this we seem to
do at once, without reckoning them. But it is not difficult
to see that this seeming instantaneousness of the perception
of small numbers is an illusion. This resembles the many
other cases in which we perform short and easy acts so
rapidly and familiarly that we are unconscious of them; as
in the acts of seeing, and of articulating our words. And
this is the more manifest, since we begin our acquaintance
with number by counting even the {143} smallest numbers.
Children and very rude savages must use an effort to reckon
even their five fingers, and find a difficulty in going
further. And persons have been known who were able by habit,
or by a peculiar natural aptitude, to count by dozens as
rapidly as common persons can by units. We may conclude,
therefore, that when we appear to catch a small number by a
single glance of the eye, we do in fact count the units of
it in a regular, though very brief succession. To count
requires an act of memory. Of this we are sensible when we
count very slowly, as when we reckon the strokes of a
church-clock; for in such a case we may forget in the
intervals of the strokes, and _miscount_. Now it will not be
doubted that the nature of the process in counting is the
same whether we count fast or slow. There is no definite
speed of reckoning at which the faculties which it requires
are changed; and therefore memory, which is requisite in
some cases, must be so in all[13\2].

[Note 13\2: I have considered Number as involving the
exercise of the sense of succession, because I cannot draw
any line between those cases of large numbers, in which, the
process of counting being performed, there is a manifest
apprehension of succession; and those cases of small
numbers, in which we seem to see the number at one glance.
But if any one holds Number to be apprehended by a direct
act of intuition, as Space and Time are, this view will not
disturb the other doctrines delivered in the text.]

The act of counting, (_one_, _two_, _three_, and so on,) is
the foundation of all our knowledge of number. The intuition
of the relations of number involves this act of counting;
for, as we have just seen, the conception of number cannot
be obtained in any other way. And thus the whole of
theoretical arithmetic depends upon an act of the mind, and
upon the conditions which the exercise of that act implies.
These have been already explained in the last chapter.

5. But if the apprehension of number be accompanied by an
act of the mind, the apprehension of _rhythm_ is so still
more clearly. All the forms of versification and the
_measures_ of melodies are the creations of man, who thus
realizes in words and sounds the {144} forms of recurrence
which rise within his own mind. When we hear in a quiet
scene any rapidly-repeated sound, as those made by the
hammer of the smith or the saw of the carpenter, every one
knows how insensibly we throw these noises into a rhythmical
form in our own apprehension. We do this even without any
suggestion from the sounds themselves. For instance, if the
beats of a clock or watch be ever so exactly alike, we still
reckon them alternately tick-_tack_, tick-_tack_. That this
is the case, may be proved by taking a watch or clock of
such a construction that the returning swing of the pendulum
is silent, and in which therefore all the beats are
rigorously alike: we shall find ourselves still reckoning
its sounds as tick-_tack_. In this instance it is manifest
that the rhythm is entirely of our own making. In melodies,
also, and in verses in which the rhythm is complex, obscure
and difficult, we perceive something is required on our
part; for we are often incapable of contributing our share,
and thus lose the sense of the measure altogether. And when
we consider such cases, and attend to what passes within us
when we catch the measure, even of the simplest and
best-known air, we shall no longer doubt that an act of our
own thoughts is requisite in such cases, as well as
impressions on the sense. And thus the conception of this
peculiar modification of time, which we have called
_rhythm_, like all the other views which we have taken of
the subject, shows that we must, in order to form such
conceptions, supply a certain idea by our own thoughts, as
well as merely receive by senses, whether external or
internal, the impressions of appearances and collections of
appearances.

{{145}}
NOTE TO CHAPTER X.

I HAVE in the last ten chapters described Space, Time, and
Number by various expressions, all intended to point out
their office as exemplifying the Ideal Element of human
knowledge. I have called them _Fundamental Ideas_; _Forms of
Perception_; _Forms of Intuition_; and perhaps other names.
I might add yet other phrases. I might say that the
properties of Space, Time, and Number are _Laws of the
Mind's Activity_ in apprehending what is. For the mind
cannot apprehend any thing or event except conformably to
the properties of space, time, and number. It is not only
that it _does_ not, but it _can_ not: and this impossibility
shows that the law is a law of the mind, and not of objects
extraneous to the mind.

It is usual for some of those who reject the doctrines here
presented to say that the axioms of geometry, and of other
sciences, are obtained by Induction from facts constantly
presented by experience. But I do not see how Induction can
prove that a proposition _must_ be true. The only
intelligible usage of the word _Induction_ appears to me to
be, that in which it is applied to a proposition which,
being separable from the facts in our apprehension, and
being compared with them, is seen to agree with them. But in
the cases now spoken of, the proposition is not separable
from the facts. We cannot infer by induction that two
straight lines cannot inclose a space, because we cannot
contemplate special cases of two lines inclosing a space, in
which it remains to be determined whether or not the
proposition, that both are straight, is true.

I do not deny that the activity of the mind by which it
perceives objects and events as related according to the
laws of space, time, and number, is awakened and developed
by being constantly exercised; and that we cannot imagine a
stage of human existence in which the powers have not been
awakened and {146} developed by such exercise. In this way,
experience and observation are necessary conditions and
prerequisites of our apprehension of geometrical (and other)
axioms. We cannot see the truth of these axioms without some
experience, because we cannot see any thing, or be human
beings, without some experience. This might be expressed by
saying that such truths are acquired necessarily _in the
course of_ all experience; but I think it is very
undesirable to apply, to such a case, the word _Induction_,
of which it is so important to us to keep the scientific
meaning free from confusion. Induction cannot give
demonstrative proofs, as I have already stated in Book 1. C.
i. sect. 3, and therefore cannot be the ground of necessary
truths.

Another expression which may be used to describe the
Fundamental Ideas here spoken of is suggested by the
language of a very profound and acute Review of the former
edition. The Reviewer holds that we pass from special
experiences to universal truths in virtue of 'the inductive
propensity--the irresistible impulse of the mind to
generalize _ad infinitum_.' I have already given reasons why
I cannot adopt the former expression; but I do not see why
space, time, number, cause, and the rest, may not be termed
_different forms_ of the _impulse of the mind to
generalize_. But if we put together all the Fundamental
Ideas as results of the Generalizing Impulse, we must still
separate them as different modes of action of that Impulse,
showing themselves in various characteristic ways in the
axioms and modes of reasoning which belong to different
sciences. The Generalizing Impulse in one case proceeds
according to the Idea of Space; in another, according to the
Idea of Mechanical Cause; and so in other subjects.

{{147}}
CHAPTER XI.

OF MATHEMATICAL REASONING.

1. _Discursive Reasoning._--WE have thus seen that our
notions of space, time, and their modifications, necessarily
involve a certain activity of the mind; and that the
conditions of this activity form the foundations of those
sciences which have the relations of space, time, and
number, for their object. Upon the fundamental principles
thus established, the various sciences which are included in
the term _Pure Mathematics_, (Geometry, Algebra,
Trigonometry, Conic Sections, and the rest of the Higher
Geometry, the Differential Calculus, and the like,) are
built up by a series of reasonings. These reasonings are
subject to the rules of Logic, as we have already remarked;
nor is it necessary here to dwell long on the nature and
rules of such processes. But we may here notice that such
processes are termed _discursive_, in opposition to the
operations by which we acquire our fundamental principles,
which are, as we have seen, _intuitive_. This opposition was
formerly very familiar to our writers; as Milton,--
. . . Thus the soul reason receives,
Discursive or intuitive.--_Paradise Lost_, v. 438.
For in such reasonings we obtain our conclusions, not by
looking at our conceptions steadily in one view, which is
_intuition_, but by passing from one view to another, like
those who run from place to place (_discursus_). Thus a
straight line may be at the same time a side of a triangle
and a radius of a circle: and in the first proposition of
Euclid a line is considered, first in one of these
relations, and then in the other, and thus the sides of a
certain triangle are proved to be equal. And by this
'discourse of reason,' as by our older {148} writers it was
termed, we set forth from those axioms which we perceive by
intuition, travel securely over a vast and varied region,
and become possessed of a copious store of mathematical
truths.

2. _Technical Terms of Reasoning._--The reasoning of
mathematics, thus proceeding from a few simple principles to
many truths, is conducted according to the rules of Logic.
If it be necessary, mathematical proofs may be reduced to
logical forms, and expressed in Syllogisms, consisting of
major, minor, and conclusion. But in most cases the
syllogism is of that kind which is called by logical writers
an _Enthymeme_; a word which implies something existing in
the thoughts only, and which designates a syllogism in which
one of the premises is understood, and not expressed. Thus
we say in a mathematical proof, 'because the point C is the
center of the circle AB, AC is equal to BC;' not stating the
_major_,--that all lines drawn from the center of a circle
to the circumference are equal; or introducing it only by a
transient reference to the definition of a circle. But the
enthymeme is so constantly used in all habitual forms of
reasoning, that it does not occur to us as being anything
peculiar in mathematical works.

The propositions which are proved to be generally true are
termed _Theorems_: but when anything is required to be done,
as to draw a line or a circle under given conditions, this
proposition is a _Problem_. A theorem requires
demonstration; a problem, solution. And for both purposes
the mathematician usually makes a _Construction_. He directs
us to draw certain lines, circles, or other curves, on which
is to be founded his demonstration that his theorem is true,
or that his problem is solved. Sometimes, too, he
establishes some _Lemma_, or preparatory proposition, before
he proceeds to his main task; and often he deduces from his
demonstration some conclusion in addition to that which was
the professed object of his proposition; and this is termed
a _Corollary_.

These technical terms are noted here, not as being very
important, but in order that they may not sound {149}
strange and unintelligible if we should have occasion to use
some of them. There is, however, one technical distinction
more peculiar, and more important.

3. _Geometrical Analysis and Synthesis._--In geometrical
reasoning such as we have described, we introduce at every
step some new consideration; and it is by combining all
these considerations, that we arrive at the conclusion, that
is, the demonstration of the proposition. Each step tends to
the final result, by exhibiting some part of the figure
under a new relation. To what we have already proved, is
added something more; and hence this process is called
_Synthesis_, or _putting together_. The proof flows on,
receiving at every turn new contributions from different
quarters; like a river fed and augmented by many tributary
streams. And each of these tributaries flows from some
definition or axiom as its fountain, or is itself formed by
the union of smaller rivulets which have sources of this
kind. In descending along its course, the synthetical proof
gathers all these accessions into one common trunk, the
proposition finally proved.

But we may proceed in a different manner. We may begin from
the formed river, and ascend to its sources. We may take the
proposition of which we require a proof, and may examine
what the supposition of its truth implies. If this be true,
then something else may be seen to be true; and from this,
something else, and so on. We may often, in this way,
discover of what simpler propositions our theorem or
solution is compounded, and may resolve these in succession,
till we come to some proposition which is obvious. This is
geometrical _Analysis_. Having succeeded in this analytical
process, we may invert it; and may descend again from the
simple and known propositions, to the proof of a theorem, or
the solution of a problem, which was our starting-place.

This process resembles, as we have said, tracing a river to
its sources. As we ascend the stream, we perpetually meet
with bifurcations; and some sagacity is needed to enable us
to see which, in each case, is the main stream: but if we
proceed in our research, we {150} exhaust the unexplored
valleys, and finally obtain a clear knowledge of the place
whence the waters flow. _Analytical_ is sometimes confounded
with _symbolical_ reasoning, on which subject we shall make
a remark in the next chapter. The object of that chapter is
to notice certain other fundamental principles and ideas,
not included in those hitherto spoken of, which we find
thrown in our way as we proceed in our mathematical
speculations. It would detain us too long, and involve us in
subtle and technical disquisitions, to examine fully the
grounds of these principles; but the Mathematics hold so
important a place in relation to the inductive sciences,
that I shall briefly notice the leading ideas which the
ulterior progress of the subject involves.

{{151}}
CHAPTER XII.

OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS.

1. _The Idea of a Limit._--THE general truths concerning
relations of space which depend upon the axioms and
definitions contained in Euclid's _Elements_, and which
involve only properties of straight lines and circles, are
termed Elementary Geometry: all beyond this belongs to the
Higher Geometry. To this latter province appertain, for
example, all propositions respecting the lengths of any
portions of curve lines; for these cannot be obtained by
means of the principles of the Elements alone. Here then we
must ask to what other principles the geometer has recourse,
and from what source these are drawn. Is there any origin of
geometrical truth which we have not yet explored?

The _Idea of a Limit_ supplies a new mode of establishing
mathematical truths. Thus with regard to the length of any
portion of a curve, a problem which we have just mentioned;
a curve is not made up of straight lines, and therefore we
cannot by means of any of the doctrines of elementary
geometry measure the length of any curve. But we may make up
a figure nearly resembling any curve by putting together
many short straight lines, just as a polygonal building of
very many sides may nearly resemble a circular room. And in
order to approach nearer and nearer to the curve, we may
make the sides more and more small, more and more numerous.
We may then possibly find some mode of measurement, some
relation of these small lines to other lines, which is not
disturbed by the multiplication of the sides, however far it
be carried. And thus, we may do what is equivalent to
measuring the curve itself; for by multiplying the {152}
sides we may approach more and more closely to the curve
till no appreciable difference remains. The curve line is
the _Limit_ of the polygon; and in this process we proceed
on the _Axiom_, that 'What is true up to the Limit is true
at the Limit.'

This mode of conceiving mathematical magnitudes is of wide
extent and use; for every curve may be considered as the
limit of some polygon; every varied magnitude, as the limit
of some aggregate of simpler forms; and thus the relations
of the elementary figures enable us to advance to the
properties of the most complex cases.

A Limit is a peculiar and fundamental conception, the use of
which in proving the propositions of the Higher Geometry
cannot be superseded by any combination of other hypotheses
and definitions[14\2]. The axiom just noticed, that what is
true up to the limit is true at the limit, is involved in
the very conception of a Limit: and this principle, with its
consequences, leads to all the results which form the
subject of the higher mathematics, whether proved by the
consideration of evanescent triangles, by the processes of
the Differential Calculus, or in any other way.

[Note 14\2: This assertion cannot be fully proved and
illustrated without a reference to mathematical reasonings
which would not be generally intelligible. I have shown the
truth of the assertion in my _Thoughts on the Study of
Mathematics_, annexed to the _Principles of English
University Education_. The proof is of this kind:--The
ultimate equality of an arc of a curve and the corresponding
periphery of a polygon, when the sides of the polygon are
indefinitely increased in number, is _evident_. But this
truth cannot be proved from any other axiom. For if we take
the supposed axiom, that a curve is always less than the
including broken line, this is not true, except with a
condition; and in tracing the import of this condition, we
find its necessity becomes evident only when we introduce a
reference to a Limit. And the same is the case if we attempt
to supersede the notion of a Limit in proving any other
simple and evident proposition in which that notion is
involved. Therefore these evident truths are _self_-evident,
_in virtue of the Idea of a Limit_.]

The ancients did not expressly introduce this conception of
a Limit into their mathematical reasonings; although in the
application of what is termed the {153} _Method of
Exhaustions_, (in which they show how to _exhaust_ the
_difference_ between a polygon and a curve, or the like,)
they were in fact proceeding upon an obscure apprehension of
principles equivalent to those of the Method of Limits. Yet
the necessary fundamental principle not having, in their
time, been clearly developed, their reasonings were both
needlessly intricate and imperfectly satisfactory. Moreover
they were led to put in the place of axioms, assumptions
which were by no means self-evident; as when Archimedes
assumed, for the basis of his measure of the circumference
of the circle, the proposition that a circular arc is
necessarily less than two lines which inclose it, joining
its extremities. The reasonings of the older mathematicians,
which professed to proceed upon such assumptions, led to
true results in reality, only because they were guided by a
latent reference to the limiting case of such assumptions.
And this latent employment of the conception of a Limit,
reappeared in various forms during the early period of
modern mathematics; as for example, in the _Method of
Indivisibles_ of Cavalleri, and the _Characteristic
Triangle_ of Barrow; till at last, Newton distinctly
referred such reasonings to the conception of a Limit, and
established the fundamental principles and processes which
that conception introduces, with a distinctness and
exactness which required little improvement to make it as
unimpeachable as the demonstrations of geometry. And when
such processes as Newton thus deduced from the conception of
a Limit, are represented by means of general algebraical
symbols instead of geometrical diagrams, we have then before
us the _Method of Fluxions_, or the _Differential Calculus_;
a mode of treating mathematical problems justly considered
as the principal weapon by which the splendid triumphs of
modern mathematics have been achieved.

2. _The Use of General Symbols._--The employment of
algebraical symbols, of which we have just spoken, has been
another of the main instruments to which the successes of
modern mathematics are owing. And here again the processes
by which we obtain our {154} results depend for their
evidence upon a fundamental conception,--the conception of
_arbitrary symbols_ as the _Signs_ of quantity and its
relations; and upon a corresponding axiom, that 'The
interpretation of such symbols must be perfectly general.'
In this case, as in the last, it was only by degrees that
mathematicians were led to a just apprehension of the
grounds of their reasoning. For symbols were at first used
only to represent numbers considered with regard to their
numerical properties; and thus the science of Algebra was
formed. But it was found, even in cases belonging to common
algebra, that the symbols often admitted of an
interpretation which went beyond the limits of the problem,
and which yet was not unmeaning, since it pointed out a
question closely analogous to the question proposed. This
was the case, for example, when the answer was a _negative
quantity_; for when Descartes had introduced the mode of
representing curves by means of algebraical relations among
the symbols of the _co-ordinates_, or distances of each of
their points from fixed lines, it was found that negative
quantities must be dealt with as not less truly significant
than positive ones. And as the researches of mathematicians
proceeded, other cases also were found, in which the
symbols, although destitute of meaning according to the
original conventions of their institution, still pointed out
truths which could be verified in other ways; as in the
cases in which what are called _impossible quantities_
occur. Such processes may usually be confirmed upon other
principles, and the truth in question may be established by
means of a demonstration in which no such seeming fallacies
defeat the reasoning. But it has also been shown in many
such cases, that the process in which some of the steps
appear to be without real meaning, does in fact involve a
valid proof of the proposition. And what we have here to
remark is, that this is not true accidentally or partially
only, but that the results of systematic symbolical
reasoning must _always_ express general truths, by their
nature; and do not, for their justification, require each of
the steps of the process to represent {155} some definite
operation upon quantity. _The absolute universality of the
interpretation of symbols_ is the fundamental principle of
their use. This has been shown very ably by Dr. Peacock in
his _Algebra_. He has there illustrated, in a variety of
ways, this principle: that 'If general symbols express an
identity when they are supposed to be of any special nature,
they must also express an identity when they are general in
their nature.' And thus, this universality of symbols is a
principle in addition to those we have already noticed; and
is a principle of the greatest importance in the formation
of mathematical science, according to the wide generality
which such science has in modern times assumed.

3. _Connexion of Symbols and Analysis._--Since in our
symbolical reasoning our symbols thus reason for us, we do
not necessarily here, as in geometrical reasoning, go on
adding carefully one known truth to another, till we reach
the desired result. On the contrary, if we have a theorem to
prove or a problem to solve which can be brought under the
domain of our symbols, we may at once state the given but
unproved truth, or the given combination of unknown
quantities, in its symbolical form. After this first
process, we may then proceed to trace, by means of our
symbols, what other truth is involved in the one just
stated, or what the unknown symbols must signify; resolving
step by step the symbolical assertion with which we began,
into others more fitted for our purpose. The former process
is a kind of _synthesis_, the latter is termed _analysis_.
And although symbolical reasoning does not necessarily imply
such analysis; yet the connexion is so familiar, that the
term _analysis_ is frequently used to designate symbolical
reasoning.

{{156}}
CHAPTER XIII.

THE DOCTRINE OF MOTION.

1. _Pure Mechanism._--THE doctrine of Motion, of which we
have here to speak, is that in which motion is considered
quite independently of its cause, force; for all
consideration of force belongs to a class of ideas entirely
different from those with which we are here concerned. In
this view it may be termed the _pure_ doctrine of motion,
since it has to do solely with space and time, which are the
subjects of pure mathematics. (See c. i. of this book.)
Although the doctrine of motion in connexion with force,
which is the subject of mechanics, is by far the most
important form in which the consideration of motion enters
into the formation of our sciences, the Pure Doctrine of
Motion, which treats of space, time, and velocity, might be
followed out so as to give rise to a very considerable and
curious body of science. Such a science is the science of
Mechanism, independent of force, and considered as the
solution of a problem which may be thus enunciated: 'To
communicate any given motion from a first mover to a given
body.' The science which should have for its object to solve
all the various cases into which this problem would ramify,
might be termed _Pure Mechanism_, in contradistinction to
_Mechanics Proper_, or _Machinery_, in which Force is taken
into consideration. The greater part of the machines which
have been constructed for use in manufactures have been
practical solutions of some of the cases of this problem. We
have also important contributions to such a science in the
works of Mathematicians; for example, the various
investigations and demonstrations which have been published
respecting the form of the Teeth {157} of Wheels, and Mr.
Babbage's memoir[15\2] on the Language of Machinery. There
are also several works which contain collections of the
mechanical contrivances which have been invented for the
purpose of transmitting and modifying motion, and these
works may be considered as treatises on the science of Pure
Mechanism. But this science has not yet been reduced to the
systematic simplicity which is desirable, nor indeed
generally recognized as a separate science. It has been
confounded, under the common name of _Mechanics_, with the
other **science, Mechanics Proper, or Machinery, which
considers the effect of _force_ transmitted by Mechanism
from one part of a material combination to another. For
example, the _Mechanical Powers_, as they are usually
termed, (the Lever, the Wheel and Axle, the Inclined Plane,
the Wedge, and the Screw,) have almost always been treated
with reference to the relation between the _Power_ and the
_Weight_, and not primarily as a mode of changing the
velocity and kind of the motion. The science of pure motion
has not generally been separated from the science of motion
viewed with reference to its causes.

[Note 15\2: _On a Method of expressing by Signs the action
of Machinery._ _Phil. Trans._ 1826, p. 250.]

Recently, indeed, the necessity of such a separation has
been seen by those who have taken a philosophical view of
science. Thus this necessity has been urged by M. Ampère, in
his _Essai sur la Philosophie des Sciences_ (1834): 'Long,'
he says, (p. 50,) 'before I employed myself upon the present
work, I had remarked that it is usual to omit, in the
beginning of all books treating of sciences which regard
motion and force, certain considerations which, duly
developed, must constitute a special science: of which
science certain parts have been treated of, either in
memoirs or in special works; such, for example, as that of
Carnot upon Motion considered Geometrically, and the essay
of Lanz and Betancourt upon the Composition of Machines.' He
then proceeds to describe this science nearly as we have
{158} done, and proposes to term it _Kinematics_
(_Cinématique_), from κίνημα, motion.

2. _Formal Astronomy._--I shall not attempt here further to
develop the form which such a science must assume. But I may
notice one very large province which belongs to it. When men
had ascertained the apparent motions of the sun, moon, and
stars, to a moderate degree of regularity and accuracy, they
tried to conceive in their minds some mechanism by which
these motions might be produced; and thus they in fact
proposed to themselves a very extensive problem in
_Kinematics_. This, indeed, was the view originally
entertained of the nature of the science of astronomy. Thus
Plato in the seventh Book of his _Republic_[16\2], speaks of
astronomy as the doctrine of the motion of solids, meaning
thereby, spheres. And the same was a proper description of
the science till the time of Kepler, and even later: for
Kepler endeavoured in vain to conjoin with the knowledge of
the motions of the heavenly bodies, those true mechanical
conceptions which converted formal into physical
astronomy[17\2].

[Note 16\2: P. 528.]

[Note 17\2: _Hist. Induc. Sc._ ii. 130.]

The astronomy of the ancients admitted none but uniform
circular motions, and could therefore be completely
cultivated by the aid of their elementary geometry. But the
pure science of motion might be extended to all motions,
however varied as to the speed or the path of the moving
body. In this form it must depend upon the doctrine of
limits; and the fundamental principle of its reasonings
would be this: That velocity is measured by the Limit of the
_space_ described, considered with reference to the _time_
in which it is described. I shall not further pursue this
subject; and in order to complete what I have to say
respecting the Pure Sciences, I have only a few words to add
respecting their bearing on Inductive Science in general.

{{159}}
CHAPTER XIV.

OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE SCIENCES.

1. ALL objects in the world which can be made the subjects
of our contemplation are subordinate to the conditions of
Space, Time, and Number; and on this account, the doctrines
of pure mathematics have most numerous and extensive
applications in every department of our investigations of
nature. And there is a peculiarity in these Ideas, which has
caused the mathematical sciences to be, in all cases, the
first successful efforts of the awakening speculative powers
of nations at the commencement of their intellectual
progress. Conceptions derived from these Ideas are, from the
very first, perfectly precise and clear, so as to be fit
elements of scientific truths. This is not the case with the
other conceptions which form the subjects of scientific
inquiries. The conception of _statical force_, for instance,
was never presented in a distinct form till the works of
Archimedes appeared: the conception of _accelerating force_
was confused, in the mind of Kepler and his contemporaries,
and only became clear enough for purposes of sound
scientific reasoning in the succeeding century: the just
conception of chemical _composition_ of elements gradually,
in modern times, emerged from the erroneous and vague
notions of the ancients. If we take works published on such
subjects before the epoch when the foundations of the true
science were laid, we find the knowledge not only small, but
worthless. The writers did not see any evidence in what we
now consider as the axioms of the science; nor any
inconsistency where we now see self-contradiction. But this
was never the case with speculations concerning {160} space
and number. From their first rise, these were true as far as
they went. The Geometry and Arithmetic of the Greeks and
Indians, even in their first and most scanty form, contained
none but true propositions. Men's intuitions upon these
subjects never allowed them to slide into error and
confusion; and the truths to which they were led by the
first efforts of their faculties, so employed, form part of
the present stock of our mathematical knowledge.

2. But we are here not so much concerned with mathematics in
their pure form, as with their application to the phenomena
and laws of nature. And here also the very earliest history
of civilization presents to us some of the most remarkable
examples of man's success in his attempts to attain to
science. Space and time, position and motion, govern all
visible objects; but by far the most conspicuous examples of
the relations which arise out of such elements, are
displayed by the ever-moving luminaries of the sky, which
measure days, and months, and years, by their motions, and
man's place on the earth by their position. Hence the
sciences of space and number were from the first cultivated
with peculiar reference to Astronomy. I have elsewhere[18\2]
quoted Plato's remark,--that it is absurd to call the
science of the relations of space _geometry_, the measure of
the earth, since its most important office is to be found in
its application to the heavens. And on other occasions also
it appears how strongly he, who may be considered as the
representative of the scientific and speculative tendencies
of his time and country, had been impressed with the
conviction, that the formation of a science of the celestial
motions must depend entirely upon the progress of
mathematics. In the Epilogue to the Dialogue on the
Laws[19\2], he declares mathematical knowledge to be the
first and main requisite for the astronomer, and describes
the portions of it which he holds necessary for astronomical
speculators to cultivate. These seem to be, Plane Geometry,
Theoretical Arithmetic, the Application of Arithmetic {161}
to planes and to solids, and finally the doctrine of
Harmonics. Indeed the bias of Plato appears to be rather to
consider mathematics as the essence of the science of
astronomy, than as its instrument; and he seems disposed, in
this as in other things, to disparage observation, and to
aspire after a science founded upon demonstration alone. 'An
astronomer,' he says in the same place, 'must not be like
Hesiod and persons of that kind, whose astronomy consists in
noting the settings and risings of the stars; but he must be
one who understands the revolutions of the celestial
spheres, each performing its proper cycle.'

[Note 18\2: _Hist. Ind. Sc._ b. iii. c. ii.]

[Note 19\2: _Epinomis_, p. 990.]

A large portion of the mathematics of the Greeks, so long as
their scientific activity continued, was directed towards
Astronomy. Besides many curious propositions of plane and
solid Geometry, to which their astronomers were led, their
Arithmetic, though very inconvenient in its fundamental
assumptions (as being sexagesimal not decimal), was
cultivated to a great extent; and the science of
Trigonometry, in which problems concerning the relations of
space were resolved by means of tables of numerical results
previously obtained, was created. Menelaus of Alexandria
wrote six Books on Chords, probably containing methods of
calculating Tables of these quantities; such Tables were
familiarly used by the later Greek astronomers. The same
author also wrote three Books on Spherical Trigonometry,
which are still extant.

3. The Greeks, however, in the first vigour of their pursuit
of mathematical truth, at the time of Plato and soon after,
had by no means confined themselves to those propositions
which had a visible bearing on the phenomena of nature; but
had followed out many beautiful trains of research,
concerning various kinds of figures, for the sake of their
beauty alone; as for instance in their doctrine of Conic
Sections, of which curves they had discovered all the
principal properties. But it is curious to remark, that
these investigations, thus pursued at first as mere matters
of curiosity and intellectual gratification, were destined,
two thousand years later, to play a very important part in
{162} establishing that system of the celestial motions
which succeeded the Platonic scheme of cycles and epicycles.
If the properties of the conic sections had not been
demonstrated by the Greeks, and thus rendered familiar to
the mathematicians of succeeding ages, Kepler would probably
not have been able to discover those laws respecting the
orbits and motions of the planets which were the occasion of
the greatest revolution that ever happened in the history of
science.

4. The Arabians, who, as I have elsewhere said, added little
of their own to the stores of science which they received
from the Greeks, did however make some very important
contributions in those portions of pure mathematics which
are subservient to astronomy. Their adoption of the Indian
mode of computation by means of the Ten Digits, 1, 2, 3, 4,
5, 6, 7, 8, 9, 0, and by the method of Local Values, instead
of the cumbrous sexagesimal arithmetic of the Greeks, was an
improvement by which the convenience and facility of
numerical calculations were immeasurably augmented. The
Arabians also rendered several of the processes of
trigonometry much more commodious, by using the Sine of an
arc instead of the Chord; an improvement which Albategnius
appears to claim for himself[20\2]; and by employing also
the Tangents of arcs, or, as they called them[21\2],
_upright shadows_.

[Note 20\2: Delambre, _Ast., M. A._, p. 12.]

[Note 21\2: _Ibid._ p. 17.]

5. The constant application of mathematical knowledge to the
researches of Astronomy, and the mutual influence of each
science on the progress of the other, has been still more
conspicuous in modern times. Newton's Method of Prime and
Ultimate Ratios, which we have already noticed as the first
correct exposition of the doctrine of a Limit, is stated in
a series of Lemmas, or preparatory theorems, prefixed to his
_Treatise on the System of the World_. Both the properties
of curve lines and the doctrines concerning force and
motion, which he had to establish, required that the common
mathematical processes should be methodized and extended. If
Newton had not been a most {163} expert and inventive
mathematician, as well as a profound and philosophical
thinker, he could never have made any one of those vast
strides in discovery of which the rapid succession in his
work strikes us with wonder[22\2]. And if we see that the
great task begun by him, goes on more slowly in the hands of
his immediate successors, and lingers a little before its
full completion, we perceive that this arises, in a great
measure, from the defect of the mathematical methods then
used. Newton's synthetical modes of investigation, as we
have elsewhere observed, were an instrument[23\2], powerful
indeed in his mighty hand, but too ponderous for other
persons to employ with effect. The countrymen of Newton
clung to it the longest, out of veneration for their master;
and English cultivators of physical astronomy were, on that
very account, left behind the progress of mathematical
science in France and Germany, by a wide interval, which
they have only recently recovered. On the Continent, the
advantages offered by a familiar use of symbols, and by
attention to their symmetry and other relations, were
accepted without reserve. In this manner the Differential
Calculus of Leibnitz, which was in its origin and
signification identical with the Method of Fluxions of
Newton, soon surpassed its rival in the extent and
generality of its application to problems. This Calculus was
applied to the science of mechanics, to which it, along with
the symmetrical use of co-ordinates, gave a new form; for it
was soon seen that the most difficult problems might in
general be reduced to finding integrals, which is the
reciprocal process of that by which differentials are found;
so that all difficulties of physical astronomy were reduced
to difficulties of symbolical calculation, these, indeed,
being often sufficiently stubborn. Clairaut, Euler, and
D'Alembert employed the increased resources of mathematical
science upon the Theory of the Moon, and other questions
relative to the system of the world; and thus began to
pursue such inquiries in the course in which mathematicians
{164} are still labouring up to the present day. This course
was not without its checks and perplexities. We have
elsewhere quoted[24\2] Clairaut's expression when he had
obtained the very complex differential equations which
contain the solution of the problem of the moon's motion:
'Now integrate them who can!' But in no very long time they
were integrated, at least approximately; and the methods of
approximation have since then been improved; so that now,
with a due expenditure of labour, they may be carried to any
extent which is thought desirable. If the methods of
astronomical observation should hereafter reach a higher
degree of exactness than they now profess, so that
irregularities in the motions of the sun, moon, and planets,
shall be detected which at present escape us, the
mathematical part of the theory of universal gravitation is
in such a condition that it can soon be brought into
comparison with the newly-observed facts. Indeed at present
the mathematical theory is in advance of such observations.
It can venture to suggest what may afterwards be detected,
as well as to explain what has already been observed. This
has happened recently; for Professor Airy has calculated the
law and amount of an inequality depending upon the mutual
attraction of the Earth and Venus; of which inequality (so
small is it,) it remains to be determined whether its effect
can be traced in the series of astronomical observations.

[Note 22\2: _Hist. Ind. Sc._ b. vii. c. ii.]

[Note 23\2: _Ibid._ p. 175.]

[Note 24\2: _Hist. Ind. Sc._ b. vi. c. vi. sect. 7.]

6. As the influence of mathematics upon the progress of
astronomy is thus seen in the cases in which theory and
observation confirm each other, so this influence appears in
another way, in the very few cases in which the facts have
not been fully reduced to an agreement with theory. The most
conspicuous case of this kind is the state of our knowledge
of the Tides. This is a portion of astronomy: for the
Newtonian theory asserts these curious phenomena to be the
result of the attraction of the sun and moon. Nor can there
be any doubt that this is true, as a general statement; yet
the subject is up to the present time a blot {165} on the
perfection of the theory of universal gravitation; for we
are very far from being able in this, as in the other parts
of astronomy, to show that theory will exactly account for
the time, and magnitude, and all other circumstances of the
phenomenon at every place on the earth's surface. And what
is the portion of our mathematics which is connected with
this solitary signal defect in astronomy? It is the
mathematics of the Motion of Fluids; a portion in which
extremely little progress has been made, and in which all
the more general problems of the subject have hitherto
remained entirely insoluble. The attempts of the greatest
mathematicians, Newton, Maclaurin, Bernoulli, Clairaut,
Laplace, to master such questions, all involve some
gratuitous assumption, which is introduced because the
problem cannot otherwise be mathematically dealt with: these
assumptions confessedly render the result defective, and how
defective, it is hard to say. And it was probably precisely
the absence of a theory which could be reasonably expected
to agree with the observations, which made Observations of
this very curious phenomenon, the Tides, to be so much
neglected as till very recently they were. Of late years
such observations have been pursued, and their results have
been resolved into empirical laws, so that the rules of the
phenomena have been ascertained, although the dependence of
these rules upon the lunar and solar forces has not been
shown. Here then we have a portion of our knowledge relating
to facts undoubtedly dependent upon universal gravitation,
in which Observation has outstripped Theory in her progress,
and is compelled to wait till her usual companion overtakes
her. This is a position of which Mathematical Theory has
usually been very impatient, and we may expect that she will
be no less so in the present instance.

7. It would be easy to show from the history of other
sciences, for example, Mechanics and Optics, how essential
the cultivation of pure mathematics has been to their
progress. The parabola was already familiar among
mathematicians when Galileo discovered that it was the
theoretical path of a Projectile; and the {166} extension
and generalization of the Laws of Motion could never have
been effected, unless the Differential and Integral Calculus
had been at hand, ready to trace the results of every
hypothesis which could be made. D'Alembert's mode of
expressing the Third Law of Motion in its most general
form[25\2], if it did not prove the law, at least reduced
the application of it to analytical processes which could be
performed in most of those cases in which they were needed.
In many instances the demands of mechanical science
suggested the extension of the methods of pure analysis. The
problem of Vibrating Strings gave rise to the Calculus of
Partial Differences, which was still further stimulated by
its application to the motions of fluids and other
mechanical problems. And we have in the writings of Lagrange
and Laplace other instances equally remarkable of new
analytical methods, to which mechanical problems, and
especially cosmical problems, have given occasion.

[Note 25\2: _Hist. Ind. Sc._ b. vi. c. vi. sect. 7.]

8. The progress of Optics as a science has, in like manner,
been throughout dependent upon the progress of pure
mathematics. The first rise of Geometry was followed by some
advances, slight ones no doubt, in the doctrine of
Reflection and in Perspective. The law of Refraction was
traced to its consequences by means of Trigonometry, which
indeed was requisite to express the law in a simple form.
The steps made in Optical science by Descartes, Newton,
Euler, and Huyghens, required the geometrical skill which
those philosophers possessed. And if Young and Fresnel had
not been, each in his peculiar way, persons of eminent
mathematical endowments, they would not have been able to
bring the Theory of Undulations and Interferences into a
condition in which it could be tested by experiments. We may
see how unexpectedly recondite parts of pure mathematics may
bear upon physical science, by calling to mind a
circumstance already noticed in the History of
Science[26\2];--that Fresnel obtained one of the {167} most
curious confirmations of the theory (the laws of Circular
Polarization by reflection) through an interpretation of an
algebraical expression, which, according to the original
conventional meaning of the symbols, involved an impossible
quantity. We have already remarked, that in virtue of the
principle of the generality of symbolical language, such an
interpretation may often point out some real and important
analogy.

[Note 26\2: _Hist. Ind. Sc._ b. ix. c. xiii. sect. 2.]

9. From this rapid sketch it may be seen how important an
office in promoting the progress of the physical sciences
belongs to mathematics. Indeed in the progress of many
sciences, every step has been so intimately connected with
some advance in mathematics, that we can hardly be surprised
if some persons have considered mathematical reasoning to be
the most essential part of such sciences; and have
overlooked the other elements which enter into their
formation. How erroneous this view is we shall best see by
turning our attention to the other Ideas besides those of
space, number, and motion, which enter into some of the most
conspicuous and admired portions of what is termed exact
science; and by showing that the clear and distinct
development of such Ideas is quite as necessary to the
progress of exact and real knowledge as an acquaintance with
arithmetic and geometry.

{{169}}
BOOK III.

THE
PHILOSOPHY
OF THE
MECHANICAL SCIENCES.

IT is only because we subject trains of phenomena, that is,
all change whatever, to the law of causality--to the
relation of cause and effect--that experience or empirical
knowledge becomes possible.

KANT, _Kr. d. R. V._ 11 Th. 1 Abth. 11 Buch. 2 Haupt.

Quicquid premit vel trahit alterum, tantundem ab eo premitur
vel trahitur ... Si corpus aliquod in corpus aliud impingens
motum ejus vi suâ quomodocunque mutaverit, idem quoque
vicissim in motu proprio eandem mutationem in partem
contrariam vi alterius (ob æqualitatem pressionis, mutuæ)
subibit ... Obtinet etiam hæc Lex in attractionibus.

NEWTON, _Princip._ ad init.

{{171}}
BOOK III.

THE PHILOSOPHY OF THE MECHANICAL SCIENCES.

CHAPTER I.

OF THE MECHANICAL SCIENCES.

IN the History of the Sciences, that class of which we here
speak occupies a conspicuous and important place; coming
into notice immediately after those parts of Astronomy which
require for their cultivation merely the ideas of space,
time, motion, and number. It appears from our History, that
certain truths concerning the _equilibrium_ of bodies were
established by Archimedes;--that, after a long interval of
inactivity, his principles were extended and pursued further
in modern times:--and that to these doctrines concerning
equilibrium and the forces which produce it, (which
constitute the science _Statics_,) were added many other
doctrines concerning the _motions_ of bodies, considered
also as produced by forces, and thus the science of
_Dynamics_ was produced. The assemblage of these sciences
composes the province of _Mechanics_. Moreover, philosophers
have laboured to make out the laws of the equilibrium of
_fluid_ as well as solid bodies; and hence has arisen the
science of _Hydrostatics_. And the doctrines of Mechanics
have been found to have a most remarkable bearing upon the
motions of the heavenly bodies; with reference to which,
indeed, they were at first principally studied. The
explanation of those cosmical facts by means of mechanical
{172} principles and their consequences, forms the science
of _Physical Astronomy_. These are the principal examples of
mechanical science; although some other portions of Physics,
as Magnetism and Electrodynamics, introduce mechanical
doctrines very largely into their speculations.

Now in all these sciences we have to consider _Forces_. In
all mechanical reasonings forces enter, either as producing
motion, or as prevented from doing so by other forces. Thus
force, in its most general sense, is the _cause_ of motion,
or of tendency to motion; and in order to discover the
principles on which the mechanical sciences truly rest, we
must examine the nature and origin of our knowledge of Causes.

In these sciences, however, we have not to deal with Cause
in its more general acceptation, in which it applies to all
kinds of agency, material or immaterial;--to the influence
of thought and will, as well as of bodily pressure and
attractive force. Our business at present is only with such
causes as immediately operate upon matter. We shall
nevertheless, in the first place, consider the nature of
Cause in its most general form; and afterwards narrow our
speculations so as to direct them specially to the
mechanical sciences.

{{173}}
CHAPTER II.

OF THE IDEA OF CAUSE.

1. WE see in the world around us a constant succession of
causes and effects connected with each other. The laws of
this connexion we learn in a great measure from experience,
by observation of the occurrences which present themselves
to our notice, succeeding one another. But in doing this,
and in attending to this succession of appearances, of which
we are aware by means of our senses, we supply from our own
minds the Idea of Cause. This Idea, as we have already shown
with respect to other Ideas, is not derived from experience,
but has its origin in the mind itself;--is introduced into
our experience by the active, and not by the passive part of
our nature.

By Cause we mean some quality, power, or efficacy, by which
a state of things produces a succeeding state. Thus the
motion of bodies from rest is produced by a cause which we
call _Force_: and in the particular case in which bodies
fall to the earth, this force is termed _Gravity_. In these
cases, the Conceptions of Force and Gravity receive their
meaning from the Idea of Cause which they involve: for Force
is conceived as the Cause of Motion. That this Idea of Cause
is not derived from experience, we prove (as in former
cases) by this consideration: that we can make assertions,
involving this idea, which are rigorously necessary and
universal; whereas knowledge derived from experience can
only be true as far as experience goes, and can never
contain in itself any evidence whatever of its necessity. We
assert that 'Every event must have a cause:' and this
proposition we know to be true, not only probably, and
generally, and as far as we can see: {174} but we cannot
suppose it to be false in any single instance. We are as
certain of it as of the truths of arithmetic or geometry. We
cannot doubt that it must apply to all events past and
future, in every part of the universe, just as truly as to
those occurrences which we have ourselves observed. _What_
causes produce what effects;--what is the cause of any
particular event;--what will be the effect of any peculiar
process;--these are points on which experience may enlighten
us. Observation and experience may be requisite, to enable
us to judge respecting such matters. But that every event
has _some_ cause, Experience cannot prove any more than she
can disprove. She can add nothing to the evidence of the
truth, however often she may exemplify it. This doctrine,
then, cannot have been acquired by her teaching; and the
Idea of Cause, which the doctrine involves, and on which it
depends, cannot have come into our minds from the region of
observation.

2. That we do, in fact, apply the Idea of Cause in a more
extensive manner than could be justified, if it were derived
from experience only, is easily shown. For from the
principle that everything must have a cause, we not only
reason concerning the succession of the events which occur
in the progress of the world, and which form the course of
experience; but we infer that the world itself must have a
cause;--that the chain of events connected by common
causation, must have a First Cause of a nature different
from the events themselves. This we are entitled to do, if
our Idea of Cause be independent of, and superior to,
experience: but if we have no Idea of Cause except such as
we gather from experience, this reasoning is altogether
baseless and unmeaning.

3. Again; by the use of our powers of observation, we are
aware of a succession of appearances and events. But none of
our senses or powers of external observation can detect in
these appearances the power or quality which we call Cause.
Cause is that which connects one event with another; but no
sense or perception discloses to us, or can disclose, any
connexion {175} among the events which we observe. We see
that one occurrence follows another, but we can never see
anything which shows that one occurrence _must_ follow
another. We have already noticed[1\3], that this truth has
been urged by metaphysicians in modern times, and generally
assented to by those who examine carefully the connexion of
their own thoughts. The arguments are, indeed, obvious
enough. One ball strikes another and causes it to move
forwards. But by what compulsion? Where is the necessity? If
the mind can see any circumstance in this case which makes
the result inevitable, let this circumstance be pointed out.
But, in fact, there is no such discoverable necessity; for
we can conceive this event not to take place at all. The
struck ball may stand still, for aught we can see. 'But the
laws of motion will not allow it to do so.' Doubtless they
will not. But the laws of motion are learnt from experience,
and therefore can prove no necessity. Why should not the
laws of motion be other than they are? Are they necessarily
true? That they are necessarily such as do actually regulate
the impact of bodies, is at least no obvious truth; and
therefore this necessity cannot be, in common minds, the
ground of connecting the impact of one ball with the motion
of another. And assuredly, if this fail, no other ground of
such necessary connexion can be shown. In this case, then,
the events are not seen to be necessarily connected. But if
this case, where one ball moves another by impulse, be not
an instance of events exhibiting a necessary connexion, we
shall look in vain for any example of such a connexion.
There is, then, no case in which events can be observed to
be necessarily connected: our idea of causation, which
implies that the event is necessarily connected with the
cause, cannot be derived from observation.

[Note 1\3: Book 3. chap. ii.]

4. But it may be said, we have not any such Idea of Cause,
implying necessary connexion with effect, and a quality by
which this connexion is produced. {176} We see nothing but
the succession of events; and by _cause_ we mean nothing but
a certain succession of events;--namely, a constant,
unvarying succession. Cause and effect are only two events
of which the second invariably follows the first. We delude
ourselves when we imagine that our idea of causation
involves anything more.

To this I reply by asking, what then is the meaning of the
maxim above quoted, and allowed by all to be universally and
necessarily true, that every event must have a cause? Let us
put this maxim into the language of the explanation just
noticed; and it becomes this:--'Every event must have a
certain other event invariably preceding it.' But why must
it? Where is the necessity? Why must like events always be
preceded by like, except so far as other events interfere?
That there is such a necessity, no one can doubt. All will
allow that if a stone ascend because it is thrown upwards in
one case, a stone which ascends in another case has also
been thrown upwards, or has undergone some equivalent
operation. All will allow that in this sense, every kind of
event must have some other specific kind of event preceding
it. But this turn of men's thoughts shows that they see in
events a connexion which is not mere succession. They see in
cause and effect, not merely what does, often or always,
precede and follow, but what _must_ precede and follow. The
events are not only conjoined, they are connected. The cause
is more than the prelude, the effect is more than the
sequel, of the fact. The cause is conceived not as a mere
occasion; it is a power, an efficacy, which has a real
operation.

5. Thus we have drawn from the maxim, that Every Effect must
have a Cause, arguments to show that we have an Idea of
Cause which is not borrowed from experience, and which
involves more than mere succession. Similar arguments might
be derived from any other maxims of universal and necessary
validity, which we can obtain concerning Cause: as, for
example, the maxims that Causes are measured by their
Effects, and that Reaction is equal and opposite to {177}
Action. These maxims we shall soon have to examine; but we
may observe here, that the necessary truth which belongs to
them, shows that they, and the Ideas which they involve, are
not the mere fruits of observation; while their meaning,
including, as it does, something quite different from the
mere conception of succession of events, proves that such a
conception is far from containing the whole import and
signification of our Idea of Cause.

The progress of the opinions of philosophers on the points
discussed in this chapter, has been one of the most
remarkable parts of the history of Metaphysics in modern
times: and I shall therefore briefly notice some of its
features.

{{178}}
CHAPTER III.

MODERN OPINIONS RESPECTING THE IDEA OF CAUSE.

1. TOWARDS the end of the seventeenth century there existed
in the minds of many of the most vigorous and active
speculators of the European literary world, a strong
tendency to ascribe the whole of our Knowledge to the
teaching of Experience. This tendency, with its
consequences, including among them the reaction which was
produced when the tenet had been pushed to a length
manifestly absurd, has exercised a very powerful influence
upon the progress of metaphysical doctrines up to the
present time. I proceed to notice some of the most prominent
of the opinions which have thus obtained prevalence among
philosophers, so far as the Idea of Cause is concerned.

Locke was one of the metaphysicians who produced the
greatest effect in diffusing this opinion, of the exclusive
dependence of our knowledge upon experience. Agreeably to
this general system, he taught[2\3] that our ideas of Cause
and Effect are got from observation of the things about us.
Yet notwithstanding this tenet of his, he endeavoured still
to employ these ideas in reasoning on subjects which are far
beyond all limits of experience: for he professed to prove,
from our idea of Causation, the existence of the Deity[3\3].

[Note 2\3: _Essay on the Human Understanding_, b. ii. c. xxvi.]

[Note 3\3: B. iv. c. x.]

Hume noticed this obvious inconsistency; but declared
himself unable to discover any remedy for a defect so fatal
to the most important parts of our knowledge. He could see,
in our belief of the succession of cause and effect, nothing
but the habit of associating in our minds what had often
been {179} associated in our experience. He therefore
maintained that we could not, with logical propriety, extend
our belief of such a succession to cases entirely distinct
from all those of which our experience consisted. We see, he
said, an actual _conjunction_ of two events; but we can in
no way detect a necessary _connexion_; and therefore we have
no means of inferring cause from effect, or effect from
cause[4\3]. The only way in which we recognize Cause and
Effect in the field of our experience, is as an unfailing
Sequence: we look in vain for anything which can assure us
of an infallible Consequence. And since experience is the
only source of our knowledge, we cannot with any justice
assert that the world in which we live must necessarily have
had a cause.

[Note 4\3: Hume's _Phil. of the Human Mind_, vol. i. p.
94.]

2. This doctrine, taken in conjunction with the known
skepticism of its author on religious points, produced a
considerable fermentation in the speculative world. The
solution of the difficulty thus thrown before philosophers,
was by no means obvious. It was vain to endeavour to find in
experience any other property of a Cause, than a constant
sequence of the effect. Yet it was equally vain to try to
persuade men that they had no idea of Cause; or even to
shake their belief in the cogency of the familiar arguments
concerning the necessity of an original cause of all that is
and happens. Accordingly these hostile and apparently
irreconcilable doctrines,--the indispensable necessity of a
cause of every event, and the impossibility of our knowing
such a necessity,--were at last allowed to encamp side by
side. Reid, Beattie, and others, formed one party, who
showed how widely and constantly the idea of a cause
pervades all the processes of the human mind: while another
sect, including Brown, and apparently Stewart, maintained
that this idea is always capable of being resolved into a
constant sequence; and these latter reasoners tried to
obviate the dangerous and shocking inferences which some
persons might try to draw from their opinion, by declaring
the {180} maxim that "Every event must have a cause," to be
an instinctive law of belief, or a fundamental principle of
the human mind[5\3].

[Note 5\3: Stewart's _Active Powers_, vol. i. p. 347.
Browne's _Lectures_, vol. i. p. 115.]

3. While this series of discussions was going on in Britain,
a great metaphysical genius in Germany was unravelling the
perplexity in another way. Kant's speculations originated,
as he informs us, in the trains of thought to which Hume's
writings gave rise; and the _Kritik der Reinen Vernunft_, or
_Examination of the Pure Reason_, was published in 1787,
with the view of showing the true nature of our knowledge.

Kant's solution of the difficulties just mentioned differs
materially from that above stated. According to Brown[6\3],
succession observed and cause inferred,--the memory of past
conjunctions of events and the belief of similar future
conjunctions,--are facts, independent, so far as we can
discover, but inseparably combined by a law of our mental
nature. According to Kant, causality is an inseparable
condition of our experience: a connexion in events is
requisite to our apprehending them _as_ events. Future
occurrences must be connected by causation as the past have
been, because we cannot think of past, present, and future,
without such connexion. We cannot fix the mind upon
occurrences, without including these occurrences in a series
of causes and effects. The relation of Causation is a
condition under which we think of events, as the relations
of space are a condition under which we see objects.

[Note 6\3: _Lectures_, vol. i. p. 114.]

4. On a subject so abstruse, it is not easy to make our
distinctions very clear. Some of Brown's illustrations
appear to approach very near to the doctrine of Kant. Thus
he says[7\3], 'The _form_ of bodies is the relation of their
elements to each other in space,--the _power_ of bodies is
their relation to each other in time.' Yet notwithstanding
such approximations in expression, the Kantian doctrine
appears to be different from {181} the views of Stewart and
Brown, as commonly understood. According to the Scotch
philosophers, the cause and the effect are two things,
connected in our minds by a law of our nature. But this view
requires us to suppose that we can conceive the law to be
absent, and the course of events to be unconnected. If we
can understand what is the special force of this law, we
must be able to imagine what the case would be if the law
were non-existing. We must be able to conceive a mind which
does not connect effects with causes. The Kantian doctrine,
on the other hand, teaches that we cannot imagine events
liberated from the connexion of cause and effect: this
connexion is a condition of our conceiving any real
occurrences: we cannot think of a real sequence of things,
except as involving the operation of causes. In the Scotch
system, the past and the future are in their nature
independent, but bound together by a rule; in the German
system, they share in a common nature and mutual relation,
by the act of thought which makes them past and future. In
the former doctrine cause is a tie which binds; in the
latter it is a character which pervades and shapes events.
The Scotch metaphysicians only assert the _universality_ of
the relation; the German attempts further to explain its
_necessity_.

[Note 7\3: _Lectures_, vol. i. p. 127.]

This being the state of the case, such illustrations as that
of Dr. Brown quoted above, in which he represents _cause_ as
a relation of the same kind with _form_, do not appear
exactly to fit his opinions. Can the relations of figure be
properly said to be connected with each other by a law of
our nature, or a tendency of our mental constitution? Can we
ascribe it to a law of our thoughts, that we believe the
three angles of a triangle to be equal to two right angles?
If so, we must give the same reason for our belief that two
straight lines cannot inclose a space; or that three and two
are five. But will any one refer us to an ultimate law of
our constitution for the belief that three and two are five?
Do we not see that they are so, as plainly as we see that
they are three and two? Can we imagine laws of our
constitution abolished, so that three and two shall {182}
make something different from five;--so that an inclosed
space shall lie between two straight lines;--so that the
three angles of a plane triangle shall be greater than two
right angles? We cannot conceive this. If the numbers _are_
three and two; if the lines _are_ straight; if the triangle
_is_ a rectilinear triangle, the consequences are
inevitable. We cannot even imagine the contrary. We do not
want a law to direct that things should be what they are.
The relation, then, of cause and effect, being of the same
kind as the necessary relations of figure and number, is not
properly spoken of as established in our minds by a special
law of our constitution: for we reject that loose and
inappropriate phraseology which speaks of the relations of
figure and number as 'determined by laws of belief.'

5. In the present work, we accept and adopt, as the basis of
our inquiry concerning our knowledge, the existence of
necessary truths concerning causes, as there exist necessary
truths concerning figure and number. We find such truths
universally established and assented to among the
cultivators of science, and among speculative men in
general. All mechanicians agree that reaction is equal and
opposite to action, both when one body presses another, and
when one body communicates motion to another. All reasoners
join in the assertion, not only that every observed change
of motion has had a cause, but that every change of motion
must have a cause. Here we have certain portions of
substantial and undoubted knowledge. Now the essential point
in the view which we must take of the idea of cause is
this,--that our view must be such as to form a solid basis
for our knowledge. We have, in the Mechanical Sciences,
certain universal and necessary truths on the subject of
causes. Now any view which refers our belief in causation to
mere experience or habit, cannot explain the possibility of
such necessary truths, since experience and habit can never
lead to a perception of necessary connexion. But a view
which teaches us to acknowledge axioms concerning cause, as
we acknowledge axioms {183} concerning space, will lead us
to look upon the science of mechanics as equally certain and
universal with the science of geometry; and will thus
materially affect our judgment concerning the nature and
claims of our scientific knowledge.

Axioms concerning Cause, or concerning Force, which as we
shall see, is a modification of Cause, will flow from an
Idea of Cause, just as axioms concerning space and number
flow from the ideas of space and number or time. And thus
the propositions which constitute the science of Mechanics
prove that we possess an idea of cause, in the same sense in
which the propositions of geometry and arithmetic prove our
possession of the ideas of space and of time or number.

6. The idea of cause, like the ideas of space and time, is a
part of the _active_ powers of the mind. The relation of
cause and effect is a relation or condition under which
events are apprehended, which relation is not given by
observation, but supplied by the mind itself. According to
the views which explain our apprehension of cause by
reference to habit, or to a supposed law of our mental
nature, causal connexion is a consequence of agencies which
the mind passively obeys; but according to the view to which
we are led, this connexion is a result of faculties which
the mind actively exercises. And thus the relation of cause
and effect is a condition of our apprehending successive
events, a part of the mind's constant and universal
activity, a source of necessary truths; or, to sum all this
in one phrase, a Fundamental Idea.

{{184}}
CHAPTER IV.

OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE.

1. _Causes are abstract Conceptions._--WE have now to
express, as well as we can, the fundamental character of
that Idea of Cause of which we have just proved the
existence. This may be done, at least for purposes of
reasoning, in this as in former instances, by means of
axioms. I shall state the principal axioms which belong to
this subject, referring the reader to his own thoughts for
the axiomatic evidence which belongs to them.

But I must first observe, that in order to express general
and abstract truths concerning cause and effect, these
terms, _cause_ and _effect_, must be understood in a general
and abstract manner. When one event gives rise to another,
the first _event_ is, in common language, often called the
cause, and the second the effect. Thus the meeting of two
billiard-balls may be said to be the cause of one of them
turning aside out of the path in which it was moving. For
our present purposes, however, we must not apply the term
cause to such occurrences as this meeting and turning, but
to a certain conception, _force_, abstracted from all such
special events, and considered as a quality or property by
which one body affects the motion of the other. And in like
manner in other cases, cause is to be conceived as some
abstract quality, power, or efficacy, by which change is
produced; a quality not identical with the events, but
disclosed by means of them. Not only is this abstract mode
of conceiving force and cause useful in expressing the
fundamental principles of science; but it supplies us with
the only mode by which such principles can be {185} stated
in a general manner, and made to lead to substantial truth
and real knowledge.

Understanding _cause_, therefore, in this sense, we proceed
to our Axioms.

2. First Axiom. _Nothing can take place without a Cause._

Every event, of whatever kind, must have a cause in the
sense of the term which we have just indicated; and that it
must, is a universal and necessary proposition to which we
irresistibly assent as soon as it is understood. We believe
each appearance to come into existence,--we conceive every
change to take place,--not only with something preceding it,
but something by which it is made to be what it is. An
effect without a cause;--an event without a preceding
condition involving the efficacy by which the event is
produced;--are suppositions which we cannot for a moment
admit. That the connexion of effect with cause is universal
and necessary, is a universal and constant conviction of
mankind. It persists in the minds of all men, undisturbed by
all the assaults of sophistry and skepticism; and, as we
have seen in the last chapter, remains unshaken, even when
its foundations seem to be ruined. This axiom expresses, to
a certain extent, our Idea of Cause; and when that idea is
clearly apprehended, the axiom requires no proof, and indeed
admits of none which makes it more evident. That
notwithstanding its simplicity, it is of use in our
speculations, we shall hereafter see; but in the first
place, we must consider the other axioms belonging to this
subject.

3. Second Axiom. _Effects are proportional to their Causes,
and Causes are measured by their Effects._

We have already said that _cause_ is that quality or power,
in the circumstances of each case, by which the effect is
produced; and this power, an abstract property of the
condition of things to which it belongs, can in no way fall
directly under the cognizance of the senses. Cause, of
whatever kind, is not apprehended as including objects and
events which share its nature by being co-extensive with
certain portions of it, as space and time are. It cannot
therefore, like them, be {186} measured by repetition of its
own parts, as space is measured by repetition of inches, and
time by repetition of minutes. Causes may be greater or
less; as, for instance, the force of a man is greater than
the force of a child. But how much is the one greater than
the other? How are we to compare the abstract conception,
force, in such cases as these?

To this, the obvious and only answer is, that we must
compare causes by means of their effects;--that we must
compare force by something which force can do. The child can
lift one fagot; the man can lift ten such fagots: we have
here a means of comparison. And whether or not the rule is
to be applied in this manner, that is, by the number of
things operated on, (a question which we shall have to
consider hereafter,) it is clear that this form of rule,
namely, a reference to some effect or other as our measure,
is the right, because the only possible form. The cause
determines the effect. The cause being the same, the effect
must be the same. The connexion of the two is governed by a
fixed and inviolable rule. It admits of no ambiguity. Every
degree of intensity in the cause has some peculiar
modification of the effect corresponding to it. Hence the
effect is an unfailing index of the amount of the cause; and
if it be a measurable effect, gives a measure of the cause.
We can have no other measure; but we need no other, for this
is exact, sufficient and complete.

It may be said, that various effects are produced by the
same cause. The sun's heat melts wax and expands
quicksilver. The force of gravity causes bodies to move
downwards if they are free, and to press down upon their
supports if they are supported. Which of the effects is to
be taken as the measure of heat, or of gravity, in these
cases? To this we reply, that if we had merely different
states of the same cause to compare, any of the effects
might be taken. The sun's heat on different days might be
measured by the expansion of quicksilver, or by the quantity
of wax melted. The force of gravity, if it were different at
different places, might be measured by the spaces through
which a given weight would bend an elastic {187} support, or
by the spaces through which a body would fall in a given
time. All these measures are consistent with the general
character of our idea of cause.

4. _Limitation of the Second Axiom._--But there may be
circumstances in the nature of the case which may further
determine the kind of effect which we must take for the
measure of the cause. For example, if causes are conceived
to be of such a nature as to be capable of addition, the
effects taken as their measure must conform to this
condition. This is the case with mechanical causes. The
weights of two bodies are the causes of the pressure which
they exert downwards; and these weights are capable of
addition. The weight of the two is the sum of the weight of
each. We are therefore not at liberty to say that weights
shall be measured by the spaces through which they bend a
certain elastic support, except we have first ascertained
that the whole weight bends it through a space equal to the
sum of the inflections produced by the separate weights.
Without this precaution, we might obtain inconsistent
results. Two weights, each of the magnitude 3 as measured by
their effects, might, if we took the inflections of a spring
for the effects, be together equal to 5 or to 7 by the same
kind of measurement. For the inflection produced by two
weights of 3 might, for aught we can see beforehand, be more
or less than twice as great as the inflection produced by
one weight of 3. That forces are capable of addition, is a
condition which limits, and, as we shall see, in some cases
rigorously fixes, the kind of effects which are to be taken
as their measures.

Causes which are thus capable of addition are to be measured
by the repeated addition of equal quantities. Two such
causes are _equal_ to each other when they produce exactly
the same effect. So far our axiom is applied directly. But
these two causes can be _added_ together; and being thus
added, they are _double_ of one of them; and the cause
composed by addition of _three_ such, is _three_ times as
great as the first; and so on for any measure whatever. By
this means, and by this {188} means only, we have a complete
and consistent measure of those causes which are so
conceived as to be subject to this condition of being added
and multiplied.

Causes are, in the present chapter, to be understood in the
widest sense of the term; and the axiom now under our
consideration applies to them, whenever they are of such a
nature as to admit of any measure at all. But the cases
which we have more particularly in view are _mechanical_
causes, the causes of the motion and of the equilibrium of
bodies. In these cases, forces are conceived as capable of
addition; and what has been said of the measure of causes in
such cases, applies peculiarly to mechanical forces. Two
weights, placed together, may be considered as a single
weight, equal to the _sum_ of the two. Two pressures,
pushing a body in the same direction at the same point, are
identical in all respects with some single pressure, their
_sum_, pushing in like manner; and this is true whether or
not they put the body in motion. In the cases of mechanical
forces, therefore, we take some certain effect, velocity
generated or weight supported, which may fix the _unit_ of
force; and we then measure all other forces by the
successive repetition of this unit, as we measure all spaces
by the successive repetition of our unit of lineal measure.

But these steps in the formation of the science of Mechanics
will be further explained, when we come to follow our axioms
concerning cause into their application in that science. At
present we have, perhaps, sufficiently explained the axiom
that causes are measured by their effects, and we now
proceed to a third axiom, also of great importance.

5. Third Axiom. _Reaction is equal and opposite to Action._

In the case of mechanical forces, the action of a cause
often takes place by an operation of one body upon another;
and in this case, the action is always and inevitably
accompanied by an _opposite_ action. If I press a stone with
my hand, the stone presses my hand in return. If one ball
strike another and put it in motion, the second ball
diminishes the motion of {189} the first. In these cases the
operation is mutual; the Action is accompanied by a
Reaction. And in all such cases the Reaction is a force of
exactly the same nature as the Action, exerted in an
opposite direction. A pressure exerted upon a body at rest
is resisted and balanced by another pressure; when the
pressure of one body puts another in motion, the body,
though it yields to the force, nevertheless exerts upon the
pressing body a force like that which it suffers.

Now the axiom asserts further, that this Reaction is
_equal_, as well as opposite, to the Action. For the
Reaction is an effect of the Action, and is determined by
it. And since the two, Action and Reaction, are forces of
the same nature, each may be considered as cause and as
effect; and they must, therefore, determine each other by a
common rule. But this consideration leads necessarily to
their equality: for since the rule is mutual, if we could
for an instant suppose the Reaction to be less than the
Action, we must, by the same rule, suppose the Action to be
less than the Reaction. And thus Action and Reaction, in
every such case, are rigorously equal to each other.

It is easily seen that this axiom is not a proposition which
is, or can be, proved by experience; but that its truth is
anterior to special observation, and depends on our
conception of Action and Reaction. Like our other axioms,
this has its source in an Idea; namely, the Idea of Cause,
under that particular condition in which cause and effect
are mutual. The necessary and universal truth which we
cannot help ascribing to the axiom, shows that it is not
derived from the stores of experience, which can never
contain truths of this character. Accordingly, it was
asserted with equal confidence and generality by those who
did not refer to experience for their principles, and by
those who did. Leonicus Tomæus, a commentator of Aristotle,
whose work was published in 1552, and therefore at a period
when no right opinions concerning mechanical reaction were
current, at least in his school, says, in his remarks on the
Author's Questions concerning the communication of motion,
that 'Reaction is equal and {190} contrary to Action.' The
same principle was taken for granted by all parties, in all
the controversies concerning the proper measure of force, of
which we shall have to speak: and would be rigorously true,
as a law of motion, whichever of the rival interpretations
of the measure of the term 'Action' we were to take.

6. _Extent of the Third Axiom._--It may naturally be asked
whether this third Axiom respecting causation extends to any
other cases than those of mechanical action, since the
notion of Cause in general has certainly a much wider
extent. For instance, when a hot body heats a cold one, is
there necessarily an equal reaction of the second body upon
the first? Does the snowball cool the boy's hand exactly as
much as the hand heats the snow? To this we reply, that, in
every case in which one body acts upon another by its
physical qualities, there must be some reaction. No body can
affect another without being itself also affected. But in
any physical change the _action_ exerted is an abstract term
which may be variously understood. The hot hand may _melt_ a
cool body, or may _warm_ it: which kind of effect is to be
taken as action? This remains to be determined by other
considerations.

In all cases of physical change produced by one body in
another, it is generally possible to assume such a meaning
of action, that the reaction shall be of the same nature as
the action; and when this is done, the third axiom of
causation, that reaction is equal to action, is universally
true. Thus if a hot body heat a cold one, the change may be
conceived as the transfer of a certain substance, _heat_ or
_caloric_, from the first body to the second. On this
supposition, the first body _loses_ just as much heat as the
other _gains_; action and reaction are equal. But if the
reaction be of a different kind to the action we can no
longer apply the axiom. If a hot body _melt_ a cold one, the
latter _cools_ the former: here, then, is reaction; but so
long as the action and reaction are stated in this form, we
cannot assert any equality between them.

In treating of the secondary mechanical sciences, we {191}
shall see further in what way we may conceive the physical
action of one body upon another, so that the same axioms
which are the basis of the science of Mechanics shall apply
to changes not at first sight manifestly mechanical.

The three axioms of causation which we have now stated are
the fundamental maxims of all reasoning concerning causes as
to their quantities; and it will be shown in the sequel that
these axioms form the basis of the science of Mechanics,
determining its form, extent, and certainty. We must,
however, in the first place, consider how we acquire those
conceptions upon which the axioms now established are to be
employed.

[2d Ed.] [The Axiom that _Reaction is equal and opposite to
Action_, may appear to be at variance with a maxim
concerning Cause which is commonly current; namely, that the
'Cause precedes Effect, and Effect follows Cause.' For it
may be said, if _A_, the Action, and _R_, the Reaction, can
be considered as mutually the cause of each other, _A_ must
precede _R_, and yet must follow it, which is impossible.
But to this I reply, that in those cases of direct Causation
to which the maxim applies, the Cause and Effect are not
successive, but simultaneous. If I press against some
obstacle, the obstacle resists and returns the pressure at
the instant it is exerted, not after any interval of time,
however small. The common maxim, that the effect follows the
cause, has arisen from the practice of considering, as
examples of cause and effect, not instantaneous forces or
causes, and the instantaneous changes which they produce;
but taking, instead of this latter, the _cumulative_ effects
produced in the course of time, and compared with like
results occurring without the action of the cause. Thus, if
we alter the length of a clock-pendulum, this change
produces, as its effect, a subsequent change of rate in the
clock: because the rate is measured by the accumulated
effects of the pendulum's gravity, before and after the
change. But the pendulum produces its mechanical effect upon
the escapement, at the moment of its contact, and each wheel
upon the next, at the moment of _its_ contact. As has {192}
been said in a Review of this work, 'The time lost in cases
of indirect physical causation is consumed in the movements
which take place among the parts of the mechanism in action,
by which the active forces so transformed into momentum are
transported over intervals of space to new points of action,
the motion of matter in such cases being regarded as a mere
carrier of force.' (_Quarterly Rev._ No. cxxxv. p. 212.)

This subject I have further treated in the _Memoirs of the
Cambridge Philosophical Society_, vol. vii. part iii.] [In
this Third Edition I add this discussion.]

_Discussion of the Question:--Are Cause and Effect
successive or simultaneous?_

I HAVE at various times laid before this Society
dissertations on the metaphysical grounds and elements of
our knowledge, and especially on the foundations of the
science of mechanics. As these speculations have not failed
to excite some attention, both here and elsewhere, I am
tempted to bring forward in the same manner some additional
disquisitions of the same kind. Indeed, the immediate
occasion of the present memoir is of itself an evidence that
such subjects are not supposed to be without their interest
for the general reader; for I am led to the views and
reasonings which I am now about to lay before the Society,
by some remarks in one of our most popular Reviews, (_The
Quarterly Review_, Article on the _History_ and _Philosophy
of the Inductive Sciences_, June 1841). A writer of singular
acuteness and comprehensiveness of view has there made
remarks upon the doctrines which I had delivered in the
_Philosophy of the Inductive Sciences_, which remarks appear
to me in the highest degree instructive and philosophical. I
am not, however, going here to discuss fully the doctrines
contained in this critique. With respect to its general
tendency, I will only observe, that the author does not
accept, in the form in which I had given it, the account of
the origin and ground of necessary and universal truths. I
had stated that our knowledge is derived from Sensations and
Ideas; and that Ideas, which are the conditions of
perception, such as _space_, _time_, _likeness_, _cause_,
make universal and necessary knowledge possible; whereas, if
knowledge were derived from Sensation alone, it could not
have those characters. I have moreover {193} enumerated a
long series of Fundamental Ideas as the bases of a
corresponding series of sciences, of which sciences I have
shown also, by an historical survey, that they claim to
possess universal truths, and have their claims allowed. I
have gone further: for I have stated the Axioms which flow
from these Fundamental Ideas, and which are the logical
grounds of necessity and universality in the truths of each
science, when the science is presented in the form of a
demonstrated system. The Reviewer does not assent to this
doctrine, nor to the argument by which it is supported;
namely, that Experience cannot lead to universal truths,
except by means of a universal Idea supplied by the mind,
and infused into the particular facts which observation
ministers. He considers that the existence of universal
truths in our knowledge may be explained otherwise. He holds
that it is a sufficient account of the matter to say that we
pass from special experience to universal truth in virtue of
'the inductive propensity--the irresistible impulse of the
mind to generalize _ad infinitum_.' I shall not here dwell
upon very strong reasons which may be assigned, as I
conceive, for not accepting this as a full and satisfactory
explanation of the difficulty. Instead of doing so, I shall
here content myself with remarking, that even if we adopt
the Reviewer's expressions, we must still contend that there
are _different forms_ of the _impulse of the mind to
generalize_, corresponding to each of the Fundamental Ideas
of our system. These Fundamental Ideas, if they be nothing
else, must at least be accepted as a classification of the
modes of action of the Inductive Propensity,--as so many
different paths and tendencies of the Generalizing Impulse:
and the Axioms which I have stated as the express results of
the Fundamental Ideas, and as the steps by which those Ideas
make universal truths possible, are still no less worthy of
notice, if they are stated as the results of our
Generalizing Impulse; and as the steps by which that
Impulse, in its many various forms, makes universal truths
possible. The Generalizing Impulse in that operation by
which it leads us to the Axioms of Geometry, and to those of
Mechanics, takes very different courses; and these courses
may well deserve to be separately studied. And perhaps, even
if we accept this view of the philosophy of our knowledge,
no simpler or clearer way can be found of describing and
distinguishing these fundamentally different operations of
the Inductive Propensity, than by saying, {194} that in the
one case it proceeds according to the Idea of Space, in
another according to the Idea of Mechanical Cause; and the
like phraseology may be employed for all the other cases.

This then being understood, my present object is to consider
some very remarkable, and, as appears to me, novel views of
the Idea of Cause which the Reviewer propounds. And these
may be best brought under our discussion by considering them
as an attempt to solve the question, Whether, according to
our fundamental apprehensions of the relation of Cause and
Effect, effect follows cause in the order of time, or is
simultaneous with it.

At first sight, this question may seem to be completely
decided by our fundamental convictions respecting cause and
effect, and by the axioms which have been propounded by
almost all writers, and have obtained universal currency
among reasoners on this subject. That the cause must precede
the effect,--that the effect must follow the cause,--are, it
might seem, self-evident truths, assumed and assented to by
all persons in all reasonings in which those notions occur.
Such a doctrine is commonly asserted in general terms, and
seems to be verified in all the applications of the idea of
cause. A heavy body produces motion by its weight; the
motion produced is subsequent in time to the pressure which
the weight exerts. In a machine, bodies push or strike each
other, and so produce a series of motions; each motion, in
this case, is the result of the motions and configurations
which have preceded it. The whole series of such motions
employs time; and this time is filled up and measured by the
series of causes and effects, the effects being, in their
turn, causes of other effects. This is the common mode of
apprehending the universal course of events, in which the
chain of causation, and the progress of time, are
contemplated as each the necessary condition and
accompaniment of the other.

But this, the Critic remarks, is not true in _direct_
causation. 'If the antecedence and consequence in question
be understood as the interposition of an interval of time,
however small, between the action of the cause and the
production of the effect, we regard it as inadmissible. In
the production of motion by force, for instance, though the
effect be cumulative with continued exertion of the cause,
yet each elementary or individual action is, to our
apprehension, _instanter_ accompanied with its corresponding
increment of momentum in the body moved. In all dynamical
{195} reasonings no one has ever thought of interposing an
instant of time between the action and its resulting
momentum; nor does it appear necessary.' This is so evident,
that it appears strange it should have the air of novelty;
yet, so far as I am aware, the matter has never before been
put in the same point of view. But this being the case, the
question occurs, how it is that time _seems_ to be employed
in the progress from cause to effect? How is it that the
opinion of the effect being subsequent to the cause has
generally obtained? And to this the Critic's answer is
obvious:--it is so in cases of indirect or of _cumulative_
effect. If a ball _A_ strikes another, _B_, and puts it in
motion, and _B_ strikes _C_, and puts it in motion, _A_'s
impact may be considered as the cause, though not the direct
cause, of _C_'s motion. Now time, namely the time of _B_'s
motion after it is struck by _A_, and before it strikes _C_,
intervenes between _A_'s impact and the beginning of _C_'s
motion: that is, between the cause and its effect. In this
sense, the effect is subsequent to the cause. Again, if a
body be put in motion by a series of impulses acting at
finite intervals of time, all in the same direction, the
motion at the end of all these intervals is the effect of
all the impulses, and exists after they have all acted. It
is the accumulated effect, and subsequent to each separate
action of the cause. But in this case, each impulse produces
its effect instantaneously, and the time is employed, not in
the transition from any cause to its effect, but in the
intervals between the action of the several causes, during
which intervals the body goes on with the velocity already
communicated to it. In each impulse, force produces motion:
and the motion goes on till a new change takes place, by the
same kind of action. The force may be said, in the language
employed by the Critic, to be transformed into momentum; and
in the successive impulses, successive portions of force are
thus transformed; while in the intervening intervals, the
force thus transformed into momentum is carried by the body
from one place to another, where a new change awaits it.
'The cause is absorbed and transformed into effect, and
therein treasured up.' Hence, as the Writer says, 'The time
lost in cases of indirect physical causation is that
consumed in the movements which take place among the parts
of the mechanism set in action, by which the active forces
so transformed into mechanism are transported over intervals
of space to new points of action, the motion of matter in
such cases being {196} regarded as a mere carrier of
force':--and when force is directly counteracted by force,
their mutual destruction must be conceived, as the Reviewer
says, to be instantaneous. We can therefore hardly resist
his conclusion, that men have been misled in assuming
sequence as a feature in the relation of cause and effect;
and we may readily assent to his suggestion, that sequence,
when observed, is to be held as a sure indication of
indirect action, accompanied with a movement of parts.

But yet if we turn for a moment to other kinds of causation,
we seem to be compelled at every step to recognize the truth
of the usual maxim upon this subject, that effects are
subsequent to causes. Is not poison, taken at a certain
moment, the cause of disorder and death which follow at a
_subsequent_ period? Is not a man's early prudence often the
cause of his prosperity in _later_ life, and his folly,
though for a moment it may produce gratification, _finally_
the cause of his ruin? And even in the case of mechanism,
if, in a clock which goes rightly, we alter the length of
the pendulum, is not this alteration the cause of an
alteration which _afterwards_ takes place in the rate of the
clock's going? Are not all these, and innumerable other
cases, instances in which the usual notion of the effect
following the cause is verified? and are they not
irreconcileable with the new doctrine of cause and effect
being simultaneous?

In order to disentangle this apparent confusion, let us
first consider the case last mentioned, of a clock, in which
some alteration is made which affects the rate of going.

So long as the parts of the clock remain unaltered, its rate
will remain unaltered; and any part which is considered as
capable of alteration, may be considered as, if we please,
the cause of the unaltered rate, by being itself unaltered.
But we do not usually introduce the positive idea of cause,
to correspond with this negation of change. If we speak of
the rate as unaltered, we may also say that it is so because
there is _no cause_ of alteration. The steady rate is the
indication of the absence of any cause of alteration; and
the rate of going measures the progress of time, in a state
of things in which causes of change are thus excluded. If an
alteration takes place in any part of the clock, once for
all, the rate is altered; but the new rate is steady as the
old rate was, and, like it, measures the uniform progress of
time. But the difference between the new rate and the old is
occasioned by {197} the difference of the parts of the
clock; and the new rate may very properly be said to be
caused by the change of the parts, and to be subsequent to
it: for it does prevail after the change, and does not
prevail before.

But how is this view to be reconciled with the one just
quoted from the Reviewer, and, as it appeared,
satisfactorily proved by him; according to which all
mechanical effects are simultaneous with their causes, and
not subsequent to them? We have here the two views in close
contact, and in seeming opposition.

In the going of a clock, the parts are in motion; and these
motions are determined by forces arising from the form and
connexion of the parts of the mechanism. Each of the forces
thus exerted at any instant produces its effect at the same
instant; and thus, so far as the term _cause_ refers to such
instantaneous forces, the cause and the effect are
simultaneous. But if such instantaneous forces act at
successive intervals of time, the motion during each
interval is unaltered, and by its uniform progress measures
the progress of time. And thus the motion of the machine
consists of a series of intervals, during each of which the
motion is uniform, and measures the time; separated from
each other by a series of changes, at each of which the
change measures the instantaneous force, and is simultaneous
with it. And if, in this case, we suppose, at any point of
time, the instantaneous forces to cease, the succession of
them being terminated, from that point of time the motion
would be uniform. And since the rate of the motion in each
interval of time is determined by the instantaneous force
which last acted and by the preceding motion, the rate of
the motion in each interval of time is determined by all the
preceding instantaneous forces. Hence, when the series of
instantaneous forces stops, the rate at which the motion
goes on permanently, from that point of time, is determined
by the antecedent series of such forces, which series may be
considered as an aggregate cause; and hence it appears, that
the _permanent_ effect is determined by the _aggregate_
cause; and in this sense the effect is subsequent to the
cause.

Thus we obtain, in this case, a solution of the difficulty
which is placed before us. The instantaneous effect or
change is simultaneous with the instantaneous force or cause
by which it is {198} produced. But if we consider a series
of such instantaneous forces as a single aggregate cause,
and the final condition as a permanent effect of this cause,
the effect is subsequent to the cause. In this case, the
cause is immediately succeeded by the effect. The cause acts
in time: the effect goes on in time. The times occupied by
the cause and by the effect succeed each other, the one
ending at the point of time at which the other begins. But
the time which the cause occupies is really composed of a
series of instants of uniform motion interposed between
instantaneous forces; and during the time that this series
of causes is going on, to make up the aggregate cause, a
series of effects is going on to make up the final effect.
There is a progressive cause and a progressive effect which
go on together, and occupy the same finite time; and this
simultaneous progression is composed of all the simultaneous
instantaneous steps of cause and effect. The aggregate cause
is the sum of the progression of causes; the final effect is
the last term of the progression of effects. At each step,
as the Reviewer says, cause is transformed into effect; and
it is treasured up in the results during the intermediate
intervals; and the time occupied is not the time which
intervenes between cause and effect at each step, but the
time which intervenes between these transformations.

I have supposed forces to act at distinct instants, and to
cease to act in the intervals between; and then, the
aggregate of such intervals to make up a finite time, during
which an aggregate force acts. But if the action of the
force be rigorously continuous, it will easily be seen that
all the consequences as to cause and effect will be the
same; the discontinuous action being merely the usual
artifice by which, in mathematical reasonings, we obtain
results respecting continuous changes. It will still be
true, that the uniform motion which takes place after a
continuous force has acted, is the effect subsequent to the
cause; while the change which takes place at any instant by
the action of the force, is the instantaneous effect
simultaneous with the cause.

It may be objected, that this solution does not appear
immediately to apply: for the motion of a clock is not
uniform during any portion of the time. The parts move by
intervals of varied motion and of rest; or by oscillations
backwards and forwards; and the succession of forces which
acts during any {199} oscillation, or any cycle of motion,
is repeated during the succeeding oscillation or cycle, and
so on indefinitely; and if an alteration be made in the
parts, it is not a change once for all, but recurs in its
operation in every cycle of the motion.

But it will be found that this circumstance does not prevent
the same explanation from being still applicable with a
slight modification. Instead of uniform motion in the
intervals of causation, we shall have to speak of _steady
going_: and instead of considering all the forces which
affect the motion as causes of change of uniform motion, we
shall have to speak of changes in the parts of the mechanism
as causes of _change of rate of going_. With this
modification, it will still be true, that any instantaneous
cause produces its instantaneous effect simultaneously,
while the permanent effect is subsequent to the change which
is its cause. The steady going of the clock is assumed as a
normal condition, in which it measures the progress of time;
and in this assumption, the notion of cause and effect is
not brought into view. But a steady rate thus denoting the
mean passage of time, a change in the rate indicates a cause
of change. The _change of rate_, as an instantaneous
_transition_ from one rate to another, is _simultaneous_
with the change in the parts. But then the _changed rate_ as
a continued _condition_ in which, no new change supervening,
the rate again measures the progress of time, is
_subsequent_ to the change of parts, for it begins when that
ends, and continues when the progress of that has ceased.

If, however, this be a satisfactory solution of the
difficulty in the case of mechanism, how shall we apply the
same views to the other cases? Growth, the effect of food,
is subsequent to the act of taking food; disorder, the
effect of poison, is subsequent to the introduction of
poison into the system. Can we say that the animal would
continue unchanged if it were not to take food; and that
food is the cause of a change, namely, of growth? This is
manifestly false; for if the animal were not to take food,
it would soon perish. But the analogy of the former case, of
the clock, will enable us to avoid this perplexity. As we
assumed a steady rate of going in the clock to be the
measure of time when we considered the effect of mechanism,
so we assume a steady rate of action in the animal functions
to be the measure of the progress of time when we consider
the causes which act upon the {200} development and health
of animals. Digestion, and of course nutrition, are a part
of this normal condition; they are involved in the steady
going of the animal mechanism, and we must suppose these
functions to go regularly on, in order that the animal may
preserve its character of animal. Food and digestion may be
considered as causes of the continued existence of the
animal, in the same way in which the form of the parts of a
clock is the cause of the steady going of a clock. And when
we come to consider causes of change, this kind of
causation, which produces a normal condition of things,
merely measuring the flow of time, is left out of our
account. We can conceive an uniform condition of animal
existence, the animal neither growing nor wasting. This
being taken as the normal condition, any deviation from this
condition indicates a cause, and is taken as the evidence
and measure of the cause of change. And thus, in a growing
animal, the food partly keeps the animal in continued animal
existence, and partly, and in addition to this, causes its
growth. Food, in the former view, is always circulating in
the system, and is supposed to be uniformly administered;
the cycles of nutrition being merged in the notion of
uniform existence, as the oscillations of the pendulum in a
clock are merged in the notion of uniform going; and the
elementary steps of nutrition which are, in this view,
supposed to take place at each instant, produce their
instantaneous effect, for they are requisite in the cycle of
animal processes which goes on from instant to instant. But
on the other hand, in considering growth, we compare the
state of an animal with a preceding state, and consider the
nutriment taken in the intervening time as the cause of the
change: hence this nutriment, as an aggregate, is considered
as the cause of growth of the animal; and in this view the
effect is subsequent to the cause. But yet here, as in the
case of mechanism, the progressive effect is simultaneous,
step by step, with the progressive cause. There is a series
of operations; as for instance, intussusception, digestion,
assimilation, growth: each of these is a progressive
operation; and in the progress of each operation, the steps
of the effect and the instantaneous forces are simultaneous.
But the end of one operation is the beginning of the next,
or at least in part, and hence we have time occupied by the
succession. The end of intussusception is the beginning of
digestion, the end of digestion the beginning of
assimilation, {201} and so on. These aggregate effects
succeed each other; and hence growth is subsequent to the
taking of food; though each instantaneous force of animal
life, no less than of mechanism, produces an effect
simultaneous with its action. Each of these separate
operations is an aggregate operation, and occupies time; and
each aggregate effect is a condition of the action of the
cause in the next operation.

Again; if an animal in a permanent condition, neither waxing
nor wasting, may be taken as the normal state in which the
functions of life measure time, in order that we may
consider growth as an effect, to be referred to food as
cause; we may, for other purposes, consider, as the normal
condition, an animal waxing and then wasting, according to
the usual law of animal life: and we must take this, the
healthy progress of an animal, as our normal condition, if
we have to consider causes which produce disease. If we have
to refer the morbid condition of an animal to the influence
of poison, for example, we must consider how far the
condition deviates from what it would have been if the
poison had not been taken into the frame. The usual progress
of the animal functions including its growth, is the measure
of time; the deviation from this usual progress is the
indication of cause; and the effect of the poison is
subsequent to the cause, because the poison acts through the
cycle of the animal functions just mentioned, which occupies
time; and because the taking the poison into the system, not
any subsequent action of the animal forces in the system, is
considered as the event which we must contemplate as a
cause. To resume the analogy of the clock: the rate of the
clock is altered by altering the parts; but this alteration
itself may occupy time; as if we alter the rate of a clock
by applying a drop of acid, which gradually eats off a part
of the pendulum, the corrosion, as an aggregate effect,
occupies time; and the rates before and after the change are
separated by this time. But the application of the drop is
the cause; and thus, in this case the final effect is
subsequent to the cause, though here, as in the case of
mechanism, the instantaneous forces always produce a
simultaneous effect.

Thus we have in every case a _uniform_ state, or a state
which is considered as uniform, or at least _normal_; and
which is taken as the indication and measure of _time_; and
we have also _change_, {202} which is contemplated as a
deviation from uniformity, and is taken as the indication
and measure of _cause_. The uniform state may be one which
never exists, being purely imaginary; as the case in which
no forces act; and the case in which animal functions go on
permanently, the animal neither growing nor wasting. The
normal state may also be a state in which change is
constantly taking place, as, in fact, even a state of motion
is a state of change; such states also are, in a further
sense, that of a clock going by starts, and that of an
animal constantly growing: in these cases the changes are
all merged in a wider view of uniformity, so that these are
taken as the normal states. And in all these cases,
successive changes which take place are separated by
intervals of time, measured by the normal progress; and each
change is produced by some _simultaneous_ instantaneous
cause. But taking the cause in a larger sense, we group
these instantaneous causes, and perhaps omit in our
contemplation some of the intervening intervals; and thus
assign the cause to a _preceding_, and the effect to a
_succeeding_ time.

I may observe further, as a corollary from what has been
said, that the measure of time is different, when we
consider different kinds of causation; and in each case, is
_homogeneous_ with the changes which causation effects. In
the consideration of mechanical causes, we measure time by
mechanical changes;--by uniform motion, or uniform
succession of cycles of motion; by the rotation of a wheel,
or the oscillation of a pendulum. But if we have to consider
physiological changes, the progress of time is
physiologically measured;--by the normal progress of vital
operations; by the circulation, digestion or development of
the organized body; by the pulse, or by the growth. These
different measures of time give to time, so far as it is
exhibited by facts and events, a different character in the
different cases. Phenomenal time has a different nature and
essence according to the kind of the changes which we
consider, and which gives us our sole phenomenal indication
of cause.

I fear that I am travelling into matters too abstruse and
metaphysical for the occasion: but before I conclude, I will
present one other aspect of the subject.

In stating the difficulty, I referred to cases of moral as
well as physical causation; as when prudence produces
prosperity, or {203} when folly produces ruin. It may be
asked, whether we are here to apply the same
explanation;--whether we are to assume a normal condition of
human existence, in which neither prudence nor folly are
displayed, neither prosperity nor adversity
produced;--whether we are to conceive the progress of such a
state to measure the progress of time, and deviations from
it to denote causes of the kind mentioned. It may be asked
further, whether, if we do make this supposition, we can
resolve the influence of such causes as prudence or
imprudence into instantaneous acts, which produce their
effects immediately: and which occupy time only by being
separated by intervals of the inactive normal moral
condition. To this I must here reply, that the discussion of
such questions would carry me too far, and would involve
speculations not included within the acknowledged domain of
this Society, from which I therefore abstain. But I may say,
before quitting the subject, that I do not think the
suppositions above suggested are untenable; and that in
order to include moral causation under the maxims of
causation in general, we must necessarily make some such
hypothesis. The peculiarity of that kind of causation which
the will and the character exert, and which is exerted upon
the will and the character, would make this case far more
complex and difficult than those already considered; but, at
the same time, would offer us the means of explaining what
may seem harsh, in the above analogy. For instance, we
should have to assume such a maxim as this: that in moral
causation, time is not to be measured by the flow of
mechanical or physiological events;--not by the clock, or by
the pulse. Moral causation has its own clock, its own pulse,
in the progress of man's moral being; and by this measure of
time is the relation of moral cause and effect to be
defined.

That in estimating moral causation, the progress of time is
necessarily estimated by moral changes, and not by
machinery,--by the progress of events, and not by the going
of the clock,--is a truth familiar as a practical maxim to
all who give their thoughts to dramatic or narrative
fictions. Who feels any thing incongruous or extravagantly
hurried in the progress of events in that great exhibition
of moral causation, the tragedy of Othello? If we were asked
what time those vast and terrible {204} and complex changes
of the being and feelings of the characters occupy, we
should say, that, measured on its own scale, the event is of
great extent;--that the transaction is of considerable
magnitude in all ways. But if, with previous critics, we
look into the progress of time by the day and the hour--what
is the measure of this history? Forty-eight hours.

{{205}}
CHAPTER V.

OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER.

1. _Force._--WHEN the faculties of observation and thought
are developed in man, the idea of causation is applied to
those changes which we see and feel in the state of rest and
motion of bodies around us. And when our abstract
conceptions are thus formed and named, we adopt the term
_Force_, and use it to denote that property which is the
cause of motion produced, changed, or prevented. This
conception is, it would seem, mainly and primarily suggested
by our consciousness of the exertions by which we put bodies
in motion. The Latin and Greek words for _Force_, Vis, Ϝὶς,
were probably, like all abstract terms, derived at first
from some sensible object. The original meaning of the Greek
word was a _muscle_ or _tendon_. Its first application as an
abstract term is accordingly to muscular force:

Δεύτερος αὖτ' Αἴας πολὺ μείζονα λᾶαν ἀείρας
ἦκ' ἐπιδινήσας, ἐπέρεισε δὲ ϜÎ͂Ν' ἀπέλεθρον.

Then Ajax a far heavier stone upheaved,
He whirled it, and impressing Force intense
Upon the mass, dismist it.

The property by which bodies affect each other's motions,
was naturally likened to that energy which we exert upon
them with similar effect: and thus the labouring horse, the
rushing torrent, the descending weight, the elastic bow,
were said to exert force. {206} Homer[8\3] speaks of the
_force_ of the river, Ϝὶς ποταμοῖο; and Hesiod[9\3] of the
_force_ of the north wind, Ϝὶς ἀνέμου βορέαο.

[Note 8\3: _Il._ xxi.]

[Note 9\3: _Op. et D._]

Thus man's general notion of force was probably first
suggested by his muscular exertions, that is, by an act
depending upon that muscular sense, to which, as we have
already seen, the perception of space is mainly due. And
this being the case, it will be easily understood that the
_Direction_ of the force thus exerted is perceived by the
muscular sense, at the same time that the force itself is
perceived; and that the direction of any other force is
understood by comparison with force which man must exert to
produce the same effect, in the same manner as force itself
is so understood.

This abstract notion of Force long remained in a very vague
and obscure condition, as may be seen by referring to the
History for the failures of attempts at a science of force
and motion, made by the ancients and their commentators in
the middle ages. By degrees, in modern times, we see the
scientific faculty revive. The conception of Force becomes
so far distinct and precise that it can be reasoned upon in
a consistent manner, with demonstrated consequences; and a
genuine science of Mechanics comes into existence. The
foundations of this science are to be found in the Axioms
concerning causation which we have already stated; these
axioms being interpreted and fixed in their application by a
constant reference to observed facts, as we shall show. But
we must, in the first place, consider further those primary
processes of observation by which we acquire the first
materials of thought on such subjects.

2. _Matter._--The conception of Force, as we have said,
arises with our consciousness of our own muscular exertions.
But we cannot imagine such exertions without also imagining
some bodily substance against which they are exercised. If
we press, we press something: if we thrust or throw, there
must be something {207} to resist the thrust or to receive
the impulse. Without body, muscular force cannot be exerted,
and force in general is not conceivable.

Thus Force cannot exist without _Body_ on which it acts. The
two conceptions, Force and Matter, are co-existent and
correlative. Force implies resistance; and the force is
effective only when the resistance is called into play. If
we grasp a stone, we have no hold of it till the closing of
the hand is resisted by the solid texture of the stone. If
we push open a gate, we must surmount the opposition which
it exerts while turning on its hinges. However slight the
resistance be, there must be some resistance, or there would
be no force. If we imagine a state of things in which
objects do not resist our touch, they must also cease to be
influenced by our strength. Such a state of things we
sometimes imagine in our dreams; and such are the poetical
pictures of the regions inhabited by disembodied spirits. In
these, the figures which appear are conspicuous to the eye,
but impalpable like shadow or smoke; and as they do not
resist the corporeal impressions, so neither do they obey
them. The spectator tries in vain to strike or to grasp
them.

Et ni docta comes tenues sine corpore vitas
Admoneat volitare cavâ sub imagine formæ,
Irruat ac frustra ferro diverberet umbras.

The Sibyl warns him that there round him fly
Bodiless things, but substance to the eye;
Else had he pierced those shapes with life-like face,
And smitten, fierce, the unresisting space.

Neque illum
Prensantem nequicquam umbras et multa volentem
Dicere, preterea vidit.

He grasps her form, and clutches but the shade.

Such may be the circumstances of the unreal world of dreams,
or of poetical fancies approaching to dreams: for in these
worlds our imaginary perceptions are bound by no rigid
conditions of force and reaction. In {208} such cases, the
mind casts off the empire of the idea of cause, as it casts
off even the still more familiar sway of the ideas of space
and time. But the character of the material world in which
we live when awake is, that we have at every instant and at
every place, force operating on matter and matter resisting
force.

3. _Solidity._--From our consciousness of muscular exertion,
we derive, as we have seen, the conception of force, and
with that also the conception of matter. We have already
shown, in a former chapter, that the same part of our frame,
the muscular system, is the organ by which we perceive
extension and the relations of space. Thus the same organ
gives us the perception of body as resisting force, and as
occupying space; and by combining these conditions we have
the conception of _solid_ extended bodies. In reality, this
resistance is inevitably presented to our notice in the very
facts from which we collect the notion of extension. For the
action of the hand and arm by which we follow the forms of
objects, implies that we apply our fingers to their surface;
and we are stopped there by the resistance which the body
offers. This resistance is precisely that which is requisite
in order to make us conscious of cur muscular effort[10\3].
Neither touch, nor any other mere passive sensation, could
produce the perception of extent, as we have already urged:
nor could the muscular sense lead to such a perception,
except the extension of the muscles were felt to be
resisted. And thus the perception of resistance enters the
mind along with the perception of extended bodies. All the
objects with which we have to do are not only extended but
solid.

[Note 10\3: Brown's _Lectures_, i. 466.]

This sense of the term _solidity_, (the general property of
all matter,) is different to that in which we oppose
_solidity_ to _fluidity_. We may avoid ambiguity by opposing
_rigid_ to _fluid_ bodies. By solid bodies, as we now speak
of them, we mean only such as resist the pressure which we
exert, so long as their parts continue in their places. By
fluid bodies, we mean those {209} whose parts are, by a
slight pressure, removed out of their places. A drop of
water ceases to prevent the contact of our two hands, not by
ceasing to have solidity in this sense, but by being thrust
out of the way. If it could remain in its place, it could
not cease to exercise its resistance to our pressure, except
by ceasing to be matter altogether.

The perception of solidity, like the perception of
extension, implies an act of the mind, as well as an
impression of the senses: as the perception of extension
implies the idea of space, so the perception of solidity
implies the idea of action and reaction. That an Idea is
involved in our knowledge on this subject, appears, as in
other instances, from this consideration, that the
convictions of persons, even of those who allow of no ground
of knowledge but experience, do in fact go far beyond the
possible limits of experience. Thus Locke says[11\3], that
'the bodies which we daily handle hinder by an
_insurmountable_ force the approach of the parts of our
hands that press them.' Now it is manifest that our
observation can never go to this length. By our senses we
can only perceive that bodies resist the greatest actual
forces that we exert upon them. But our conception of force
carries us further: and since, so long as the body is there
to receive the action of the force, it must suffer the whole
of that action, and must react as much as it suffers: it is
therefore true, that so long as the body remains there, the
force which is exerted upon it can never surmount the
resistance which the body exercises. And thus this doctrine,
that bodies resist the intrusion of other bodies by an
insurmountable force, is, in fact, a consequence of the
axiom that the reaction is always equal to the action.

[Note 11\3: _Essay_, b. ii. c. 4.]

4. _Inertia._--But this principle of the equality of action
and reaction appears also in another way. Not only when we
exert force upon bodies at rest, but when, by our exertions,
we put them in motion, they react. If we set a large stone
in motion, the stone {210} resists; for the operation
requires an effort. By increasing the effort, we can
increase the effect, that is, the motion produced; but the
resistance still remains. And the greater the stone moved,
the greater is the effort requisite to move it. There is, in
every case, a resistance to motion, which shows itself, not
in preventing the motion, but in a reciprocal force, exerted
backwards upon the agent by which the motion is produced.
And this resistance resides in each portion of matter, for
it is increased as we add one portion of matter to another.
We can push a light boat rapidly through the water; but we
may go on increasing its freight, till we are barely able to
stir it. This property of matter, then, by which it resists
the reception of motion, or rather by which it reacts and
requires an adequate force in order that any motion may
result, is called its inertness, or _inertia_. That matter
has such a property, is a conviction flowing from that idea
of a reaction equal and opposite to the action, which the
conception of all force involves. By what laws this inertia
depends on the magnitude, form, and material of the body,
must be the subject of our consideration hereafter. But that
matter has this inertia, in virtue of which, as the matter
is greater, the velocity which the same effort can
communicate to it is less, is a principle inseparable from
the notion of matter itself.

Hermann says that Kepler first introduced this 'most
significant' _inertia_. Whether it is to be found in earlier
writers I know not; Kepler certainly does use it familiarly
in those attempts to assign physical reasons for the motions
of the planets which were among the main occasions of the
discovery of the true laws of mechanics. He assumes the
slowness of the motions of the planets to increase, (other
causes remaining the same,) as the inertia increases; and
though, even in this assumption, there is an errour
involved, (if we adopt that interpretation of the term
_inertia_ to which subsequent researches led,) the
introduction of such a word was one step in determining and
expressing those laws of motion which depend on the
fundamental principle of the equality of action and
reaction. {211}

5. We have thus seen, I trust in a satisfactory manner, the
origin of our conceptions of Force, Matter, Solidity, and
Inertness. It has appeared that the organ by which we obtain
such conceptions is that very muscular frame, which is the
main instrument of our perceptions of space; but that,
besides bodily sensations, these ideal conceptions, like all
the others which we have hitherto considered, involve also
an habitual activity of the mind, giving to our sensations a
meaning which they could not otherwise possess. And among
the ideas thus brought into play, is an idea of action with
an equal and opposite reaction, which forms a foundation for
universal truths to be hereafter established respecting the
conceptions thus obtained.

We must now endeavour to trace in what manner these
fundamental principles and conceptions are unfolded by means
of observation and reasoning, till they become an extensive
yet indisputable science.

{{212}}
CHAPTER VI.

OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS.

1. _Object of the Chapter._--IN the present and the
succeeding chapters we have to show how the general axioms
of Causation enable us to construct the science of
Mechanics. We have to consider these axioms as moulding
themselves, in the first place, into certain fundamental
mechanical principles, which are of evident and necessary
truth in virtue of their dependence upon the general axioms
of Causation; and thus as forming a foundation for the whole
structure of the science;--a system of truths no less
necessary than the fundamental principles, because derived
from these by rigorous demonstration.

This account of the construction of the science of
Mechanics, however generally treated, cannot be otherwise
than technical in its details, and will probably be
imperfectly understood by any one not acquainted with
Mechanics as a mathematical science.

I cannot omit this portion of my survey without rendering my
work incomplete; but I may remark that the main purpose of
it is to prove, in a more particular manner, what I have
already declared in general, that there are, in Mechanics no
less than in Geometry, fundamental principles of axiomatic
evidence and necessity;--that these principles derive their
axiomatic character from the Idea which they involve,
namely, the Idea of Cause;--and that through the combination
of principles of this kind, the whole science of Mechanics,
including its most complex and remote results, exists as a
body of solid and universal truths. {213}

2. _Statics and Dynamics._--We must first turn our attention
to a technical distinction of Mechanics into two portions,
according as the forces about which we reason produce rest,
or motion; the former portion is termed _Statics_, the
latter _Dynamics_. If a stone fall, or a weight put a
machine in motion, the problem belongs to Dynamics; but if
the stone rest upon the ground, or a weight be merely
supported by a machine, without being raised higher, the
question is one of Statics.

3. _Equilibrium._--In Statics, forces _balance_ each other,
or keep each other _in equilibrium_. And forces which
directly balance each other, or keep each other in
equilibrium, are necessarily and manifestly equal. If we see
two boys pull at two ends of a rope so that neither of them
in the smallest degree prevails over the other, we have a
case in which two forces are in equilibrium. The two forces
are evidently equal, and are a statical exemplification of
action and reaction, such as are spoken of in the third
axiom concerning causes. Now the same exemplification occurs
in every case of equilibrium. No point or body can be kept
at rest except in virtue of opposing forces acting upon it;
and these forces must always be equal in their opposite
effect. When a stone lies on the floor, the weight of the
stone downwards is opposed and balanced by an equal pressure
of the floor upwards. If the stone rests on a slope, its
tendency to slide is counteracted by some equal and opposite
force, arising, it may be, from the resistance which the
sloping ground opposes to any motion along its surface.
Every case of rest is a case of equilibrium: every case of
equilibrium is a case of equal and opposite forces.

The most complex frame-work on which weights are supported,
as the roof of a building, or the cordage of a machine, are
still examples of equilibrium. In such cases we may have
many forces all combining to balance each other; and the
equilibrium will depend on various conditions of direction
and magnitude among the forces. And in order to understand
what are these conditions, we must ask, in the first place,
what {214} we understand by the magnitude of such
forces;--what is the measure of statical forces.

4. _Measure of Statical Forces._--At first we might expect,
perhaps, that since statical forces come under the general
notion of Cause, the mode of measuring them would be derived
from the second axiom of Causation, that causes are measured
by their effects. But we find that the application of this
axiom is controlled by the limitation which we noticed,
after stating that axiom; namely, the condition that the
causes shall be capable of addition. Further, as we have
seen, a statical force produces no other effect than this,
that it balances some other statical force; and hence the
measure of statical forces is necessarily dependent upon
their balancing, that is, upon the equality of action and
reaction.

That _statical forces are capable of addition_ is involved
in our conception of such forces. When two men pull at a
rope in the same direction, the forces which they exert are
added together. When two heavy bodies are put into a basket
suspended by a string, their weights are added, and the sum
is supported by the string.

Combining these considerations, it will appear that the
measure of statical forces is necessarily given at once by
the fundamental principle of the equality of action and
reaction. Since two opposite forces which balance each other
are equal, each force is measured by that which it balances;
and since forces are capable of addition, a force of any
magnitude is measured by adding together a proper number of
such equal forces. Thus a heavy body which, appended to some
certain elastic branch of a tree, would bend it down through
one inch, may be taken as a unit of weight. Then if we
remove this first body, and find a second heavy body which
will also bend the branch through the same space, this is
also a unit of weight; and in like manner we might go on to
a third and a fourth equal body; and adding together the
two, or the three, or the four heavy bodies, we have a force
twice, or three times, or four times the unit of weight. And
with {215} such a collection of heavy bodies, or _weights_,
we can readily measure all other forces; for the same
principle of the equality of action and reaction leads at
once to this maxim, that any statical force is measured by
the weight which it would support.

As has been said, it might at first have been supposed that
we should have to apply, in this case, the axiom that causes
are measured by their effects in another manner; that thus,
if that body were a unit of weight which bent the bough of a
tree through one inch, _that_ body would be _two_ units
which bent it through _two_ inches, and so on. But, as we
have already stated, the measures of weight must be subject
to this condition, that they are susceptible of being added:
and therefore we cannot take the deflexion of the bough for
our measure, till we have ascertained, that which experience
alone can teach us, that under the burden of two equal
weights, the deflexion will be twice as great as it is with
one weight, which is not true, or at least is neither
obviously nor necessarily true. In this, as in all other
cases, although causes must be measured by their effects, we
learn from experience only how the effects are to be
interpreted, so as to give a true and consistent measure.

With regard, however, to the measure of statical force, and
of weight, no difficulty really occurred to philosophers
from the time when they first began to speculate on such
subjects; for it was easily seen that if we take any uniform
material, as wood, or stone, or iron, portions of this which
are geometrically equal, must also be equal in statical
effect; since this was implied in the very hypothesis of a
uniform material And a body ten times as large as another of
the same substance, will be of ten times the weight. But
before men could establish by reasoning the conditions under
which weights would be in equilibrium, some other principles
were needed in addition to the mere measure of forces. The
principles introduced for this purpose still resulted from
the conception of equal action and reaction; but it required
no small clearness of thought to select them rightly, and to
employ them {216} successfully. This, however, was done, to
a certain extent, by the Greeks; and the treatise of
Archimedes _On the Center of Gravity_, is founded on
principles which may still be considered as the genuine
basis of statical reasoning. I shall make a few remarks on
the most important principle among those which Archimedes
thus employs.

5. _The Center of Gravity._--The most important of the
principles which enter into the demonstration of Archimedes
is this: that "Every body has a center of gravity;" meaning
by the center of gravity, a point at which the whole matter
of the body may be supposed to be collected, to all intents
and purposes of statical reasoning. This principle has been
put in various forms by succeeding writers: for instance, it
has been thought sufficient to assume a case much simpler
than the general one; and to assert that two _equal_ bodies
have their center of gravity in the point midway between
them. It is to be observed, that this assertion not only
implies that the two bodies will _balance_ upon a support
placed at that midway point, but also, that they will
exercise, upon such a support, a _pressure equal to their
sum_; for this point being the center of gravity, the whole
matter of the two bodies may be conceived to be collected
there, and therefore the whole weight will press there. And
thus the principle in question amounts to this, that _when
two equal heavy bodies are supported on the middle point
between them, the pressure upon the support is equal to the
sum of the weights of the bodies_.

A clear understanding of the nature and grounds of this
principle is of great consequence: for in it we have the
foundation of a large portion of the science of Mechanics.
And if this principle can be shown to be necessarily true,
in virtue of our Fundamental Ideas, we can hardly doubt that
there exist many other truths of the same kind, and that no
sound view of the evidence and extent of human knowledge can
be obtained, so long as we mistake the nature of these, its
first principles. {217}

The above principle, that the pressure on the support is
equal to the sum of the bodies supported, is often stated as
an axiom in the outset of books on Mechanics. And this
appears to be the true place and character of this
principle, in accordance with the reasonings which we have
already urged. The axiom depends upon our conception of
action and reaction. That the two weights are supported,
implies that the supporting force must be equal to the force
or weight supported.

In order further to show the foundation of this principle,
we may ask the question:--If it be not an axiom, deriving
its truth from the fundamental conception of equal action
and reaction, which equilibrium always implies, what is the
origin of its certainty? The principle is never for an
instant denied or questioned: it is taken for granted, even
before it is stated. No one will doubt that it is not only
true, but true with the same rigour and universality as the
axioms of Geometry. Will it be said, that it is borrowed
from experience? Experience could never prove a principle to
be universally and rigorously true. Moreover, when from
experience we prove a proposition to possess great exactness
and generality, we approach by degrees to this proof: the
conviction becomes stronger, the truth more secure, as we
accumulate trials. But nothing of this kind is the case in
the instance before us. There is no gradation from less to
greater certainty;--no hesitation which precedes confidence.
From the first, we know that the axiom is exactly and
certainly true. In order to be convinced of it, we do not
require many trials, but merely a clear understanding of the
assertion itself.

But in fact, not only are trials not necessary to the proof,
but they do not strengthen it. Probably no one ever made a
trial for the purpose of showing that the pressure upon the
support is equal to the sum of the two weights. Certainly no
person with clear mechanical conceptions ever wanted such a
trial to convince him of the truth; or thought the truth
clearer after the trial had been made. If to such a person,
an {218} experiment were shown which seemed to contradict
the principle, his conclusion would be, not that the
principle was doubtful, but that the apparatus was out of
order. Nothing can be less like collecting truth from
experience than this.

We maintain, then, that this equality of mechanical action
and reaction, is one of the principles which do not flow
from, but regulate our experience. To this principle, the
facts which we observe must conform; and we cannot help
interpreting them in such a manner that they shall be
exemplifications of the principle. A mechanical pressure not
accompanied by an equal and opposite pressure, can no more
be given by experience, than two unequal right angles. With
the supposition of such inequalities, space ceases to be
space, force ceases to be force, matter ceases to be matter.
And this equality of action and reaction, considered in the
case in which two bodies are connected so as to act on a
single support, leads to the axiom which we have stated
above, and which is one of the main foundations of the
science of Mechanics.

[2d ed.] [To the doctrine that mechanical principles, such
as the one here under consideration (that the pressure on
the point of support is equal to the sum of the weights),
are derived from our Ideas, and do not flow from but
regulate our experience, objections are naturally made by
those who assert all our knowledge to be derived from
experience. How, they ask, can we know the properties of
pressures, levers and the like, except from experience? What
but experience can possibly inform us that a force applied
transversely to a lever will have any tendency to turn the
lever on its center? This cannot be, except we suppose in
the lever tenacity, rigidity and the like, which are
qualities known only by experience. And it is obvious that
this line of argument might be carried on through the whole
subject.

My answer to this objection is a remark of the same kind as
one which I have made respecting the Ideas of Space, Time,
and Number, in the last Book. The mind, in apprehending
events as causes {219} and effects, is governed by Laws of
its own Activity; and these Laws govern the results of the
mind's action; and make these results conform to the Axioms
of Causation. But this activity of the mind is awakened and
developed by being exercised; and in dealing with the
examples of cause and effect here spoken of, (namely,
pressure and resistance, force and motion,) the mind's
activity is necessarily governed also by the bodily powers
of perception and action. We are human beings only in so far
as we have existed in space and time; and of our human
faculties, developed by our existence in space and time,
space and time are necessary conditions. In like manner, we
are human beings only in so far as we have bodies, and
bodily organs; and our bodies necessarily imply material
objects external to us. And hence our human faculties,
developed by our bodily existence in a material world, have
the conditions of matter for their necessary Laws. I have
already said (chap. v.) that our conception of Force arises
with our consciousness of our own muscular exertions;--that
Force cannot be conceived without Resistance to exercise
itself upon;--and that this resistance is supplied by
Matter. And thus the conception of Matter, and of the most
general modes in which Matter receives, resists, and
transmits force, are parts of our constitution which, though
awakened and unfolded by our being in a material world, are
not distinguishable from the original structure of the mind.
I do not ascribe to the mind _innate_ Ideas--Ideas which it
would have, even if it had no intercourse with the world of
space, time, and matter; because we cannot imagine a mind in
such a state. But I attempt to point out and classify those
Conditions of all Experience, to which the intercourse of
all minds with the material world has necessarily given rise
in all. Truths _thus_ necessarily acquired in the course of
all experience, cannot be said to be learnt _from
experience_, in the same sense in which particular facts, at
definite times, are learnt from experience--learnt by some
persons and not by others--learnt with more or less of
certainty. These latter _special truths of_ {220}
_experience_ will be very important subjects of our
consideration; but our whole chance of discussing them with
any profit depends upon our keeping them distinct from the
_necessary and universal conditions of experience_. Here, as
everywhere, we must keep in view the fundamental antithesis
of Ideas and Facts.]

6. _Oblique Forces._--By the aid of the above axiom and a
few others, the Greeks made some progress in the science of
Statics. But after a short advance, they arrived at another
difficulty, that of Oblique Forces, which they never
overcame; and which no mathematician mastered till modern
times. The unpublished manuscripts of Leonardo da Vinci,
written in the fifteenth century, and the works of Stevinus
and Galileo, in the sixteenth, are the places in which we
find the first solid grounds of reasoning on the subject of
forces acting obliquely to each other. And from that period,
mathematicians, having thus become possessed of all the
mechanical principles which are requisite in problems
respecting equilibrium, soon framed a complete science of
Statics. Succeeding writers presented this science in forms
variously modified; for it was found, in Mechanics as in
Geometry, that various propositions might be taken as the
starting points; and that the collection of truths which it
was the mechanician's business to include in his course,
might thus be traversed by various routes, each path
offering a series of satisfactory demonstrations. The
fundamental conceptions of force and resistance, like those
of space and number, could be contemplated under different
aspects, each of which might be made the basis of axioms, or
of principles employed as axioms. Hence the grounds of the
truth of Statics may be stated in various ways; and it would
be a task of some length to examine all these completely,
and to trace them to their Fundamental Ideas. This I shall
not undertake here to do; but the philosophical importance
of the subject makes it proper to offer a few remarks on
some of the main principles involved in the different modes
of presenting Statics as a rigorously demonstrated science.
{221}

7. _A Force may be supposed to act at any Point of its
Direction._--It has been stated in the history of
Mechanics[12\3], that Leonardo da Vinci and Galileo obtained
the true measure of the effect of oblique forces, by
reasonings which were, in substance, the same. The principle
of these reasonings is that expressed at the head of this
paragraph; and when we have a little accustomed ourselves to
contemplate our conceptions of force, and its action on
matter, in an abstract manner, we shall have no difficulty
in assenting to the principle in this general form. But it
may, perhaps, be more obvious at first in a special case.

[Note 12\3: _Hist. Ind. Sc._ b. vi. c. i. sect. 2.]

If we suppose a wheel, moveable about its axis, and carrying
with it in its motion a weight, (as, for example, one of the
wheels by means of which the large bells of a church are
rung,) this weight may be supported by means of a rope (not
passing along the circumference of the wheel, as is usual in
the case of bells,) but fastened to one of the spokes of the
wheel. Now the principle which is enunciated above asserts,
that if the rope pass in a straight line across several of
the spokes of the wheel, it makes no difference in the
mechanical effect of the force applied, for the purpose of
putting the bell in motion, to _which_ of these spokes the
rope is _fastened_. In each case, the fastening of the rope
to the wheel merely serves to enable the force to produce
motion about the center; and so long as the force acts in
the same line, the effect is the same, at whatever point of
the rope the line of action finishes.

This axiom very readily aids us in estimating the effect of
oblique forces. For when a force acts on one of the arms of
a lever at any oblique angle, we suppose another arm
projecting from the center of motion, like another spoke of
the same wheel, so situated that it is perpendicular to the
force. This arm we may, with Leonardo, call the _virtual
lever_; for, by the axiom, we may suppose the force to act
where the line of its direction meets this arm; and thus we
reduce the case {222} to that in which the force acts
perpendicularly on the arm.

The ground of this axiom is, that matter, in Statics, is
necessarily conceived as _transmitting_ force. That force
can be transmitted from one place to another, by means of
matter;--that we can push with a rod, pull with a rope,--are
suppositions implied in our conceptions of force and matter.
Matter is, as we have said, that which receives the
impression of force, and the modes just mentioned, are the
simplest ways in which that impression operates. And since,
in any of these cases, the force might be resisted by a
reaction equal to the force itself, the reaction in each
case would be equal, and, therefore, the action in each case
is necessarily equal; and thus the forces must be
transmitted, from one point to another, without increase or
diminution.

This property of matter, of transmitting the action of
force, is of various kinds. We have the coherence of a rope
which enables us to pull, and the rigidity of a staff, which
enables us to push with it in the direction of its length;
and again, the same staff has a rigidity of another kind, in
virtue of which we can use it as a lever; that is, a
rigidity to resist flexure, and to transmit the force which
turns a body round a fulcrum. There is, further, the
rigidity by which a solid body resists _twisting_. Of these
kinds of rigidity, the first is that to which our axiom
refers; but in order to complete the list of the elementary
principles of Statics, we ought also to lay down axioms
respecting the other kinds of rigidity[13\3]. These,
however, I shall not here state, as they do not involve any
new principle. Like the one just considered, they form part
of our fundamental conception of matter; they are not the
results of any experience, but are the hypotheses to which
we are irresistibly led, when we would liberate our
reasonings concerning force and matter from a dependence on
the special results of experience. We cannot even {223}
conceive (that is, if we have any clear mechanical
conceptions at all) the force exerted by the point of a
staff and resisting the force which we steadily impress on
the head of it, to be different from the impressed force.

[Note 13\3: Such axioms are given in a little work (_The
Mechanical Euclid_) which I published on the Elements of
Mechanics.]

8. _Forces may have equivalent Forces substituted for them.
The Parallelogram of Forces._--It has already been observed,
that in order to prove the doctrines of Statics, we may take
various principles as our starting points, and may still
find a course of demonstration by which the leading
propositions belonging to the subject may be established.
Thus, instead of beginning our reasonings, as in the last
section we supposed them to commence, with the case in which
forces act upon different points of the same body in the
same line of force, and counteract each other in virtue of
the intervening matter by which the effect of force is
transferred from one point to another; we may suppose
different forces to act at the same point, and may thus
commence our reasonings with a case in which we have to
contemplate force, without having to take into our account
the resistance or rigidity of matter. Two statical forces,
thus acting at a mathematical point, are equivalent, in all
respects, to some single force acting at the same point; and
would be kept in equilibrium by a force equal and opposite
to that single force. And the rule by which the single force
is derived from the two, is commonly termed _the
parallelogram of forces_; the proposition being this,--That
if the two forces be represented in magnitude and direction
by the two sides of a parallelogram, the resulting force
will be represented in the same manner by the diagonal of
the parallelogram. This proposition has very frequently been
made, by modern writers, the commencement of the science of
Mechanics: a position for which, by its simplicity, it is
well suited; although, in order to deduce from it the other
elementary propositions of the science, as, for instance,
those respecting the lever, we require the axiom stated in
the last section.

9. _The Parallelogram of Forces is a necessary Truth._--In
the series of discussions in which we are {224} here
engaged, our main business is to ascertain the nature and
grounds of the certainty of scientific truths. We have,
therefore, to ask whether this proposition, the
parallelogram of forces, be a necessary truth; and if so, on
what grounds its necessity ultimately rests. We shall find
that this, like the other fundamental doctrines of Statics,
justly claim a demonstrative certainty. Daniel Bernoulli, in
1726, gave the first proof of this important proposition on
pure statical principles; and thus, as he says[14\3],
'proved that statical theorems are not less necessarily true
than geometrical are.' If we examine this proof of
Bernoulli, in order to discover what are the principles on
which it rests, we shall find that the reasoning employs in
its progress such axioms as this;--That if from forces which
are in equilibrium at a point be taken away other forces
which are in equilibrium at the same point, the remainder
will be in equilibrium; and generally;--That if forces can
be resolved into other equivalent forces, these may be
separated, grouped, and recombined, in any new manner, and
the result will still be identical with what it was at
first. Thus in Bernoulli's proof, the two forces to be
compounded are represented by P and Q; P is resolved into
two other forces, X and U; and Q into two others, Y and V,
under certain conditions. It is then assumed that these
forces may be grouped into the pairs X, Y, and U, V: and
when it has been shown that X and Y are in equilibrium, they
may, by what has been said, be removed, and the forces, P,
Q, are equivalent to U, V; which, being in the same
direction by the course of the construction, have a result
equal to their sum.

[Note 14\3: _Comm. Petrop._ vol. i.]

It is clear that the principles here assumed are genuine
axioms, depending upon our conception of the nature of
equivalence of forces, and upon their being capable of
addition and composition. If the forces, P, Q, be
_equivalent_ to forces X, U, Y, V, they are equivalent to
these forces added and compounded in any order; just as a
geometrical figure is, by our conception of {225} space,
equivalent to its parts added together in any order. The
apprehension of forces as having magnitude, as made up of
parts, as capable of composition, leads to such axioms in
Statics, in the same manner as the like apprehension of
space leads to the axioms of Geometry. And thus the truths
of Statics, resting upon such foundations, are independent
of experience in the same manner in which geometrical truths
are so.

The proof of the parallelogram of forces thus given by
Daniel Bernoulli, as it was the first, is also one of the
most simple proofs of that proposition which have been
devised up to the present day. Many other demonstrations,
however, have been given of the same proposition. Jacobi, a
German mathematician, has collected and examined eighteen of
these[15\3]. They all depend either upon such principles as
have just been stated; That forces may in every way be
replaced by those which are equivalent to them;--or else
upon those previously stated, the doctrine of the lever, and
the transfer of a force from one point to another of its
direction. In either case, they are necessary results of our
statical conceptions, independent of any observed laws of
motion, and indeed, of the conception of actual motion
altogether.

[Note 15\3: These are by the following mathematicians; D.
Bernoulli (1726); Lambert (1771); Scarella (1756); Venini
(1764); Araldi (1806); Wachter (1815); Kaestner; Marini;
Eytelwein; Salimbeni; Duchayla; two different proofs by
Foncenex (1760); three by D'Alembert; and those of Laplace
and M. Poisson.]

There is another class of alleged proofs of the
parallelogram of forces, which involve the consideration of
the motion produced by the forces. But such reasonings are,
in fact, altogether irrelevant to the subject of Statics. In
that science, forces are not measured by the motion which
they produce, but by the forces which they will balance, as
we have already seen. The combination of two forces employed
in producing motion in the same body, either simultaneously
or successively, {226} belongs to that part of Mechanics
which has motion for its subject, and is to be considered in
treating of the laws of motion. The composition of motion,
(as when a man moves in a ship while the ship moves through
the water,) has constantly been confounded with the
composition of force. But though it has been done by very
eminent mathematicians, it is quite necessary for us to keep
the two subjects distinct, in order to see the real nature
of the evidence of truth in either case. The conditions of
equilibrium of two forces on a lever, or of three forces at
a point, can be established without any reference whatever
to any motions which the forces might, under _other_
circumstances, produce. And because this can be done, to do
so is the only scientific procedure. To prove such
propositions by any other course, would be to support truth
by extraneous and inconclusive reasons; which would be
foreign to our purpose, since we seek not only knowledge,
but the grounds of our knowledge.

10. _The Center of gravity seeks the lowest place._--The
principles which we have already mentioned afford a
sufficient basis for the science of Statics in its most
extensive and varied applications; and the conditions of
equilibrium of the most complex combinations of machinery
may be deduced from these principles with a rigour not
inferior to that of geometry. But in some of the more
complex cases, the results of long trains of reasoning may
be foreseen, in virtue of certain maxims which appear to us
self-evident, although it may not be easy to trace the exact
dependence of these maxims upon our fundamental conceptions
of force and matter. Of this nature is the maxim now
stated;--That in any combination of matter any how
supported, the Center of Gravity will descend into the
lowest position which the connexion of the parts allows it
to assume by descending. It is easily seen that this maxim
carries to a much greater extent the principle which the
Greek mathematicians assumed, that every body has a Center
of Gravity, that is, a point in which, if the whole matter
of the body be collected, the effect will remain unchanged.
For the Greeks asserted this of a {227} single rigid mass
only; whereas, in the maxim now under our notice, it is
asserted of any masses, connected by strings, rods, joints,
or in any manner. We have already seen that more modern
writers on mechanics, desirous of assuming as fundamental no
wider principles than are absolutely necessary, have not
adopted the Greek axiom in all its generality, but have only
asserted that two _equal_ weights have a center of gravity
midway between them. Yet the principle that every body,
however irregular, has a center of gravity, and will be
supported if that center is supported, and not otherwise, is
so far evident, that it might be employed as a fundamental
truth, if we could not resolve it into any simpler truths:
and, historically speaking, it was assumed as evident by the
Greeks. In like manner the still wider principle, that a
collection of bodies, as, for instance, a flexible chain
hanging upon one or more supports, has a center of gravity;
and that this point will descend to the lowest possible
situation, as a single body would do, has been adopted at
various periods in the history of mechanics; and especially
at conjunctures when mathematical philosophers have had new
and difficult problems to contend with. For in almost every
instance it has only been by repeated struggles that
philosophers have reduced the solution of such problems to a
clear dependence upon the most simple axioms.

11. _Stevinus's Proof for Oblique Forces._--We have an
example of this mode of dealing with problems, in Stevinus's
mode of reasoning concerning the Inclined Plane; which, as
we have stated in the History of Mechanics, was the first
correct published solution of that problem. Stevinus
supposes a loop of chain, or a loop of string loaded with a
series of equal balls at equal distances, to hang over the
Inclined Plane; and his reasoning proceeds upon this
assumption,--That such a loop so hanging will find a certain
position in which it will rest: for otherwise, says
he[16\3], its motion must go on for ever, which is absurd.
It may be asked how {228} this absurdity of a perpetual
motion appears; and it will perhaps be added, that although
the impossibility of a machine with such a condition may be
proved as a remote result of mechanical principles, this
impossibility can hardly be itself recognized as a
self-evident truth. But to this we may reply, that the
impossibility is really evident in the case contemplated by
Stevinus; for we cannot conceive a loop of chain to go on
through all eternity, sliding round and round upon its
support, by the effect of its own weight. And the ground of
our conviction that this cannot be, seems to be this
consideration; that when the chain moves by the effect of
its weight, we consider its motion as the result of an
effort to reach some certain position, in which it can rest;
just as a single ball in a bowl moves till it comes to rest
at the lowest point of the bowl. Such an effect of weight in
the chain, we may represent to ourselves by conceiving all
the matter of the chain to be collected in one single point,
and this single heavy point to hang from the support in some
way or other, so as fitly to represent the mode of support
of the chain. In whatever manner this heavy point (the
center of gravity of the chain) be supported and controlled
in its movements, there will still be some position of rest
which it will seek and find. And thus there will be some
corresponding position of rest for the chain; and the
interminable shifting from one position to another, with no
disposition to rest in any position, cannot exist.

[Note 16\3: Stevin. _Statique_, livre i. prop. 19.]

Thus the demonstration of the property of the Inclined Plane
by Stevinus, depends upon a principle which, though far from
being the simplest of those to which the case can be
reduced, is still both true and evident: and the evidence of
this principle, depending upon the assumption of a center of
gravity, is of the same nature as the evidence of the Greek
statical demonstrations, the earliest real advances in the science.

12. _Principle of Virtual Velocities._--We have referred
above to an assertion often made, that we may, from the
simple principles of Mechanics, demonstrate the
impossibility of a perpetual motion. In reality, {229}
however, the simplest proof of that impossibility, in a
machine acted upon by weight only, arises from the very
maxim above stated, that the center of gravity seeks and
finds the lowest place; or from some similar proposition.
For if, as is done by many writers, we profess to prove the
impossibility of a perpetual motion by means of that
proposition which includes the conditions of equilibrium,
and is called the _Principle of Virtual Velocities_[17\3],
we are under the necessity of first proving in a general
manner that principle. And if this be done by a mere
enumeration of cases, (as by taking those five cases which
are called the _Mechanical Powers_,) there may remain some
doubts whether the enumeration of possible mechanical
combinations be complete. Accordingly, some writers have
attempted independent and general proofs of the Principle of
Virtual Velocities; and these proofs rest upon assumptions
of the same nature as that now under notice. This is, for
example, the case with Lagrange's proof, which depends upon
what he calls the _Principle of Pulleys_. For this principle
is,--That a weight any how supported, as by a string passing
round any number of pulleys any how placed, will be at rest
then only, when it cannot get lower by any small motion of
the pulleys. And thus the maxim that a weight will descend
if it can, is assumed as the basis of this proof.

[Note 17\3: See _Hist. Ind Sc._ b. vi. c. ii. sect. 4.]

There is, as we have said, no need to assume such principles
as these for the foundation of our mechanical science. But
it is, on various accounts, useful to direct our attention
to those cases in which truths, apprehended at first in a
complex and derivative form, have afterwards been reduced to
their simpler elements;--in which, also, sagacious and
inventive men have fixed upon those truths as self-evident,
which now appear to us only certain in virtue of
demonstration. In these cases we can hardly doubt that such
men were led to assert the doctrines which they discovered,
not by any capricious conjecture of arbitrary selection, but
by having a keener and deeper insight than other persons
{230} into the relations which were the object of their
contemplation; and in the science now spoken of, they were
led to their assumptions by possessing clearly and
distinctly the conceptions of mechanical cause and
effect,--action and reaction,--force, and the nature of its
operation.

13. _Fluids press Equally in all Directions._--The doctrines
which concern the equilibrium of fluids depend on principles
no less certain and simple than those which refer to the
equilibrium of solid bodies; and the Greeks, who, as we have
seen, obtained a clear view of some of the principles of
Statics, also made a beginning in the kindred subject of
Hydrostatics. We still possess a treatise of Archimedes _On
Floating Bodies_, which contains correct solutions of
several problems belonging to this subject, and of some
which are by no means easy. In this treatise, the
fundamental assumption is of this kind: 'Let it be assumed
that the nature of a fluid is such, that the parts which are
less pressed yield to those which are more pressed.' In this
assumption or axiom it is implied that a pressure exerted
upon a fluid in one direction produces a pressure in another
direction; thus, the weight of the fluid which arises from a
downward force produces a lateral pressure against the sides
of the containing vessel. Not only does the pressure thus
diverge from its original direction into all other
directions, but the pressure is in all directions exactly
equal, an equal extent of the fluid being taken. This
principle, which was involved in the reasoning of
Archimedes, is still to the present day the basis of all
hydrostatical treatises, and is expressed, as above, by
saying that _fluids press equally in all directions_.

Concerning this, as concerning previously-noticed
principles, we have to ask whether it can rightly be said to
be derived from experience. And to this the answer must
still be, as in the former cases, that the proposition is
not one borrowed from experience in any usual or exact sense
of the phrase. I will endeavour to illustrate this. There
are many elementary propositions in physics, our knowledge
of which {231} indisputably depends upon experience; and in
these cases there is no difficulty in seeing the evidence of
this dependence. In such cases, the _experiments_ which
prove the law are prominently stated in treatises upon the
subject: they are given with exact measures, and with an
account of the means by which errours were avoided: the
experiments of more recent times have either rendered more
certain the law originally asserted, or have pointed out
some correction of it as requisite: and the names, both of
the discoverers of the law and of its subsequent reformers,
are well known. For instance, the proposition that 'The
elastic force of air varies as the density,' was first
proved by Boyle, by means of operations of which the detail
is given in his _Defence_ of his _Pneumatical
Experiments_[18\3]; and by **Mariotte in his _Traité de
l'Équilibre des Liquides_, from whom it has generally been
termed Mariotte's law. After being confirmed by many other
experimenters, this law was suspected to be slightly
inaccurate, and a commission of the French Academy of
Sciences was appointed, consisting of several distinguished
philosophers[19\3], to ascertain the truth or falsehood of
this suspicion. The result of their investigations appeared
to be, that the law is exact, as nearly as the inevitable
inaccuracies of machinery and measures will allow us to
judge. Here we have an example of a law which is of the
simplest kind and form; and which yet is not allowed to rest
upon its simplicity or apparent probability, but is
rigorously tested by experience. In this case, the
assertion, that the law depends upon experience, contains a
reference to plain and notorious passages in the history of
science.

[Note 18\3: Shaw's _Boyle_, Vol. ii. p. 671.]

[Note 19\3: The members were Prony, Arago, Ampère, Girard,
and Dulong. The experiments were extended to a pressure of
twenty-seven atmospheres; and in no instance did the
difference between the observed and calculated elasticity
amount to one-hundredth of the whole; nor did the difference
appear to increase with the increase of pressure.--Fechner,
_Repertorium_, i. 110.]

Now with regard to the principle that fluids press equally
in all directions, the case is altogether different. {232}
It is, indeed, often asserted in works on hydrostatics, that
the principle is collected from experience, and sometimes a
few experiments are described as exhibiting its effect; but
these are such as to illustrate and explain, rather than to
prove, the truth of the principle: they are never related to
have been made with that exactness of precaution and
measurement, or that frequency of repetition, which are
necessary to establish a purely experimental truth. Nor did
such experiments occur as important steps in the history of
science. It does not appear that Archimedes thought
experiment necessary to confirm the truth of the law as he
employed it: on the contrary, he states it in exactly the
same shape as the axioms which he employs in statics, and
even in geometry; namely, as an assumption. Nor does any
intelligent student of the subject find any difficulty in
assenting to this fundamental principle of hydrostatics as
soon as it is propounded to him. Experiment was not
requisite for its discovery; experiment is not necessary for
its proof at present; and we may add, that experiment,
though it may make the proposition the more readily
intelligible, can add nothing to our conviction of its truth
when it is once understood.

14. _Foundation of the above Axiom._--But it will naturally
be asked, What then is the ground of our conviction of this
doctrine of the equal pressure of a fluid in all directions?
And to this I reply, that the reasons of this conviction are
involved in our idea of a fluid, which is considered as
matter, and therefore as capable of receiving, resisting,
and transmitting force according to the general conception
of matter; and which is also considered as matter which has
its parts perfectly moveable among one another. For it
follows from these suppositions, that if the fluid be
confined, a pressure which thrusts in one side of the
containing vessel, may cause any other side to bulge
outwards, if there be a part of the surface which has not
strength to resist this pressure from within. And that this
pressure, when thus transferred into a direction different
from the original one, is not altered in intensity, {233}
depends upon this consideration; that any difference in the
two pressures would be considered as a defect of _perfect_
fluidity, since the fluidity would be still more complete,
if this entire and undiminished transmission of pressure in
all directions were supposed. If, for instance, the lateral
pressure were less than the vertical, this could be
conceived no other way than as indicating some rigidity or
adhesion of the parts of the fluid. When the fluidity is
perfect, the two pressures which act in the two different
parts of the fluid exactly balance each other: they are the
action and the reaction; and must hence be equal by the same
necessity as two directly opposite forces in statics.

But it may be urged, that even if we grant that this
conception of a perfect fluid, as a body which has its parts
perfectly moveable among each other, leads us necessarily to
the principle of the equality of hydrostatic pressure in all
directions, still this conception itself is obtained from
experience, or suggested by observation. And to this we may
reply, that the conception of a fluid, as contemplated in
mechanical theory, cannot be said to be derived from
experience, except in the same manner as the conception of a
solid and rigid body may be said to be acquired by
experience. For if we imagine a vessel full of small, smooth
spherical balls, such a collection of balls would approach
to the nature of a fluid, in having its parts moveable among
each other; and would approach to perfect fluidity, as the
balls became smoother and smaller. And such a collection of
balls would also possess the statical properties of a fluid;
for it would transmit pressure out of a vertical into a
lateral (or any other) direction, in the same manner as a
fluid would do. And thus a collection of solid bodies has
the same property which a fluid has; and the science of
Hydrostatics borrows from experience no principles beyond
those which are involved in the science of Statics
respecting solids. And since in this latter portion of
science, as we have already seen, none of the principles
depend for their evidence upon any special experience, the
doctrines of Hydrostatics also are not {234} proved by
experience, but have a necessary truth borrowed from the
relations of our ideas.

It is hardly to be expected that the above reasoning will,
at first sight, produce conviction in the mind of the
reader, except he have, to a certain extent, acquainted
himself with the elementary doctrines of the science of
Hydrostatics as usually delivered; and have followed, with
clear and steady apprehension, some of the trains of
reasoning by which the pressures of fluids are determined;
as, for instance, the explanation of what is called _the
Hydrostatic Paradox_. The necessity of such a discipline in
order that the reader may enter fully into this part of our
speculations, naturally renders them less popular; but this
disadvantage is inevitable in our plan. We cannot expect to
throw light upon philosophy by means of the advances which
have been made in the mathematical and physical sciences,
except we really understand the doctrines which have been
firmly established in those sciences. This preparation for
philosophizing may be somewhat laborious; but such labour is
necessary if we would pursue speculative truth with all the
advantages which the present condition of human knowledge
places within our reach.

We may add, that the consequences to which we are directed
by the preceding opinions, are of very great importance in
their bearing upon our general views respecting human
knowledge. I trust to be able to show, that some important
distinctions are illustrated, some perplexing paradoxes
solved, and some large anticipations of the future extension
of our knowledge suggested, by means of the conclusions to
which the preceding discussions have conducted us. But
before I proceed to these general topics, I must consider
the foundations of some of the remaining portions of the
science of Mechanics.

{{235}}
CHAPTER VII.

OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS.

1. IN the History of Mechanics, I have traced the steps by
which the three Laws of Motion and the other principles of
mechanics were discovered, established, and extended to the
widest generality of form and application. We have, in these
laws, examples of principles which were, historically
speaking, obtained by reference to experience. Bearing in
mind the object and the result of the preceding discussions,
we cannot but turn with much interest to examine these
portions of science; to inquire whether there be any real
difference in the grounds and nature between the knowledge
thus obtained, and those truths which we have already
contemplated; and which, as we have seen, contain their own
evidence, and do not require proof from experiment.

2. _The First Law of Motion._--The first law of motion is,
that _When a body moves not acted upon by any force, it will
go on perpetually in a straight line, and with a uniform
velocity._ Now what is the real ground of our assent to this
proposition? That it is not at first sight a self-evident
truth, appears to be clear; since from the time of Aristotle
to that of Galileo the opposite assertion was held to be
true; and it was believed that all bodies in motion had, by
their own nature, a constant tendency to move more and more
slowly, so as to stop at last. This belief, indeed, is
probably even now entertained by most persons, till their
attention is fixed upon the arguments by which the first law
of motion is established. It is, however, not difficult to
lead any person of a speculative habit {236} of thought to
see that the retardation which constantly takes place in the
motion of all bodies when left to themselves, is, in
reality, the effect of extraneous forces which destroy the
velocity. A top ceases to spin because the friction against
the ground and the resistance of the air gradually diminish
its motion, and not because its motion has any internal
principle of decay or fatigue. This may be shown, and was,
in fact, shown by Hooke before the Royal Society, at the
time when the laws of motion were still under discussion, by
means of experiments in which the weight of the top is
increased, and the resistance to motion offered by its
support, is diminished; for by such contrivances its motion
is made to continue much longer than it would otherwise do.
And by experiments of this nature, although we can never
remove the whole of the external impediments to continued
motion, and although, consequently, there will always be
some retardation; and an end of the motion of a body left to
itself, however long it may be delayed, must at last come;
yet we can establish a conviction that if all resistance
could be removed, there would be no diminution of velocity,
and thus the motion would go on for ever.

If we call to mind the axioms which we formerly stated, as
containing the most important conditions involved in the
idea of Cause, it will be seen that our conviction in this
case depends upon the first axiom of Causation, that nothing
can happen without a cause. Every change in the velocity of
the moving body must have a cause; and if the change can, in
any manner, be referred to the presence of other bodies,
these are said to exert _force_ upon the moving body: and
the conception of force is thus evolved from the general
idea of cause. _Force is any cause which has motion, or
change of motion, for its effect_; and thus, all the change
of velocity of a body which can be referred to extraneous
bodies,--as the air which surrounds it, or the support on
which it rests,--is considered as the effect of forces; and
this consideration is looked upon as explaining the
difference between the motion which really takes places in
the experiment, and that motion {237} which, as the law
asserts, would take place if the body were not acted on by
any forces.

Thus the truth of the first law of motion depends upon the
axiom that no change can take place without a cause; and
follows from the definition of force, if we suppose that
there can be none but an _external_ cause of change. But in
order to establish the law, it was necessary further to be
assured that there is no _internal_ cause of change of
velocity belonging to all matter whatever, and operating in
such a manner that the mere progress of time is sufficient
to produce a diminution of velocity in all moving bodies. It
appears from the history of mechanical science, that this
latter step required a reference to observation and
experiment; and that the first law of motion is so far,
historically at least, dependent upon our experience.

But notwithstanding this historical evidence of the need
which we have of a reference to observed facts, in order to
place this first law of motion out of doubt, it has been
maintained by very eminent mathematicians and philosophers,
that the law is, in truth, evident of itself, and does not
really rest upon experimental proof. Such, for example, is
the opinion of d'Alembert[20\3], who offers what is called
an _à priori_ proof of this law; that is, a demonstration
derived from our ideas alone. When a body is put in motion,
either, he says, the cause which puts it in motion at first,
suffices to make it move one foot, or the continued action
of the cause during this foot is requisite for the motion.
In the first case, the same reason which made the body
proceed to the end of the first foot will hold for its going
on through a second, a third, a fourth foot, and so on for
any number. In the second case, the same reason which made
the force continue to act during the first foot, will hold
for its acting, and therefore for the body moving during
each succeeding foot. And thus the body, once beginning to
move, must go on moving for ever.

[Note 20\3: _Dynamique._]

{238} It is obvious that we might reply to this argument,
that the reasons for the body proceeding during each
succeeding foot may not necessarily be all the same; for
among these reasons may be the time which has elapsed; and
thus the velocity may undergo a change as the time proceeds:
and we require observation to inform us that it does not do so.

Professor Playfair has presented nearly the same argument,
although in a different and more mathematical form[21\3]. If
the velocity change, says he, it must change according to
some expression of calculation depending upon the time, or,
in mathematical language, must be a _function_ of the time.
If the velocity diminish as the time increases, this may be
expressed by stating the velocity in each case as a certain
number, from which another quantity, or _term_, increasing
as the time increases, is subtracted. But, Playfair adds,
there is no condition involved in the nature of the case, by
which the _coefficients_, or numbers which are to be
employed, along with the number representing the time, in
calculating this second term, can be determined to be of one
magnitude rather than of any other. Therefore he infers
there can be no such coefficients, and that the velocity is
in each case equal to some constant number, independent of
the time; and is therefore the same for all times.

[Note 21\3: _Outlines of Natural Philosophy_, p. 26.]

In reply to this we may observe, that the circumstance of
_our not seeing_ in the nature of the case anything which
determines for us the coefficients above spoken of, cannot
prove that they have not some certain value _in nature_. We
do not see in the nature of the case anything which should
determine a body to fall sixteen feet in a second of time,
rather than one foot or one hundred feet: yet in fact the
space thus run through by falling bodies is determined to a
certain magnitude. It would be easy to assign a mathematical
expression for the velocity of a body, implying that
one-hundredth of the velocity, or any other {239} fraction,
is lost in each second[22\3]: and where is the absurdity of
supposing such an expression really to represent the
velocity?

[Note 22\3: This would be the case, if, _t_ being the
number of seconds elapsed, and _C_ some constant quantity,
the velocity were expressed by this mathematical formula,
_C_(99/100)^_t_.]

Most modern writers on mechanics have embraced the opposite
opinion, and have ascribed our knowledge of this first law
of motion to experience. Thus M. Poisson, one of the most
eminent of the mathematicians who have written on this
subject, says[23\3], "We cannot affirm _à priori_ that the
velocity communicated to a body will not become slower and
slower of itself, and end by being entirely extinguished. It
is only by experience and induction that this question can
be decided."

[Note 23\3: Poisson, _Dynamique_, ed. 2, art. 113.]

Yet it cannot be denied that there is much force in those
arguments by which it is attempted to show that the First
Law of Motion, such as we find it, is more consonant to our
conceptions than any other would be. The Law, as it exists,
is the most simple that we can conceive. Instead of having
to determine by experiments what is the law of the natural
change of velocity, we find the Law to be that it does not
change at all. To a certain extent, the Law depends upon the
evident axiom, that no change can take place without a
cause. But the question further occurs, whether the mere
lapse of time may not be a cause of change of velocity. In
order to ensure this, we have recourse to experiment; and
the result is that time alone does not produce any such
change. In addition to the conditions of change which we
collect from our own Ideas, we ask of Experience what other
conditions and circumstances she has to offer; and the
answer is, that she can point out none; When we have removed
the alterations which external causes, in our very
conception of them, occasion, there are no longer any
alterations. Instead of having to guide ourselves {240} by
experience, we learn that on this subject she has nothing to
tell us. Instead of having to take into account a number of
circumstances, we find that we have only to reject all
circumstances. The velocity of a body remains unaltered by
time alone, of whatever kind the body itself be.

But the doctrine that time alone is not a cause of change of
velocity in any body is further recommended to us by this
consideration;--that time is conceived by us not as a cause,
but only as a condition of other causes producing their
effects. Causes operate in time; but it is only when the
cause exists, that the lapse of time can give rise to
alterations. When therefore all external causes of change of
velocity are supposed to be removed, the velocity must
continue identical with itself, whatever the time which
elapses. An eternity of negation can produce no positive
result.

Thus, though the discovery of the First Law of Motion was
made, historically speaking, by means of experiment, we have
now attained a point of view in which we see that it might
have been certainly known to be true independently of
experience. This law in its ultimate form, when completely
simplified and steadily contemplated, assumes the character
of a self-evident truth. We shall find the same process to
take place in other instances. And this feature in the
progress of science will hereafter be found to suggest very
important views with regard both to the nature and prospects
of our knowledge.

3. _Gravity is a Uniform Force._--We shall find observations
of the same kind offering themselves in a manner more or
less obvious, with regard to the other principles of
Dynamics. The determination of the laws according to which
bodies fall downwards by the common action of gravity, has
already been noticed in the History of Mechanics[24\3], as
one of the earliest positive advances in the doctrine of
motion. These laws were first rightly stated by Galileo, and
{241} established by reasoning and by experiment, not
without dissent and controversy. The amount of these
doctrines is this: That gravity is a uniform accelerating
force; such a _uniform force_ having this for its character,
that it _makes the velocity increase in exact proportion to
the time of motion_. The relation which the spaces described
by the body bear to the times in which they are described,
is obtained by mathematical deduction from this definition
of the force.

[Note 24\3: _Hist. Ind. Sc._ b. vi. c. ii. sect. 2.]

The clear Definition of a uniform accelerating force, and
the Proposition that gravity is such a force, were
co-ordinate and contemporary steps in this discovery. In
defining accelerating force, reference, tacit or express,
was necessarily made to the second of the general axioms
respecting causation,--That causes are measured by their
effects. Force, in the cases now under our notice, is
conceived to be, as we have already stated, (p. 236,) any
cause which, acting from without, changes the motion of a
body. It must, therefore, in this acceptation, be measured
by the magnitude of the changes which are produced. But in
what manner the changes of motion are to be employed as the
measures of force, is learnt from observation of the facts
which we see taking place in the world. Experience
_interprets_ the axiom of causation, from which otherwise we
could not deduce any real knowledge. We may assume, in
virtue of our general conceptions of force, that under the
same circumstances, a greater change of motion implies a
greater force producing it; but what are we to expect when
the circumstances change? The weight of a body makes it fall
from rest at first, and causes it to move more quickly as it
descends lower. We may express this by saying, that gravity,
the universal force which makes all terrestrial bodies fall
when not supported, by its continuous action first _gives_
velocity to the body when it has none, and afterwards _adds_
velocity to that which the body already has. But how is the
velocity added proportioned to the velocity which already
exists? Force acting on a body at rest, and on a body in
motion, appears under very different {242} conditions;--how
are the effects related? Let the force be conceived to be in
both cases the same, since force is conceived to depend upon
the extraneous bodies, and not upon the condition of the
moving mass itself. But the force being the same, the
effects may still be different. It is at first sight
conceivable that the body, acted upon by the same gravity,
may receive a less addition of velocity when it is already
moving in the direction in which this gravity impels it; for
if we ourselves push a body forwards, we can produce little
additional effect upon it when it is already moving rapidly
away from us. May it not be true, in like manner, that
although gravity be always the same force, its effect
depends upon the velocity which the body under its influence
already possesses?

Observation and reasoning combined, as we have said, enabled
Galileo to answer these questions. He asserted and proved
that we may consistently and properly measure a force by the
velocity which is by it generated in a body, in some certain
time, as one second; and further, that if we adopt this
measure, gravity will be a force of the same value under all
circumstances of the body which it affects; since it
appeared that, in fact, a falling body does receive equal
increments of velocity in equal times from first to last.

If it be asked whether we could have known, anterior to, or
independent of, experiment, that gravity is a uniform force
in the sense thus imposed upon the term; it appears clear
that we must reply, that we could not have attained to such
knowledge, since other laws of the motion of bodies
downwards are easily conceivable, and nothing but
observation could inform us that one of these laws does not
prevail in fact. Indeed, we may add, that the assertion that
the force of gravity is uniform, is so far from being
self-evident, that it is not even true; for gravity varies
according to the distance from the center of the earth; and
although this variation is so small as to be, in the case of
falling bodies, imperceptible, it negatives the rigorous
uniformity of the force as completely, though {243} not to
the same extent, as if the weight of a body diminished in a
marked degree, when it was carried from the lower to the
upper room of a house. It cannot, then, be a truth
independent of experience, that gravity is uniform.

Yet, in fact, the assertion that gravity is uniform was
assented to, not only before it was proved, but even before
it was clearly understood. It was readily granted by all,
that bodies which fall freely are _uniformly_ accelerated;
but while some held the opinion just stated, that uniformly
accelerated motion is that in which the velocity increases
in proportion to the _time_, others maintained, that _that_
is uniformly accelerated motion, in which the velocity
increases in proportion to the _space_; so that, for
example, a body in falling vertically through twenty feet
should acquire twice as great a velocity as one which falls
through ten feet.

These two opinions are both put forward by the interlocutors
of Galileo's Dialogue on this subject[25\3]. And the latter
supposition is rejected, the author showing, not that it is
inconsistent with experience, but that it is impossible in
itself: inasmuch as it would inevitably lead to the
conclusion, that the fall through a large and a small
vertical space would occupy exactly the same time.

[Note 25\3: _Dialogo_, iii. p. 95.]

Indeed, Galileo assumes his definition of uniformly
accelerated motion as one which is sufficiently recommended
by its own simplicity. 'If we attend carefully,' he says,
'we shall find that no mode of increase of velocity is more
simple than that which adds equal increments in equal times.
Which we may easily understand if we consider the close
affinity of time and motion: for as the uniformity of motion
is defined by the equality of spaces described in equal
times, so we may conceive the uniformity of acceleration to
exist when equal velocities are added in equal times.'

Galileo's mode of supporting his opinion, that bodies
falling by the action of gravity are thus uniformly {244}
accelerated, consists, in the first place, in adducing the
maxim that nature always employs the most simple
means[26\3]. But he is far from considering this a decisive
argument. 'I,' says one of his speakers, 'as it would be
very unreasonable in me to gainsay this or any other
definition which any author may please to make, since they
are all arbitrary, may still, without offence, doubt whether
such a definition, conceived and admitted in the abstract,
fits, agrees, and is verified in that kind of accelerated
motion which bodies have when they descend naturally.'

[Note 26\3: _Dialogo_, iii. p. 91.]

The experimental proof that bodies, when they fall
downwards, are uniformly accelerated, is (by Galileo)
derived from the inclined plane; and therefore assumes the
proposition, that if such uniform acceleration prevail in
vertical motion, it will also hold when a body is compelled
to describe an oblique rectilinear path. This proposition
may be shown to be true, if (assuming by anticipation the
Third Law of Motion, of which we shall shortly have to
speak,) we introduce the conception of a uniform statical
force as the cause of uniform acceleration. For the force on
the inclined plane bears a constant proportion to the
vertical force, and this proportion is known from statical
considerations. But in the work of which we are speaking,
Galileo does not introduce this abstract conception of force
as the foundation of his doctrines. Instead of this, he
proposes, as a postulate sufficiently evident to be made the
basis of his reasonings, That bodies which descend down
inclined planes of different inclinations, but of the same
vertical height, all acquire the same velocity[27\3]. But
when this postulate has been propounded by one of the
persons of the dialogue, another interlocutor says, 'You
discourse very probably; but besides this likelihood, I wish
to augment the probability so far, that it shall be almost
as complete as a necessary demonstration.' He then proceeds
to describe a very ingenious and simple experiment, which
shows that when a body is made to swing upwards at the end
of {245} a string, it attains to the same height, whatever
is the path it follows, so long as it starts from the lowest
point with the same velocity. And thus Galileo's postulate
is experimentally confirmed, so far as the force of gravity
can be taken as an example of the forces which the postulate
contemplates: and conversely, gravity is proved to be a
uniform force, so far as it can be considered clear that the
postulate is true of uniform forces.

[Note 276\3: _Dialogo_, iii. p. 36.]

When we have introduced the conception and definition of
accelerating force, Galileo's postulate, that bodies
descending down inclined planes of the same vertical height,
acquire the same velocity, may, by a few steps of reasoning,
be demonstrated to be true of uniform forces: and thus the
proof that gravity, either in vertical or oblique motion, is
a uniform force, is confirmed by the experiment above
mentioned; as it also is, on like grounds, by many other
experiments, made upon inclined planes and pendulums.

Thus the propriety of Galileo's conception of a uniform
force, and the doctrine that gravity is a uniform force,
were confirmed by the same reasonings and experiments. We
may make here two remarks; _First_, that the conception,
when established and rightly stated, appears so simple as
hardly to require experimental proof; a remark which we have
already made with regard to the First Law of Motion: and
_Second_, that the discovery of the real law of nature was
made by assuming propositions which, without further proof,
we should consider as very precarious, and as far less
obvious, as well as less evident, than the law of nature in
its simple form.

4. _The Second Law of Motion._--When a body, instead of
falling downwards from rest, is thrown in any direction, it
describes a curve line, till its motion is stopped. In this,
and in all other cases in which a body describes a curved
path in free space, its motion is determined by the Second
Law of Motion. The law, in its general form, is as
follows:--When a body is thus cast forth and acted upon by a
force in a direction {246} transverse to its motion, the
result is, That _there is combined with the motion with
which the body is thrown, another motion, exactly the same
as that which the same force would have communicated to a
body at rest_.

It will readily be understood that the basis of this law is
the axiom already stated, that effects are measured by their
causes. In virtue of this axiom, the effect of gravity
acting upon a body in a direction transverse to its motion,
must measure the accelerative or deflective force of gravity
under those circumstances. If this effect vary with the
varying velocity and direction of the body thus acted upon,
the deflective force of gravity also will vary with those
circumstances. The more simple supposition is, that the
deflective force of gravity is the same, whatever be the
velocity and direction of the body which is subjected to its
influence: and this is the supposition which we find to be
verified by facts. For example, a ball let fall from the top
of a ship's upright mast, when she is sailing steadily
forward, will fall at the foot of the mast, just as if it
were let fall while the ship were at rest; thus showing that
the motion which gravity gives to the ball is compounded
with the horizontal motion which the ball shares with the
ship from the first. This general and simple conception of
motions as _compounded_ with one another, represents, it is
proved, the manner in which the motion produced by gravity
modifies any other motion which the body may previously have had.

The discussions which terminated in the general reception of
this Second Law of Motion among mechanical writers, were
much mixed up with the arguments for and against the
Copernican system, which system represented the earth as
revolving upon its axis. For the obvious argument against
this system was, that if each point of the earth's surface
were thus in motion from west to east, a stone dropt from
the top of a tower would be left behind, the tower moving
away from it: and the answer was, that by this law of
motion, the stone would have the earth's motion impressed
upon it, as well as that motion which would {247} arise from
its gravity to the earth; and that the motion of the stone
relative to the tower would thus be the same as if both
earth and tower were at rest. Galileo further urged, as a
presumption in favour of the opinion that the two
motions,--the circular motion arising from the rotation of
the earth, and the downward motion arising from the gravity
of the stone, would be compounded in the way we have
described, (neither of them disturbing or diminishing the
other,)--that the first motion was in its own nature not
liable to any change or diminution[28\3], as we learn from
the First Law of Motion. Nor was the subject lightly
dismissed. The experiment of the stone let fall from the top
of the mast was made in various forms by Gassendi; and in
his Epistle, _De Motu impresso a Motore translato_, the rule
now in question is supported by reference to these
experiments. In this manner, the general truth, the Second
Law of Motion, was established completely and beyond
dispute.

[Note 28\3: _Dialogo_, ii. p. 114.]

But when this law had been proved to be true in a general
sense, with such accuracy as rude experiments, like those of
Galileo and Gassendi, would admit, it still remained to be
ascertained (supposing our knowledge of the law to be the
result of experience alone,) whether it were true with that
precise and rigorous exactness which more refined modes of
experimenting could test. We so willingly believe in the
simplicity of laws of nature, that the rigorous accuracy of
such a law, known to be at least approximately true, was
taken for granted, till some ground for suspecting the
contrary should appear. Yet calculations have not been
wanting which might confirm the law as true to the last
degree of accuracy. Laplace relates (_Syst. du Monde_, livre
iv. chap. 16,) that at one time he had conceived it possible
that the effect of gravity upon the moon might be slightly
modified by the moon's direction and velocity; and that in
this way an explanation might be found for the moon's
_acceleration_ (a deviation of her observed from her
calculated place, which long {248} perplexed
mathematicians). But it was after some time discovered that
this feature in the moon's motion arose from another cause;
and the second law of motion was confirmed as true in the
most rigorous sense.

Thus we see that although there were arguments which might
be urged in favour of this law, founded upon the necessary
relations of ideas, men became convinced of its truth only
when it was verified and confirmed by actual experiment. But
yet in this case again, as in the former ones, when the law
had been established beyond doubt or question, men were very
ready to believe that it was not a mere result of
observation,--that the truth which it contained was not
derived from experience,--that it might have been assumed as
true in virtue of reasonings anterior to experience,--and
that experiments served only to make the law more plain and
intelligible, as visible diagrams in geometry serve to
illustrate geometrical truths; our knowledge not being (they
deemed) in mechanics, any more than in geometry, borrowed
from the senses. It was thought by many to be self-evident,
that the effect of a force in any direction cannot be
increased or diminished by any motion transverse to the
direction of the force which the body may have at the same
time: or, to express it otherwise, that if the motion of the
body be compounded of a horizontal and vertical motion, the
vertical motion alone will be affected by the vertical
force. This principle, indeed, not only has appeared evident
to many persons, but even at the present day is assumed as
an axiom by many of the most eminent mathematicians. It is,
for example, so employed in the _Mécanique Céleste_ of
Laplace, which may be looked upon as the standard of
mathematical mechanics in our time; and in the _Mécanique
Analytique_ of Lagrange, the most consummate example which
has appeared of subtilty of thought on such subjects, as
well as of power of mathematical generalization[29\3]. And
{249} thus we have here another example of that circumstance
which we have already noticed in speaking of the First Law
of Motion, (Art. 2 of this chapter,) and of the Law that
Gravity is a uniform Force, (Art. 3); namely, that the law,
though historically established by experiments, appears,
when once discovered and reduced to its most simple and
general form, to be self-evident. I am the more desirous of
drawing attention to this feature in various portions of the
history of science, inasmuch as it will be found to lead to
some very extensive and important views, hereafter to be
considered.

[Note 29\3: I may observe that the rule that we may
_compound_ motions, as the Law supposes, is involved in the
step of _resolving_ them; which is done in the passage to
which I refer. (_Méc. Analyt._ ptie. i. sect. i. art. 3. p.
225.) 'Si on conçoit que le mouvement d'un corps et les
forces qui le sollicitent soient _decomposées_ suivant trois
lignes droites perpendiculaires entre elles, on pourra
considérer séparément les mouvemens et les forces relatives
à chacun de ces trois directions. Car à cause de la
perpendicularité des directions il est visible que chacun de
ces mouvemens partiels peut être regardé comme indépendant
des deux autres, et qu'il ne peut recevoir d'altération que
de la part de la force qui agit dans la direction de ce
mouvement; l'on peut conclure que ces trois mouvemens
doivent suivre, chacun en particulier, les lois des
mouvemens rectilignes accélérés ou retardés par les forces
données.' Laplace makes the same assumption in effect,
(_Méc. Cél._ p. i. liv. i. art. 7), by resolving the forces
which act upon a point in three rectangular directions, and
reasoning separately concerning each direction. But in his
mode of treating the subject is involved a principle which
belongs to the Third Law of Motion, namely, the doctrine
that the velocity is as the force, of which we shall have to
speak elsewhere.]

5. _The Third Law of Motion._--We have, in the definition of
Accelerating Force, a measure of Forces, so far as they are
concerned in producing motion. We had before, in speaking of
the principles of statics, defined the measure of Forces or
Pressures, so far as they are employed in producing
equilibrium. But these two aspects of Force are closely
connected; and we require a law which shall lay down the
rule of their connexion. By the same kind of muscular
exertion by which we can support a heavy stone, we can also
put it in motion. The question then occurs, how is the rate
and manner of its motion determined? The answer to this
question is contained in the Third Law {250} of Motion, and
it is to this effect: that the _Momentum_ which any pressure
produces in the mass in a given time is proportional to the
pressure. By _Momentum_ is meant the product of the numbers
which express the velocity and the mass of the body: and
hence, if the mass of the body be the same in the instances
which we compare, the rule is,--That _the velocity is as the
force which produces it_; and this is one of the simplest
ways of expressing the Third Law of Motion.

In agreement with our general plan, we have to ask, What is
the ground of this rule? What is the simplest and most
satisfactory form to which we can reduce the proof of it?
Or, to take an instance; if a double pressure be exerted
against a given mass, so disposed as to be capable of
motion, why must it produce twice the velocity in the same time?

To answer this question, suppose the double pressure to be
resolved into two single pressures: one of these will
produce a certain velocity; and the question is, why an
equal pressure, acting upon the same mass, will produce an
equal velocity _in addition_ to the former? Or, stating the
matter otherwise, the question is, why each of the two
forces will produce its separate effect, unaltered by the
simultaneous action of the other force?

This statement of the case makes it seem to approach very
near to such cases as are included in the Second Law of
Motion, and therefore it might appear that this Third Law
has no grounds distinct from the Second. But it must be
recollected that the word _force_ has a different meaning in
this case and in that; in this place it signifies
_pressure_; in the statement of the Second Law its import
was _accelerative_ or _deflective force_, measured by the
velocity or deflexion generated. And thus the Third Law of
Motion, so far as our reasonings yet go, appears to rest on
a foundation different from the Second.

Accordingly, that part of the Third Law of Motion which we
are now considering, that the velocity generated is as the
force, was obtained, in fact, by a separate train of
research. The first exemplification of this {251} law which
was studied by mathematicians, was the motion of bodies upon
inclined planes: for the force which urges a body down an
inclined plane is known by statics, and hence the velocity
of its descent was to be determined. Galileo
originally[30\3] in his attempts to solve this problem of
the descent of a body down an inclined plane, did not
proceed from the principle which we have stated, (the
determination of the force which acts down the inclined
plane from statical considerations,) obvious as it may seem;
but assumed, as we have already seen, a proposition
apparently far more precarious;--namely, that a body sliding
down a smooth inclined plane acquires always the same
velocity, so long as the _vertical_ height fallen through is
the same. And this conjecture (for at first it was nothing
more than a conjecture) he confirmed by an ingenious
experiment; in which bodies acquired or lost the same
velocity by descending or ascending through the same height,
although their paths were different in other respects.

[Note 30\3: _Dial. della Sc. Nuov._ iii. p. 96. See _Hist.
Ind. Sci._ b. vi. c. ii. sect. 5.]

This was the form in which the doctrine of the motion of
bodies down inclined planes was at first presented in
Galileo's _Dialogues_ on the Science of Motion. But his
disciple Viviani was dissatisfied with the assumption thus
introduced; and in succeeding editions of the _Dialogues_,
the apparent chasm in the reasoning was much narrowed, by
making the proof depend upon a principle nearly identical
with the third law of motion as we have just stated it. In
the proof thus added, 'We are agreed,' says the
interlocutor[31\3], 'that in a moving body the impetus,
energy, momentum, or propension to motion, is as great as is
the force or least resistance which suffices to sustain it;'
and the impetus or momentum, in the course of the proof,
being taken to be as the velocity produced in a given time,
it is manifest that the principle so stated amounts to this;
that the velocity produced is as the statical force. And
thus this law of motion appears, {252} in the school of
Galileo, to have been suggested and established at first by
experiment, but afterwards confirmed and demonstrated by _à
priori_ considerations.

[Note 31\3: _Dialogo_, p. 104.]

We see, in the above reasoning, a number of abstract terms
introduced which are not, at first at least, very distinctly
defined, as _impetus_, _momentum_, &c. Of these, _momentum_
has been selected, to express that quantity which, in a
moving body, measures the statical force impressed upon the
body. This quantity is, as we have just seen, proportional
to the velocity in a given body. It is also, in different
bodies, proportional to the mass of the body. This part of
the third law of motion follows from our conception of
matter in general as consisting of parts capable of
addition. A double pressure must be required to produce the
same velocity in a double mass; for if the mass be halved,
each half will require an equal pressure; and the addition,
both of the pressures and of the masses, will take place
without disturbing the effects.

The measure of the quantity of matter of a body considered
as affecting the velocity which pressure produces in the
body, is termed its _inertia_, as we have already stated (c.
v.). Inertia is the property by which a large mass of matter
requires a greater force than a small mass, to give it an
equal velocity. It belongs to each portion of matter; and
portions of inertia are added whenever portions of matter
are added. Hence _inertia is as the quantity of matter_;
which is only another way of expressing this third law of
motion, so far as quantity of matter is concerned.

But how do we know the quantity of matter of a body? We may
reply, that we take the weight as the measure of the
quantity of matter: but we may then be again asked, how it
appears that the weight is proportional to the inertia;
which it must be, in order that the quantity of matter may
be proportional to both one and the other. We answer, that
this appears to be true experimentally, because all bodies
fall with equal velocities by gravity, when the known causes
of difference are removed. The observations of falling {253}
bodies, indeed, are not susceptible of much exactness: but
experiments leading to the same result, and capable of great
precision, were made upon pendulums by Newton; as he relates
in his _Principia_, Book III. prop. 6. They all agreed, he
says, with perfect accuracy: and thus the weight and the
inertia are proportional in all cases, and therefore each
proportional to the quantity of matter as measured by the other.

The conception of inertia, as we have already seen in
chapter V., involves the notion of action and reaction; and
thus the laws which involve inertia depend upon the idea of
mutual causation. The rule, that the velocity is as the
force, depends upon the principle of causation, that the
effect is proportional to the cause; the effect being here
so estimated as to be consistent both with the other laws of
motion and with experiment.

But here, as in other cases, the question occurs again; Is
experiment really requisite for the proof of this law? If we
look to authorities, we shall be not a little embarrassed to
decide. D'Alembert is against the necessity of experimental
proof. 'Why,' says he[32\3], 'should we have recourse to
this principle employed, at the present day, by everybody,
that the force is proportional to the velocity? ... a
principle resting solely upon this vague and obscure axiom,
that the effect is proportional to the cause. We shall not
examine here,' he adds, 'if this principle is necessarily
true; we shall only avow that the proofs which have hitherto
been adduced do not appear to us unexceptionable: nor shall
we, with some geometers, adopt it as a purely contingent
truth; which would be to ruin the certainty of mechanics,
and to reduce it to be nothing more than an experimental
science. We shall content ourselves with observing,' he
proceeds, 'that certain or doubtful, clear or obscure, it is
useless in mechanics, and consequently ought to be banished
from the science.' Though D'Alembert rejects the third law
of motion in this form, he accepts one of {254} equivalent
import, which appears to him to possess axiomatic certainty;
and this procedure is in consistence with the course which
he takes, of claiming for the science of mechanics more than
mere experimental truth. On the contrary, Laplace considers
this third law as established by experiment. 'Is the force,'
he says'[33\3], 'proportioned to the velocity? This,' he
replies, 'we cannot know _à priori_, seeing that we are in
ignorance of the nature of moving force: we must therefore,
for this purpose, recur to experience; for all which is not
a necessary consequence of the few data we have respecting
the nature of things, is, for us, only a result of
observation.' And again he says[34\3], 'Here, then, we have
two laws of motion,--the law of inertia [the first law of
motion], and the law of the force proportional to the
velocity,--which are given by observation. They are the most
natural and the most simple laws which we can imagine, and
without doubt they flow from the very nature of matter; but
this nature being unknown, they are, for us, only observed
facts: the only ones, however, which Mechanics borrows from
experience.'

[Note 32\3: _Dynamique_, Pref. p. x.]

[Note 33\3: _Méc. Cél._ p. 15.]

[Note 34\3: p. 18.]

It will appear, I think, from the views given in this and
several other parts of the present work, that we cannot with
justice say that we have very 'few data respecting the
nature of things,' in speculating concerning the laws of the
universe; since all the consequences which flow from the
relations of our fundamental ideas, necessarily regulate our
knowledge of things, so far as we have any such knowledge.
Nor can we say that the nature of matter is unknown to us,
in any sense in which we can conceive knowledge as possible.
The nature of matter is no more unknown than the nature of
space or of number. In our conception of matter, as of space
and of number, are involved certain relations, which are the
necessary groundwork of our knowledge; and anything which is
independent of these relations, is not unknown, but
inconceivable. {255}

It must be already clear to the reader, from the phraseology
employed by these two eminent mathematicians, that the
question respecting the formation of the third law of motion
can only be solved by a careful consideration of what we
mean by observation and experience, nature and matter. But
it will probably be generally allowed, that, taking into
account the explanations already offered of the necessary
conditions of experience and of the conception of inertia,
this law of motion, that the inertia is as the quantity of
matter, is almost or altogether self-evident.

6. _Action and Reaction are Equal in Moving Bodies._--When
we have to consider bodies as acting upon one another, and
influencing each other's motions, the third law of motion is
still applied; but along with this, we also employ the
general principle that action and reaction are equal and
opposite. Action and reaction are here to be understood as
momentum produced and destroyed, according to the measure of
action established by the Third Law of Motion: and the cases
in which this principle is thus employed form so large a
portion of those in which the third law of motion is used,
that some writers (Newton at the head of them) have
stated the equality of action and reaction as the third law
of motion.

The third law of motion being once established, the equality
of action and reaction, in the sense of momentum gained and
lost, necessarily follows. Thus, if a weight hanging by a
string over the edge of a smooth level table draw another
weight along the table, the hanging weight moves more slowly
than it would do if not so connected, and thus loses
velocity by the connexion; while the other weight gains by
the connexion all the velocity which it has, for if left to
itself it would rest. And the pressures which restrain the
descent of the first body and accelerate the motion of the
second, are equal at all instants of time, for each of these
pressures is the tension of the string: and hence, by the
third law of motion, the momentum gained by the one body,
and the momentum lost by the other in virtue of the action
of this string, are equal. And similar {256} reasoning may
be employed in any other case where bodies are connected.

The case where one body does not push or draw, but _strikes_
another, appeared at first to mechanical reasoners to be of
a different nature from the others; but a little
consideration was sufficient to show that a blow is, in
fact, only a short and violent pressure; and that,
therefore, the general rule of the equality of momentum lost
and gained applies to this as well as to the other cases.

Thus, in order to determine the case of the direct action of
bodies upon one another, we require no new law of motion.
The equality of action and reaction, which enters
necessarily into every conception of mechanical operation,
combined with the measure of action as given by the third
law of motion, enables us to trace the consequences of every
case, whether of pressure or of impact.

7. _D'Alembert's Principle._--But what will be the result
when bodies do not act directly upon each other, but are
_indirectly_ connected in any way by levers, strings,
pulleys, or in any other manner, so that one part of the
system has a mechanical advantage over another? The result
must still be determined by the principle that action and
reaction balance each other. The action and reaction, being
pressures in one sense, must balance each other by the laws
of statics, for these laws determine the equilibrium of
pressure. Now action and reaction, according to their
measures in the Third Law of Motion, are momentum gained and
lost, when the action is direct; and except the indirect
action introduce some modification of the law, they must
have the same measure still. But, in fact, we cannot well
conceive any modification of the law to take place in this
case; for direct action is only one (the ultimate) case of
indirect action. Thus if two heavy bodies act at different
points of a lever, the action of each on the other is
indirect; but if the two points come together, the action
becomes direct. Hence the rule must be that which we have
already stated; for if the rule were false for indirect
action, it would {257} also be false for direct action, for
which case we have shown it to be true. And thus we obtain
the general principle, that in any system of bodies which
act on each other, action and reaction, estimated by
momentum gained and lost, balance each other according to
the laws of equilibrium. This principle, which is so general
as to supply a key to the solution of all possible
mechanical problems, is commonly called _D'Alembert's
Principle_. The experimental proofs which convinced men of
the truth of the Third Law of Motion were, many or most of
them, proofs of the law in this extended sense. And thus the
proof of D'Alembert's Principle, both from the idea of
mechanical action and from experience, is included in the
proof of the law already stated.

8. _Connexion of Dynamical and Statical Principles._--The
principle of equilibrium of D'Alembert just stated, is the
law which he would substitute for the Third Law of Motion;
and he would thus remove the necessity for an independent
proof of that law. In like manner, the Second Law of Motion
is by some writers derived from the principle of the
composition of statical forces; and they would thus
supersede the necessity of a reference to experiment in that
case. Laplace takes this course, and thus, as we have seen,
rests only the First and Third Law of Motion upon
experience. Newton, on the other hand, recognizes the same
connexion of propositions, but for a different purpose; for
he derives the composition of statical forces from the
Second Law of Motion.

The close connexion of these three principles, the
composition of (statical) forces, the composition of
(accelerating) forces with velocities, and the measure of
(moving) forces by velocities, cannot be denied; yet it
appears to be by no means easy to supersede the necessity of
independent proofs of the last two of these principles. Both
may be proved or illustrated by experiment: and the
experiments which prove the one are different from those
which establish the other. For example, it appears by easy
calculations, that when we apply our principles to the
oscillations of a pendulum, {258} the Second Law is proved
by the fact, that the oscillations take place at the same
rate in an east and west, and in a north and south
direction: under the same circumstances, the Third Law is
proved by our finding that the time of a small oscillation
is proportional to the square root of the length of a
pendulum; and similar differences might be pointed out in
other experiments, as to their bearing upon the one law or
the other.

9. _Mechanical Principles become gradually more simple and
more evident._--I will again point out in general two
circumstances which I have already noticed in particular
cases of the laws of motion.--Truths are often at first
assumed in a form which is far from being the most obvious
or simple;--and truths once discovered are gradually
simplified, so as to assume the appearance of self-evident
truths.

The former circumstance is exemplified in several of the
instances which we have had to consider. The assumption,
that a perpetual motion is impossible, preceded the
knowledge of the first law of motion. The assumed equality
of the velocities acquired down two inclined planes of the
same height, was afterwards reduced to the third law of
motion by Galileo himself. In the History[35\3], we have
noted Huyghens's assumption of the equality of the actual
descent and potential ascent of the center of gravity: this
was afterwards reduced by Herman and the Bernoullis, to the
statical equivalence of the solicitations of gravity and the
vicarious solicitations of the effective forces which act on
each point; and finally to the principle of D'Alembert,
which asserts that the motions gained and lost balance each
other.

[Note 35\3: B. vi. c. v. sect. 2.]

This early assertion of principles which now appear neither
obvious nor self-evident, is not to be considered as a
groundless assumption on the part of the discoverers by whom
it was made. On the contrary, it is evidence of the deep
sagacity and clear thought which were {259} requisite in
order to make such discoveries. For these results are really
rigorous consequences of the laws of motion in their
simplest form: and the evidence of them was probably
present, though undeveloped, in the minds of the
discoverers. We are told of geometrical students, who, by a
peculiar aptitude of mind, perceived the evidence of some of
the more advanced propositions of geometry without going
through the introductory steps. We must suppose a similar
aptitude for mechanical reasonings, which, existing in the
minds of Stevinus, Galileo, Newton, and Huyghens, led them
to make those assumptions which finally resolved themselves
into the laws of motion.

We may observe further, that the simplicity and evidence
which the laws of mechanics have at length assumed, are much
favoured by the usage of words among the best writers on
such subjects. Terms which originally, and before the laws
of motion were fully known, were used in a very vague and
fluctuating sense, were afterwards limited and rendered
precise, so that assertions which at first appear identical
propositions become distinct and important principles. Thus
_force_, _motion_, _momentum_, are terms which were
employed, though in a loose manner, from the very outset of
mechanical speculation. And so long as these words retained
the vagueness of common language, it would have been a
useless and barren truism to say that 'the momentum is
proportional to the force,' or that 'a body loses as much
motion as it communicates to another.' But when 'momentum'
and 'quantity of motion' are defined to mean the product of
mass and velocity, these two propositions immediately become
distinct statements of the third law of motion and its
consequences. In like manner, the assertion that 'gravity is
a uniform force' was assented to, before it was settled what
a uniform force was; but this assertion only became
significant and useful when that point had been properly
determined. The statement that 'when different motions are
communicated to the same body their effects are {260}
compounded,' becomes the second law of motion, when we
define what composition of motions is. And the same process
may be observed in other cases.

And thus we see how well the form which science ultimately
assumes is adapted to simplify knowledge. The definitions
which are adopted, and the terms which become current in
precise senses, produce a complete harmony between the
matter and the form of our knowledge; so that truths which
were at first unexpected and recondite, became familiar
phrases, and after a few generations sound, even to common
ears, like identical propositions.

10. _Controversy of the Measure of Force._--In the History
of Mechanics[36\3], we have given an account of the
controversy which, for some time, occupied the
mathematicians of Europe, whether the forces of bodies in
motion should be reckoned proportional to the velocity, or
to the square of the velocity. We need not here recall the
events of this dispute; but we may remark, that its history,
as a metaphysical controversy, is remarkable in this
respect, that it has been finally and completely settled;
for it is now agreed among mathematicians that both sides
were right, and that the results of mechanical action may be
expressed with equal correctness by means of _momentum_ and
of _vis viva_. It is, in one sense, as D'Alembert has
said[37\3], a dispute about words; but we are not to infer
that, on that account, it was frivolous or useless; for such
disputes are one principal means of reducing the principles
of our {261} knowledge to their utmost simplicity and
clearness. The terms which are employed in the science of
mechanics are now liberated for ever, in the minds of
mathematicians, from that ambiguity which was the
battleground in the war of the _vis viva_.

[Note 36\3: B. vi. c. v. sect. 2.]

[Note 37\3: D'Alembert has also remarked (_Dynamique_, Pref.
xxi.) that this controversy 'shows how little justice and
precision there is in the pretended axiom that causes are
proportional to their effects.' But this reflection is by no
means well founded. For since both measures are true, it
appears that causes may be _justly_ measured by their
effects, even when very different kinds of effects are
taken. That the axiom does not point out one _precise_
measure, till illustrated by experience or by other
considerations, we grant: but the same thing occurs in the
application of other axioms also.]

But we may observe that the real reason of this controversy
was exactly that tendency which we have been noticing;--the
disposition of man to assume in his speculations certain
general propositions as true, and to fix the sense of terms
so that they shall fall in with this truth. It was agreed,
on all hands, that in the mutual action of bodies the same
quantity of force is always preserved; and the question was,
by which of the two measures this rule could best be
verified. We see, therefore, that the dispute was not
concerning a definition merely, but concerning a definition
combined with a general proposition. Such a question may be
readily conceived to have been by no means unimportant; and
we may remark, in passing, that such controversies, although
they are commonly afterwards stigmatized as quarrels about
words and definitions, are, in reality, events of
considerable consequence in the history of science; since
they dissipate all ambiguity and vagueness in the use of
terms, and bring into view the conditions under which the
fundamental principles of our knowledge can be most clearly
and simply presented.

It is worth our while to pause for a moment on the prospect
that we have thus obtained, of the advance of knowledge, as
exemplified in the history of Mechanics. The general
transformation of our views from vague to definite, from
complex to simple, from unexpected discoveries to
self-evident truths, from seeming contradictions to
identical propositions, is very remarkable, but it is by no
means peculiar to our subject. The same circumstances, more
or less prominent, more or less developed, appear in the
history of other sciences, according to the point of advance
which each has reached. They bear upon very important
doctrines respecting the prospects, the {262} limits, and
the very nature of our knowledge. And though these doctrines
require to be considered with reference to the whole body of
science, yet the peculiar manner in which they are
illustrated by the survey of the history of Mechanics, on
which we have just been engaged, appears to make this a
convenient place for introducing them to the reader.

{{263}}
CHAPTER VIII.

OF THE PARADOX OF UNIVERSAL PROPOSITIONS OBTAINED FROM
EXPERIENCE.

1. IT was formerly stated[38\3] that experience cannot
establish any universal or necessary truths. The number of
trials which we can make of any proposition is necessarily
limited, and observation alone cannot give us any ground of
extending the inference to untried cases. Observed facts
have no visible bond of necessary connexion, and no exercise
of our senses can enable us to discover such connexion. We
can never acquire from a mere observation of facts, the
right to assert that a proposition is true in all cases, and
that it could not be otherwise than we find it to be.

[Note 38\3: B. i. c. iv. Of Experience]

Yet, as we have just seen in the history of the laws of
motion, we may go on collecting our knowledge from
observation, and enlarging and simplifying it, till it
approaches or attains to complete universality and seeming
necessity. Whether the laws of motion, as we now know them,
can be rigorously traced to an absolute necessity in the
nature of things, we have not ventured absolutely to
pronounce. But we have seen that some of the most acute and
profound mathematicians have believed that, for these laws
of motion, or some of them, there was such a demonstrable
necessity compelling them to be such as they are, and no
other. Most of those who have carefully studied the
principles of Mechanics will allow that some at least of the
primary laws of motion approach very near to this character
of necessary truth; and will confess that it would be
difficult to imagine any other consistent {264} scheme of
fundamental principles. And almost all mathematicians will
allow to these laws an absolute universality; so that we may
apply them without scruple or misgiving, in cases the most
remote from those to which our experience has extended. What
astronomer would fear to refer to the known laws of motion,
in reasoning concerning the double stars; although these
objects are at an immeasurably remote distance from that
solar system which has been the only field of our
observation of mechanical facts? What philosopher, in
speculating respecting a magnetic fluid, or a luminiferous
ether, would hesitate to apply to it the mechanical
principles which are applicable to fluids of known
mechanical properties? When we assert that the quantity of
motion in the world cannot be increased or diminished by the
mutual actions of bodies, does not every mathematician feel
convinced that it would be an unphilosophical restriction to
limit this proposition to such modes of action as we have tried?

Yet no one can doubt that, in historical fact, these laws
were collected from experience. That such is the case, is no
matter of conjecture. We know the time, the persons, the
circumstances, belonging to each step of each discovery. I
have, in the History, given an account of these discoveries;
and in the previous chapters of the present work, I have
further examined the nature and the import of the principles
which were thus brought to light.

Here, then, is an apparent contradiction. Experience, it
would seem, has done that which we had proved that she
cannot do. She has led men to propositions, universal at
least, and to principles which appear to some persons
necessary. What is the explanation of this contradiction,
the solution of this paradox? Is it true that Experience can
reveal to us universal and necessary truths? Does she
possess some secret virtue, some unsuspected power, by which
she can detect connexions and consequences which we have
declared to be out of her sphere? Can she see more than mere
appearances, and observe more than mere facts? Can {265} she
penetrate, in some way, to the nature of things?--descend
below the surface of phenomena to their causes and origins,
so as to be able to say what can and what can not be;--what
occurrences are partial, and what universal? If this be so,
we have indeed mistaken her character and powers; and the
whole course of our reasoning becomes precarious and
obscure. But, then, when we return upon our path we cannot
find the point at which we deviated, we cannot detect the
false step in our deduction. It still seems that by
experience, strictly so called, we cannot discover necessary
and universal truths. Our senses can give us no evidence of
a necessary connexion in phenomena. Our observation must be
limited, and cannot testify concerning anything which is
beyond its limits. A general view of our faculties appears
to prove it to be impossible that men should do what the
history of the science of mechanics shows that they have done.

2. But in order to try to solve this Paradox, let us again
refer to the History of Mechanics. In the cases belonging to
that science, in which propositions of the most
unquestionable universality, and most approaching to the
character of necessary truths, (as, for instance, the laws
of motion,) have been arrived at, what is the source of the
axiomatic character which the propositions thus assume? The
answer to this question will, we may hope, throw some light
on the perplexity in which we appear to be involved.

Now the answer to this inquiry is, that the laws of motion
borrow their axiomatic character from their being merely
_interpretations_ of the Axioms of Causation. Those axioms,
being exhibitions of the Idea of Cause under various
aspects, are of the most rigorous universality and
necessity. And so far as the laws of motion are
exemplifications of those axioms, these laws must be no less
universal and necessary. How these axioms are to be
understood;--in what sense _cause_ and _effect_, _action_
and _reaction_, are to be taken, experience and observation
did, in fact, teach inquirers on this subject; and without
this teaching, the laws of motion could never have been
distinctly known. If two forces {266} act together, each
must produce its effect, by the axiom of causation; and,
therefore, the effects of the separate forces must be
_compounded_. But a long course of discussion and experiment
must instruct men of what kind this _composition_ of forces
is. Again; action and reaction must be equal; but much
thought and some trial were needed to show what _action_ and
_reaction_ are. Those metaphysicians who enunciated Laws of
motion without reference to experience, propounded only such
laws as were vague and inapplicable. But yet these persons
manifested the indestructible conviction, belonging to man's
speculative nature, that there exist Laws of motion, that
is, universal formulæ, connecting the causes and effects
when motion takes place. Those mechanicians, again, who,
observed facts involving equilibrium and motion, and stated
some narrow rules, without attempting to ascend to any
universal and simple principle, obtained laws no less barren
and useless than the metaphysicians; for they could not tell
in what new cases, or whether in any, their laws would be
verified;--they needed a more general rule, to show them the
limits of the rule they had discovered. They went wrong in
each attempt to solve a new problem, because their
interpretation of the terms of the axioms, though true,
perhaps, in certain cases, was not right in general.

Thus Pappus erred in attempting to interpret as a case of
the lever, the problem of supporting a weight upon an
inclined plane; thus Aristotle erred in interpreting the
doctrine that the weight of bodies is the cause of their
fall; thus Kepler erred in interpreting the rule that the
velocity of bodies depends upon the force; thus
Bernoulli[39\3] erred in interpreting the equality of action
and reaction upon a lever in motion. In each of these
instances, true doctrines, already established, (whether by
experiment or otherwise,) were erroneously applied. And the
error was corrected by further reflection, which pointed out
that another mode of interpretation was requisite, in order
that the axiom {267} which, was appealed to in each case
might retain its force in the most general sense. And in the
reasonings which avoided or corrected such errors, and which
led to substantial general truths, the object of the
speculator always was to give to the acknowledged maxims
which the Idea of Cause suggested, such a signification as
should be consistent with their universal validity. The rule
was not accepted as particular at the outset, and afterwards
generalized more and more widely; but from the very first,
the universality of the rule was assumed, and the question
was, how it should be understood so as to be universally
true. At every stage of speculation, the law was regarded as
a general law. This was not an aspect which it gradually
acquired, by the accumulating contributions of experience,
but a feature of its original and native character. _What_
should happen universally, experience might be needed to
show: but that what happened should happen _universally_,
was implied in the nature of knowledge. The universality of
the laws of motion was not gathered from experience, however
much the laws themselves might be so.

[Note 39\3: _Hist. Ind. Sc._ b. vi. c. v. sect. 2.]

3. Thus we obtain the solution of our Paradox, so far as the
case before us is concerned. The laws of motion borrow their
_form_ from the Idea of Causation, though their _matter_ may
be given by experience: and hence they possess a
universality which experience cannot give. They are
certainly and universally valid; and the only question for
observation to decide is, how they are to be understood.
They are like general mathematical formulæ, which are known
to be true, even while we are ignorant what are the unknown
quantities which they involve. It must be allowed, on the
other hand, that so long as these formulæ are not
interpreted by a real study of nature, they are not only
useless but prejudicial; filling men's minds with vague
general terms, empty maxims, and unintelligible
abstractions, which they mistake for knowledge. Of such
perversion of the speculative propensities of man's nature,
the world has seen too much in all ages. Yet we must not, on
that account, despise these forms of {268} truth, since
without them, no general knowledge is possible. Without
general terms, and maxims, and abstractions, we can have no
science, no speculation; hardly, indeed, consistent thought
or the exercise of reason. The course of real knowledge is,
to obtain from thought and experience the right
interpretation of our general terms, the real import of our
maxims, the true generalizations which our abstractions
involve.

4. If it be asked, How Experience is able to teach us to
interpret aright the general terms which the Axioms of
Causation involve;--whence she derives the light which she
is to throw on these general notions; the answer is
obvious;--namely, that the relations of causation are the
_conditions_ of Experience;--that the general notions are
_exemplified_ in the particular cases of which she takes
cognizance. The events which take place about us, and which
are the objects of our observation, we cannot conceive
otherwise than as subject to the laws of cause and effect.
Every event must have a cause;--Every effect must be
determined by its cause;--these maxims are true of the
phenomena which form the materials of our experience. It is
precisely to them, that these truths apply. It is in the
world which we have before our eyes, that these propositions
are universally verified; and it is therefore by the
observation of what we see, that we must learn how these
propositions are to be understood. Every fact, every
experiment, is an example of these statements; and it is
therefore by attention to and familiarity with facts and
experiments, that we learn the signification of the
expressions in which the statements are made; just as in any
other case we learn the import of language by observing the
manner in which it is applied in known cases. Experience is
the interpreter of nature; it being understood that she is
to make her interpretation in that comprehensive phraseology
which is the genuine language of science.

5. We may return for an instant to the objection, that
experience cannot give us general truths, since, after any
number of trials confirming a rule, we may for aught we can
foresee, have one which violates the {269} rule. When we
have seen a thousand stones fall to the ground, we may see
one which does not fall under the same apparent
circumstances. How then, it is asked, can experience teach
us that _all_ stones, rigorously speaking, will fall if
unsupported? And to this we reply, that it is not true that
we can conceive one stone to be suspended in the air, while
a thousand others fall, without believing some peculiar
cause to support it; and that, therefore, such a supposition
forms no exception to the law, that gravity is a force by
which _all_ bodies are urged downwards. Undoubtedly we can
conceive a body, when dropt or thrown, to move in a line
quite different from other bodies: thus a certain
missile[40\3] used by the natives of Australia, and lately
brought to this country, when thrown from the hand in a
proper manner, describes a curve, and returns to the place
from whence it was thrown. But did any one, therefore, even
for an instant suppose that the laws of motion are different
for this and for other bodies? On the contrary, was not
every person of a speculative turn immediately led to
inquire how it was that the known causes which modify
motion, the resistance of the air and the other causes,
produced in this instance so peculiar an effect? And if the
motion had been still more unaccountable, it would not have
occasioned any uncertainty whether it were consistent with
the agency of gravity and the laws of motion. If a body
suddenly alter its direction, or move in any other
unexpected manner, we never doubt that there is a cause of
the change. We may continue quite ignorant of the nature of
this cause, but this ignorance never occasions a moment's
doubt that the cause exists and is exactly suited to the
effect. And thus experience can prove or discover to us
general rules, but she can never prove that general rules do
not exist. Anomalies, exceptions, unexplained phenomena, may
remind us that we have much still to learn, but they can
never make us suppose that truths are not universal. We may
observe facts that show us we have not fully {270}
understood the meaning of our general laws, but we can never
find facts which show our laws to have no meaning. Our
experience is bound in by the limits of cause and effect,
and can give us no information concerning any region where
that relation does not prevail. The whole series of external
occurrences and objects, through all time and space, exists
only, and is conceived only, as subject to this relation;
and therefore we endeavour in vain to imagine to ourselves
when and where and how exceptions to this relation may
occur. The assumption of the connexion of cause and effect
is essential to our experience, as the recognition of the
maxims which express this connexion is essential to our
knowledge.

[Note 40\3: Called the Bo-me-rang.]

6. I have thus endeavoured to explain in some measure how,
at least in the field of our mechanical knowledge,
experience can discover universal truths, though she cannot
give them their universality; and how such truths, though
borrowing their form from our ideas, cannot be understood
except by the actual study of external nature. And thus with
regard to the laws of motion, and other fundamental
principles of Mechanics, the analysis of our ideas and the
history of the progress of the science well illustrate each
other.

If the paradox of the discovery of universal truths by
experience be thus solved in one instance, a much wider
question offers itself to us;--How far the difficulty, and
how far the solution, are applicable to other subjects. It
is easy to see that this question involves most grave and
extensive doctrines with regard to the whole compass of
human knowledge: and the views to which we have been led in
the present Book of this work are, we trust, fitted to throw
much light upon the general aspect of the subject. But after
discussions so abstract, and perhaps obscure, as those in
which we have been engaged for some chapters, I willingly
postpone to a future occasion an investigation which may
perhaps appear to most readers more recondite and difficult
still. And we have, in fact, many other special fields of
knowledge to survey, before we are led by the order of our
subject, to {271} those general questions and doctrines,
those antitheses brought into view and again resolved, which
a view of the whole territory of human knowledge suggests,
and by which the nature and conditions of knowledge are
exhibited.

Before we quit the subject of mechanical science we shall
make a few remarks on another doctrine which forms part of
the established truths of the science, namely, the doctrine
of universal gravitation.

{{272}}
CHAPTER IX.

OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL GRAVITATION.

THE doctrine of universal gravitation is a feature of so
much importance in the history of science that we shall not
pass it by without a few remarks on the nature and evidence
of the doctrine.

1. To a certain extent the doctrine of the attraction of
bodies according to the law of the inverse square of the
distance, exhibits in its progress among men the same
general features which we have noticed in the history of the
laws of motion. This doctrine was maintained _à priori_ on
the ground of its simplicity, and was asserted positively,
even before it was clearly understood:--notwithstanding this
anticipation, its establishment on the ground of facts was a
task of vast labour and sagacity:--when it had been so
established in a general way, there occurred at later
periods, an occasional suspicion that it might be
approximately true only:--these suspicions led to further
researches, which showed the rule to be rigorously
exact:--and at present there are mathematicians who
maintain, not only that it is true, but that it is a
necessary property of matter. A very few words on each of
these points will suffice.

2. I have shown in the _History of Science_[41\3], that the
attraction of the sun according to the inverse square of the
distance, had been divined by Bullialdus, Hooke, Halley, and
others, before it was proved by Newton. Probably the reason
which suggested this conjecture was, that gravity might be
considered {273} as a sort of emanation; and that thus, like
light or any other effect diffused from a center, it must
follow the law just stated, the efficacy of the force being
weakened in receding from the center, exactly in proportion
to the space through which it is diffused. It cannot be
denied that such a view appears to be strongly recommended
by analogy.

[Note 41\3: B. vii. c. i.]

When it had been proved by Newton that the planets were
really retained in their elliptical orbits by a central
force, his calculations also showed that the above-stated
_law_ of the force must be at least very approximately
correct, since otherwise the aphelia of the orbits could not
be so nearly at rest as they were. Yet when it seemed as if
the motion of the moon's apogee could not be accounted for
without some new supposition, the _à priori_ argument in
favour of the inverse square did not prevent Clairaut from
trying the hypothesis of a small term added to that which
expressed the ancient law: but when, in order to test the
accuracy of this hypothesis, the calculation of the motion
of the moon's apogee was pushed to a greater degree of
exactness than had been obtained before, it was found that
the new term vanished of itself; and that the inverse square
now accounted for the whole of the motion. And thus, as in
the case of the second law of motion, the most scrupulous
examination terminated in showing the simplest rule to be
rigorously true.

3. Similar events occurred in the history of another part of
the law of gravitation: namely, that the attraction is
proportional to the quantity of matter attracted. This part
of the law may also be thus stated, That the weight of
bodies arising from gravity is proportional to their
inertia; and thus, that the _accelerating force_ on all
bodies under the same circumstances is the same. Newton made
experiments which proved this with regard to terrestrial
bodies; for he found that, at the end of equal strings,
balls of all substances, gold, silver, lead, glass, wood,
&c., oscillated in equal times[42\3]. But a few years ago,
doubts {274} arose among the German astronomers whether this
law was rigorously true with regard to the planetary bodies.
Some calculations appeared to prove, that the attraction of
Jupiter as shown by the perturbations which he produces in
the small planets Juno, Vesta, and Pallas, was different
from the attraction which he exerts on his own satellites.
Nor did there appear to these philosophers anything
inconceivable in the supposition that the attraction of a
planet might be thus _elective_. But when Mr. Airy obtained
a more exact determination of the mass of Jupiter, as
indicated by his effect on his satellites, it was found that
this suspicion was unfounded; and that there was, in this
case, no exception to the universality of the rule, that
this cosmical attraction is in the proportion of the
attracted mass.

[Note 42\3: _Prin._ lib. iii. prop. 6.]

4. Again: when it had thus been shown that a mutual
attraction of parts, according to the law above mentioned,
prevailed throughout the extent of the solar system, it
might still be doubted whether the same law extended to
other regions of the universe. It might have been perhaps
imagined that each fixed star had its peculiar law of force.
But the examination of the motions of double stars about
each other, by the two Herschels and others, appears to show
that these bodies describe ellipses as the planets do; and
thus extends the law of the inverse squares to parts of the
universe immeasurably distant from the whole solar system.

5. Since every doubt which has been raised with regard to
the universality and accuracy of the law of gravitation, has
thus ended in confirming the rule, it is not surprizing that
men's minds should have returned with additional force to
those views which had at first represented the law as a
necessary truth, capable of being established by reason
alone. When it had been proved by Newton that gravity is
really a _universal_ attribute of matter as far as we can
learn, his pupils were not content without maintaining it to
be an _essential_ quality. This is the doctrine held by
Cotes in the preface to the second edition of the
_Principia_ (1712): {275} 'Gravity,' he says, 'is a primary
quality of bodies, as extension, mobility, and
impenetrability are.' But Newton himself by no means went so
far. In his second Letter to Bentley (1693), he says, 'You
sometimes speak of gravity as essential and inherent to
matter; pray do not ascribe that notion to me. The cause of
gravity,' he adds, 'I do not pretend to know, and would take
more time to consider of it.'

Cotes maintains his opinion by urging, that we learn by
_experience_ that all bodies possess gravity, and that we do
not learn in any other way that they are extended, moveable,
or solid. But we have already seen, that the ideas of space,
time, and reaction, on which depend extension, mobility, and
solidity, are not results, but conditions, of experience. We
cannot conceive a body except as extended; we cannot
conceive it to exert mechanical action except with some kind
of solidity. But so far as our conceptions of body have
hitherto been developed, we find no difficulty in conceiving
two bodies which do not attract each other.

6. Newton lays down, in the second edition of the
_Principia_, this 'Rule of Philosophizing' (book iii.); that
'The qualities of bodies which cannot be made more or less
intense, and which belong to all bodies on which we are able
to make experiments, are to be held to be qualities of all
bodies in general.' And this Rule is cited in the sixth
Proposition of the Third Book of the _Principia_, (Cor. 2,)
in order to prove that gravity, proportional to the quantity
of matter, may be asserted to be a quality of all bodies
universally. But we may remark that a Rule of
Philosophizing, itself of precarious authority, cannot
authorize us in ascribing universality to an empirical
result. Geometrical and statical properties are seen to be
necessary, and _therefore_ universal: but Newton appears
disposed to assert a like universality of gravity, quite
unconnected with any necessity. It would be a very
inadequate statement, indeed a false representation, of
statical truth, if we were to say, that because every body
which has hitherto been tried _has been found_ to have a
center of gravity, we venture to assert that all bodies
whatever {276} have a center of gravity. And if we are ever
able to assert the absolute universality of the law of
gravitation, we shall have to rest this truth upon the
clearer development of our ideas of matter and force; not
upon a Rule of Philosophizing, which, till otherwise proved,
must be a mere rule of prudence, and which the opponent may
refuse to admit.

7. Other persons, instead of asserting gravity to be in its
own nature essential to matter, have made hypotheses
concerning some mechanism or other, by which this mutual
attraction of bodies is produced[43\3]. Thus the Cartesians
ascribed to a vortex the tendency of bodies to a center;
Newton himself seems to have been disposed to refer this
tendency to the elasticity of an ether; Le Sage propounded a
curious hypothesis, in which this attraction is accounted
for by the impulse of infinite streams of particles flowing
constantly through the universe in all directions. In these
speculations, the force of gravity is resolved into the
pressure or impulse of solids or fluids. On the other hand,
hypotheses have been propounded, in which the solidity, and
other physical qualities of bodies, have been explained by
representing the bodies as a collection of points, from
which points, repulsive, as well as attractive, forces
emanate. This view of the constitution of bodies was
maintained and developed by Boscovich, and is hence termed
'Boscovich's Theory:' and the discussion of it will more
properly come under our review at a future period, when we
speak of the question whether bodies are made up of atoms.
But we may observe, that Newton himself appears to have
inclined, as his followers certainly did, to this mode of
contemplating the physical properties of bodies. In his
Preface to the _Principia_, after speaking of the central
forces which are exhibited in cosmical phenomena, he says:
'Would that we could derive the other phenomena of Nature
from mechanical principles by the same mode of reasoning.
For many things move me {277} so that I suspect all these
phenomena may depend upon certain forces, by which the
particles of bodies, through causes not yet known, are
either impelled to each other and cohere according to
regular figures, or are repelled and recede from each other:
which forces being unknown, philosophers have hitherto made
their attempts upon nature in vain.'

[Note 43\3: See Vince, _Observations on the Hypothesis
respecting Gravitation_, and the Critique of that work,
_Edinb. Rev._ vol. xiii.]

8. But both these hypotheses;--that by which cohesion and
solidity are reduced to attractive and repulsive forces, and
that by which attraction is reduced to the impulse and
pressure of media;--are hitherto merely modes of
representing mechanical laws of nature; and cannot, either
of them, be asserted as possessing any evident truth or
peremptory authority to the exclusion of the other. This
consideration may enable us to estimate the real weight of
the difficulty felt in assenting to the mutual attraction of
bodies not in contact with each other; for it is often urged
that this attraction of bodies at a distance is an absurd
supposition.

The doctrine is often thus stigmatized, both by popular and
by learned writers. It was long received as a maxim in
philosophy (as Monboddo informs us[44\3]), that a body
cannot act _where_ it is not, any more than _when_ it is
not. But to this we reply, that time is a necessary
condition of our conception of causation, in a different
manner from space. The action of force can only be conceived
as taking place in a succession of moments, in each of which
cause and effect immediately succeed each other: and thus
the interval of time between a cause and its remote effect
is filled up by a continuous succession of events connected
by the same chain of causation. But in space, there is no
such visible necessity of continuity; the action and
reaction may take place at a distance from each other; all
that is necessary being that they be equal and opposite.

[Note 44\3: _Ancient Metaphysics_, vol. ii. p. 175.]

Undoubtedly the existence of attraction is rendered more
acceptable to common apprehension by supposing {278} some
intermediate machinery,--a cord, or rod, or fluid,--by which
the forces may be conveyed from one point to another. But
such images are rather fitted to satisfy those prejudices
which arise from the earlier application of our ideas of
force, than to exhibit the real nature of those ideas. If we
suppose two bodies to pull each other by means of a rod or
cord, we only suppose, in addition to those equal and
opposite forces acting upon the two bodies, (which forces
are alone essential to mutual attraction) a certain power of
resisting transverse pressure at every point of the
intermediate line: which additional supposition is entirely
useless, and quite unconnected with the essential conditions
of the case. When the Newtonians were accused of introducing
into philosophy an unknown cause which they termed
_attraction_, they justly replied that they knew as much
respecting attraction as their opponents did about impulse.
In each case we have a knowledge of the conception in
question so far as we clearly apprehend it under the
conditions of those axioms of mechanical causation which
form the basis of our science on such subjects.

Having thus examined the degree of certainty and generality
to which our knowledge of the law of universal gravitation
has been carried, by the progress of mechanical discovery
and speculation up to the present time, we might proceed to
the other branches of science, and examine in like manner
their grounds and conditions. But before we do this, it will
be worth our while to attend for a moment to the effect
which the progress of mechanical ideas among mathematicians
and mechanical philosophers has produced upon the minds of
other persons, who share only in an indirect and derivative
manner in the influence of science.

{{279}}
CHAPTER X.

OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS.

1. WE have seen how the progress of knowledge upon the
subject of motion and force has produced, in the course of
the world's history, a great change in the minds of acute
and speculative men; so that such persons can now reason
with perfect steadiness and precision upon subjects on
which, at first, their thoughts were vague and confused; and
can apprehend, as truths of complete certainty and evidence,
laws which it required great labour and time to discover.
This _complete_ development and clear manifestation of
mechanical ideas has taken place only among mathematicians
and philosophers. But yet a progress of thought upon such
subjects,--an advance from the obscure to the clear, and
from errour to truth,--may be traced in the world at large,
and among those who have not directly cultivated the exact
sciences. This diffused and collateral influence of science
manifests itself, although in a wavering and fluctuating
manner, by various indications, at various periods of
literary history. The opinions and reasonings which are put
forth upon mechanical subjects, and above all, the adoption,
into common language, of terms and phrases belonging to the
prevalent mechanical systems, exhibit to us the most
profound discoveries and speculations of philosophers in
their effect upon more common and familiar trains of
thought. This effect is by no means unimportant, and we
shall point out some examples of such indications as we have
mentioned.

2. The discoveries of the ancients in speculative mechanics
were, as we have seen, very scanty; and {280} hardly
extended their influence to the unmathematical world. Yet
the familiar use of the term 'center of gravity' preserved
and suggested the most important part of what the Greeks had
to teach. The other phrases which they employed, as
_momentum_, _energy_, _virtue_, _force_, and the like, never
had any exact meaning, even among mathematicians; and
therefore never, in the ancient world, became the means of
suggesting just habits of thought. I have pointed out, in
the History of Science, several circumstances which appear
to denote the general confusion of ideas which prevailed
upon mechanical subjects during the times of the Roman
empire. I have there taken as one of the examples of this
confusion, the fable narrated by Pliny and others concerning
the echineïs, a small fish, which was said to stop a ship
merely by sticking to it[45\3]. This story was adduced as
betraying the absence of any steady apprehension of the
equality of action and reaction; since the fish, except it
had some immoveable obstacle to hold by, must be pulled
forward by the ship, as much as it pulled the ship backward.
If the writers who speak of this wonder had shown any
perception of the necessity of a reaction, either produced
by the rapid motion of the fish's fins in the water, or in
any other way, they would not be chargeable with this
confusion of thought; but from their expressions it is, I
think, evident that they saw no such necessity[46\3]. Their
idea of mechanical action was not sufficiently distinct to
enable them to see the absurdity of {281} supposing an
intense pressure with no obstacle for it to exert itself
against.

[Note 45\3: _Hist. Ind. Sc._ b. iv. c. i. sect. 2.]

[Note 46\3: See Prof. Powell, _On the Nature and Evidence of
the Laws of Motion_. _Reports of the Ashmolean Society_.
Oxford. 1837. Professor Powell has made an objection to my
use of this instance of confusion of thought; the remark in
the text seems to me to justify what I said in the History.
As an evidence that the fish was not supposed to produce its
effect by its muscular power acting on the water, we may
take what Pliny says, _Nat. Hist._ xxxii. 1, 'Domat mundi
rabiem, nullo suo labore; non retinendo, aut alio modo quam
adhærendo:' and also what he states in another place (ix.
41), that when it is preserved in pickle, it may be used in
recovering gold which has fallen into a deep well. All this
implies adhesion alone, with no conception of reaction.]

3. We may trace, in more modern times also, indications of a
general ignorance of mechanical truths. Thus the phrase of
shooting at an object 'point-blank,' implies the belief that
a cannon-ball describes a path of which the first portion is
a straight line. This errour was corrected by the true
mechanical principles which Galileo and his followers
brought to light; but these principles made their way to
popular notice, principally in consequence of their
application to the motions of the solar system, and to the
controversies which took place respecting those motions.
Thus by far the most powerful argument against the reception
of the Copernican system of the universe, was that of those
who asked, Why a stone dropt from a tower was not left
behind by the motion of the earth? The answer to this
question, now universally familiar, involves a reference to
the true doctrine of the composition of motions. Again;
Kepler's persevering and strenuous attempts[47\3] to frame a
physical theory of the universe were frustrated by his
ignorance of the first law of motion, which informs us that
a body will retain its velocity without any maintaining
force. He proceeded upon the supposition that the sun's
force was requisite to _keep up_ the motion of the planets,
as well as to deflect and modify it; and he was thus led to
a system which represented the sun as carrying round the
planets in their orbits by means of a _vortex_, produced by
his revolution. The same neglect of the laws of motion
presided in the formation of Descartes' system of vortices.
Although Descartes had enunciated in words the laws of
motion, he and his followers showed that they had not the
practical habit of referring to these mechanical principles;
and dared not trust the planets to move in free space
without some surrounding machinery to support them[48\3].

[Note 47\3: _Hist. Ind. Sc._ b. v. c. iv. and b. vii. c. i.]

[Note 48\3: I have, in the History, applied to Descartes the
character which Bacon gives to Aristotle, 'Audax simul et
pavidus:' though he was bold enough to enunciate the laws of
motion without knowing them aright, he had not the courage
to leave the planets to describe their orbits by the agency
of those laws, without the machinery of contact.]

{282} 4. When at last mathematicians, following Newton, had
ventured to consider the motion of each planet as a
mechanical problem not different in its nature from the
motion of a stone cast from the hand; and when the solution
of this problem and its immense consequences had become
matters of general notoriety and interest; the new views
introduced, as is usual, new terms, which soon became
extensively current. We meet with such phrases as 'flying
off in the tangent,' and 'deflexion from the tangent;' with
antitheses between 'centripetal' and 'centrifugal force,' or
between 'projectile' and 'central force.' 'Centers of
force,' 'disturbing forces,' 'perturbations,' and
'perturbations of higher orders,' are not unfrequently
spoken of: and the expression 'to gravitate,' and the term
'universal gravitation,' acquired a permanent place in the
language.

Yet for a long time, and even up to the present day, we find
many indications that false and confused apprehensions on
such subjects are by no means extirpated. Arguments are
urged against the mechanical system of the universe,
implying in the opponents an absence of all clear mechanical
notions. Many of this class of writers retrograde to
Kepler's point of view. This is, for example, the case with
Lord Monboddo, who, arguing on the assumption that force is
requisite to maintain, as well as to deflect motion,
produced a series of attacks upon the Newtonian philosophy;
which he inserted in his _Ancient Metaphysics_, published in
1779 and the succeeding years. This writer (like Kepler),
measures force by the velocity which the body _has_[49\3],
not by that which it _gains_. Such a use of language would
prevent our obtaining any laws of motion at all.
Accordingly, the author, in the very next page to that which
I have just quoted, abandons this measure of force, and, in
curvilinear motion, measures {283} force by 'the fall from
the extremity of the arc.' Again; in his objections to the
received theory, he denies that curvilinear motion is
compounded, although his own mode of considering such motion
assumes this composition in the only way in which it was
ever intended by mathematicians. Many more instances might
be adduced to show that a want of cultivation of the
mechanical ideas rendered this philosopher incapable of
judging of a mechanical system.

[Note 49\3: _Anc. Met._ vol. ii. b. v. c. vi. p. 413.]

The following extract from the _Ancient Metaphysics_, may be
sufficient to show the value of the author's criticism on
the subjects of which we are now speaking. His object is to
prove that there do not exist a centripetal and a
centrifugal force in the case of elliptical motion. 'Let any
man move in a circular or elliptical line described to him;
and he will find no tendency in himself either to the center
or from it, much less both. If indeed he attempt to make the
motion with great velocity, or if he do it carelessly and
inattentively, he may go out of the line, either towards the
center or from it: but this is to be ascribed, not to the
nature of the motion, but to our infirmity; or perhaps to
the animal form, which is more fitted for progressive motion
in a right line than for any kind of curvilinear motion. But
this is not the case with a sphere or spheroid, which is
equally adapted to motion in all directions[50\3].' We need
hardly remind the reader that the manner in which a man
running round a small circle, finds it necessary to lean
inwards, in order that there may be a centripetal
inclination to counteract the centrifugal force, is a
standard example of our mechanical doctrines; and this fact
(quite familiar in practice as well as theory) is in direct
contradiction of Lord Monboddo's assertion.

[Note 50\3: _Anc. Met._ vol. i. b. ii. c. 19, p. 264.]

5. A similar absence of distinct mechanical thought appears
in some of the most celebrated metaphysicians of Germany. I
have elsewhere noted[51\3] the opinion expressed by Hegel,
that the glory which belongs to {284} Kepler has been
unjustly transferred to Newton; and I have suggested, as the
explanation of this mode of thinking, that Hegel himself, in
the knowledge of mechanical truth, had not advanced beyond
Kepler's point of view. Persons who possess conceptions of
space and number, but who have not learnt to deal with ideas
of force and causation, may see more value in the
discoveries of Kepler than in those of Newton. Another
exemplification of this state of mind may be found in
Professor Schelling's speculations; for instance, in his
_Lectures on the Method of Academical Study_. In the twelfth
Lecture, on the study of Physics and Chemistry, he says, (p.
266,) 'What the mathematical natural philosophy has done for
the knowledge of the laws of the universe since the time
that they were discovered by his (Kepler's) godlike genius,
is, as is well known, this: it has attempted a construction
of those laws which, according to its foundations, is
altogether empirical. We may assume it as a general rule,
that in any proposed construction, that which is not a pure
general form cannot have any scientific import or truth. The
foundation from which the centrifugal motion of the bodies
of the world is derived, is no necessary form, it is an
empirical fact. The Newtonian attractive force, even if it
be a necessary assumption for a merely reflective view of
the subject, is still of no significance for the Reason,
which recognizes only absolute relations. The grounds of the
Keplerian laws can be derived, without any empirical
appendage, purely from the doctrine of Ideas, and of the two
Unities, which are in themselves one Unity, and in virtue of
which each being, while it is absolute in itself, is at the
same time in the absolute, and reciprocally.'

[Note 51\3: _Hist. Ind. Sc._ b. vii. c. ii. sect. 5.]

It will be observed, that in this passage our mechanical
laws are objected to because they are not necessary results
of our ideas; which, however, as we have seen, according to
the opinion of some eminent mechanical philosophers, they
are. But to assume this evident necessity as a condition of
every advance in science, is to mistake the last, perhaps
unattainable step, for the first, which lies before our
feet. And, {285} without inquiring further about 'the
Doctrine of the two Unities,' or the manner in which from
that doctrine we may deduce the Keplerian laws, we may be
well convinced that such a doctrine cannot supply any
sufficient reason to induce us to quit the inductive path by
which all scientific truth up to the present time has been
acquired.

6. But without going to schools of philosophy opposed to the
Inductive School, we may find many loose and vague habits of
thinking on mechanical subjects among the common classes of
readers and reasoners. And there are some familiar modes of
employing the phraseology of mechanical science, which are,
in a certain degree, chargeable with inaccuracy, and may
produce or perpetuate confusion. Among such cases we may
mention the way in which the centripetal and centrifugal
forces, and also the projectile and central forces of the
planets, are often compared or opposed. Such antitheses
sometimes proceed upon the false notion that the two members
of these pairs of forces are of the same kind: whereas on
the contrary the _projectile_ force is a hypothetical
impulsive force which may, at some former period, have
caused the motion to begin; while the _central_ force is an
actual force, which must act continuously and during the
whole time of the motion, in order that the motion may go on
in the curve. In the same manner the _centrifugal_ force is
not a distinct force in a strict sense, but only a certain
result of the first law of motion, measured by the portion
of _centripetal_ force which counteracts it. Comparisons of
quantities so heterogeneous imply confusion of thought, and
often suggest baseless speculations and imagined reforms of
the received opinions.

7. I might point out other terms and maxims, in addition to
those already mentioned, which, though formerly employed in
a loose and vague manner, are now accurately understood and
employed by all just thinkers; and thus secure and diffuse a
right understanding of mechanical truths. Such are
_momentum_, _inertia_, _quantity of matter_, _quantity of
motion_; that _force is proportional to its effects_; that
_action and_ {286} _reaction are equal_; that _what is
gained in force by machinery is lost in time_; that _the
quantity of motion in the world cannot be either increased
or diminished_. When the expression of the truth thus
becomes easy and simple, clear and convincing, the meanings
given to words and phrases by discoverers glide into the
habitual texture of men's reasonings, and the effect of the
establishment of true mechanical principles is felt far from
the school of the mechanician. If these terms and maxims are
understood with tolerable clearness, they carry the
influence of truth to those who have no direct access to its
sources. Many an extravagant project in practical machinery,
and many a wild hypothesis in speculative physics, has been
repressed by the general currency of such maxims as we have
just quoted.

8. Indeed so familiar and evident are the elementary truths
of mechanics when expressed in this simple form, that they
are received as truisms; and men are disposed to look back
with surprise and scorn at the speculations which were
carried on in neglect of them. The most superficial reasoner
of modern times thinks himself entitled to speak with
contempt and ridicule of Kepler's hypothesis concerning the
physical causes of the celestial motions: and gives himself
credit for intellectual superiority, because he sees, as
self-evident, what such a man could not discover at all. It
is well for such a person to recollect, that the real cause
of his superior insight is not the pre-eminence of his
faculties, but the successful labours of those who have
preceded him. The language which he has learnt to use
unconsciously, has been adapted to, and moulded on,
ascertained truths. When he talks familiarly of
"accelerating forces" and "deflexions from the tangent," he
is assuming that which Kepler did not know, and which it
cost Galileo and his disciples so much labour and thought to
establish. Language is often called an instrument of
thought; but it is also the nutriment of thought; or rather,
it is the atmosphere in which thought lives: a medium
essential to the activity of our speculative power, although
invisible {287} and imperceptible in its operation; and an
element modifying, by its qualities and changes, the growth
and complexion of the faculties which it feeds. In this way
the influence of preceding discoveries upon subsequent ones,
of the past upon the present, is most penetrating and
universal, though most subtle and difficult to trace. The
most familiar words and phrases are connected by
imperceptible ties with the reasonings and discoveries of
former men and distant times. Their knowledge is an
inseparable part of ours; the present generation inherits
and uses the scientific wealth of all the past. And this is
the fortune, not only of the great and rich in the
intellectual world: of those who have the key to the ancient
storehouses, and who have accumulated treasures of their
own;--but the humblest inquirer, while he puts his
reasonings into words, benefits by the labours of the
greatest discoverers. When he counts his little wealth, he
finds that he has in his hands coins which bear the image
and superscription of ancient and modern intellectual
dynasties; and that in virtue of this possession,
acquisitions are in his power, solid knowledge within his
reach, which none could ever have attained to, if it were
not that the gold of truth, once dug out of the mine,
circulates more and more widely among mankind.

9. Having so fully examined, in the preceding instances, the
nature of the progress of thought which science implies,
both among the peculiar cultivators of science, and in that
wider world of general culture which receives only an
indirect influence from scientific discoveries, we shall not
find it necessary to go into the same extent of detail with
regard to the other provinces of human knowledge. In the
case of the Mechanical Sciences, we have endeavoured to
show, not only that Ideas are requisite in order to form
into a science the Facts which nature offers to us, but that
we can advance, almost or quite, to a complete
identification of the Facts with the Ideas. In the sciences
to which we now proceed, we shall not seek to fill up the
chasm by which Facts and Ideas are separated; but we shall
endeavour to detect the Ideas which our {288} knowledge
involves, to show how essential these are; and in some
respects to trace the mode in which they have been gradually
developed among men.

10. The motions of the heavenly bodies, their laws, their
causes, are among the subjects of the first division of the
Mechanical Sciences; and of these sciences we formerly
sketched the history, and have now endeavoured to exhibit
the philosophy. If we were to take any other class of
motions, _their_ laws and causes might give rise to sciences
which would be mechanical sciences in exactly the same sense
in which Physical Astronomy is so. The phenomena of magnets,
of electrical bodies, of galvanical apparatus, seem to form
obvious materials for such sciences; and if they were so
treated, the philosophy of such branches of knowledge would
naturally come under our consideration at this point of our
progress.

But on looking more attentively at the sciences of
Electricity, Magnetism, and Galvanism, we discover cogent
reasons for transferring them to another part of our
arrangement; we find it advisable to associate them with
Chemistry, and to discuss their principles when we can
connect them with the principles of chemical science. For
though the first steps and narrower generalizations of these
sciences depend upon mechanical ideas, the highest laws and
widest generalizations which we can reach respecting them,
involve chemical relations. The progress of these portions
of knowledge is in some respects opposite to the progress of
Physical Astronomy. In this, we begin with phenomena which
appear to indicate peculiar and various qualities in the
bodies which we consider, (namely, the heavenly bodies,) and
we find in the end that all these qualities resolve
themselves into one common mechanical property, which exists
alike in all bodies and parts of bodies. On the contrary, in
studying magnetical and electrical laws, we appear at first
to have a single extensive phenomenon, attraction and
repulsion: but in our attempts to generalize this
phenomenon, we find that it is governed by conditions
depending upon something quite separate from the bodies
themselves, upon {289} the presence and distribution of
peculiar and transitory agencies; and, so far as we can
discover, the general laws of these agencies are of a
_chemical_ nature, and are brought into action by peculiar
properties of special substances. In cosmical phenomena,
everything, in proportion as it is referred to mechanical
principles, tends to simplicity,--to permanent uniform
forces,--to one common, positive, property. In magnetical
and electrical appearances, on the contrary, the application
of mechanical principles leads only to a new complexity,
which requires a new explanation; and this explanation
involves changeable and various forces,--gradations and
oppositions of qualities. The doctrine of the universal
gravitation of matter is a simple and ultimate truth, in
which the mind can acquiesce and repose. We rank gravity
among the mechanical attributes of matter, and we see no
necessity to derive it from any ulterior properties. Gravity
belongs to matter, independent of any conditions. But the
_conditions_ of magnetic or electrical activity require
investigation as much as the _laws_ of their action. Of
these conditions no mere mechanical explanation can be
given; we are compelled to take along with us chemical
properties and relations also: and thus magnetism,
electricity, galvanism, are _mechanico-chemical sciences_.

11. Before considering these, therefore, I shall treat of
what I shall call _Secondary Mechanical Sciences_; by which
expression I mean the sciences depending upon certain
qualities which our senses discover to us in
bodies;--_Optics_, which has visible phenomena for its
subject; _Acoustics_, the science of hearing; the doctrine
of _Heat_, a quality which our touch recognizes: to this
last science I shall take the liberty of sometimes giving
the name _Thermotics_, analogous to the names of the other
two. If our knowledge of the phenomena of Smell and Taste
had been successfully cultivated and systematized, the
present part of our work would be the place for the
philosophical discussion of those sensations as the subjects
of science.

The branches of knowledge thus grouped in one class involve
common Fundamental Ideas, from which {290} their principles
are derived in a mode analogous, at least in a certain
degree, to the mode in which the principles of the
mechanical sciences are derived from the fundamental ideas
of causation and reaction. We proceed now to consider these
Fundamental Ideas, their nature, development, and
consequences.

{{291}}
BOOK IV.

THE
PHILOSOPHY
OF THE
SECONDARY
MECHANICAL SCIENCES.

Πάσχοντος γάρ τι τοῦ αἰσθητικοῦ γίνεται τὸ ὁρᾶν· ὑπ' αὐτοῦ
μὲν οὖν τοῦ ὁρωμένου χρώματος ἀδύνατον· λείπεται δὴ ὑπὸ _τοῦ
μεταξύ_, ὥστ' ἀναγκαῖόν τι εἶναι _μεταξύ_· κενοῦ δὲ
γενομένου οὐχ ὅτι ἀκριβῶς, ἀλλ' ὅλως οὐθὲν ὀφθήσεται. δι' ἣν
μὲν οὖν αἰτίαν τὸ χρῶμα ἀναγκαῖον ἐν φωτὶ ὁρᾶσθαι, εἴρηται.
πῦρ δὲ ἐν ἀμφοῖν ὁρᾶται, καὶ ἐν σκότει καὶ ἐν φωτί, καὶ
τοῦτο _ἐξ ἀνάγκης_· τὸ γὰρ διαφανὲς ὑπὸ τούτου γίνεται
διαφανές. ὁ δ' αὐτὸς λόγος καὶ περὶ ψόφου καὶ ὀσμῆς ἐστιν·
οὐθὲν γὰρ αὐτῶν ἁπτόμενον τοῦ αἰσθητηρίου ποιεῖ τὴν
αἴσθησιν, ἀλλ' ὑπὸ μὲν ὀσμῆς καὶ ψόφου _τὸ μεταξὺ_ κινεῖται,
ὑπὸ δὲ τούτου τῶν αἰσθητηρίων ἑκάτερον· ὅταν δ' ἐπ' αὐτό τις
ἐπιθῇ τὸ αἰσθητήριον τὸ ψοφοῦν ἢ τὸ ὄζον, οὐδεμίαν αἴσθησιν
ποιήσει.

ARISTOT. _De Anima_, II. 7.

{{293}} BOOK IV.

THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.

CHAPTER I.

OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED.

1. _Of Primary and Secondary Qualities._--IN the same way in
which the mechanical sciences depend upon the Idea of Cause,
and have their principles regulated by the development of
that Idea, it will be found that the sciences which have for
their subject Sound, Light, and Heat, depend for _their_
principles upon the Fundamental Idea of Media by means of
which we perceive those qualities. Like the idea of cause,
this idea of a medium is unavoidably employed, more or less
distinctly, in the common, unscientific operations of the
understanding; and is recognized as an express principle in
the earliest speculative essays of man. But here also, as in
the case of the mechanical sciences, the development of the
idea, and the establishment of the scientific truths which
depend upon it, was the business of a succeeding period, and
was only executed by means of long and laborious researches,
conducted with a constant reference to experiment and
observation.

Among the most prominent manifestations of the influence of
the idea of a medium of which we have now to speak, is the
distinction of the qualities of bodies into _primary_, and
_secondary_ qualities. This distinction has {294} been
constantly spoken of in modern times: yet it has often been
a subject of discussion among metaphysicians whether there
be really such a distinction, and what the true difference
is. Locke states it thus[1\4]: Original or Primary qualities
of bodies are 'such as are utterly inseparable from the body
in what estate soever it may be,--such as sense constantly
finds in every particle of matter which has bulk enough to
be perceived, and the mind finds inseparable from every
particle of matter, though less than to make itself singly
perceived by our senses:' and he enumerates them as
solidity, extension, figure, motion or rest, and number.
Secondary qualities, on the other hand, are such 'which in
truth are nothing in the objects themselves, but powers to
produce various sensations in us by their primary qualities,
_i.e._ by the bulk, figure, texture, and motion of their
insensible parts, as colours, sounds, tastes, &c.'

[Note 1\4: _Essay_, b. ii. ch. viii. s. 9, 10.]

Dr. Reid[2\4], reconsidering this subject, puts the
difference in another way. There is, he says, a real
foundation for the distinction of Primary and Secondary
qualities, and it is this: 'That our senses give us a direct
and distinct notion of the primary qualities, and inform us
what they are in themselves; but of the secondary qualities,
our senses give us only a relative and obscure notion. They
inform us only that they are qualities that affect us in a
certain manner, that is, produce in us a certain sensation;
but as to what they are in themselves, our senses leave us
in the dark.'

[Note 2\4: _Essays_, b. ii. c. xvii.]

Dr. Brown[3\4] states the distinction somewhat otherwise. We
give the name of Matter, he observes, to that which has
extension and resistance: these, therefore, are Primary
qualities of matter, because they compose our definition of
it. All other qualities are Secondary, since they are
ascribed to bodies only because we find them associated with
the primary qualities which form our notion of those bodies.

[Note 3\4: _Lectures_, ii. 12.]

{295} It is not necessary to criticize very strictly these
various distinctions. If it were, it would be easy to find
objections to them. Thus Locke, it may be observed, does not
point out any _reason_ for believing that his secondary
qualities are produced by the primary. How are we to learn
that the colour of a rose arises from the bulk, figure,
texture, and motion of its particles? Certainly our senses
do not teach us this; and in what other way, on Locke's
principles, can we learn it? Reid's statement is not more
free from the same objection. How does it appear that our
notion of Warmth is relative to our own sensations more than
our notion of Solidity? And if we take Brown's account, we
may still ask whether our selection of certain qualities to
form our idea and definition of Matter be arbitrary and
without reason? If it be, how can it make a real
distinction? if it be not, what is the reason?

I do not press these objections, because I believe that any
of the above accounts of the distinction of Primary and
Secondary qualities is right in the main, however imperfect
it may be. The difference between such qualities as
Extension and Solidity on the one hand, and Colour or
Fragrance on the other, is assented to by all, with a
conviction so firm and indestructible, that there must be
some fundamental principle at the bottom of the belief,
however difficult it may be to clothe the principle in
words. That successive efforts to express the real nature of
the difference were made by men so clear-sighted and acute
as those whom I have quoted, even if none of them are
satisfactory, shows how strong and how deeply-seated is the
perception of truth which impels us to such attempts.

The most obvious mode of stating the difference of Primary
and Secondary qualities, as it naturally offers itself to
speculative minds, appears to be that employed by Locke,
slightly modified. Certain of the qualities of bodies, as
their bulk, figure, and motion, are perceived immediately in
the bodies themselves. Certain other qualities as sound,
colour, heat, are {296} perceived by means of some medium.
Our conviction that this is the case is spontaneous and
irresistible; and this difference of qualities immediately
and mediately perceived is the distinction of Primary and
Secondary qualities. We proceed further to examine this
conviction.

2. _The Idea of Externality._--In reasoning concerning the
Secondary Qualities of bodies, we are led to assume the
bodies to be external to us, and to be perceived by means of
some Medium intermediate between us and them. These
assumptions are fundamental conditions of perception,
inseparable from perception even in thought.

That objects are _external_ to us, that they are _without_
us, that they have _outness_, is as clear as it is that
these words have any meaning at all. This conviction is,
indeed, involved in the exercise of that faculty by which we
perceive all things as existing in space; for by this
faculty we place ourselves and other objects in one common
space, and thus they are exterior to us. It may be remarked
that this apprehension of objects as external to us,
although it assumes the idea of space, is far from being
implied in the idea of space. The objects which we
contemplate are considered as existing in space, and by that
means become invested with certain mutual relations of
position; but when we consider them as existing without
_us_, we make the additional step of supposing _ourselves_
and the objects to exist in one common space. The question
respecting the Ideal Theory of Berkeley has been mixed up
with the recognition of this condition of the externality of
objects. That philosopher maintained, as is well known, that
the perceptible qualities of bodies have no existence except
in a perceiving mind. This system has often been understood
as if he had imagined the world to be a kind of optical
illusion, like the images which we see when we shut our
eyes, appearing to be without us, though they are only in
our organs; and thus this Ideal System has been opposed to a
belief in an external world. In truth, however, no such
opposition exists. The Ideal System is an attempt to explain
the {297} mental process of perception, and to get over the
difficulty of mind being affected by matter. But the author
of that system did not deny that objects were perceived
under the conditions of space and mechanical
causation;--that they were _external_ and _material_ so far
as those words describe perceptible qualities. Berkeley's
system, however visionary or erroneous, did not prevent his
entertaining views as just, concerning optics or acoustics,
as if he had held any other doctrine of the nature of
perception.

But when Berkeley's theory was understood as a denial of the
existence of objects without us, how was it answered? If we
examine the answers which are given by Reid and other
philosophers to this hypothesis, it will be found that they
amount to this: that objects _are_ without us, since we
_perceive_ that they are so; that we perceive them to be
external, by the same act by which we perceive them to be
objects. And thus, in this stage of philosophical inquiry,
the externality of objects is recognized as one of the
inevitable conditions of our perception of them; and hence
the Idea of Externality is adopted as one of the necessary
foundations of all reasoning concerning all objects
whatever.

3. _Sensation by a Medium._--Objects, as we have just seen,
are necessarily apprehended as _without_ us; and in general,
as removed from us by a great or small distance. Yet they
affect our bodily senses; and this leads us irresistibly to
the conviction that they are perceived by means of something
intermediate. Vision, or hearing, or smell, or the warmth of
a fire, must be communicated to us by some Medium of
Sensation. This unavoidable belief appears in all attempts,
the earliest and the latest alike, to speculate upon such
subjects. Thus, for instance, Aristotle says[4\4], 'Seeing
takes place in virtue of some action which the sentient
organ suffers: now it cannot suffer action from the colour
of the object directly: the only remaining possible case
then is, that it is acted upon by an {298} intervening
Medium; there must then be an intervening Medium.' 'And the
same may be said,' he adds, 'concerning sounding and odorous
bodies; for these do not produce sensation by touching the
sentient organ, but the intervening Medium is acted on by
the sound or the smell, and the proper organ, by the Medium
... In sound the Medium is air; in smell we have no name for
it.' In the sense of taste, the necessity of a Medium is not
at first so obviously seen, because the object tasted is
brought into contact with the organ; but a little attention
convinces us that the taste of a solid body can only be
perceived when it is conveyed in some liquid vehicle. Till
the fruit is crushed, and till its juices are pressed out,
we do not distinguish its flavour. In the case of heat, it
is still more clear that we are compelled to suppose some
invisible fluid, or other means of communication, between
the distant body which warms us and ourselves.

[Note 4\4: Περὶ Ψυχῆς. ii. 7. See the motto to this Book.]

It may appear to some persons that the assumption of an
intermedium between the object perceived and the sentient
organ results from the principles which form the basis of
our mechanical reasonings,--that every change must have a
cause, and that bodies can act upon each other only by
contact. It cannot be denied that this principle does offer
itself very naturally as the ground of our belief in media
of sensation; and it appears to be referred to for this
purpose by Aristotle in the passage quoted above. But yet we
cannot but ask, Does the principle, that matter produces its
effect by contact only, manifestly apply here? When we so
apply it, we include _sensation_ among the _effects_ which
material contact produces;--a case so different from any
merely mechanical effect, that the principle, so employed,
appears to acquire a new signification. May we not, then,
rather say that we have here a new axiom,--That sensation
implies a material cause immediately acting on the
organ,--than a new application of our former
proposition,--That all mechanical change implies contact?

The solution of this doubt is not of any material
consequence to our reasonings; for whatever be the {299}
ground of the assumption, it is certain that we do assume
the existence of media by which the sensations of sight,
hearing, and the like, are produced; and it will be seen
shortly that principles inseparably connected with this
assumption are the basis of the sciences now before us.

This assumption makes its appearance in the physical
doctrines of all the schools of philosophy. It is exhibited
perhaps most prominently in the tenets of the Epicureans,
who were materialists, and extended to all kinds of
causation the axiom of the existence of a corporeal
mechanism by which alone the effect is produced. Thus,
according to them, vision is produced by certain images or
material films which flow from the object, strike upon the
eyes, and so become sensible. This opinion is urged with
great detail and earnestness by Lucretius, the poetical
expositor of the Epicurean creed among the Romans. His
fundamental conviction of the necessity of a material medium
is obviously the basis of his reasoning, though he attempts
to show the existence of such a medium by facts. Thus he
argues[5\4], that by shouting loud we make the throat sore;
which shows, he says, that the voice must be material, so
that it can hurt the passage in coming out.
Haud igitur dubium est quin voces verbaque constent
Corporeis e principiis ut lædere possint.

[Note 5\4: _De Rerum Naturâ_, Lib. iv. 529.]

4. _The Process of Perception of Secondary Qualities._--The
likenesses or representatives of objects by which they
affect our senses were called by some writers _species_, or
_sensible species_, a term which continued in use till the
revival of science. It may be observed that the conception
of these _species_ as films cast off from the object, and
retaining its shape, was different, as we have seen, from
the view which Aristotle took, though it has sometimes been
called the Peripatetic doctrine[6\4]. We may add that the
expression was latterly applied to express the supposition
of an emanation of any kind, and implied little {300} more
than that supposition of a Medium of which we are now
speaking. Thus Bacon, after reviewing the phenomena of
sound, says[7\4], 'Videntur motus soni fieri per _species
spirituales_: ita enim loquendum donec certius quippiam
inveniatur.'

[Note 6\4: Brown, vol. ii. p. 98.]

[Note 7\4: _Hist. Son. et Aud._ vol. ix. p. 87.]

Though the fundamental principles of several sciences depend
upon the assumption of a Medium of Perception, these
principles do not at all depend upon any special view of the
Process of our perceptions. The mechanism of that process is
a curious subject of consideration; but it belongs to
physiology, more properly than either to metaphysics, or to
those branches of physics of which we are now speaking. The
general nature of the process is the same for all the
senses. The object affects the appropriate intermedium; the
medium, through the proper organ, the eye, the ear, the
nose, affects the nerves of the particular sense; and, by
these, in some way, the sensation is conveyed to the mind,
But to treat the _impression_ upon the nerves as the _act_
of sensation which we have to consider, would be to mistake
our object, which is not the constitution of the human body,
but of the human mind. It would be to mistake one link of
the chain for the power which holds the end of the chain. No
anatomical analysis of the corporeal conditions of vision,
or hearing, or feeling warm, is necessary to the sciences of
Optics, or Acoustics, or Thermotics.

Not only is this physiological research an extraneous part
of our subject, but a partial pursuit of such a research may
mislead the inquirer. We perceive objects _by means of_
certain media, and _by means of_ certain impressions on the
nerves: but we cannot with propriety say that we perceive
either the media or the impressions on the nerves. What
person in the act of seeing is conscious of the little
coloured spaces on the retina? or of the motions of the
bones of the auditory apparatus whilst he is hearing?
Surely, no one. This may appear obvious enough, and yet a
writer of no common acuteness, Dr. Brown, has put forth
several {301} very strange opinions, all resting upon the
doctrine that the coloured spaces on the retina are the
_objects_ which we perceive; and there are some supposed
difficulties and paradoxes on the same subject which have
become quite celebrated (as upright vision with inverted
images), arising from the same confusion of thought.

As the consideration of the difficulties which have arisen
respecting the Philosophy of Perception may serve still
further to illustrate the principles on which we necessarily
reason respecting the secondary qualities of bodies, I shall
here devote a few pages to that subject.

{{302}}
CHAPTER II.

ON PECULIARITIES IN THE PERCEPTIONS OF THE DIFFERENT SENSES.

1. WE cannot doubt that we perceive all secondary qualities
by means of immediate impressions made, through the proper
medium of sensation, upon our organs. Hence all the senses
are sometimes vaguely spoken of as modifications of the
sense of feeling. It will, however, be seen, on reflection,
that this mode of speaking identifies in words things which
in our conceptions have nothing in common. No impression on
the organs of touch can be conceived as having any
resemblance to colour or smell. No effort, no ingenuity, can
enable us to describe the impressions of one sense in terms
borrowed from another.

The senses have, however, each its peculiar powers, and
these powers may be in some respects compared, so as to show
their leading resemblances and differences, and the
characteristic privileges and laws of each. This is what we
shall do as briefly as possible.

SECT. I.--_Prerogatives of Sight._

THE sight distinguishes colours, as the hearing
distinguishes tones; the sight estimates degrees of
brightness, the ear, degrees of loudness; but with several
resemblances, there are most remarkable differences between
these two senses.

2. _Position._--The sight has this peculiar prerogative,
that it apprehends the _place_ of its objects directly and
primarily. We see _where_ an object is at the same instant
that we see what it is. If we see two objects, we see their
relative position. We cannot help {303} perceiving that one
is above or below, to the right or to the left of the other,
if we perceive them at all.

There is nothing corresponding to this in sound. When we
hear a noise, we do not necessarily assign a place to it. It
may easily happen that we cannot tell from which side a
thunder-clap comes. And though we often can judge in what
direction a voice is heard, this is a matter of secondary
impression, and of inference from concomitant circumstances,
not a primary fact of sensation. The judgments which we form
concerning the position of sounding bodies are obtained by
the conscious or unconscious comparison of the impressions
made on the two ears, and on the bones of the head in
general; they are not inseparable conditions of hearing. We
may hear sounds, and be uncertain whether they are 'above,
around, or underneath!' but the moment anything visible
appears, however unexpected, we can say, 'see _where_ it
comes!'

Since we can see the relative position of things, we can see
_figure_, which is but the relative position of the
different parts of the boundary of the object. And thus the
whole visible world exhibits to us a scene of various
shapes, coloured and shaded according to their form and
position, but each having relations of position to all the
rest; and altogether, entirely filling up the whole range
which the eye can command.

3. _Distance._--The distance of objects from us is no matter
of immediate perception, but is a judgment and inference
formed from our sensations, in something of the same way as
our judgment of position by the ear, though more precise.
That this is so, was most distinctly shown by Berkeley, in
his _New Theory of Vision_. The elements on which we form
our judgment are, the effort by which we fix both eyes on
the same object, the effort by which we adjust each eye to
distinct vision, and the known forms, colours, and parts of
objects, as compared with their appearance. The right
interpretation of the information which these circumstances
give us respecting the true distances and forms of things,
is gradually learnt by experience, the lesson being begun in
our earliest infancy, and inculcated upon us every hour
during which we {304} use our eyes. The completeness with
which the lesson is learnt is truly admirable; for we forget
that our conclusion is obtained indirectly, and mistake a
judgment on evidence for an intuitive perception. This,
however, is not more surprizing than the rapidity and
unconsciousness of effort with which we understand the
meaning of the speech that we hear, or the book that we
read. In both cases, the habit of interpretation is become
as familiar as the act of perception. And this is the case
with regard to vision. We see the breadth of the street as
clearly and readily as we see the house on the other side of
it. We see the house to be square, however obliquely it be
presented to us. Indeed the difficulty is, to recover the
consciousness of our real and original sensations;--to
discover what is the _apparent_ relation of the lines which
appear before us. As we have already said, (book ii. chap.
6) in the common process of vision we suppose ourselves to
see that which cannot be seen; and when we would make a
picture of an object, the difficulty is to represent what is
visible and no more.

But perfect as is our habit of interpreting what we
perceive, we could not interpret if we did not perceive. If
the eye did not apprehend visible position, it could not
infer actual position, which is collected from visible
position as a consequence: if we did not see apparent
figure, we could not arrive at any opinion concerning real
form. The perception of place, which is the prerogative of
the eye, is the basis of all its other superiority.

The precision with which the eye can judge of apparent
position is remarkable. If we had before us two stars
distant from each other by one-twentieth of the moon's
diameter, we could easily decide the apparent direction of
the one from the other, as above or below, to the right or
left. Yet eight millions of stars might be placed in the
visible hemisphere of the sky at such distances from each
other; and thus the eye would recognize the relative
position in a portion of its range not greater than one
eight-millionth of the whole. Such is the accuracy of the
sense of vision in this {305} respect; and, indeed, we might
with truth have stated it much higher. Our judgment of the
position of distant objects in a landscape depends upon
features far more minute than the magnitude we have here
described.

As our object is to point out principally the differences of
the senses, we do not dwell upon the delicacy with which we
distinguish tints and shades, but proceed to another sense.

SECT. II.--_Prerogatives of Hearing._

THE sense of hearing has two remarkable prerogatives; it can
perceive a definite and peculiar relation between certain
tones, and it can clearly perceive two tones together; in
both these circumstances it is distinguished from vision,
and from the other senses.

4. _Musical intervals._--We perceive that two tones have, or
have not, certain definite relations to each other, which we
call _Concords_: one sound is a _Fifth_, an _Octave_, &c.,
above the other. And when this is the case, our perception
of the relation is extremely precise. It is easy to perceive
when a fifth is out of tune by one-twentieth of a tone; that
is, by one-seventieth of itself. To this there is nothing
analogous in vision. Colours have certain vague relations to
one another; they look well together, by contrast or by
resemblance; but this is an indefinite, and in most cases a
casual and variable feeling. The relation of _complementary_
colours to one another, as of red to green, is somewhat more
definite; but still, has nothing of the exactness and
peculiarity which belongs to a musical concord. In the case
of the two sounds, there is an exact point at which the
relation obtains; when by altering one note we pass this
point, the concord does not gradually fade away, but
instantly becomes a discord; and if we go further still, we
obtain another concord of quite a different character.

We learn from the theory of sound that concords occur when
the times of vibration of the notes have exact simple
ratios; an octave has these times as 1 to {306} 2; a fifth,
as 2 to 3. According to the undulatory theory of light, such
ratios occur in colours, yet the eye is not affected by them
in any peculiar way. The times of the undulations of certain
red and certain violet rays are as 2 to 3, but we do not
perceive any peculiar harmony or connexion between those
colours.

5. _Chords._--Again, the ear has this prerogative, that it
can apprehend two notes together, yet distinct. If two
notes, distant by a fifth from each other, are sounded on
two wind instruments, both they and their musical relation
are clearly perceived. There is not a mixture, but a
concord, a musical interval. In colours, the case is
otherwise. If blue and yellow fall on the same spot, they
form green; the colour is simple to the eye; it can no more
be decomposed by the vision than if it were the simple green
of the prismatic spectrum: it is impossible for us, by
sight, to tell whether it is so or not.

These are very remarkable differences of the two senses: two
colours can be compounded into an apparently simple one; two
sounds cannot: colours pass into each other by gradations
and intermediate tints; sounds pass from one concord to
another by no gradations: the most intolerable discord is
that which is near a concord. We shall hereafter see how
these differences affect the _scales_ of sound and of
colour.

6. _Rhythm._--We might remark, that as we see objects in
_space_, we hear sounds in _time_; and that we thus
introduce an arrangement among sounds which has several
analogies with the arrangement of objects in space. But the
conception of time does not seem to be peculiarly connected
with the sense of hearing; a faculty of apprehending tone
and time, or in musical phraseology _tune_ and _rhythm_, are
certainly very distinct. I shall not, therefore, here dwell
upon such analogies.

The other Senses have not any peculiar prerogatives, at
least none which bear on the formation of science. I may,
however, notice, in the feeling of heat, this circumstance;
that it presents us with two opposites, heat and cold, which
graduate into each other. This {307} is not quite peculiar,
for vision also exhibits to us white and black, which are
clearly opposites, and which pass into each other by the
shades of gray.

SECT. III.--_The Paradoxes of Vision._

7. _First Paradox of Vision. Upright Vision._--All our
senses appear to have this in common; That they act by means
of organs, in which a bundle of nerves receives the
impression of the appropriate medium of the sense. In the
construction of these organs there are great differences and
peculiarities, corresponding, in part at least, to the
differences in the information given. Moreover, in some
cases, as we have noted in the case of audible position and
visible distance, that which seems to be a perception is
really a judgment founded on perceptions of which we are not
directly aware. It will be seen, therefore, that with
respect to the peculiar powers of each sense, it may be
asked;--whether they can be explained by the construction of
the peculiar organ;--whether they are acquired judgments and
not direct perceptions;--or whether they are inexplicable in
either of these ways, and cannot, at present at least, be
resolved into anything but conditions of the intellectual
act of perception.

Two of these questions with regard to vision, have been much
discussed by psychological writers: the cause of our seeing
objects upright by inverted images on the retina; and of our
seeing single with two such images.

Physiologists have very completely explained the exquisitely
beautiful mechanism of the eye, considered as analogous to
an optical instrument; and it is indisputable that by means
of certain transparent lenses and humours, an inverted image
of the objects which are looked at is formed upon the
_retina_, or fine net-work of nerve, with which the back of
the eye is lined. We cannot doubt that the impression thus
produced on these nerves is essential to the act of vision;
and so far as we consider the nerves {308} themselves to
feel or perceive by contact, we may say that they perceive
this image, or the affections of light which it indicates.
But we cannot with any propriety say that _we_ perceive, or
that our mind perceives, this image; for we are not
conscious of it, and none but anatomists are aware of its
existence: we perceive _by means_ of it.

A difficulty has been raised, and dwelt upon in a most
unaccountable manner, arising from the neglect of this
obvious distinction. It has been asked, how is it that we
see an object, a man for instance, upright, when the
immediate object of our sensation, the image of the man on
our retina, is inverted? To this we must answer, that we see
him upright _because_ the image is inverted; that the
inverted image is the necessary means of seeing an upright
object. This is granted, and where then is the difficulty?
Perhaps it may be put thus: How is it that we do not judge
the man to be inverted, since the sensible image is so? To
this we may reply, that we have no notion of _upright_ or
inverted, except that which is founded on experience, and
that all our experience, without exception, must have taught
us that such a sensible image belongs to a man who is in an
upright position. Indeed, the contrary judgment is not
conceivable; a man is upright whose head is upwards and his
feet downwards. But what are the sensible images of
_upwards_ and _downwards_? Whatever be our standard of up
and down, the sensible representation of _up_ will be an
image moving on the retina towards the lower side, and the
sensible representation of _down_ will be a motion towards
the upper side. The head of the man's image is towards the
image of the sky, its feet are towards the image of the
ground; how then should it appear otherwise than upright? Do
we expect that the whole world should appear inverted? Be it
so: but if the whole be inverted, how is the relation of the
parts altered? Do we expect that we should think our own
persons in particular? This cannot be, for we look at them
as we do at other objects. Do we expect that things should
appear to fall {309} upwards? Surely not. For what do we
know of upwards, except that it is the direction in which
bodies do _not_ fall? In short, the whole of this
difficulty, though it has in no small degree embarrassed
metaphysicians, appears to result from a very palpable
confusion of ideas; from an attempt at comparison of what
_we_ see, with that which the retina feels, as if they were
separately presentable. It is a sufficient explanation to
say, that we do not see the image on the retina, but see by
_means_ of it. The perplexity does not require much more
skill to disentangle, than it does to see that a word
written in _black_ ink, may signify _white_[8\4].

[Note 8\4: The explanation of our seeing objects erect when
the image is inverted has been put very simply, by saying,
'We _call_ that the _lower_ end of an object which is next
the ground.' The observer cannot look into his own eye; he
knows _by experience_ what kind of image corresponds to a
man in an upright position. The anatomist tells him that
this image is _inverted_: but this does not disturb the
process of judging by experience. It does not appear why any
one should be perplexed at the notion of seeing objects
erect by means of inverted images, rather than at the notion
of seeing objects large by means of small images; or cubical
and pyramidal, by means of images on a spherical surface; or
green and red, by means of images on a black surface. Indeed
some persons have contrived to perplex themselves with these
latter questions, as well as the first.

The above explanation is not at all affected, as to its
substance, if we adopt Sir David Brewster's expression, and
say that the _line of visible direction_ is a line passing
through the center of the spherical surface of the retina,
and therefore of course perpendicular to the surface. In
speaking of 'the inverted image,' it has always been
supposed to be determined by such lines; and though the
point where they intersect may not have been ascertained
with exactness by previous physiologists, the philosophical
view of the matter was not in any degree vitiated by this
imperfection.]

8. _Second Paradox of Vision. Single Vision._--(1.) _Small
or Distant Objects._--The other difficulty, why with two
images on the retina we see only one object, is of a much
more real and important kind. This effect is manifestly
limited by certain circumstances of a very precise nature;
for if we direct our eyes at an object which is very near
the eye, we see {310} all other objects double. The fact is
not, therefore, that we are incapable of receiving two
impressions from the two images, but that, under certain
conditions, the two impressions form one. A little attention
shows us that these conditions are, that with both eyes we
should look at the same object; and again, we find that to
look at an object with either eye, is to direct the eye so
that the image falls on or near a particular point about the
middle of the retina. Thus these middle points in the two
retinas correspond, and we see an image single when the two
images fall on the corresponding points.

Again, as each eye judges of position, and as the two eyes
judge similarly, an object will be seen in the same place by
one eye and by the other, when the two images which it
produces are _similarly situated_ with regard to the
_corresponding points_ of the retina[9\4].

[Note 9\4: The explanation of single vision with two eyes
may be put in another form. Each eye judges immediately of
the relative position of all objects within the field of its
direct vision. Therefore when we look with both eyes at a
_distant_ prospect (so distant that the distance between the
eyes is small in comparison) the two prospects, being
similar collections of forms, will coincide altogether, if a
corresponding point in one and in the other coincide. If
this be the case, the two images of every object will fall
upon corresponding points of the retina, and will appear
single.

If the two prospects seen by the two eyes do not exactly
coincide, in consequence of nearness of the objects, or
distortion of the eyes, but if they nearly coincide, the
stronger image of an object absorbs the weaker, and the
object is seen single; yet modified by the combination, as
will be seen when we speak of the single vision of near
objects. When the two images of an object are considerably
apart, we see it double.

This explanation is not different in substance from the one
given in the text; but perhaps it is better to avoid the
assertion that the law of corresponding points is 'a
distinct and original principle of our constitution,' as I
had stated in the first edition. The simpler mode of stating
the law of our constitution appears to be to say, that each
eye determines similarly the position of objects; and that
when the positions of an object, as seen by the two eyes,
coincide (or nearly coincide) the object is seen single.]

This is the Law of Single Vision, at least so far as regards
small objects; namely, objects so small that in
contemplating them we consider their position only, {311}
and not their solid dimensions. Single vision in such cases
is a result of the law of vision simply: and it is a mistake
to call in, as some have done, the influence of habit and of
acquired judgments, in order to determine the result in such
cases.

To ascribe the apparent singleness of objects to the
impressions of vision corrected by the experience of
touch[10\4], would be to assert that a person who had not
been in the habit of handling what he saw, would see all
objects double; and also, to assert that a person beginning
with the double world which vision thus offers to him,
would, by the continued habit of handling objects, gradually
and at last learn to see them single. But all the facts of
the case show such suppositions to be utterly fantastical.
No one can, in this case, go back from the habitual judgment
of the singleness of objects, to the original and direct
perception of their doubleness, as the draughtsman goes back
from judgments to perception, in representing solid
distances and forms by means of perspective pictures. No one
can point out any case in which the habit is imperfectly
formed; even children of the most tender age look at an
object with both eyes, and see it as one.

[Note 10\4: See Brown, vol. ii. p. 81.]

In cases when the eyes are distorted (in squinting), one eye
only is used, or if both are employed, there is double
vision; and thus any derangement of the correspondence of
motion in the two eyes will produce double-sightedness.

Brown is one of those[11\4] who assert that two images
suggest a single object because we have _always found_ two
images to belong to a single object. He urges as an
illustration, that the _two_ words 'he conquered,' by custom
excite exactly the same notion as the _one_ Latin word
'vicit;' and thus that two visual images, by the effect of
habit, produce the same belief of a single object as one
tactual impression. But in order to make this pretended
illustration of any value, it ought to be true that when a
person has thoroughly learnt the Latin language, he can no
longer distinguish {312} any separate meaning in 'he' and in
'conquered.' We can by no effort perceive the double
sensation, when we look _at_ the object with the two eyes.
Those who squint, learn by habit to see objects single: but
the habit which they acquire is that of attending to the
impressions of one eye only at once, not of combining the
two impressions. It is obvious, that if each eye spreads
before us the same visible scene, with the same objects and
the same relations of place, then, if one object in each
scene coincide, the whole of the two visible impressions
will be coincident. And here the remarkable circumstance is,
that not only each eye judges for itself of the relations of
position which come within its field of view; but that there
is a superior and more comprehensive faculty which combines
and compares the two fields of view; which asserts or denies
their coincidence; which contemplates, as in a relative
position to one another, these two visible worlds, in which
all other relative position is given. This power of
confronting two sets of visible images and figured spaces
before a purely intellectual tribunal, is one of the most
remarkable circumstances in the sense of vision.

[Note 11\4: _Lectures_, vol. ii. p. 81.]

9. (2.) _Near Objects._--We have hitherto spoken of the
singleness of objects whose images occupy corresponding
positions on the retina of the two eyes. But here occurs a
difficulty. If an object of moderate size, a small thick
book for example, be held at a little distance from the
eyes, it produces an image on the retina of each eye; and
these two images are perspective representations of the book
from different points of view, (the positions of the two
eyes,) and are therefore of different forms. Hence the two
images cannot occupy corresponding points of the retina
throughout their whole extent. If the central parts of the
two images occupy corresponding points, the boundaries of
the two wall not correspond. How is it then consistent with
the law above stated that in this case the object appears
single?

It may be observed, that the two images in such a case will
differ most widely when the object is not a {313} mere
surface, but a solid. If a book, for example, be held with
one of its upright edges towards the face, the right eye
will see one side more directly than the left eye, and the
left eye will see another side more directly, and the
outline of the two images upon the two retinas will exhibit
this difference. And it may be further observed, that this
difference in the images received by the two eyes, is a
plain and demonstrative evidence of the solidity of the
object seen; since nothing but a solid object could (without
some special contrivance) produce these different forms of
the images in the two eyes.

Hence the absence of exact coincidence in the two images on
the retina is the necessary condition of the solidity of the
object seen, and must be one of the indications by means of
which our vision apprehends an object as solid. And that
this is so, Mr. Wheatstone has proved experimentally, by
means of some most ingenious and striking contrivances. He
has devised[12\4] an instrument (the _stereoscope_) by which
two images (drawn in outline) differing exactly as much as
the two images of a solid body seen near the face would
differ, are conveyed, one to one eye, and the other to the
other. And it is found that when this is effected, the
object which the images represent is not only seen single,
but is apprehended as solid with a clearness and reality of
conviction quite distinct from any impression which a mere
perspective representation can give.

[Note 12\4: _Phil. Trans._ 1839.]

At the same time it is found that the object is then only
apprehended as single when the two images are such as are
capable of being excited by one single object placed in
solid space, and seen by the two eyes. If the images differ
more or otherwise than this condition allows, the result is,
that both are seen, their lines crossing and interfering
with one another.

It may be observed, too, that if an object be of such large
size as not to be taken in by a single glance of the eyes,
it is no longer apprehended as single by a direct act of
perception; but its parts are looked at {314} separately and
successively, and the impressions thus obtained are put
together by a succeeding act of the mind. Hence the objects
which are directly seen as solid, will be of moderate size;
in which case it is not difficult to show that the outlines
of the two images will differ from each other only slightly.

Hence we are led to the following, as the Law of Single
Vision for _near_ objects:--When the two images in the two
eyes are situated (part for part) nearly, but not exactly,
upon corresponding points, the object is apprehended as
single, if the two images are such as are or would be given
by a single solid object seen by the two eyes separately:
and in this case the object is necessarily apprehended as solid.

This law of vision does not contradict that stated above for
distant objects: for when an object is removed to a
considerable distance, the images in the two eyes coincide
exactly, and the object is seen as single, though without
any direct apprehension of its solidity. The first law is a
special case of the second. Under the condition of _exactly_
corresponding points, we have the perception of singleness,
but no evidence of solidity. Under the condition of _nearly_
corresponding points, we may have the perception of
singleness, and with it, of solidity.

We have before noted it as an important feature in our
visual perception, that while we have two distinct
impressions upon the sense, which we can contemplate
separately and alternately, (the impressions on the two
eyes,) we have a higher perceptive faculty which can
recognize these two impressions, exactly similar to each
other, as only two images of one and the same assemblage of
objects. But we now see that the faculty by which we
perceive visible objects can do much more than this:--it can
not only unite two impressions, and recognize them as
belonging to one object in virtue of their coincidence, but
it can also unite and identify them, even when they do not
exactly coincide. It can correct and adjust their small
difference, so that they are both apprehended as
representations of the same figure. It can infer from them a
real form, not {315} agreeing with either of them; and a
solid space, which they are quite incapable of exemplifying.
The visual faculty decides whether or not the two ocular
images can be pictures of the same solid object, and if they
can, it undoubtingly and necessarily accepts them as being
so. This faculty operates as if it had the power of calling
before it all possible solid figures, and of ascertaining by
trial whether any of those will, at the same time, fit both
the outlines which are given by the sense. It assumes the
reality of solid space, and, if it be possible, reconciles
the appearances with that reality. And thus an activity of
the mind of a very remarkable and peculiar kind is exercised
in the most common act of seeing.

10. It may be said that this doctrine, of such a visual
faculty as has been described, is very vague and obscure,
since we are not told what are its limits. It adjusts and
corrects figures which _nearly_ coincide, so as to identify
them. But _how_ nearly, it may be asked, must the figures
approach each other, in order that this adjustment may be
possible? What discrepance renders impossible the
reconcilement of which we speak? Is it not impossible to
give a definite answer to these questions, and therefore
impossible to lay down definitely such laws of vision as we
have stated? To this I reply, that the indefiniteness thus
objected to us, is no new difficulty, but one with which
philosophers are familiar, and to which they are already
reconciled. It is, in fact, no other than the indefiniteness
of the limits of distinct vision. How near to the face must
an object be brought, so that we shall cease to see it
distinctly? The distance, it will be answered, is
indefinite: it is different for different persons; and for
the same person, it varies with the degree of effort,
attention, and habit. But this indefiniteness is only the
indefiniteness, in another form, of the deviation of the two
ocular images from one another: and in reply to the question
concerning them we must still say, as before, that in
doubtful cases, the power of apprehending an object as
single, when this _can_ be done, will vary with effort,
attention, and habit. The assumption {316} that the apparent
object exists as a real figure, in real space, is to be
verified, if possible; but, in extreme cases, from the
unfitness of the point of view, or from any other cause of
visual confusion or deception, the existence of a real
object corresponding to the appearance may be doubtful; as
in any other kind of perception it may be doubtful whether
our senses, under disadvantageous circumstances, give us
true information. The vagueness of the limits, then, within
which this visual faculty can be successfully exercised, is
no valid argument against the existence of the faculty, or
the truth of the law which we have stated concerning its
action.

SECT. IV.--_The Perception of Visible Figure._

11. _Visible Figure._--There is one tenet on the subject of
vision which appears to me so extravagant and
unphilosophical, that I should not have thought it necessary
to notice it, if it had not been recently promulgated by a
writer of great acuteness in a book which has obtained, for
a metaphysical work, considerable circulation. I speak of
Brown's opinion[13\4] that we have no immediate perception
of visible figure. I confess myself unable to comprehend
fully the doctrine which he would substitute in the place of
the one commonly received. He states it thus[14\4]: 'When
the simple affection of sight is blended with the ideas of
suggestion [those arising from touch, &c.] in what are
termed the acquired perceptions of vision, as, for example,
in the perception of a sphere, it is colour only which is
blended with the large convexity, and not a small coloured
plane.' The doctrine which Brown asserts in this and similar
passages, appears to be, that we do not by vision perceive
_both_ colour and _figure_; but that the colour which we see
is blended with the figure which we learn the existence of
by other means, as by touch. But if this were possible when
we can call in other perceptions, how is it possible when we
cannot or do not touch the object? {317} Why does the moon
appear round, gibbous, or horned? What sense besides vision
suggests to us the idea of her figure? And even in objects
which we can reach, what is that circumstance in the sense
of vision which suggests to us that the colour belongs to
the sphere, except that we see the colour where we see the
sphere? If we do not see figure, we do not see position; for
figure is the relative position of the parts of a boundary.
If we do not see position, why do we ascribe the yellow
colour to the sphere on our left, rather than to the cube on
our right? We _associate_ the colour with the object, says
Dr. Brown; but if his opinion were true, we could not
associate two colours with two objects, for we could not
apprehend the colours as occupying two different places.

[Note 13\4: _Lectures_, vol. ii. p. 82.]

[Note 14\4: _Ib._ vol. ii. p. 90.]

The whole of Brown's reasoning on this subject is so
irreconcilable with the first facts of vision, that it is
difficult to conceive how it could proceed from a person who
has reasoned with great acuteness concerning touch. In order
to prove his assertion, he undertakes to examine the only
reasons which, he says[15\4], he can imagine for believing
the immediate perception of visible figure: (1) That it is
absolutely impossible, in our present sensations of sight,
to separate colour from extension; and (2) That there are,
in fact, figures on the retina corresponding to the apparent
figures of objects.

[Note 15\4: _Lectures_, vol. ii. p. 83.]

On the subject of the first reason, he says, that the figure
which we perceive as associated with colour, is the real,
and not the apparent figure. 'Is there,' he asks, 'the
slightest consciousness of a perception of visible figure,
corresponding to the affected portion of the retina?' To
which, though he seems to think an affirmative answer
impossible, we cannot hesitate to reply, that there is
undoubtedly such a consciousness; that though obscured by
being made the ground of habitual inference as to the real
figure, this consciousness is constantly referred to by the
draughtsman, and easily recalled by any one. We may separate
colour, he says {318} again[16\4], from the figures on the
retina, as we may separate it from length, breadth, and
thickness, which we do not see. But this is altogether
false: we cannot separate colour from length, breadth, and
thickness, _in any other way_, than by transferring it to
the visible figure which we do see. He cannot, he allows,
separate the colour from the visible form of the trunk of a
large oak; but just as little, he thinks, can he separate it
from the convex mass of the trunk, which (it is allowed on
all hands) he does not immediately see. But in this he is
mistaken: for if he were to make a _picture_ of the oak, he
would separate the colour from the convex shape, which he
does not imitate, but he could not separate it from the
visible figure, which he does imitate; and he would then
perceive that the fact that he _has not_ an immediate
perception of the convex form, is necessarily connected with
the fact that he _has_ an immediate perception of the
apparent figure; so far is the rejection of immediate
perception in the former case from being a reason for
rejecting it in the latter.

[Note 16\4: _Lectures_, vol. ii. p. 84.]

Again, with regard to the second argument. It does not, he
says, follow, that because a certain figured portion of the
retina is affected by light, we should see such a figure;
for if a certain figured portion of the olfactory organ were
affected by odours, we should not acquire by smell any
perception of such figure[17\4]. This is merely to say, that
because we do not perceive position and figure by one sense,
we cannot do so by another sense. But this again is
altogether erroneous. It is an office of our sight to inform
us of position, and consequently of figure; for this
purpose, the organ is so constructed that the position of
the object determines the position of the point of the
retina affected. There is nothing of this kind in the organ
of smell; objects in different positions and of different
forms do not affect different parts of the olfactory nerve,
or portions of different shape. Different objects, remote
from each other, if perceived by smell, affect the same
{319} part of the olfactory organs. This is all quite
intelligible; for it is not the office of smell to inform us
of position. Of what use or meaning would be the curious and
complex structure of the eye, if it gave us only such vague
and wandering notions of the colours and forms of the
flowers in a garden, as we receive from their odours when we
walk among them blindfold? It is, as we have said, the
_prerogative_ of vision to apprehend position: the places of
objects on the retina give this information. We do not
suppose that the affection of a certain shape of nervous
expanse will necessarily and in all cases give us the
impression of figure; but we know that in vision it does;
and it is clear that if we did not acquire our acquaintance
with visible figure in this way, we could not acquire it in
any way[18\4].

[Note 17\4: _Ib._ p. 87.]

[Note 18\4: When Brown says further (p. 87), that we can
indeed show the image in the dissected eye; but that 'it is
not in the dissected eye that vision takes place;' it is
difficult to see what his drift is. Does he doubt that there
is an image formed in the living as completely as in the
dissected eye?]

The whole of this strange mistake of Brown's appears to
arise from the fault already noticed;--that of considering
the image on the retina as the _object_ instead of the
_means_ of vision. This indeed is what he says: 'the true
object of vision is not the distant body itself, but the
light that has reached the expansive termination of the
optic nerve[19\4].' Even if this were so, we do not see why
we should not perceive the position of the impression on
this expanded nerve. But as we have already said, the
impression on the nerve is the means of vision, and enables
us to assign a place, or at least a direction, to the object
from which the light proceeds, and thus makes vision
possible. Brown, indeed, pursues his own peculiar view till
he involves the subject in utter confusion. Thus he
says[20\4], 'According to the common theory [that figure can
be perceived by the eye,] a visible sphere is at once to my
perception convex and plane; and if the sphere be a one, it
is perceived at once to be a sphere of {320} many feet in
diameter, and a plane circular surface of the diameter of a
quarter of an inch.' It is easy to deduce these and greater
absurdities, if we proceed on his strange and baseless
supposition that the object and the image on the retina are
_both_ perceived. But who is conscious of the image on the
retina in any other way than as he sees the object by means
of it?

[Note 19\4: _Lectures_, vol. ii. p. 57.]

[Note 20\4: _Ib._ vol. ii. p. 89.]

Brown seems to have imagined that he was analysing the
perception of figure 'in the same manner in which Berkeley
had analyzed the perception of distance. He ought to have
recollected that such an undertaking, to be successful,
required him to show _what_ elements he analyzed it _into_.
Berkeley analyzed the perception of real figure into the
interpretation of visible figure according to certain rules
which he distinctly stated. Brown analyzes the perception of
visible figure into no elements. Berkeley says, that we do
not directly perceive distance, but that we perceive
something else, from which we infer distance, namely,
visible figure and colour, and our own efforts in seeing;
Brown says, that we do not see figure, but infer it; what
then do we see, which we infer it from? To this he offers no
answer. He asserts the seeming perception of visible figure
to be a result of 'association;'--of 'suggestion.' But what
meaning can we attach to this? Suggestion requires something
which suggests; and not a hint is given what it is which
suggests position. Association implies two things
associated; what is the sensation which we associate with
form? What is that visual perception which is not figure,
and which we mistake for figure? What perception is it that
suggests a square to the eye? What impressions are those
which have been associated with a visible triangle, so that
the revival of the impressions revives the notion of the
triangle? Brown has nowhere pointed out such perceptions and
impressions; nor indeed was it possible for him to do so;
for the only visual perceptions which he allows to remain,
those of colour, most assuredly do not suggest visible
figures by their differences; red is not associated with
square rather than with round, or with round rather than
square. On the contrary, the {321} eye, constructed in a
very complex and wonderful manner in order that it may give
to us directly the perception of position as well as of
colour, has it for one of its prerogatives to give us this
information; and the perception of the relative position of
each part of the visible boundary of an object constitutes
the perception of its apparent figure; which faculty we
cannot deny to the eye without rejecting the plain and
constant evidence of our senses, making the mechanism of the
eye unmeaning, confounding the object with the means of
vision, and rendering the mental process of vision utterly
unintelligible.

Having sufficiently discussed the processes of perception, I
now return to the consideration of the Ideas which these
processes assume.

{{322}}
CHAPTER III.

SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE
IDEA OF A MEDIUM.

1. IN what precedes, we have shown by various considerations
that we necessarily and universally assume the perception of
secondary qualities to take place by means of a medium
interjacent between the object and the person perceiving.
Perception is affected by various peculiarities, according
to the nature of the quality perceived: but in all cases a
medium is equally essential to the process.

This principle, which, as we have seen, is accepted as
evident by the common understanding of mankind, is confirmed
by all additional reflection and discipline of the mind, and
is the foundation of all the theories which have been
proposed concerning the processes by which the perception
takes place, and concerning the modifications of the
qualities thus perceived. The medium, and the mode in which
the impression is conveyed through the medium, seem to be
different for different qualities; but the existence of the
medium leads to certain necessary conditions or
alternatives, which have successively made their appearance
in science, in the course of the attempts of men to theorize
concerning the principal secondary qualities, sound, light,
and heat. We must now point out some of the ways, at first
imperfect and erroneous, in which the consequences of the
fundamental assumption were traced.

2. _Sound._--In all cases the medium of sensation, whatever
it is, is supposed to produce the effect of conveying
secondary qualities to our perception by means of its
primary qualities. It was conceived to operate {323} by the
size, form, and motion of its parts. This is a fundamental
principle of the class of sciences of which we have at
present to speak.

It was assumed from the first, as we have seen in the
passage lately quoted from Aristotle[21\4], that in the
conveyance of _sound_, the medium of communication was the
air. But although the first theorists were right so far,
that circumstance did not prevent their going entirely wrong
when they had further to determine the nature of the
process. It was conceived by Aristotle that the air acted
after the manner of a rigid body;--like a staff, which,
receiving an impulse at one end, transmits it to the other.
Now this is altogether an erroneous view of the manner in
which the air conveys the impulse by which sound is
perceived. An approach was made to the true view of this
process, by assimilating it to the diffusion of the little
circular waves which are produced on the surface of still
water when a stone is dropt into it. These little waves
begin from the point thus disturbed, and run outwards,
expanding on every side, in concentric circles, till they
are lost. The propagation of sound through the air from the
point where it is produced, was compared by Vitruvius to
this diffusion of circular waves in water; and thus the
notion of a propagation of impulse by the _waves_ of a fluid
was introduced, in the place of the former notion of the
impulse of an unyielding body.

[Note 21\4: _Supr._ p. 297.]

But though, taking an enlarged view of the nature of the
progress of a wave, this is a just representation of the
motion of air in conveying sound, we cannot suppose that the
process was, at the period of which we speak, rightly
understood. For the waves of water were contemplated only as
affecting the surface of the water; and as the air has no
surface, the communication must take place by means of an
internal motion, which can bear only a remote and obscure
resemblance to the waves which we see. And even with regard
to the waves of water, the mechanism by which they are {324}
produced and transferred was not at all understood; so that
the comparison employed by Vitruvius must be considered
rather as a loose analogy than as an exact scientific
explanation.

No correct account of such motions was given, till the
formation of the science of Mechanics in modern times had
enabled philosophers to understand more distinctly the mode
in which motion is propagated through a fluid, and to
discern the forces which the process calls into play, so as
to continue the motion once begun. Newton introduced into
this subject the exact and rigorous conception of an
_Undulation_, which is the true key to the explanation of
impulses conveyed through a fluid.

Even at the present day, the right apprehension of the
nature of an Undulation transmitted through a fluid is found
to be very difficult for all persons except those whose
minds have been duly disciplined by mathematical studies.
When we see a wave run along the surface of water, we are
apt to imagine at first that a portion of the fluid is
transferred bodily from one place to another. But with a
little consideration we may easily satisfy ourselves that
this is not so: for if we look at a field of standing corn,
when a breeze blows over it, we see waves like those of
water run along its surface. Yet it is clear that in this
case the separate stalks of corn only bend backwards and
forwards, and no portion of the grain is really conveyed
from one part of the field to the other. This is obvious
even to popular apprehension. The poet speaks of
. . . . The rye,
That stoops its head when whirlwinds rave
And springs again in eddying wave
As each wild gust sweeps by.
Each particle of the mass in succession has a small motion
backwards and forwards; and by this means a large ridge made
by many such particles runs along the mass to any distance.
This is the true conception of an undulation in general.

Thus, when an Undulation is propagated in a fluid, it is not
_matter_, but _form_, which is transmitted from {325} one
place to another. The particles along the line of each wave
assume a certain arrangement, and this arrangement passes
from one part to another, the particles changing their
places only within narrow limits, so as to lend themselves
successively to the arrangements by which the successive
waves, and the intervals between the waves, are formed.

When such an Undulation is propagated through air, the wave
is composed, not, as in water, of particles which are higher
than the rest, but of particles which are closer to each
other than the rest. The wave is not a ridge of elevation,
but a line of condensation; and as in water we have
alternately elevated and depressed lines, we have in air
lines alternately condensed and rarefied. And the motion of
the particles is not, as in water, up and down, in a
direction transverse to that of the wave which runs
forwards; in the motion of an undulation through air the
motion of each particle is alternately forwards and
backwards, while the motion of the undulation is constantly
forwards.

This precise and detailed account of the Undulatory Motion
of air by which sound is transmitted was first given by
Newton. He further attempted to determine the motions of the
separate particles, and to point out the force by which each
particle affects the next, so as to continue the progress of
the undulation once begun. The motions of each particle must
be oscillatory; he assumed the oscillations to be governed
by the simplest law of oscillation which had come under the
notice of mathematicians, (that of small vibrations of a
pendulum;) and he proved that in this manner the forces
which are called into play by the contraction and expansion
of the parts of the elastic fluid are such as the
continuance of the motion requires.

Newton's proof of the exact law of Oscillatory Motion of the
aërial particles was not considered satisfactory by
succeeding mathematicians; for it was found that the same
result, the development of forces adequate to continue the
motion, would follow if any other law of the motion were
assumed. Cramer proved this by a sort of _parody_ on
Newton's proof, in which, by the {326} alteration of a few
phrases in this formula of demonstration, it was made to
establish an entirely different conclusion.

But the general conception of an Undulation as presented by
Newton was, as from its manifest mechanical truth it could
not fail to be, accepted by all mathematicians; and in
proportion as the methods of calculating the motions of
fluids were further improved, the necessary consequences of
this conception, in the communication of sound through air,
were traced by unexceptionable reasoning. This was
especially done by Euler and Lagrange, whose memoirs on such
motions of fluids are some of the most admirable examples
which exist, of refined mathematical methods applied to the
solution of difficult mechanical problems.

But the great step in the formation of the theory of sound
was undoubtedly that which we have noticed, the introduction
of the Conception of an Undulation such as we have attempted
to describe it:--a state, condition, or arrangement of the
particles of a fluid, which is transferred from one part of
space to another by means of small motions of the particles,
altogether distinct from the movement of the Undulation
itself. This is a conception which is not obvious to common
apprehension. It appears paradoxical at first sight to speak
of a large _wave_ (as the tide-wave) running up a river at
the rate of twenty miles an hour, while the _stream_ of the
river is all the while flowing downwards. Yet this is a very
common fact. And the conception of such a motion must be
fully mastered by all who would reason rightly concerning
the mechanical transmission of impressions through a medium.

We have described the motion of sound as produced by small
motions of the particle forwards and backwards, while the
waves, or condensed and rarefied lines, move constantly
forwards. It may be asked what right we have to suppose the
motion to be of this kind, since when sound is heard, no
such motions of the particles of air can be observed, even
by refined methods of observation. Thus Bacon declares
himself against the hypothesis of such a vibration, since,
as he remarks, it {327} cannot be perceived in any visible
impression upon the flame of a candle. And to this we reply,
that the supposition of this Vibration is made in virtue of
a principle which is involved in the original assumption of
a medium; namely, That _a Medium, in conveying Secondary
qualities, operates by means of its Primary qualities_, the
bulk, figure, motion, and other mechanical properties of its
parts. This is an Axiom belonging to the Idea of a Medium.
In virtue of this axiom it is demonstrable that the motion
of the air, when any how disturbed, must be such as is
supposed in our acoustical reasonings. For the elasticity of
the parts of the air, called into play by its expansion and
contraction, lead, by a mechanical necessity, to such a
motion as we have described. We may add that, by proper
contrivances, this motion may be made perceptible in its
visible effects. Thus the theory of sound, as an impression
conveyed through air, is established upon evident general
principles, although the mathematical calculations which are
requisite to investigate its consequences are, some of them,
of a very recondite kind.

3. _Light._--The early attempts to explain Vision
represented it as performed by means of material rays
proceeding _from_ the eye, by the help of which the eye felt
out the form and other visible qualities of an object, as a
blind man might do with his staff. But this opinion could
not keep its ground long: for it did not even explain the
fact that light is necessary to vision. Light, as a peculiar
medium, was next assumed as the machinery of vision; but the
mode in which the impression was conveyed through the medium
was left undetermined, and no advance was made towards sound
theory, on that subject, by the ancients.

In modern times, when the prevalent philosophy began to
assume a mechanical turn (as in the theories of Descartes),
light was conceived to be a material substance which is
emitted from luminous bodies, and which is also conveyed
from all bodies to the eye, so as to render them visible.
The various changes of direction by which the rays of light
are affected, (reflection, {328} refraction, &c.,) Descartes
explained, by considering the particles of light as small
globules, which change their direction when they impinge
upon other bodies, according to the laws of Mechanics.
Newton, with a much more profound knowledge of Mechanics
than Descartes possessed, adopted, in the most mature of his
speculations, nearly the same view of the nature of light;
and endeavoured to show that reflection, refraction, and
other properties of light, might be explained as the effects
which certain forces, emanating from the particles of
bodies, produce upon the luminiferous globules.

But though some of the properties of light could thus be
accounted for by the assumption of particles emitted from
luminous bodies, and reflected or refracted by forces, other
properties came into view which would not admit of the same
explanation. The phenomena of _diffraction_ (the fringes
which accompany shadows) could never be truly represented by
such an hypothesis, in spite of many attempts which were
made. And the _colours of thin plates_, which show the rays
of light to be affected by an alternation of two different
conditions at small intervals along their length, led Newton
himself to incline, often and strongly, to some hypothesis
of undulation. The _double refraction_ of Iceland spar, a
phenomenon in itself very complex, could, it was found by
Huyghens, be expressed with great simplicity by a certain
hypothesis of undulations.

Two hypotheses of the nature of the luminiferous medium were
thus brought under consideration; the one representing Light
as Matter emitted from the luminous object, the other, as
Undulations propagated through a fluid. These two hypotheses
remained in presence of each other during the whole of the
last century, neither of them gaining any material advantage
over the other, though the greater part of mathematicians,
following Newton, embraced the emission theory. But at the
beginning of the present century, an additional class of
phenomena, those of the _interference_ of two rays of light,
were brought under {329} consideration by Dr. Young; and
these phenomena were strongly in favour of the undulatory
theory, while they were irreconcilable with the hypothesis
of emission. If it had not been for the original bias of
Newton and his school to the other side, there can be little
doubt that from this period light as well as sound would
have been supposed to be propagated by undulations; although
in this case it was necessary to assume as the vehicle of
such undulations a special medium or _ether_. Several points
of the phenomena of vision no doubt remained unexplained by
the undulatory theory, as absorption, and the natural
colours of bodies; but such facts, though they did not
confirm, did not evidently contradict the theory of a
Luminiferous Ether; and the facts which such a theory did
explain, it explained with singular happiness and accuracy.

But before this Undulatory Theory could be generally
accepted, it was presented in an entirely new point of view
by being combined with the facts of _polarization_. The
general idea of polarization must be illustrated hereafter;
but we may here remark that Young and Fresnel, who had
adopted the undulatory theory, after being embarrassed for
some time by the new facts which were thus presented to
their notice, at last saw that these facts might be
explained by conceiving the vibrations to be transverse to
the ray, the motions of the particles being not backwards
and forwards in the line in which the impulse travels, but
to the right and left of that line. This conception of
_transverse vibrations_, though quite unforeseen, had
nothing in it which was at all difficult to reconcile with
the general notion of an undulation. We have described an
undulation, or wave, as a certain condition or arrangement
of the particles of the fluid successively transferred from
one part of space to another: and it is easily conceivable
that this arrangement or wave may be produced by a lateral
transfer of the particles from their quiescent positions.
This conception of transverse vibrations being accepted, it
was found that the explanation of the phenomena of
polarization and of those of interference led to the same
theory {330} with a correspondence truly wonderful; and this
coincidence in the views, collected from two quite distinct
classes of phenomena, was justly considered as an almost
demonstrative evidence of the truth of this undulatory
theory.

It remained to be considered whether the doctrine of
transverse vibrations in a fluid could be reconciled with
the principles of Mechanics. And it was found that by making
certain suppositions, in which no inherent improbability
existed, the hypothesis of transverse vibrations would
explain the laws, both of interference and of polarization
of light, in air and in crystals of all kinds, with a
surprizing fertility and fidelity.

Thus the Undulatory Theory of Light, like the Undulatory
Theory of Sound, is recommended by its conformity to the
fundamental principle of the Secondary Mechanical Sciences,
that the medium must be supposed to transmit its peculiar
impulses according to the laws of Mechanics. Although no one
had previously dreamt of qualities being conveyed through a
medium by such a process, yet when it is once suggested as
the only mode of explaining some of the phenomena, there is
nothing to prevent our accepting it entirely, as a
satisfactory theory for all the known laws of Light.

4. _Heat._--With regard to Heat as with regard to Light, a
fluid medium was necessarily assumed as the vehicle of the
property. During the last century, this medium was supposed
to be an emitted fluid. And many of the ascertained Laws of
Heat, those which prevail with regard to its radiation more
especially, were well explained by this hypothesis[22\4].
Other effects of heat, however, as for instance _latent
heat_[23\4], and the change of _consistence_ of
bodies[24\4], were not satisfactorily brought into connexion
with the hypothesis; while {331} _conduction_[25\4], which
at first did not appear to result from the fundamental
assumption, was to a certain extent explained as internal
radiation.

[Note 22\4: See the Account of the Theory of Exchanges,
_Hist. Ind. Sc._ b. x. c. i. sect. 2.]

[Note 23\4: _Ib._ c. ii. sect. 3.]

[Note 24\4: _Ib._ c. ii. sect. 2.]

[Note 25\4: _Ib._ c. i. sect. 7.]

But it was by no means clear that an Undulatory Theory of
Heat might not be made to explain these phenomena equally
well. Several philosophers inclined to such a theory; and
finally, Ampère showed that the doctrine that the heat of a
body consists in the undulations of its particles propagated
by means of the undulations of a medium, might be so
adjusted as to explain all which the theory of emission
could explain, and moreover to account for facts and laws
which were out of the reach of that theory. About the same
time it was discovered by Prof. Forbes and M. Nobili that
radiant heat is, under certain circumstances, polarized. Now
polarization had been most satisfactorily explained by means
of transverse undulations in the case of light; while all
attempts to modify the emission theory so as to include
polarization in it, had been found ineffectual. Hence this
discovery was justly considered as lending great countenance
to the opinion that Heat consists in the vibrations of its
proper medium.

But what is this medium? Is it the same by which the
impressions of Light are conveyed? This is a difficult
question; or rather it is one which we cannot at present
hope to answer with certainty. No doubt the connexion
between Light and Heat is so intimate and constant, that we
can hardly refrain from considering them as affections of
the same medium. But instead of attempting to erect our
systems on such loose and general views of connexion, it is
rather the business of the philosophers of the present day
to determine the laws of the operation of heat, and its real
relation to light, in order that we may afterwards be able
to connect the theories of the two qualities. Perhaps in a
more advanced state of our knowledge we may be able to state
it as an Axiom, that two Secondary Qualities, which are
intimately connected in their causes and effects, must be
affections of the same Medium. {332} But at present it does
not appear safe to proceed upon such a principle, although
many writers, in their speculations both concerning Light
and Heat, and concerning other properties, have not
hesitated to do so.

Some other consequences follow from the Idea of a Medium
which must be the subject of another chapter.

{{333}}
CHAPTER IV.

OF THE MEASURE OF SECONDARY QUALITIES.

SECT. I.--_Scales of Qualities in general._

THE ultimate object of our investigation in each of the
Secondary Mechanical Sciences, is the nature of the
processes by which the special impressions of sound, light,
and heat, are conveyed, and the modifications of which these
processes are susceptible. And of this investigation, as we
have seen, the necessary basis is the principle, that these
impressions are transmitted by means of a medium. But before
we arrive at this ultimate object, we may find it necessary
to occupy ourselves with several intermediate objects:
before we discover the _cause_, it may be necessary to
determine the _laws_ of the phenomena. Even if we cannot
immediately ascertain the mechanism of light or heat, it may
still be interesting and important to arrange and measure
the effects which we observe.

The idea of a Medium affects our proceeding in this research
also. We cannot measure Secondary qualities in the same
manner in which we measure Primary qualities, by a mere
addition of parts. There is this leading and remarkable
difference, that while both classes of qualities are
susceptible of changes of magnitude, primary qualities
increase by addition of _extension_, secondary, by
augmentation of _intensity_. A space is doubled when another
equal space is placed by its side; one weight joined to
another makes up the sum of the two. But when one degree of
warmth is combined with another, or one shade of red colour
with another, we cannot in like manner talk of the _sum_.
The component parts do not evidently retain their {334}
separate existence; we cannot separate a strong green colour
into two weaker ones, as we can separate a large force into
two smaller. The increase is absorbed into the previous
amount, and is no longer in evidence as a part of the whole.
And this is the difference which has given birth to the two
words _extended_, and _intense_. That is extended which has
'partes extra partes,' parts outside of parts: that is
intense which becomes stronger by some indirect and
unapparent increase of agency, like the stretching of the
internal springs of a machine, as the term _intense_
implies. Extended magnitudes can at will be resolved into
the parts of which they were originally composed, or any
other which the nature of their extension admits; their
proportion is apparent; they are directly and at once
subject to the relations of number. Intensive magnitudes
cannot be resolved into smaller magnitudes; we can see that
they differ, but we cannot tell in what proportion; we have
no direct measure of their quantity. How many times hotter
than blood is boiling water? The answer cannot be given by
the aid of our feelings of heat alone.

The difference, as we have said, is connected with the
fundamental principle that we do not perceive Secondary
qualities directly, but through a Medium. We have no natural
apprehension of light, or sound, or heat, as they exist in
the bodies from which they proceed, but only as they affect
our organs. We can only measure them, therefore, by some
_Scale_ supplied by their effects. And thus while extended
magnitudes, as space, time, are measurable directly and of
themselves; intensive magnitudes, as brightness, loudness,
heat, are measurable only by artificial means and
conventional scales. Space, time, measure themselves: the
repetition of a smaller space, or time, while it composes a
larger one, measures it. But for light and heat we must have
Photometers and Thermometers, which measure something which
is assumed to be an indication of the quality in question.
In the one case, the mode of applying the measure, and the
meaning of the number resulting, are seen by intuition; in
the {335} other, they are consequences of assumption and
reasoning. In the one case, they are _Units_, of which the
extension is made up; in the other, they are _Degrees_ by
which the intensity ascends.

2. When we discover any property in a sensible quality,
which at once refers us to number or space, we readily take
this property as a measure; and thus we make a transition
from quality to quantity. Thus Ptolemy in the third chapter
of the First Book of his _Harmonics_ begins thus: 'As to the
differences which exist in sounds both in _quality_ and in
_quantity_, if we consider that difference which refers to
the acuteness and graveness, we cannot at once tell to which
of the above two classes it belongs, till we have considered
the causes of such symptoms.' But at the end of the chapter,
having satisfied himself that grave sounds result from the
magnitude of the string or pipe, other things being equal,
he infers, 'Thus the difference of acute and grave appears
to be a difference of _quantity_.'

In the same manner, in order to form Secondary Mechanical
Sciences respecting any of the other properties of bodies,
we must reduce these properties to a dependence upon
quantity, and thus make them subject to measurement. We
cannot obtain any sciential truths respecting the comparison
of sensible qualities, till we have discovered measures and
scales of the qualities which we have to consider; and
accordingly, some of the most important steps in such
sciences have been the establishment of such measures and
scales, and the invention of the requisite instruments.

The formation of the mathematical sciences which rest upon
the measures of the intensity of sensible qualities took
place mainly in the course of the last century. Perhaps we
may consider Lambert, a mathematician who resided in
Switzerland, and published about 1750, as the person who
first clearly felt the importance of establishing such
sciences. His Photometry, Pyrometry, and Hygrometry, are
examples of the systematic reduction of sensible qualities
(light, heat, moisture) to modes of numerical measurement.
{336}

We now proceed to speak of such modes of measurement with
regard to the most obvious properties of bodies.

SECT. II.--_The Musical Scale._

3. THE establishment of the _Harmonic Canon_, that is, of a
Scale and Measure of the musical place of notes, in the
relation of _high_ and _low_, was the first step in the
science of Harmonics. The perception of the differences and
relations of musical sounds is the office of the sense of
hearing; but these relations are fixed, and rendered
accurately recognizable by artificial means. 'Indeed, in all
the senses,' as Ptolemy truly says in the opening of his
Harmonics, 'the sense discovers what is approximately true,
and receives accuracy from another quarter: the reason
receives the approximately-true from another quarter, and
discovers the accurate truth.' We can have no measures of
sensible qualities which do not ultimately refer to the
sense;--whether they do this immediately, as when we refer
Colours to an assumed Standard; or mediately, as when we
measure Heat by Expansion, having previously found by an
appeal to sense that the expansion increases with the heat.
Such relations of sensible qualities cannot be described in
words, and can only be apprehended by their appropriate
faculty. The faculty by which the relations of sounds are
apprehended is a _musical ear_ in the largest acceptation of
the term. In this signification the faculty is nearly
universal among men; for all persons have musical ears
sufficiently delicate to understand and to imitate the
modulations corresponding to various emotions in speaking;
which modulations depend upon the succession of acuter and
graver tones. These are the relations now spoken of, and
these are plainly perceived by persons who have very
imperfect musical ears, according to the common use of the
phrase. But the relations of tones which occur in speaking
are somewhat indefinite; and in forming that musical scale
which is the basis of our science upon the subject, we {337}
take the most definite and marked of such relations of
notes; such as occur, not in speaking but in singing. Those
musical relations of two sounds which we call the _octave_,
the _fifth_, the _fourth_, the _third_, are recognized after
a short familiarity with them. These _chords_ or _intervals_
are perceived to have each a peculiar character, which
separates them from the relations of two sounds taken at
random, and makes it easy to know them when sung or played
on an instrument; and for most persons, not difficult to
sing the sounds in succession exactly, or nearly correct.
These musical relations, or _concords_, then, are the
groundwork of our musical series of sounds. But how are we
to name these indescribable sensible characters? how to
refer, with unerring accuracy, to a type which exists only
in our own perceptions? We must have for this purpose a
_Scale_ and a _Standard_.

The Musical Scale is a series of eight notes, ascending by
certain steps from the first or key-note to the octave above
it, each of the notes being fixed by such distinguishable
musical relations as we have spoken of above. We may call
these notes C, D, E, F, G, A, B, _c_; and we may then say
that G is determined by its being a fifth above C; D by its
being a fourth below G; E by its being a third above C; and
similarly of the rest. It will be recollected that the terms
a _fifth_, a _fourth_, a _third_, have hitherto been
introduced as expressing certain simple and indescribable
musical relations among sounds, which might have been
indicated by any other names. Thus we might call the fifth
the _dominant_, and the fourth the _subdominant_, as is done
in one part of musical science. But the names we have used,
which are the common ones, are in fact derived from the
number of notes which these intervals include in the scale
obtained in the above manner. The notes, C, D, E, F, G,
being five, the interval from C to G is a fifth, and so of
the rest. The fixation of this scale gave the means of
describing exactly any note which occurs in the scale, and
the method is easily applicable to notes above and below
this range; for in a series of sounds higher or lower by an
octave than {338} this standard series, the ear discovers a
recurrence of the same relations so exact, that a person may
sometimes imagine he is producing the same notes as another
when he is singing the same air an octave higher. Hence the
next eight notes may be conveniently denoted by a repetition
of the same letters, as the first; thus, C, D, E, F, G, A,
B, _c_, _d_, _e_, _f_, _g_, _a_, _b_; and it is easy to
devise a continuation of such cycles. And other admissible
notes are designated by a further modification of the
standard ones, as by making each note _flat_ or _sharp_;
which modification it is not necessary here to consider,
since our object is only to show how a standard is
attainable, and how it serves the ends of science.

We may observe, however, that the above is not an exact
account of the first, or early Greek scale; for that scale
was founded on a primary division of the interval of two
octaves (the extreme range which it admitted) into five
_tetrachords_, each tetrachord including the interval of a
fourth. All the notes of this series had different names
borrowed from this division[26\4]; thus _mese_ was the
middle or key-note; the note below it was _lichanos mesôn_,
the next below was _parypate mesôn_, the next lower, _hypate
mesôn_. The fifth above _mese_ was _nete diazeugmenôn_, the
octave was _nete hyperbolæôn_.

[Note 26\4: Burney's _History of Music_, vol. i. p. 28.]

4. But supposing a complete system of such denominations
established, how could it be with certainty and rigour
applied? The human ear is fallible, the organs of voice
imperfectly obedient; if this were not so, there would be no
such thing as a _good_ ear or a _good_ voice. What means can
be devised of finding at will a _perfect_ concord, a fifth
or a fourth? Or supposing such concords fixed by an
acknowledged authority, how can they be referred to, and the
authority adduced? How can we enact a Standard of sounds?

A Standard was discovered in the _Monochord_. A musical
string properly stretched, may be made to produce different
notes, in proportion as we intercept a longer or shorter
portion, and make this portion {339} vibrate. The relation
of the length of the strings which thus sound the two notes
G and C is fixed and constant, and the same is true of all
other notes. Hence the musical interval of any notes of
which we know the places in the musical scale, may be
reproduced by measuring the lengths of string which are
known to give them. If C be of the length 180, D is 160, E
is 144, F is 135, G is 120; and thus the musical relations
are reduced to numerical relations, and the monochord is a
complete and perfect _Tonometer_.

We have here taken the length of the string as the measure
of the tone: but we may observe that there is in us a
necessary tendency to assume that the ground of this measure
is to be sought in some ulterior cause; and when we consider
the matter further, we find this cause in the frequency of
these vibrations of the string. The truth that the same note
must result from the same frequency of vibration is readily
assented to on a slight suggestion of experience. Thus
Mersenne[27\4], when he undertakes to determine the
frequency of vibrations of a given sound, says 'Supponendum
est quoscunque nervos et quaslibet chordas unisonum
facientes eundem efficere numerum recursuum eodem vel equali
tempore, quod perpetuâ constat experientiâ.' And he proceeds
to apply it to cases where experience could not verify this
assertion, or at least had not verified it, as to that of pipes.

[Note 27\4: _Harmonia_, lib. ii. prop. 19.]

The pursuit of these numerical relations of tones forms the
science of Harmonics; of which here we do not pretend to
give an account, but only to show, how the invention of a
Scale and Nomenclature, a Standard and Measure of the tone
of sounds, is its necessary basis. We will therefore now
proceed to speak of another subject; _colour_.

SECT. III.--_Scales of Colour._

5. _The Prismatic Scale of Colour._--A SCALE of Colour must
depend originally upon differences {340} discernible by the
eye, as a scale of notes depends on differences perceived by
the ear. In one respect the difficulty is greater in the
case of the visible qualities, for there are no relations of
colour which the eye peculiarly singles out and
distinguishes, as the ear selects and distinguishes an
octave or a fifth. Hence we are compelled to take an
arbitrary scale; and we have to find one which is fixed, and
which includes a proper collection of colours. The
_prismatic spectrum_, or coloured image produced when a
small beam of light passes obliquely through any transparent
surface (as the surface of a prism of glass,) offers an
obvious Standard as far as it is applicable. Accordingly
colours have, for various purposes, been designated by their
place in the spectrum, ever since the time of Newton; and we
have thus a means of referring to such colours as are
included in the series _red_, _orange_, _yellow_, _green_,
_blue_, _violet_, _indigo_, and the intermediate tints.

But this scale is not capable of numerical precision. If the
spectrum could be exactly defined as to its extremities, and
if these colours occupied always the same proportional part
of it, we might describe any colour in the above series by
the measure of its position. But the fact is otherwise. The
spectrum is too indefinite in its boundaries to afford any
distinct point from which we may commence our measures; and
moreover the spectra produced by different transparent
bodies differ from each other. Newton had supposed that the
spectrum and its parts were the same, so long as the
refraction was the same; but his successors discovered that,
with the same amount of refraction in different kinds of
glass, there are different magnitudes of the spectrum; and
what is still worse with reference to our present purpose,
that the spectra from different glasses have the colours
distributed in different proportions. In order, therefore,
to make the spectrum the scale of colour, we must assume
some fixed substance; for instance, we may take water, and
thus a series approaching to the colours of the _rainbow_
will be our standard. But we should still have an extreme
difficulty in applying such a rule. The distinctions of
{341} colour which the terms of common language express, are
not used with perfect unanimity or with rigorous precision.
What one person calls _bluish green_ another calls _greenish
blue_. Nobody can say what is the precise boundary between
red and orange. Thus the prismatic scale of colour was
incapable of mathematical exactness, and this inconvenience
was felt up to our own times.

But this difficulty was removed by a curious discovery of
Wollaston and Fraunhofer; who found that there are, in the
solar spectrum, certain fine black Lines which occupy a
definite place in the series of colours, and can be observed
with perfect precision. We have now no uncertainty as to
what coloured light we are speaking of, when we describe it
as that part of the spectrum in which Fraunhofer's Line C or
D occurs. And thus, by this discovery, the prismatic
spectrum of sunlight became, for certain purposes, an exact
_Chromatometer_.

6. _Newton's Scale of Colours._--Still, such a standard,
though definite, is arbitrary and seemingly anomalous. The
lines A, B, C, D, &c., of Fraunhofer's spectrum are
distributed without any apparent order or law; and we do
not, in this way, obtain numerical measures, which is what,
in all cases, we desire to have. Another discovery of
Newton, however, gives us a spectrum containing the same
colours as the prismatic spectrum, but produced in another
way, so that the colours have a numerical relation. I speak
of the laws of the _Colours of Thin Plates_. The little
rainbows which we sometimes see in the cracks of broken
glass are governed by fixed and simple laws. The kind of
colour produced at any point depends on the thickness of the
thin plate of air included in the fissure. If the thickness
be eight-millionths of an inch, the colour is orange, if
fifteen-millionths of an inch, we have green, and so on; and
thus these numbers, which succeed each other in a regular
order from red to indigo, give a numerical measure of each
colour; which measure, when we pursue the subject, we find
is one of the bases of all optical theory. The series of
colours obtained from plates of air of gradually increasing
thickness is called {342} _Newton's Scale of Colours_; but
we may observe that this is not precisely what we are here
speaking of, a scale of _simple_ colours; it is a series
produced by certain combinations, resulting from the
repetition of the first spectrum, and is mainly useful as a
standard for similar phenomena, and not for colour in
general. The real scale of colour is to be found, as we have
said, in the numbers which express the thickness of the
producing film;--in the length of a _fit_ in Newton's
phraseology, or the length of an _undulation_ in the modern
theory.

7. _Scales of Impure Colours._--The standards just spoken of
include (mainly at least) only pure and simple colours; and
however complete these standards may be for certain objects
of the science of optics, they are insufficient for other
purposes. They do not enable us to put in their place mixed
and impure colours. And there is, in the case of colour, a
difficulty already noticed, which does not occur in the case
of sound; two notes, when sounded together, are not
necessarily heard as one; they are recognized as still two,
and as forming a concord or a discord. But two colours form
a single colour; and the eye cannot, in any way, distinguish
between a green compound of blue and yellow, and the simple,
undecomposable green of the spectrum. By composition of
three or more colours, innumerable new colours may be
generated which form no part of the prismatic series; and by
such compositions is woven the infinitely varied web of
colour which forms the clothing of nature. How are we to
classify and arrange all the possible colours of objects, so
that each shall have a place and name? How shall we find a
_chromatometer_ for impure as well as for pure colour?

Though no optical investigations have depended on a scale of
impure colours, such a scale has been wanted and invented
for other purposes; for instance, in order to identify and
describe objects of natural history. Not to speak of earlier
essays, we may notice Werner's Nomenclature of Colours,
devised for the purpose of describing minerals. This scale
of colour was far superior to any which had previously been
promulgated. {343} It was, indeed, arbitrary in the
selection of its degrees, and in a great measure in their
arrangement; and the colours were described by the usual
terms, though generally with some added distinction; as
_blackish green_, _bluish green_, _apple-green_,
_emerald-green_. But the great merit of the scale was its
giving a _fixed_ conventional meaning to these terms, so
that they lost much of their usual vagueness. Thus
_apple-green_ did not mean the colour of any green apple
casually taken; but a certain definite colour which the
student was to bear in mind, whether or not he had ever seen
an apple of that exact hue. The words were not a
description, but a _record_ of the colour: the memory was to
retain a _sensation_, not a name.

The imperfection of the system (arising from its arbitrary
form) was its incompleteness: however well it served for the
reference of the colours which it did contain, it was
applicable to no others; and thus though Werner's
enumeration extended to more than a hundred colours, there
occur in nature a still greater number which cannot be
exactly described by means of it.

In such cases the unclassed colour is, by the Wernerians,
defined by stating it as intermediate between two others:
thus we have an object described as _between emerald-green
and grass-green_. The eye is capable of perceiving a
gradation from one colour to another; such as may be
produced by a gradual mixture in various ways. And if we
image to ourselves such a mixture, we can compare with it a
given colour. But in employing this method we have nothing
to tell us in what part of the scale we must seek for an
approximation to our unclassed colour. We have no rule for
discovering where we are to look for the boundaries of the
definition of a colour which the Wernerian series does not
supply. For it is not always between contiguous members of
the series that the undescribed colour is found. If we place
emerald-green between apple-green and grass-green, we may
yet have a colour intermediate between emerald-green and
leek-green; and, in fact, the Wernerian series of colours is
destitute {344} of a principle of self-arrangement and
gradation; and is thus necessarily and incurably imperfect.

8. We should have a complete Scale of Colours, if we could
form a series including all colours, and arranged so that
each colour was intermediate in its tint between the
adjacent terms of the series; for then, whether we took many
or few of the steps of the series for our standard terms,
the rest could be supplied by the law of continuity; and any
given colour would either correspond to one of the steps of
our scale or fall between two intermediate ones. The
invention of a Chromatometer for Impure Colours, therefore,
requires that we should be able to form all possible colours
by such intermediation in a systematic manner; that is, by
the mixture or combination of certain elementary colours
according to a simple rule: and we are led to ask whether
such a process has been shown to be possible.

The colours of the prismatic spectrum obviously do form a
continuous series; green is intermediate between its
neighbours yellow and blue, orange between red and yellow;
and if we suppose the two ends of the spectrum bent round to
meet each other, so that the arrangement of the colours may
be circular, the violet and indigo will find their
appropriate place between the blue and red. And all the
interjacent tints of the spectrum, as well as the ones just
named, will result from such an arrangement. Thus all the
_pure_ colours are produced by combinations two and two of
three primary colours, Red, Yellow, and Blue: and the
question suggests itself whether these three are not really
the only Primary Colours, and whether all the impure colours
do not arise from mixtures of the three in various
proportions. There are various modes in which this
suggestion may be applied to the construction of a scale of
colours; but the simplest, and the one which appears really
to verify the conjecture that all possible colours may be so
exhibited, is the following. A certain combination of red,
yellow, and blue, will produce black, or pure grey, and when
diluted, will give all the shades of grey which intervene
between {345} black and white. By adding various shades of
grey, then, to pure colours, we may obtain all the possible
ternary combinations of red, yellow, and blue; and in this
way it is found that we exhaust the range of colours. Thus
the circle of pure colours of which we have spoken may be
accompanied by several other circles, in which these colours
are tinged with a less or greater shade of grey; and in this
manner it is found that we have a perfect chromatometer;
every possible colour being exhibited either exactly or by
means of approximate and contiguous limits. The arrangement
of colours has been brought into this final and complete
form by M. Merimée, whose Chromatic Scale is published by M.
Mirbel in his _Elements of Botany_. We may observe that such
a standard affords us a numerical exponent for every colour
by means of the proportions of the three primary colours
which compose it; or, expressing the same result otherwise,
by means of the pure colour which is involved, and the
proportion of grey by which it is rendered impure. In such a
scale the fundamental elements would be the precise tints of
red, yellow, and blue which are found or assumed to be
primary; the numerical exponents of each colour would depend
upon the arbitrary number of degrees which we interpose
between each two primary colours; and between each pure
colour and absolute blackness. No such numerical scale has,
however, as yet, obtained general acceptation[28\4].

[Note 28\4: The reference to _Fraunhofer's Lines_, as a
means of determining the place of a colour in the prismatic
series, has been objected to, because, as is asserted, the
colours which are in the neighbourhood of each line vary
with the position of the sun, state of the atmosphere and
the like. It is very evident that coloured light refracted
by the prism will not give the same spectrum as white light.
The spectrum given by white light is of course the one here
meant. It is an usual practice of optical experimenters to
refer to the colours of such a spectrum, defining them by
Fraunhofer's Lines.

I do not know whether it needs explanation that the 'first
spectrum' in Newton's rings is a ring of the prismatic
colours.

I have not had an opportunity of consulting Lambert's
_Photometria, sive de mensura et gradibus luminis, colorum,
et umbræ_, published in 1760, nor Mayer's _Commentatio de
Affinitate Colorum_, (1758), in which, I believe, he
describes a chromatometer. The present work is not intended
to be complete as a history; and I hope I have given
sufficient historical detail to answer its philosophical
purpose.]

{346} SECT. IV.--_Scales of Light._

9. _Photometer._--ANOTHER instrument much needed in optical
researches is a _Photometer_, a measure of the intensity of
light. In this case, also, the organ of sense, the eye, is
the ultimate judge; nor has any effect of light, as light,
yet been discovered which we can substitute for such a
judgment. All instruments, such as that of Leslie, which
employ the heating effect of light, or at least all that
have hitherto been proposed, are inadmissible as
photometers. But though the eye can judge of two surfaces
illuminated by light of the same colour, and can determine
when they are equally bright, or which is the brighter, the
eye can by no means decide at sight the proportion of
illumination. How much in such judgments we are affected by
contrast, is easily seen when we consider how different is
the apparent brightness of the moon at mid-day and at
midnight, though the light which we receive from her is, in
fact, the same at both periods. In order to apply a scale in
this case, we must take advantage of the known numerical
relations of light. We are certain that if all other
illumination be excluded, two equal luminaries, under the
same circumstances, will produce an illumination twice as
great as one does; and we can easily prove, from
mathematical considerations, that if light be not enfeebled
by the medium through which it passes, the illumination on a
given surface will diminish as the square of the distance of
the luminary increases. If, therefore, we can by taking a
fraction thus known of the illuminating effect of one
luminary, make it equal to the total effect of another, of
which equality the eye is a competent judge, we compare the
effects of the two luminaries. In order to make this
comparison we may, with Rumford, look at the shadows of the
same object made by the two lights, {347} or with Ritchie,
we may view the brightness produced on two contiguous
surfaces, framing an apparatus so that the equality may be
brought about by proper adjustment; and thus a measure will
become practicable. Or we may employ other methods as was
done by Wollaston[29\4], who reduced the light of the sun by
observing it as reflected from a bright globule, and thus
found the light of the sun to be 10,000,000,000 times that
of Sirius, the brightest fixed star. All these methods are
inaccurate, even as methods of comparison; and do not offer
any fixed or convenient numerical standard; but none better
have yet been devised[30\4].

[Note 29\4: _Phil. Trans._ 1820, p. 19.]

[Note 30\4: Improved Photometers have been devised by
Professor Wheatstone, Professor Potter, and Professor
Steinheil; but they depend upon principles similar to those
mentioned in the text.]

10. _Cyanometer._--As we thus measure the brightness of a
colourless light, we may measure the intensity of any
particular colour in the same way; that is, by applying a
standard exhibiting the gradations of the colour in question
till we find a shade which is seen to agree with the
proposed object. Such an instrument we have in the
_Cyanometer_, which was invented by Saussure for the purpose
of measuring the intensity of the blue colour of the sky. We
may introduce into such an instrument a numerical scale, but
the numbers in such a scale will be altogether arbitrary.

SECT. V.--_Scales of Heat._

11. _Thermometers._--WHEN we proceed to the sensation of
heat, and seek a measure of that quality, we find, at first
sight, new difficulties. Our sensations of this kind are
more fluctuating than those of vision; for we know that the
same object may feel warm to one hand and cold to another at
the same instant, if the hands have been previously cooled
and warmed respectively. Nor can we obtain here, as in the
case of light, self-evident numerical relations of the heat
communicated in given circumstances; for we know that the
{348} effect so produced will depend on the warmth of the
body to be heated, as well as on that of the source of heat;
the summer sun, which warms our bodies, will not augment the
heat of a red-hot iron. The cause of the difference of these
cases is, that bodies do not receive the whole of their
heat, as they receive the whole of their light, from the
immediate influence of obvious external agents. There is no
readily-discovered absolute cold, corresponding to the
absolute darkness which we can easily produce or imagine.
Hence we should be greatly at a loss to devise a
_Thermometer_, if we did not find an indirect effect of heat
sufficiently constant and measurable to answer this purpose.
We discover, however, such an effect in the _expansion_ of
bodies by the effect of heat.

12. Many obvious phenomena show that air, under given
circumstances, expands by the effect of heat; the same is
seen to be true of liquids, as of water, and spirit of wine;
and the property is found to belong also to the metallic
fluid, quicksilver. A more careful examination showed that
the increase of bulk in some of these bodies by increase of
Heat was a fact of a nature sufficiently constant and
regular to afford a means of measuring that previously
intangible quality; and the Thermometer was invented. There
were, however, many difficulties to overcome, and many
points to settle, before this instrument was fit for the
purposes of science.

An explanation of the way in which this was done necessarily
includes an important chapter of the history of Thermotics.
We must now, therefore, briefly notice historically the
progress of the Thermometer. The leading steps of this
progress, after the first invention of the instrument,
were--The establishment of _fixed points_ in the
thermometric scale--The _comparison of the scales_ of
different substances--And the reconcilement of these
differences by some method of interpreting them as
indications of the absolute _quantity of heat_.

13. It would occupy too much space to give in detail the
history of the successive attempts by which {349} these
steps were effected. A thermometer is described by Bacon
under the title _Vitrum Calendare_; this was an air
thermometer. Newton used a thermometer of linseed oil, and
he perceived that the first step requisite to give value to
such an instrument was to fix its scale; accordingly he
proposed his _Scala Graduum Caloris_[31\4]. But when
thermometers of different liquids were compared, it
appeared, from their discrepancies, that this fixation of
the scale of heat was more difficult than had been supposed.
It was, however, effected. Newton had taken freezing water,
or rather thawing snow, as the zero of his scale, which is
really a fixed point; Halley and Amontons discovered (in
1693 and 1702) that the heat of boiling water is another
fixed point; and Daniel Gabriel Fahrenheit, of Dantzig, by
carefully applying these two standard points, produced,
about 1714, thermometers, which were constantly consistent
with each other. This result was much admired at the time,
and was, in fact, the solution of the problem just stated,
the _fixation of the scale of heat_.

[Note 31\4: _Phil. Trans._ 1701.]

14. But the scale thus obtained is a conventional not a
natural scale. It depends upon the fluid employed for the
thermometer. The progress of expansion from the heat of
freezing to that of boiling water is different for mercury,
oil, water, spirit of wine, air. A degree of heat which is
half-way between these two standard points according to a
mercurial thermometer, will be below the half-way point in a
spirit thermometer, and above it in an air thermometer. Each
liquid has its own _march_ in the course of its expansion.
Deluc and others compared the marches of various liquids,
and thus made what we may call a _concordance_ of
thermometers of various kinds.

15. Here the question further occurs: Is there not some
_natural measure_ of the degrees of heat? It appears certain
that there must be such a measure, and that by means of it
all the scales of different liquids must be reconciled. Yet
this does not seem to have occurred at once to men's minds.
Deluc, in speaking {350} of the researches which we have
just mentioned, says[32\4], 'When I undertook these
experiments, it never once came into my thoughts that they
could conduct me with any probability to a table of real
degrees of heat. But hope grows with success, and desire
with hope.' Accordingly he pursued this inquiry for a long
course of years.

[Note 32\4: _Modif. de l'Atmosph._ 1782, p. 303.]

What are the principles by which we are to be guided to the
true measure of heat? Here, as in all the sciences of this
class, we have the general principle, that the secondary
quality, Heat, must be supposed to be perceived in some way
by a material Medium or Fluid. If we take that which is,
perhaps, the simplest form of this hypothesis, that the heat
depends upon the _quantity_ of this fluid, or _Caloric_,
which is present, we shall find that we are led to
propositions which may serve as a foundation for a natural
measure of heat. The _Method of Mixtures_ is one example of
such a result. If we mix together two pints of water, one
hot and one cold, is it not manifest that the temperature of
the mixture must be midway between the two? Each of the two
portions brings with it its own heat. The whole heat, or
caloric, of the mixture is the sum of the two; and the heat
of each half must be the half of this sum, and therefore its
temperature must be intermediate between the temperatures of
the equal portions which were mixed. Deluc made experiments
founded upon this principle, and was led by them to conclude
that 'the dilatations of mercury follow an accelerated march
for successive equal augmentations of heat.'

But there are various circumstances which prevent this
method of mixtures from being so satisfactory as at first
sight it seems to promise to be. The different capacities
for heat of different substances, and even of the same
substance at different temperatures, introduce much
difficulty into the experiments; and this path of inquiry
has not yet led to a satisfactory result. {351}

16. Another mode of inquiring into the natural measure of
heat is to seek it by researches on the _law of cooling_ of
hot bodies. If we assume that the process of cooling of hot
bodies consists in a certain material heat flying off, we
may, by means of certain probable hypotheses, determine
mathematically the law according to which the temperature
decreases as time goes on; and we may assume _that_ to be
the true measure of temperature which gives to the
experimental law of cooling the most simple and probable
form.

It appears evident from the most obvious conceptions which
we can form of the manner in which a body parts with its
superabundant heat, that the hotter a body is, the faster it
cools; though it is not clear without experiment, by what
law the rate of cooling will depend upon the heat of the
body. Newton took for granted the most simple and seemingly
natural law of this dependence: he supposed the rate of
cooling to be _proportional_ to the temperature, and from
this supposition he could deduce the temperature of a hot
iron, calculating from the original temperature and the time
during which it had been cooling. By calculation founded on
such a basis, he graduated his thermometer.

17. But a little further consideration showed that the rate
of cooling of a hot body depended upon the temperature of
the surrounding bodies, as well as upon its own temperature.
Prevost's _Theory of Exchanges_[33\4] was propounded with a
view of explaining this dependence, and was generally
accepted. According to this theory, all bodies radiate heat
to one another, and are thus constantly giving and receiving
heat; and a body which is hotter than surrounding bodies,
cools itself, and warms the surrounding, bodies, by an
exchange of heat for heat, in which they are the gainers.
Hence if _θ_ be the temperature of the bodies, or of the
space, by which the hot body is surrounded, and _θ_ + _t_ the
temperature of the hot body, the rate of cooling will depend
{352} upon the excess of the radiation for a temperature _θ_ +
_t_, above the radiation for a temperature _θ_.

[Note 33\4: _Recherches sur la Chaleur_, 1791. _Hist. Ind.
Sc._ b. x. c. i. sect. 2.]

Accordingly, in the admirable researches of MM. Dulong and
Petit upon the cooling of bodies, it was assumed that the
rate of cooling of the hot body was represented by the
excess of F(_θ_ + _t_) above F(_θ_); where F represented some
mathematical _function_, that is, some expression obtained
by arithmetical operations from the temperatures _θ_ + _t_ and
_θ_; although what these operations are to be, was left
undecided, and was in fact determined by the experiments.
And the result of their investigations was, that the
function is of this kind: when the temperature increases by
equal intervals, the function increases in a continued
geometric proportion[34\4]. This was, in fact, the same law
which had been assumed by Newton and others, with this
difference, that _they_ had neglected the term which depends
upon the temperature of the surrounding space.

[Note 34\4: The formula for the rate of cooling is _ma^(θ +
t) - ma^θ_, where the quantity _m_ depends upon the nature
of the body, the state of its surface, and other
circumstances.--_Ann. Chim._ vii. 150.]

18. This law falls in so well with the best conceptions we
can form of the mechanism of cooling upon the supposition of
a radiant fluid caloric, that it gives great probability to
the scale of temperature on which the simplicity of the
result depends. Now the temperatures in the formulæ just
referred to were expressed by means of the _air
thermometer_. Hence MM. Dulong and Petit justly state, that
while all different substances employed as thermometers give
different laws of thermotical phenomena, their own success
in obtaining simple and general laws by means of the air
thermometer, is a strong recommendation of that as the
_natural scale of heat_. They add[35\4], 'The well-known
uniformity of the principal physical properties of all
gases, and especially the perfect identity of their laws of
dilatation by heat, [a very important discovery of {353}
Dalton and Gay Lussac[36\4],] make it very probable that in
this class of bodies the disturbing causes have not the same
influence as in solids and liquids; and consequently that
the changes of bulk produced by the action of heat are here
in a more immediate dependence on the force which produces them.'

[Note 35\4: _Annales de Chimie_, vii. 153.]

[Note 36\4: _Hist. Ind. Sc._ b. x. c. ii. sect. 1.]

19. Still we cannot consider this point as settled till we
obtain a more complete theoretical insight into the nature
of heat itself. If it be true that heat consists in the
vibrations of a fluid, then, although, as Ampère has
shown[37\4], the laws of radiation will, on mathematical
grounds, be the same as they are on the hypothesis of
emission, we cannot consider the natural scale of heat as
determined, till we have discovered some means of measuring
the caloriferous vibrations as we measure luminiferous
vibrations. We shall only know what the quantity of heat is
when we know what heat itself is;--when we have obtained a
theory which satisfactorily explains the manner in which the
substance or medium of heat produces its effects. When we
see how radiation and conduction, dilatation and
liquefaction, are all produced by mechanical changes of the
same fluid, we shall then see what the nature of that change
is which dilatation really measures, and what relation it
bears to any more proper standard of heat.

[Note 37\4: _Ib._ c. iv.]

We may add, that while our thermotical theory is still so
imperfect as it is, all attempts to divine the true nature
of the relation between light and heat are premature, and
must be in the highest degree insecure and visionary.
Speculations in which, from the general assumption of a
caloriferous and luminiferous medium, and from a few facts
arbitrarily selected and loosely analysed, a general theory
of light and heat is asserted, are entirely foreign to the
course of inductive science, and cannot lead to any stable
and substantial truth.

20. _Other Instruments for measuring Heat._--It does not
belong to our present purpose to speak of {354} instruments
of which the object is to measure, not sensible qualities,
but some effect or modification of the cause by which such
qualities are produced: such, for instance, are the
_Calorimeter_, employed by Lavoisier and Laplace, in order
to compare the _Specific Heat_ of different substances; and
the _Actinometer_, invented by Sir John Herschel, in order
to determine the _effect of the Sun's Rays_ by means of the
heat which they communicate in a given time; which effect
is, as may readily be supposed, very different under
different circumstances of atmosphere and position. The laws
of such effects may be valuable contributions to our
knowledge of heat, but the interpretation of them must
depend on a previous knowledge of the relations which
temperature bears to heat, according to the views just
explained.

SECT. VI.--_Scales of other Qualities._

21. BEFORE quitting the subject of the measures of sensible
qualities, we may observe that there are several other such
qualities for which it would be necessary to have scales and
means of measuring, in order to make any approach to science
on such subjects. This is true, for instance, of Tastes and
Smells. Indeed some attempts have been made towards a
classification of the Tastes of sapid substances, but these
have not yet assumed any satisfactory or systematic
character; and I am not aware that any instrument has been
suggested for _measuring_ either the Flavour or the Odour of
bodies which possess such qualities.

22. _Quality of Sounds._--The same is true of that kind of
difference in sounds which is peculiarly termed their
_Quality_; that character by which, for instance, the sound
of a flute differs from that of a hautbois, when the note is
the same; or a woman's voice from a boy's.

23. _Articulate Sounds._--There is also in sounds another
difference, of which the nature is still obscure, but in
reducing which to rule, and consequently to measure, some
progress has nevertheless been made. {355} I speak of the
differences of sound considered as _articulate_.
Classifications of the sounds of the usual alphabets have
been frequently proposed; for instance, that which arranges
the _Consonants_ in the following groups,:

Sharp. Flat. Sharp Aspirate. Flat Aspirate. Nasal.
p b ph (_f_) bh (_v_) m
k g (hard) kh gh ng
t d th (sharp) th (flat) n
s z sh zh

It is easily perceived that the relations of the sounds in
each of these horizontal lines are analogous; and
accordingly the rules of derivation and modification of
words in several languages proceed upon such analogies. In
the same manner the _Vowels_ may be arranged in an order
depending on their sound. But to make such arrangements
fixed and indisputable, we ought to know the mechanism by
which such modifications are caused. Instruments have been
invented by which some of these sounds can be imitated; and
if such instruments could be made to produce the above
series of articulate sounds, by connected and regular
processes, we should find, in the process, a _measure_ of
the sound produced. This has been in a great degree effected
for the Vowels by Professor Willis's artificial mode of
imitating them. For he finds that if a musical reed be made
to sound through a cylindrical pipe, we obtain by gradually
lengthening the cylindrical pipe, the series of vowels I, E,
A, O, U, with intermediate sounds[38\4]. In this instrument,
then, the length of the pipe would determine the vowel, and
might be used numerically to express it. Such an instrument
so employed would be a measure of vowel quality, and might
be called a _Phthongometer_.

[Note 38\4: _Camb. Trans._ vol. iii. p. 239.]

Our business at present, however, is not with instruments
which might be devised for measuring sensible qualities, but
with those which have been so used, and have thus been the
basis of the sciences in which {356} such qualities are
treated of; and this we have now done sufficiently for our
present purpose.

24. There is another Idea which, though hitherto very
vaguely entertained, has had considerable influence in the
formation, both of the sciences spoken of in the present
Book, and on others which will hereafter come under our
notice: namely, the Idea of Polarity. This Idea will be the
subject of the ensuing Book. And although this Idea forms a
part of the basis of various other extensive portions of
science, as Optics and Chemistry, it occupies so peculiarly
conspicuous a place in speculations belonging to what I have
termed the Mechanico-Chemical Sciences, (Magnetism and
Electricity,) that I shall designate the discussion of the
Idea of Polarity as the Philosophy of those Sciences.

{{357}}
BOOK V.

THE
PHILOSOPHY
OF THE
MECHANICO-CHEMICAL SCIENCES.

En donnant à ces côtés le nom de _poles_, j'appelerai
_polarisation_ la modification qui donne à la lumière des
propriétés relatives à ces poles. J'ai tardé jusqu'à présent
à admettre ce terme dans la description des phénomènes
physiques dont il est question; je n'ai pas osé l'introduire
dans les mémoires où j'ai publié mes dernières expériences;
mais les variétés qu'offre ce nouveau phénomène, et la
difficulté de les décrire, me forcent à admettre cette
nouvelle expression, qui signifie simplement la modification
que la lumière a subie en acquérant de nouvelles propriétés
qui ne sont pas relatives à la direction du rayon, mais
seulement à ses côtés considérés à angles droits et dans un
plan perpendiculaire à sa direction.

Malus (1811), _Mém. de Inst._ tom. xi. p. 106.

{{359}}
BOOK V.

THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.

CHAPTER I.

ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA OF
POLARITY.

1. IN some of the mechanical sciences, as Magnetism and
Optics, the phenomena are found to depend upon position (the
position of the magnet, or of the ray of light,) in a
peculiar alternate manner. This dependence, as it was first
apprehended, was represented by means of certain conceptions
of space and force, as for instance by considering the two
_Poles_ of a magnet. But in all such modes of representing
these alternations by the conceptions borrowed from other
ideas, a closer examination detected something superfluous
and something defective; and in proportion as the view which
philosophers took of this relation was gradually purified
from these incongruous elements, and was rendered more
general and abstract by the discovery of analogous
properties in new cases, it was perceived that the relation
could not be adequately apprehended without considering it
as involving a peculiar and independent Idea, which we may
designate by the term _Polarity_.

We shall trace some of the forms in which this Idea has
manifested itself in the history of science. In doing so we
shall not begin, as in other Books of this work we have
done, by speaking of the notion as it is {360} employed in
common use: for the relation of Polarity is of so abstract
and technical a nature, that it is not employed, at least in
any distinct and obvious manner, on any ordinary or
practical occasions. The idea belongs peculiarly to the
region of speculation: in persons of common habits of
thought it is probably almost or quite undeveloped; and even
most of those whose minds have been long occupied by
science, find a difficulty in apprehending it in its full
generality and abstraction, and stript of all irrelevant
hypothesis.

2. _Magnetism._--The name and the notion of _Poles_ were
first adopted in the case of a magnet. If we have two
magnets, their extremities attract and repel each other
alternatively. If the first end of the one attract the first
end of the other, it repels the second end, and conversely.
In order to express this rule conveniently, the two ends of
each magnet are called the _north pole_ and the _south pole_
respectively, the denominations being borrowed from the
poles of the earth and heavens. 'These poles,' as Gilbert
says[1\5], 'regulate the motions of the celestial spheres
and of the earth. In like manner the magnet has its poles, a
northern and a southern one; certain and determined points
constituted by nature in the stone, the primary terms of its
motions and effects, the limits and governors of many
actions and virtues.'

[Note 1\5: _De Magn._ lib. i. c. iii.]

The nature of the opposition of properties of which we speak
may be stated thus:
The North pole of one magnet attracts the South pole of another
magnet.
The North pole of one magnet _repels_ the North pole of another
magnet.
The South pole of one magnet repels the South pole of another
magnet.
The South pole of one magnet _attracts_ the North pole of
another magnet.

It will be observed that the contrariety of position which
is indicated by putting the South pole for the North pole in
either magnet, is accompanied by the {361} opposition of
mechanical effect which is expressed by changing attraction
into repulsion and repulsion into attraction: and thus we
have the general feature of Polarity,--A contrast of
properties corresponding to a contrast of positions.

3. _Electricity._--When the phenomena of Electricity came to
be studied, it appeared that they involved relations in some
respects Analogous to those of magnetism.

Two kinds of electricity were distinguished, the positive
and the negative; and it appeared that two bodies electrized
positively, or two electrized negatively, repelled each
other, like two north or two south magnetic poles; while a
positively and a negatively electrized body attracted each
other, like the north and south poles of two magnets. In
conductors of an oblong form, the electricity could easily
be made to distribute itself so that one end should be
positively and one end negatively electrized; and then such
conductors acted on each other exactly as magnets would do.

But in conductors, however electrized, there is no peculiar
point which can permanently be considered as the _pole_. The
distribution of electricity in the conductor depends upon
external circumstances: and thus, although the phenomena
offer the general character of _polarity_--alternative
results corresponding to alternative positions,--they cannot
be referred to poles. Some other mode of representing the
forces must be adopted than that which makes them emanate
from permanent points as in a magnet.

The phenomena of attraction and repulsion in electrized
bodies were conveniently represented by means of the
hypothesis of _two_ electric _fluids_, a positive and a
negative one, which were supposed to be distributed in the
bodies. Of these fluids, it was supposed that each repelled
its own parts and attracted those of the opposite fluid: and
it was found that this hypothesis explained all the obvious
laws of electric action. Here then we have the phenomena of
polarization explained by a new kind of machinery:--two
opposite fluids {362} distributed in bodies, and supplying
them, so to speak, with their polar forces. This hypothesis
not only explains electrical attraction, but also the
electrical spark: namely, thus: when two bodies, of which
the neighbouring surfaces are charged with the two opposite
fluids, approach near to each other, the mutual attraction
of the fluids becomes more and more intense, till at last
the excess of fluid on the one body breaks through the air
and rushes to the other body, in a form accompanied by light
and noise. When this transfer has taken place, the
attraction ceases, the positive and the negative fluid
having neutralized each other. Their effort was to unite;
and this union being effected, there is no longer any force
in action. Bodies in their natural unexcited condition may
be considered as occupied by a combination of the two
fluids: and hence we see how the production of either kind
of electricity is necessarily accompanied with the
production of an equivalent amount of the opposite kind.

4. _Voltaic Electricity._--Such is the case in Franklinic
electricity,--that which is excited by the common electrical
machine. In studying Voltaic electricity, we are led to the
conviction that the fluid which is in a condition of
momentary _equilibrium_ in electrized conductors, exists in
the state of a _Current_ in the voltaic circuit. And here we
find polar relations of a new kind existing among the
forces. Two voltaic Currents _attract_ each other when they
are moving in the _same_, and _repel_ each other when they
are moving in _opposite_, directions.

But we find, in addition to these, other polar relations of
a more abstruse kind, and which the supposition of two
fluids does not so readily explain. For instance, if such
fluids existed, distinct from each other, it might be
expected that it would be possible to exhibit one of them
separate from the other. Yet in all the phenomena of
electromotive currents, we attempt in vain to obtain one
kind of electricity separately. 'I have not,' says Mr.
Faraday[2\5], 'been able to find a {363} single fact which
could be adduced to prove the theory of two electricities
rather than one, in electric currents; or, admitting the
hypothesis of two electricities, have I been able to
perceive the slightest grounds that one electricity can be
more powerful than the other, or that it can be present
without the other, or that it can be varied or in the
slightest degree affected without a corresponding variation
in the other.' 'Thus,' he adds, 'the polar character of the
powers is rigorous and complete.' Thus, we too may remark,
all the superfluous and precarious parts gradually drop off
from the hypothesis which we devise in order to represent
polar phenomena; and the abstract notion of Polarity--of
equal and opposite powers called into existence by a common
condition--remains unincumbered with extraneous machinery.

[Note 2\5: _Researches_, 516.]

5. _Light._--Another very important example of the
application of the Idea of Polarity is that supplied by the
discovery of the polarization of light. A ray of light may,
by various processes, be modified, so that it has different
properties according to its different _sides_, although this
difference is not perceptible by any common effects. If, for
instance, a ray thus modified, pass perpendicularly through
a circular glass, and fall upon the eye, we may turn the
glass round and round in its frame, and we shall make no
difference in the brightness of the spot which we see. But
if, instead of a glass, we look through a longitudinal slice
of tourmaline, the spot is alternately dark and bright as we
turn the crystal through successive quadrants. Here we have
a contrast of Properties (dark and bright) corresponding to
a contrast of positions, (the position of a line east and
west being contrasted with the position north and south,)
which, as we have said, is the general character of
Polarity. It was with a view of expressing this character
that the term _Polarization_ was originally introduced.
Malus was forced by his discoveries into the use of this
expression. 'We find,' he says, in 1811, 'that light
acquires properties which are relative only to the sides of
the ray,--which are the same for the north and south sides
of the ray, (using {364} the points of the compass for
description's sake only,) and which are different when we go
from the north and south to the east or to the west sides of
the ray. I shall give the name of _poles_ to these sides of
the ray, and shall call _polarization_ the modification
which gives to light these properties relative to these
poles. I have _put off_ hitherto the admission of this term
into the description of the physical phenomena with which we
have to do: I did not _dare_ to introduce it into the
Memoirs in which I published my last observations: but the
variety of forms in which this new phenomenon appears, and
the difficulty of describing them, compel me to admit this
new expression; which signifies simply the modification
which light has undergone in acquiring new properties which
are not relative to the direction of the ray, but only to
its sides considered at right angles to each other, and in a
plane perpendicular to its direction.'

The theory which represents light as an emission of
particles was in vogue at the time when Malus published his
discoveries; and some of his followers in optical research
conceived that the phenomena which he thus described
rendered it necessary to ascribe poles and an axis to each
particle of light. On this hypothesis, light would be
polarized when the axes of all the particles were in the
same direction: and, making such a supposition, it may
easily be conceived capable of transmission through a
crystal whose axis is parallel to that of the luminous
particles, and intransmissible when the axis of the crystal
is in a position transverse to that of the particles.

The hypothesis of particles possessing _poles_ is a rude and
arbitrary assumption, in this as in other cases; but it
serves to convey the general notion of polarity, which is
the essential feature of the phenomena. The term
'polarization of light has sometimes been complained of in
modern times as hypothetical and obscure. But the real cause
of obscurity was, that the Idea of Polarity was, till
lately, very imperfectly developed in men's minds. As we
have seen, the general notion of Polarity,--opposite
properties in opposite {365} directions,--exactly describes
the character of the optical phenomena to which the term is
applied.

It is to be recollected that in optics we never speak of the
_poles_, but of the _plane of polarization_ of a ray. The
word _sides_, which Newton and Malus have used, neither of
them appears to have been satisfied with; Newton, in
employing it, had recourse to the strange Gallicism of
speaking of the _coast_ of usual and of unusual refraction
of a crystal.

The modern theory of optics represents the plane of
polarization of light as depending, not on the position in
which the axes of the luminiferous particles lie, but on the
_direction_ of those _transverse vibrations_ in which light
consists. This theory is, as we have stated in the History,
recommended by an extraordinary series of successes in
accounting for the phenomena. And this hypothesis of
transverse vibrations shows us another mechanical mode,
(besides the hypothesis of particles with axes,) by which we
may represent the polarity of a ray. But we may remark that
the general notion of Polarity, as applied to light in such
cases, would subsist, even if the undulatory theory were
rejected. The idea is, as we have before said, independent
of all hypothetical machinery.

I need not here refer to the various ways in which light may
be polarized; as, for instance, by being reflected from the
surface of water, or of glass, at certain angles, by being
transmitted, through crystals, and in other ways. In all
cases the modification produced, the polarization, is
identically the same property. Nor need I mention the
various kinds of phenomena which appear as contrasts in the
result; for these are not merely light and dark, or white
and black, but red and green, and generally, a colour and
its _complementary_ colour, exhibited in many complex and
varied configurations. These multiplied modes in which
polarized light presents itself add nothing to the original
conception of Polarization: and I shall therefore pass on to
another subject.

6. _Crystallization._--Bodies which are perfectly
crystallized exhibit the most complete regularity and {366}
symmetry of form; and this regularity not only appears in
their outward shape, but pervades their whole texture, and
manifests itself in their cleavage, their transparency, and
in the uniform and determinate optical properties which
exist in every part, even in the smallest fragment of the
mass. If we conceive crystals as composed of particles, we
must suppose these particles to be arranged in the most
regular manner; for example, if we suppose each particle to
have an axis, we must suppose all these axes to be parallel;
for the direction of the axis of the particles is indicated
by the physical and optical properties of the crystal, and
therefore this direction must be the same for every portion
of the crystal. This parallelism of the axes of the
particles may be conceived to result from the circumstance
of each particle having poles, the opposite poles attracting
each other. In virtue of forces acting as this hypothesis
assumes, a collection of small _magnetic_ particles would
arrange themselves in parallel positions; and such a
collection of magnetic particles offers a sort of image of a
crystal. Thus we are led to conceive the particles of
crystals as polarized, and as determined in their
crystalline positions by polar forces. This mode of
apprehending the constitution of crystals has been adopted
by some of our most eminent philosophers. Thus Berzelius
says[3\5], 'It is demonstrated, that the regular forms of
bodies presuppose an effort of their atoms to touch each
other by preference in certain points; that is, they are
founded upon a Polarity;'--he adds, 'a polarity which can be
no other than an electric or magnetic polarity.' In this
latter clause we have the identity of different kinds of
polarity asserted; a principle which we shall speak of in
the next chapter. But we may remark, that even without
dwelling upon this connexion, any notion which we can form
of the structure of Crystals necessarily involves the idea
of Polarity. Whether this polarity necessarily requires us
to believe crystals to be composed of Atoms which exert an
effort to touch {367} each other in certain points by
preference, is another question. And, in agreement with what
has been said respecting other kinds of polarity, we shall
probably find, on a more profound examination of the
subject, that while the Idea of Polarity is essential, the
machinery by which it is thus expressed is precarious and
superfluous.

[Note 3\5: _Essay on the Theory of Chemical Properties_,
1820, p. 113.]

7. _Chemical Affinity._--We shall have, in the next Book, to
speak of Chemical Affinity at some length; but since the
ultimate views to which philosophers have been led, induce
them to consider the forces of Affinity as Polar Forces, we
must enumerate these among the examples of Polarity. In
chemical processes, opposites tend to unite, and to
neutralize each other by their union. Thus an _acid_ or an
_alkali_ combine with vehemence, and form a compound, a
neutral salt, which is neither acid nor alkaline.

This conception of contrariety and mutual neutralization,
involves the Idea of Polarity. In the conception as
entertained by the earlier chemists, the Idea enters very
obscurely: but in the attempts which have more recently been
made to connect this relation (of acid and base), with other
relations, the chemical elements have been conceived as
composed of particles which possess poles; _like_ poles
repelling, and _unlike_ attracting each other, as they do in
magnetic and electric phenomena. This is, however, a rude
and arbitrary way of expressing Polarity, and, as may be
easily shown, involves many difficulties which do not belong
to the Idea itself. Mr. Faraday, who has been led by his
researches to a conviction of the polar nature of the forces
of chemical affinity, has expressed their character in a
more general manner, and without any of the machinery of
particles indued with poles. According to his view, chemical
synthesis and analysis must always be conceived as taking
place in virtue of equal and opposite forces, by which the
particles are united or separated. These forces, by the very
circumstance of their being polar, may be transferred from
point to point. For if we conceive a string of particles,
and if the positive force of the first particle {368} be
liberated and brought into action, its negative force also
must be set free: this negative force neutralizes the
positive force of the next particle, and therefore the
negative force of this particle (before employed in
neutralizing its positive force) is set free: this is in the
same way transferred to the next particle, and so on. And
thus we have a positive force active at one extremity of a
line of particles, corresponding to a negative force at the
other extremity, all the intermediate particles reciprocally
neutralizing each other's action. This conception of the
transfer of chemical action was indeed at an earlier period
introduced by Grotthus[4\5], and confirmed by Davy. But in
Mr. Faraday's hands we see it divested of all that is
superfluous, and spoken of, not as a line of particles, but
as 'an axis of power, having [at every point] contrary
forces, exactly equal, in opposite directions.'

[Note 4\5: DUMAS, _Leçons sur la Philosophie Chimique_, p. 401.]

8. _General Remarks._--Thus, as we see, the notion of
Polarity is applicable to many large classes of phenomena.
Yet the Idea in a distinct and general form is only of late
growth among philosophers. It has gradually been abstracted
and refined from many extraneous hypotheses which were at
first supposed to be essential to it. We have noticed some
of these hypotheses;--as the poles of a _body_; the poles of
the _particles_ of a fluid; _two_ opposite fluids; a single
fluid in _excess_ and _defect_; transverse _vibrations_. To
these others might be added. Thus Dr. Prout[5\5] assumes
that the polarity of molecules results from their _rotation_
on their axes, the opposite motions of contiguous molecules
being the cause of opposite (positive and negative)
polarities.

[Note 5\5: _Bridgewater Treatise_, p. 559.]

But none of these hypotheses can be proved by the fact of
Polarity alone; and they have been in succession rejected
when they had been assumed on that ground. Thus Davy, in
1826, speaking of chemical forces says[6\5], 'In assuming
the idea of two ethereal, subtile, elastic {369} fluids,
attractive of the particles of each other, and repulsive as
to their own particles, capable of combining in different
proportions with bodies, and according to their proportions
giving them their specific qualities and rendering them
equivalent masses, it would be natural to refer the action
of the poles to the repulsions of the substances combined
with the excess of one fluid, and the attractions of those
united to the excess of the other fluid; and a history of
the phenomena, not unsatisfactory to the reason, might in
this way be made out. But as it is possible likewise to take
an entirely different view of the subject, on the idea of
the dependence of the results upon the primary attractive
powers of the parts of the combination on a single subtile
fluid, I shall not enter into any discussion on this obscure
part of the theory.' Which of these theories will best
represent the case, will depend upon the consideration of
other facts, in combination with the polar phenomena, as we
see in the history of optical theory. In like manner Mr.
Faraday proved by experiment[7\5] the errour of all theories
which ascribe electro-chemical decomposition to the
attraction of the poles of the voltaic battery.

[Note 6\5: _Phil. Tr._ 1826, p. 415.]

[Note 7\5: _Researches_, p. 495, &c.]

In order that they may distinctly image to themselves the
Idea of Polarity, men clothe it in some of the forms of
machinery above spoken of; yet every new attempt shows them
the unnecessary difficulties in which they thus involve
themselves. But on the other hand it is difficult to
apprehend this Idea divested of all machinery; and to
entertain it in such a form that it shall apply at the same
time to magnetism and electricity, galvanism and chemistry,
crystalline structure and light. The Idea of _Polarity_
becomes most pure and genuine, when we entirely reject the
conception of _Poles_, as Faraday has taught us to do in
considering electro-chemical decomposition; but it is only
by degrees and by effort that we can reach this point of
abstraction and generality. {370}

9. There is one other remark which we may here make. It was
a maxim commonly received in the ancient schools of
philosophy, that 'Like attracts Like:' but as we have seen,
the universal maxim of Polar Phenomena is, that Like
_repels_ Like, and attracts Unlike. The north pole attracts
the south pole, the positive fluid attracts the negative
fluid; opposite elements rush together; opposite motions
reduce each other to rest. The permanent and stable course
of things is that which results from the balance and
neutralization of contrary tendencies. Nature is constantly
labouring after repose by the effect of such tendencies; and
so far as Polar Forces enter into her economy, she seeks
harmony by means of discord, and unity by opposition.

Although the Idea of Polarity is as yet somewhat vague and
obscure, even in the minds of the cultivators of physical
science, it has nevertheless given birth to some general
principles which have been accepted as evident, and have had
great influence on the progress of science. These we shall
now consider.

{{371}}
CHAPTER II.

OF THE CONNEXION OF POLARITIES.

1. IT has appeared in the preceding chapter that in cases in
which the phenomena suggest to us the idea of Polarity, we
are also led to assume some material machinery as the mode
in which the polar forces are exerted. We assume, for
instance, globular particles which possess poles, or the
vibrations of a fluid, or two fluids attracting each other;
in every case, in short, some hypothesis by which the
existence and operation of the Polarity is embodied in
geometrical and mechanical properties of a medium; nor is it
possible for us to avoid proceeding upon the conviction that
some such hypothesis must be true; although the nature of
the connexion between the mechanism and the phenomena must
still be indefinite and arbitrary.

But since each class of Polar Phenomena is thus referred to
an ulterior cause, of which we know no more than that it has
a polar character, it follows that _different_ Polarities
may result from the _same_ cause manifesting its polar
character under different aspects. Taking, for example, the
hypothesis of globular particles, if electricity result from
an action dependent upon the _poles_ of each globule,
magnetism may depend upon an action in the _equator_ of each
globule; or taking the supposition of transverse vibrations,
if polarized light result directly from such _vibrations_,
crystallization may have reference to the _axes_ of the
elasticity of the _medium_ by which the vibrations are
rendered transverse,--so far as the polar character only of
the phenomena is to be accounted for. I say this _may_ be
so, _in so far_ only as the polar character of the phenomena
is concerned; for whether the relation of {372} electricity
to magnetism, or of crystalline forces to light, can really
be explained by such hypotheses, remains to be determined by
the facts themselves. But since the first necessary feature
of the hypothesis is, that it shall give polarity, and since
an hypothesis which does this, may, by its mathematical
relations, give polarities of different kinds and in
different directions, any two co-existent kinds of polarity
may result from the same cause, manifesting itself in
various manners.

The conclusion to which we are led by these general
considerations is, that two co-existing classes of polar
phenomena _may_ be effects of the same cause. But those who
have studied such phenomena more deeply and attentively
have, in most or in all cases, arrived at the conviction
that the various kinds of Polarity in such cases _must_ be
connected and fundamentally identical. As this conviction
has exercised a great influence, both upon the discoveries
of new facts and upon the theoretical speculations of modern
philosophers, and has been put forward by some writers as a
universal principle of science, I will consider some of the
cases in which it has been thus applied.

2. _Connexion of Magnetic and Electric Polarity._--The polar
phenomena of electricity and magnetism are clearly analogous
in their laws: and obvious facts showed at an early period
that there was some connexion between the two agencies.
Attempts were made to establish an evident and definite
relation between the two kinds of force, which attempts
proceeded upon the principle now under
consideration;--namely, that in such cases, the two kinds of
Polarity must be connected. Professor Œrsted, of Copenhagen,
was one of those who made many trials founded upon this
conviction: yet all these were long unsuccessful. At length,
in 1820, he discovered that a galvanic current, passing at
right angles near to a magnetic needle, exercises upon it a
powerful deflecting force. The connexion once detected
between magnetism and galvanism was soon recognized as
constant and universal. It was represented in different
hypothetical modes by different persons; some considering
the galvanic {373} current as the primitive axis, and the
magnet as constituted of galvanic currents passing round it
at right angles to the magnetic axis; while others conceived
the magnetic axis as the primitive one, and the electric
current as implying a magnetic current round the wire. So
far as many of the general relations of these two kinds of
force were concerned, either mode of representation served
to express them; and thus the assumption that the two
Polarities, the magnetic and the electric, were
fundamentally identical, was verified, so far as the
phenomena of magnetic attraction, and the like, were
concerned.

I need not here mention how this was further confirmed by
the experiments in which, by means of the forces thus
brought into view, a galvanic wire was made to revolve round
a magnet, and a magnet round a galvanic wire;--in which
artificial magnets were constructed of coils of galvanic
wire;--and finally, in which the galvanic spark was obtained
from the magnet. The identity which sagacious speculators
had divined even before it was discovered, and which they
had seen to be universal as soon as it was brought to light,
was completely manifested in every imaginable form.

The relation of the electric and magnetic Polarities was
found to be, that they were _transverse_ to each other, and
this relation exhibited under various conditions of form and
position of the apparatus, gave rise to very curious and
unexpected perplexities. The degree of complication which
this relation may occasion, may be judged of from the number
of constructions and modes of conception offered by Œrsted,
Wollaston, Faraday, and others, for the purpose of framing a
technical memory of the results. The magnetic polarity gives
us the north and south poles of the needle; the electric
polarity makes the current positive and negative; and these
pairs of opposites are connected by relations of situation,
as above and below, right and left; and give rise to the
resulting motion of the needle one way or the other. {374}

3. Ampère, by framing his hypotheses of the action of
voltaic currents and the constitution of magnets, reduced
all these technical rules to rigorous deductions from one
general principle. And thus the vague and obscure persuasion
that there _must_ be _some_ connexion between Electricity
and Magnetism, so long an idle and barren conjecture, was
unfolded into a complete theory, according to which magnetic
and electromotive actions are only two different
manifestations of the same forces; and all the
above-mentioned complex relations of polarities are reduced
to one single polarity, that of the electro-dynamic current.

4. As the Idea of Polarity was thus firmly established and
clearly developed, it became an instrument of reasoning.
Thus it led Ampère to maintain that the original or
elementary forces in electro-dynamic action could not be as
M. Biot thought they were, a statical _couple_, but must be
directly opposite to each other. The same idea enabled Mr.
Faraday to carry on with confidence such reasonings as the
following[8\5]: 'No other known power has like direction
with that exerted between an electric current and a magnetic
pole; it is tangential, while all other forces acting at a
distance are direct. Hence if a magnetic pole on one side of
a revolving plate follow its course by reason of its
obedience to the tangential force exerted upon it by the
very current of electricity which it has itself caused; a
similar pole on the other side of the plate should
immediately set it free from this force; for the currents
which have to be formed by the two poles are in contrary
directions.' And in Article 1114 of his _Researches_, the
same eminent philosopher infers that if electricity and
magnetism are considered as the results of a peculiar agent
or condition, exerted in determinate directions
perpendicular to each other, one must be by some means
convertible into the other; and this he was afterwards able
to prove to be the case in fact.

[Note 8\5: _Researches_, 244.]

{375} Thus the principle that the Co-existent Polarities of
magnetism and electricity are connected and fundamentally
identical, is not only true, but is far from being either
vague or barren. It has been a fertile source both of
theories which have, at present, a very great probability,
and of the discovery of new and striking facts. We proceed
to consider other similar cases.

5. _Connexion of Electrical and Chemical Polarities._--The
doctrine that the chemical forces by which the elements of
bodies are held together or separated, are identical with
the polar forces of electricity, is a great discovery of
modern times; so great and so recent, indeed, that probably
men of science in general have hardly yet obtained a clear
view and firm hold of this truth. This doctrine is now,
however, entirely established in the minds of the most
profound and philosophical chemists of our time. The
complete development and confirmation of this as of other
great truths, was preceded by more vague and confused
opinions gradually tending to this point; and the progress
of thought and of research was impelled and guided, in this
as in similar cases, by the persuasion that these
co-existent polarities could not fail to be closely
connected with each other. While the ultimate and exact
theory to which previous incomplete and transitory theories
tended is still so new and so unfamiliar, it must needs be a
matter of difficulty and responsibility for a common reader
to describe the steps by which truth has advanced from point
to point. I shall, therefore, in doing this, guide myself
mainly by the historical sketches of the progress of this
great theory, which, fortunately for us, have been given us
by the two philosophers who have played by far the most
important parts in the discovery, Davy and Faraday.

It will be observed that we are concerned here with the
progress of theory, and not of experiment, except so far as
it is confirmatory of theory. In Davy's Memoir[9\5] of 1826,
on the Relations of Electrical and {376} Chemical Changes,
he gives the historical details to which I have alluded.
Already in 1802 he had conjectured that all chemical
decompositions might be polar. In 1806 he attempted to
confirm this conjecture, and succeeded, to his own
satisfaction, in establishing[10\5] that the combinations
and decompositions by electricity were referable to the law
of electrical attractions and repulsions; and advanced the
hypothesis (as he calls it), that chemical and electrical
attractions were produced by the same cause, acting in one
case on particles, in the other on masses. This hypothesis
was most strikingly confirmed by the author's being able to
use electrical agency as a more powerful means of chemical
decomposition than any which had yet been applied.
'Believing,' he adds, 'that our philosophical systems are
exceedingly imperfect, I never attached much importance to
this hypothesis; but having formed it after a copious
induction of facts, and having gained by the application of
it a number of practical results, and considering myself as
much the author of it as I was of the decomposition of the
alkalies, and having developed it in an elementary work as
far as the present state of chemistry seemed to allow, I
have never,' he says, 'criticised or examined the manner in
which different authors have adopted or explained it,
contented, if in the hands of others, it assisted the
arrangements of chemistry or mineralogy, or became an
instrument of discovery.' When the doctrine had found an
extensive acceptance among chemists, attempts were made to
show that it had been asserted by earlier writers: and
though Davy justly denies all value to these pretended
anticipations, they serve to show, however dimly, the
working of that conviction of the Connexion of Co-existent
Properties which all along presided in men's minds during
this course of investigation. 'Ritter and Winterl have been
quoted,' Davy says[11\5], 'among other persons, as having
imagined or anticipated the relation between electrical
powers and chemical affinities before the discovery of the
pile {377} of Volta. But whoever will read with attention
Ritter's "Evidence that Galvanic action exists in organised
nature," and **Winterl's _Prolusiones ad Chemiam sæculi decimi
noni_, will find nothing to justify this opinion.' He then
refers to the Queries of Newton at the end of his Optics.
'These,' he says, 'contain more grand and speculative views
that might be brought to bear upon this question than any
found in the works of modern electricians; but it is very
unjust to the experimentalists who by the laborious
application of new instruments, have discovered novel facts
and analogies, to refer them to any such suppositions as
that all attractions, chemical, electrical, magnetical, and
gravitative, may depend upon the same cause.' It is
perfectly true, that such vague opinions, though arising
from that tendency to generalize which is the essence of
science, are of no value except so far as they are both
rendered intelligible, and confirmed by experimental
research.

[Note 9\5: _Phil. Trans._ 1826, p. 383.]

[Note 10\5: _Phil. Trans._ 1826, p. 389.]

[Note 11\5: _Ibid._ p. 384.]

The phenomena of chemical decomposition by means of the
voltaic pile, however, led other persons to views very
similar to those of Davy. Thus Grotthus in 1805[12\5]
published an hypothesis of the same kind. 'The pile of
Volta,' he says, 'is an electrical magnet, of which each
element, that is, each pair of plates, has a positive and a
negative pole. The consideration of this polarity suggested
to me the idea that a similar polarity may come into play
between the elementary particles of water when acted upon by
the same electrical agent; and I avow that this thought was
for me a flash of light.'

[Note 12\5: _Ann. Chim._ lxviii. 54.]

6. The thought, however, though thus brought into being, was
very far from being as yet freed from vagueness,
superfluities, and errours. I have elsewhere noticed[13\5]
Faraday's remark on Davy's celebrated Memoir of 1806; that
'the mode of action by which the effects take place is
stated very generally, so generally, indeed, that probably a
dozen precise schemes of electro-chemical action might be
drawn up, differing {378} essentially from each other, yet
all agreeing with the statement there given.' When Davy and
others proceeded to give a little more definiteness and
precision to the statement of their views, they soon
introduced into the theory features which it was afterwards
found necessary to abandon. Thus[14\5] both Davy, Grotthus,
Riffault, and Chompré, ascribed electrical decomposition to
the action of the _poles_, and some of them even pretended
to assign the proportion in which the force of the pole
diminishes as the distance from it increases. Faraday, as I
have already stated, showed that the polarity must be
considered as residing not only in what had till then been
called the _poles_, but at every point of the circuit. He
ascribed[15\5] electro-chemical decomposition to internal
forces, residing in the _particles_ of the matter under
decomposition, not to external forces, exerted by the poles.
Hence he shortly afterwards[16\5] proposed to reject the
word _poles_ altogether, and to employ instead, the term
_electrode_, meaning the doors or passages (of whatever
surface formed) by which the decomposed elements pass out.
What have been called the _positive_ and _negative_ poles he
further termed the _Anode_ and _Cathode_; and he introduced
some other changes in nomenclature connected with these. He
then, as I have related in the History[17\5], invented the
Volta-electrometer, which enabled him to measure the
quantity of voltaic action, and this he found to be
identical with the quantity of chemical affinity; and he was
thus led to the clearest view of the truth towards which he
and his predecessors had so long been travelling, that
electrical and chemical forces are identical[18\5].

[Note 13\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 1.]

[Note 14\5: See Faraday's Historical Sketch, _Researches_,
481-492.]

[Note 15\5: Art. 524.]

[Note 16\5: In 1834. Eleventh Series of Researches. Art. 662.]

[Note 17\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 2.]

[Note 18\5: Arts. 915, 916, 917.]

7. It will, perhaps, be said that this beautiful train of
discovery was entirely due to experiment, and not to any _à
priori_ conviction that co-existent polarities {379} must be
connected. I trust I have sufficiently stated that such an
_à priori_ principle could not be proved, nor even
understood, without a most laborious and enlightened use of
experiment; but yet I think that the doctrine, when once
fully unfolded, exhibited clearly, and established as true,
takes possession of the mind with a more entire conviction
of its certainty and universality, in virtue of the
principle we are now considering. When the theory has
assumed so simple a form, it appears to derive immense
probability (to say the least) from its simplicity. Like the
laws of motion, when stated in its most general form, it
appears to carry with it its own evidence. And thus this
great theory borrows something of its character from the
Ideas which it involves, as well as from the Experiments by
which it was established.

8. We may find in many of Mr. Faraday's subsequent
reasonings, clear evidence that this idea of the Connexion
of Polarities, as now developed, is not limited in its
application to facts already known experimentally, but, like
other ideas, determines the philosopher's researches into
the unknown, and gives us the _form_ of knowledge even
before we possess the _matter_. Thus, he says, in his
Thirteenth Series[19\5], 'I have long sought, and still
seek, for an effect or condition which shall be to statical
electricity what magnetic force is to current electricity;
for as the lines of discharge are associated with a certain
transverse effect, so it appeared to me impossible but that
the lines of tension or of inductive action, which of
necessity precede the discharge, should also have their
correspondent transverse condition or effect.' Other similar
passages might be found.

[Note 19\5: Art. 1658.]

I will now consider another case to which we may apply the
Principle of Connected Polarities.

9. _Connexion of Chemical and Crystalline Polarities._--The
close connexion between the Chemical Affinity and the
Crystalline Attraction of elements cannot be overlooked.
Bodies never crystallize but when their elements combine
chemically; and solid bodies which {380} combine, when they
do it most completely and exactly, also crystallize. The
forces which _hold together_ the elements of a crystal of
alum are the same forces which make it a _crystal_. There is
no distinguishing between the two sets of forces.

Both _chemical_ and _crystalline_ forces are _polar_, as we
stated in the last chapter; but the polarity in the two
cases is of a different kind. The polarity of chemical
forces is then put in the most distinct form, when it is
identified with electrical polarity; the polarity of the
particles of crystals has reference to their geometrical
form. And it is clear that these two kinds of polarity must
be connected. Accordingly, Berzelius expressly asserts[20\5]
the necessary identity of these two polarities. 'The regular
forms of bodies suppose a polarity which _can be_ no other
than an electric or magnetic polarity.' This being so
seemingly inevitable, we might expect to find the electric
forces manifesting some relation to the definite directions
of crystalline forms. Mr. Faraday tried, but in vain, to
detect some such relation. He attempted to ascertain[21\5]
whether a cube of rock crystal transmitted the electrical
force of tension with different intensity along and across
the axis of the crystal. In the first specimen there seemed
to be some difference; but in other experiments, made both
with rock crystal and with calc spar, this difference
disappeared. Although therefore we may venture to assert
that there must be some very close connexion between
electrical and crystalline forces, we are, as yet, quite
ignorant what the nature of the connexion is, and in what
kind of phenomena it will manifest itself.

[Note 20\5: _Essay on Chemical Prop._ 113.]

[Note 21\5: _Researches_. Art. 1689.]

10. _Connexion of Crystalline and Optical
Polarities._--Crystals present to us _optical_ phenomena
which have a manifestly polar character. The double
refraction, both of uniaxal and of biaxal crystals, is
always accompanied with opposite polarization of the two
rays; and in this and in other ways light is polarized in
directions dependent upon the axes of the crystalline form,
that is, on the directions of the polarities of the {381}
crystalline particles. The identity of these two kinds of
polarity (crystalline and optical) is too obvious to need
insisting on; and it is not necessary for us here to decide
by what hypothesis this identity may most properly be
represented. We may hereafter perhaps find ourselves
justified in considering the crystalline forces as
determining the _elasticity_ of the luminiferous ether to be
different in _different directions_ within the crystal, and
thus as determining the refraction and polarization of the
light which the crystal transmits. But at present we merely
note this case as an additional example of the manifest
connexion and fundamental identity of two co-existent
polarities.

11. _Connexion of Polarities in general._--Thus we find that
the Connexion of different kinds of Polarities, magnetic,
electric, chemical, crystalline, and optical, is certain as
a truth of experimental science. We have attempted to show
further that in the minds of several of the most eminent
discoverers and philosophers, such a conviction is something
more than a mere empirical result: it is a principle which
has regulated their researches while it was still but
obscurely seen and imperfectly unfolded, and has given to
their theories a character of generality and self-evidence
which experience alone cannot bestow.

It will, perhaps, be said that these doctrines,--that
scientific researches may usefully be directed by principles
in themselves vague and obscure;--that theories may have an
evidence superior to and anterior to experience;--are
doctrines in the highest degree dangerous, and utterly at
variance with the soundest maxims of modern times respecting
the cultivation of science.

In the justice and wisdom of this caution I entirely agree:
and although I have shown that this principle of the
_Connexion of Polarities_, rightly interpreted and
established in each case by experiment, involves profound
and comprehensive truths; I think it no less important to
remark that, at least in the present stage of our knowledge,
we can make no use of this principle without taking care, at
every step, to determine by {382} clear and decisive
experiments, its proper meaning and application. All
endeavours to proceed otherwise have led, and must lead, to
ignorance and confusion. Attempts to deduce from our bare
Idea of Polarity, and our fundamental convictions respecting
the connexion of polarities, theories concerning the forces
which really exist in nature, can hardly have any other
result than to bewilder men's minds, and to misdirect their
efforts.

So far, indeed, as this persuasion of a connexion among
apparently different kinds of agencies, impels men, engaged
in the pursuit of knowledge, to collect observations, to
multiply, repeat, and vary experiments, and to contemplate
the result of these in all aspects and relations, it may be
an occasion of the most important discoveries. Accordingly
we find that the great laws of phenomena which govern the
motions of the planets about the sun, were first discovered
by Kepler, in consequence of his scrutinizing the recorded
observations with an intense conviction of the existence of
geometrical and arithmetical harmonies in the solar system.
Perhaps we may consider the discovery of the connexion of
magnetism and electricity by Professor Œrsted in 1820, as an
example somewhat of the same kind; for he also was a
believer in certain comprehensive but undefined relations
among the properties of bodies; and in consequence of such
views entertained great admiration for the _Prologue to the
Chemistry of the Nineteenth Century_, of Winterl, already
mentioned. M. Œrsted, in 1803, published a summary of this
work; and in so doing, praised the views of Winterl as far
more profound and comprehensive than those of Lavoisier.
Soon afterwards a Review of this publication appeared in
France[22\5], in which it was spoken of as a work only fit
for the dark ages, and as the indication of a sect which had
for some time 'ravaged Germany,' and inundated that country
with extravagant and unintelligible mysticism. It was,
therefore, a kind of triumph to M. Œrsted to be, after {383}
some years' labour, the author of one of the most remarkable
and fertile physical discoveries of his time.

[Note 22\5: _Ann. Chim._, Tom. 1. (1804), p. 191.]

12. It was not indeed without some reason that certain of
the German philosophers were accused of dealing in doctrines
vast and profound in their aspect, but, in reality,
indefinite, ambiguous, and inapplicable. And the most
prominent of such doctrines had reference to the principle
now under our consideration; they represented the properties
of bodies as consisting in certain polarities, and professed
to deduce, from the very nature of things, with little or no
reference to experiment, the existence and connexion of
these polarities. Thus Schelling, in his _Ideas towards a
Philosophy of Nature_, published in 1803, says[23\5],
'Magnetism is the universal act of investing Multiplicity
with Unity; but the universal form of the reduction of
Multiplicity to Unity is the Line, pure Longitudinal
Extension: hence Magnetism is determination of pure
Longitudinal Extension; and as this manifests itself by
absolute Cohesion, Magnetism is the determination of
absolute Cohesion.' And as Magnetism was, by such reasoning,
conceived to be proved as a universal property of matter,
Schelling asserted it to be a confirmation of his views when
it was discovered that other bodies besides iron are
magnetic. In like manner he used such expressions as the
following[24\5]: 'The threefold character of the Universal,
the Particular, and the Indifference of the two,--as
expressed in their Identity, is Magnetism, as expressed in
their Difference, is Electricity, and as expressed in the
Totality, is Chemical Process. Thus these forms are only one
form; and the Chemical Process is a mere transfer of the
three Points of Magnetism into the Triangle of Chemistry.'

[Note 23\5: P. 223.]

[Note 24\5: P. 486.]

It was very natural that the chemists should refuse to
acknowledge, in this fanciful and vague language,
(delivered, however, it is to be recollected, in 1803,) an
anticipation of Davy's doctrine of the identity of
electrical and chemical forces, or of Œrsted's {384}
electro-magnetic agency. Yet it was perhaps no less natural
that the author of such assertions should look upon every
great step in the electro-chemical theory as an illustration
of his own doctrines. Accordingly we find Schelling
welcoming, with a due sense of their importance, the
discoveries of Faraday. When he heard of the experiment in
which electricity was produced from common magnetism, he
fastened with enthusiasm upon the discovery, even before he
knew any of its details, and proclaimed it at a public
meeting of a scientific body[25\5] as one of the most
important advances of modern science. We have (he thus
reasoned) three effects of polar forces;--Electro-chemical
Decomposition, Electrical Action, Magnetism. Volta and Davy
had confirmed experimentally the identity of the two former
agencies: Œrsted showed that a closed voltaic circuit
acquired magnetic properties: but in order to exhibit the
identity of electric and magnetic action it was requisite
that electric forces should be extricated from magnetic.
This great step Faraday, he remarked, had made, in producing
the electric spark by means of magnets.

[Note 25\5: Ueber Faraday's _Neueste Entdeckung_. München. 1832.]

13. Although conjectures and assertions of the kind thus put
forth by Schelling involve a persuasion of the pervading
influence and connexion of polarities, which persuasion has
already been confirmed in many instances, they involve this
principle in a manner so vague and ambiguous that it can
rarely, in such a form, be of any use or value. Such views
of polarity can never teach us in what cases we are and in
what we are not expected to find polar relations; and indeed
tend rather to diffuse error and confusion, than to promote
knowledge. Accordingly we cannot be surprized to find such
doctrines put forward by their authors as an evidence of the
small value and small necessity of experimental science.
This is done by the celebrated metaphysician Hegel, in his
_Encyclopædia_[26\5]. 'Since,' {385} says he, 'the plane of
incidence and of reflection in simple reflection is the same
plane, when a second reflector is introduced which further
distributes the illumination reflected from the first, the
position of the first plane with respect to the second
plane, containing the direction of the first reflection and
of the second, has its influence upon the position,
illumination or darkening of the object as it appears by the
second reflection. This influence must be the strongest when
the two planes are what we must call _negatively_ related to
each other:--that is, when they are at right angles.' 'But,'
he adds, 'when men infer (as Malus has done) from the
modification which is produced by this situation, in the
illumination of the reflection, that the molecules of light
in themselves, that is, on their different sides, possess
different physical energies; and when on this foundation,
along with the phenomena of entoptical colours therewith
connected, a wide labyrinth of the most complex theory is
erected; we have then one of the most remarkable examples of
the _inferences_ of physics from experiment.' If Hegel's
reasoning prove anything, it must prove that polarization
always accompanies reflection under such circumstances as he
describes: yet all physical philosophers know that in the
case of metals, in which the reflection is most complete,
light is not completely polarized at any angle; and that in
other substances the polarization depends upon various
circumstances which show how idle and inapplicable is the
account which he thus gives of the property. His
self-complacent remark about the inferences of physics from
experiment, is intended to recommend by comparison his own
method of considering the nature of 'things in themselves;'
a mode of obtaining physical truth which had been more than
exhausted by Aristotle, and out of which no new attempts
have extracted anything of value since his time.

[Note 26\5: Sec. 278.]

14. Thus the general conclusion to which we are led on this
subject, is, that the persuasion of the existence and
Connexion or Identity of various Polarities in nature,
although very naturally admitted, and in many {386} cases
interpreted and confirmed by observed facts, is of itself,
so far as we at present possess it, a very insecure guide to
scientific doctrines. When it is allowed to dictate our
theories, instead of animating and extending our
experimental researches, it leads only to errour, confusion,
obscurity, and mysticism.

This Fifth Book, on the subject of Polarities, is a short
one compared with most of the others. This arises in a great
measure from the circumstance that the Idea of Polarity has
only recently been apprehended and applied, with any great
degree of clearness, among physical philosophers; and is
even yet probably entertained in an obscure and ambiguous
manner by most experimental inquirers. I have been desirous
of not attempting to bring forward any doctrines upon the
subject, except such as have been fully illustrated and
exemplified by the acknowledged progress of the physical
sciences. If I had been willing to discuss the various
speculations which have been published respecting the
universal prevalence of Polarities in the universe, and
their results in every province of nature, I might easily
have presented this subject in a more extended form; but
this would not have been consistent with my plan of tracing
the influence of scientific Ideas only so far as they have
really aided in disclosing and developing scientific truths.
And as the influence of this Idea is clearly distinguishable
both from those which precede and those which follow, in the
character of the sciences to which it gives rise, and as it
appears likely to be hereafter of great extent and
consequence, it seemed better to treat of it in a separate
Book, although of a brevity disproportioned to the rest.

END OF VOL. I.

Cambridge: Printed at the University Press.

HISTORY
OF
SCIENTIFIC IDEAS.

VOLUME II.

Cambridge;
PRINTED BY C. J. CLAY, M.A.
AT THE UNIVERSITY PRESS.

HISTORY
OF
SCIENTIFIC IDEAS.

BY WILLIAM WHEWELL, D.D.,
MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.

BEING THE FIRST PART OF THE PHILOSOPHY
OF THE INDUCTIVE SCIENCES.

_THE THIRD EDITION._

IN TWO VOLUMES.

ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ

VOLUME II.

LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1858.

CONTENTS
OF
THE SECOND VOLUME.

BOOK VI.

THE PHILOSOPHY OF CHEMISTRY.

PAGE
CHAP. I. ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION 3

_Art._ 1. Fundamental Ideas of Chemistry.
2. Elements.
3. Do Compounds resemble their Elements?
4. The Three Principles.
5. A Modern Errour.
6. Are Compounds determined by the Figure of Elements?
7. Crystalline Form depends on Figure of Elements.
8. Are Compounds determined by Mechanical Attraction
of Elements?
9. Newton's followers.
10. Imperfection of their Hypotheses.

CHAP. II. ESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF
CHEMICAL AFFINITY 15

_Art._ 1. Early Chemists.
2. Chemical Affinity.
3. Affinity or Attraction?
4. Affinity preferable.
5. Analysis is possible.
{vi}
6. Affinity is Elective.
7. Controversy on this.
8. Affinity is Definite.
9. Are these Principles necessarily true?
10. Composition determines Properties.
11. Comparison on this subject.
12. Composition determines Crystalline Form.

CHAP. III. OF THE IDEA OF SUBSTANCE 29

_Art._ 1. Indestructibility of Substance.
2. The Idea of Substance.
3. Locke's Denial of Substance.
4. Is all Substance heavy?
Note on Sir W. Hamilton's objections 37

CHAP. IV. APPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY 39

_Art._ 1. A Body is Equal to its Elements.
2. Lavoisier.
3. Are there Imponderable Elements?
4. Faraday's views.
5. Composition of Water.
6. Heat in Chemistry.

CHAP. V. THE ATOMIC THEORY 48

_Art._ 1. The Theory on Chemical Grounds.
2. Hypothesis of Atoms.
3. Its Chemical Difficulties.
4. Grounds of the Atomic Doctrine.
5. Ancient Atomists.
6. Francis Bacon.
7. Modern Atomists.
8. Arguments for and against.
9. Boscovich's Theory.
10. Molecular Hypothesis.
11. Poisson's Inference.
12. Wollaston's Argument.
13. Properties are Permanent.
{vii}
BOOK VII.

THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.

CHAP. I. EXPLICATION OF THE IDEA OF SYMMETRY 67

_Art._ 1. Symmetry, what.
2. Kinds of Symmetry.
3. Examples in Nature.
4. Vegetables and Animals.
5. Symmetry a Fundamental Idea.
6. Result of Symmetry.

CHAP. II. APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS 75

_Art._ 1. 'Fundamental Forms.'
2. Their use.
3. 'Systems of Crystallization.'
4. Cleavage.
5. Other Properties.

CHAP. III. SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS 80

_Art._ 1. Integrant Molecules.
2. Difficulties of the Theory.
3. Merit of the Theory.
4. Wollaston's Hypothesis.
5. Maxim for such Hypotheses.
6. Dalton's Hypothesis.
7. Ampère's Hypothesis.
8. Difficulty of such Hypotheses.
9. Isomorphism.
{viii}
BOOK VIII.

PHILOSOPHY OF THE CLASSIFICATORY SCIENCES.

CHAP. I. THE IDEA OF LIKENESS AS GOVERNING THE USE OF
COMMON NAMES 95

_Art._ 1. Object of the Chapter.
2. Unity of the Individual.
3. Condition of Unity.
4. Kinds.
5. Not made by Definitions.
6. Condition of the Use of Terms.
7. Terms may have different Uses.
8. Gradation of Kinds.
9. Characters of Kinds.
10. Difficulty of Definitions.
11. 'The Five Words.'

CHAP. II. THE METHODS OF NATURAL HISTORY, AS REGULATED
BY THE IDEA OF LIKENESS 108

_Sect._ I. _Natural History in General._
_Art._ 1. Idea of Likeness in Natural History.
2. Condition of its Use.

_Sect._ II. _Terminology._
_Art._ 3. Meaning of the word.

_Sect._ III. _The Plan of the System._
_Art._ 4. Its Meaning.
5. Latent Reference to Natural Affinity.
6. Natural Classes.
7. Artificial Classes.
8. Are Genera Natural?
9. Natural History and Mathematics.
10. Natural Groups given by Type, not by Definition.
11. Physiography.
12. Artificial and Natural Systems.
{ix}
_Sect._ IV. _Methods of framing Natural Systems._
_Art._ 13. Method of Blind Trial.
14. Method of General Comparison.

_Sect._ V. _Gradation of Groups._
_Art._ 15. Series of Subdivisions.
16. What is a Species?
17. The _words_ 'Species' and 'Genus.'
18. Varieties. Races.

_Sect._ VI. _Nomenclature._
_Art._ 19. Binary Nomenclature.

_Sect._ VII. _Diagnosis._
_Art._ 20. Characteristick and Systematick.

CHAP. III. APPLICATION OF THE NATURAL HISTORY METHOD
TO MINERALOGY 138

_Art._ 1. Mohs's System.
2. His 'Characteristick.'
3. Mineral _Species_ not yet well fixed.
4. _Orders_ of Minerals.
5. Nomenclature of Minerals.
6. M. Necker's 'Règne Mineral.'
7. Inconvenience of taking a Chemical Basis of
Mineral Systems.
8. Relation of Natural History and Chemistry.
9. What is a Mineralogical Individual?
10. A well-formed Crystal is an Individual.
11. Not the Integrant Molecules,
12. Nor the Cleavage Forms.
13. Compound Crystals are not Individuals.
14. Crystalline Forms are sufficiently complete for
this.
15. Including aggregate Masses.
16. Do Artificial Crystals belong to Mineralogy?
17. The Mineralogical Individual extends as far as
the same Crystalline Axes extend.
18. Artificial Crystals do belong to Mineralogy:
{x}
19. Cannot be excluded.
20. Species to be determined by the Crystalline Power.
21. Secondary Derivative Forms are Varieties:
22. Are not Species, as M. Necker holds.

CHAP. IV. OF THE IDEA OF NATURAL AFFINITY 159

_Art._ 1. The Idea of Affinity
2. Is not to be made out by Arbitrary Rules.
3. Functions of Living things are many,
4. But all lead to the same arrangement.
5. This is Cuvier's principle:
6. And Decandolle's.
7. Is this applicable to Inorganic Bodies?
8. Yes; by the agreement of Physical and
Chemical Arrangement.

BOOK IX.

THE PHILOSOPHY OF BIOLOGY.

CHAP. 1. ANALOGY OF BIOLOGY WITH OTHER SCIENCES. 169

_Art._ 1. Biology involves the Idea of Life.
2. This Idea to be historically traced.
3. The Idea at first expressed by means of other
Ideas.
4. Mystical, Mechanical, Chemical, and Vital
Fluid Hypotheses.

CHAP. II. SUCCESSIVE BIOLOGICAL HYPOTHESES 174

_Sect._ I. _The Mystical School._

_Sect._ II. _The Iatrochemical School._

_Sect._ III. _The Iatromathematical School._

_Sect._ IV. _The Vital Fluid School._

_Sect._ V. _The Psychical School._
{xi}

CHAP. III. ATTEMPTS TO ANALYSE THE IDEA OF LIFE 195

_Art._ 1. Definitions of Life,
2. By Stahl, Humboldt, Kant.
3. Definition of Organization by Kant.
4. Life is a System of Functions.
5. Bichat. _Sum_ of Functions.
6. Use of Definition.
7. Cuvier's view.
8. Classifications of Functions.
9. Vital, Natural, and Animal Functions.
10. Bichat. Organic and Animal Life.
11. Use of this Classification.

CHAP. IV. ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES,
AND FIRST, OF ASSIMILATION AND SECRETION 203

_Sect._ I. _Course of Biological Research._
_Art._ 1. Observation and New Conceptions.

_Sect._ II. _Attempts to form a distinct Conception
of Assimilation and Secretion._
_Art._ 2. The Ancients.
3. Buffon. Interior Mould.
4. Defect of this view.
5. Cuvier. Life a Vortex.
6. Defect of this view.
7. Schelling. Matter and Form.
8. Life a constant Form of circulating Matter, &c.

_Sect._ III. _Attempts to conceive the Forces of
Assimilation and Secretion._
_Art._ 9. Assimilation is a Vital Force.
10. The name 'Assimilation.'
11. Several processes involved in Assimilation.
12. _Absorption_. Endosmose.
13. Absorption involves a Vital Force.
14. _Secretion_. Glands.
15. Motions of Vital Fluids.
{xii}
_Sect._ IV. _Attempts to conceive the Process of Generation._
_Art._ 16. 'Reproduction' figuratively used for Generation.
17. Nutrition different from
18. Generation.
19. Generations successively included.
20. Pre-existence of Germs.
21. Difficulty of this view.
22. Communication of Vital Forces.
23. Close similarity of Nutrition and Generation.
24. The Identity of the two Processes exemplified.

CHAP. V. ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL
FORCES, _continued_.--VOLUNTARY MOTION. 222

_Art._ 1. Voluntary Motion one of the animal Functions.
2. Progressive knowledge of it.
3. Nervous Fluid not electric.
4. Irritability. Glisson.
5. Haller.
6. Contractility.
7. Organic Sensibility and Contractility not separable.
8. Improperly described by Bichat.
9. Brown.
10. Contractility a peculiar Power.
11. Cuvier's view.
12. Elementary contractile Action.
13. Strength of Muscular Fibre.
14. Sensations become Perceptions
15. By means of Ideas;
16. And lead to Muscular Actions.
17. Volition comes between Perception and Action.
18. Transition to Psychology,
19. A center is introduced.
20. The central consciousness may be obscure.
21. Reflex Muscular Action.
22. Instinct.
23. Difficulty of conceiving Instinct.
24. Instinct opposed to Insight.
{xiii}

CHAP. VI. OF THE IDEA OF FINAL CAUSES 239

_Art._ 1. Organization. Parts are Ends and Means.
2. Not merely mutually dependent.
3. Not merely mutually Cause and Effect.
4. Notion of _End_ not derived from Facts.
5. This notion has regulated Physiology.
6. Notion of Design comes from within.
7. Design not understood by Savages.
8. Design opposed to Morphology.
9. Impression of Design when fresh.
10. Acknowledgement of an End by adverse Physiologists.
11. This included in the Notion of Disease.
12. It belongs to organized Creatures only.
13. The term Final _Cause_.
14. Law and Design.
15. Final Causes and Morphology.
16. Expressions of physiological Ends.
17. The Conditions of Existence.
18. The asserted presumption of Teleology.
19. Final Causes in other subjects.
20. Transition to Palætiology.

BOOK X.

THE PHILOSOPHY OF PALÆTIOLOGY.

CHAP. I. OF PALÆTIOLOGICAL SCIENCES IN GENERAL. 257

_Art._ 1. Description of Palætiology.
2. Its Members.
3. Other Members.
4. Connexion of the whole subject.
5. We shall take Material Sciences only;
6. But these are connected with others.

CHAP. II. OF THE THREE MEMBERS OF A PALÆTIOLOGICAL SCIENCE 263

_Art._ 1. Divisions of such Sciences.
2. The Study of Causes.
3. Ætiology.
{xiv}
4. Phenomenology requires Classification. Phenomenal
Geology.
5. Phenomenal Uranology.
6. Phenomenal Geography of Plants and Animals.
7. Phenomenal Glossology.
8. The Study of Phenomena leads to Theory.
9. No sound Theory without Ætiology.
10. Causes in Palætiology.
11. Various kinds of Cause.
12. Hypothetical Order of Palætiological Causes.
13. Mode of Cultivating Ætiology:--In Geology:
14. In the Geography of Plants and Animals:
15. In Languages.
16. Construction of Theories.
17. No sound Palætiological Theory yet extant.

CHAP. III. OF THE DOCTRINE OF CATASTROPHES AND THE
DOCTRINE OF UNIFORMITY 284

_Art._ 1. Doctrine of Catastrophes.
2. Doctrine of Uniformity.
3. Is Uniformity probable _a priori_?
4. Cycle of Uniformity indefinite.
5. Uniformitarian Arguments are Negative only.
6. Uniformity in the Organic World.
7. Origin of the present Organic World.
8. Nebular Origin of the Solar System.
9. Origin of Languages.
10. No Natural Origin discoverable.

CHAP. IV. OF THE RELATION OF TRADITION TO PALÆTIOLOGY 297

_Art._ 1. Importance of Tradition.
2. Connexion of Tradition and Science.
3. Natural and Providential History of the World.
4. The Sacred Narrative.
5. Difficulties in interpreting the Sacred Narrative.
6. Such Difficulties inevitable.
7. Science tells us nothing concerning Creation.
{xv}
8. Scientific views, when familiar, do not disturb
the authority of Scripture.
9. When should Old Interpretations be given up?
10. In what Spirit should the Change be accepted?
11. In what Spirit should the Change be urged?
12. Duty of Mutual forbearance.
13. Case of Galileo.

CHAP. V. OF THE CONCEPTION OF A FIRST CAUSE 316

_Art._ 1. The Origin of things is not naturally discoverable;
2. Yet has always been sought after.
3. There must be a First Cause.
4. This is an Axiom.
5. Involved in the proof of a Deity.
6. The mind is not satisfied without it.
7. The Whole Course of Nature must have a Cause.
8. Necessary Existence of God.
9. Forms of the Proof.
10. Idea of a First Cause is Necessary.
11. Conception of a First Cause.
12. The First Cause in all Sciences is the same.
13. We are thus led to Moral Subjects.

Conclusion of this History.

{{1}}
BOOK VI.

THE
PHILOSOPHY
OF
CHEMISTRY.

A PHILOSOPHER was asked:--How much does smoke weigh? He
answered: Subtract from the weight of the fuel the weight of
the ashes, and thou hast the weight of the smoke. Thus he
assumed as incontrovertible that, even in the fire, the
Substance does not perish, only its Form undergoes a change.
In like manner the proposition, _Nothing can come of
Nothing_ was only another consequence of the Principle of
Permanence, or rather of the Principle of the Enduring
Existence of the same subject with different appearances.

Kant, _Kritik d. r. Vern._

{{3}}
BOOK VI.

THE PHILOSOPHY OF CHEMISTRY.

CHAPTER I.

ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION.

1. WE have now to bring into view, if possible, the Ideas
and General Principles which are involved in Chemistry,--the
science of the composition of bodies. For in this as in
other parts of human knowledge, we shall find that there are
certain Ideas, deeply seated in the mind, though shaped and
unfolded by external observation, which are necessary
conditions of the existence of such a science. These Ideas
it is, which impel man to such a knowledge of the
Composition of bodies, which give _meaning_ to _facts_
exhibiting this composition, and _universality_ to _special_
truths discovered by experience. These are the Ideas of
_Element_ and of _Substance_.

Unlike the Idea of Polarity, of which we treated in the last
Book, these Ideas have been current in men's minds from very
early times, and formed the subject of some of the first
speculations of philosophers. It happened however, as might
have been expected, that in the first attempts they were not
clearly distinguished from other notions, and were
apprehended and applied in an obscure and confused manner.
We cannot better exhibit the peculiar character and meaning
of these Ideas than by tracing the form which they have
assumed {4} and the efficacy which they have exerted in
these successive essays. This, therefore, I shall endeavour
to do, beginning with the Idea of Element.

2. That bodies are composed or made up of certain parts,
elements, or principles, is a conception which has existed
in men's minds from the beginning of the first attempts at
speculative knowledge. The doctrine of the Four Elements,
Earth, Air, Fire and Water, of which all things in the
universe were supposed to be constituted, is one of the
earliest forms in which this conception was systematized;
and this doctrine is stated by various authors to have
existed as early as the times of the ancient Egyptians[1\6].
The words usually employed by Greek writers to express these
elements are ἀρχὴ a _principle_ or _beginning_, and
στοιχεῖον, which probably meant a _letter_ (of a word)
before it meant an _element_ of a compound. For the
resolution of a word into its letters is undoubtedly a
remarkable instance of a successful analysis performed at an
early stage of man's history; and might very naturally
supply a metaphor to denote the analysis of substances into
their intimate parts, when men began to contemplate such an
analysis as a subject of speculation. The Latin word
_elementum_ itself, though by its form it appears to be a
derivative abstract term, comes from some root now obsolete;
probably[2\6] from a word signifying _to grow_ or _spring up_.

[Note 1\6: Gilbert's _Phys._ 1. i. c. iii.]

[Note 2\6: Vossius _in voce_. "Conjecto esse ab antiqua voco
_eleo_ pro _oleo_, id est _cresco_: a qua signiflcatione
proles, _suboles_, _adolescens_: ut ab _juratum_,
_juramentum_; ab _adjutum_, _adjumentum_: sic ab _eletum_,
_elementum_: quia inde omnia crescunt ac nascuntur."]

The mode in which elements form the compound bodies and
determine their properties was at first, as might be
expected, vaguely and variously conceived. It will, I trust,
hereafter be made clear to the reader that the relation of
the elements to the compound involves a peculiar and
appropriate Fundamental Idea, not susceptible of being
correctly represented by any comparison or combination of
other ideas, and guiding us to clear and definite results
only when it is illustrated {5} and nourished by an abundant
supply of experimental facts. But at first the peculiar and
special notion which is required in a just conception of the
constitution of bodies was neither discerned nor suspected;
and up to a very late period in the history of chemistry,
men went on attempting to apprehend the constitution of
bodies more clearly by substituting for this obscure and
recondite idea of Elementary Composition, some other idea
more obvious, more luminous, and more familiar, such as the
ideas of Resemblance, Position, and mechanical Force. We
shall briefly speak of some of these attempts, and of the
errours which were thus introduced into speculations on the
relations of elements and compounds.

3. _Compounds assumed to resemble their Elements._--The
first notion was that compounds derive their qualities from
their elements by _resemblance_:--they are hot in virtue of
a hot element, heavy in virtue of a heavy element, and so
on. In this way the doctrine of the _four elements_ was
framed; for every body is either hot or cold, moist or dry;
and by combining these qualities in all possible ways, men
devised four elementary substances, as has been stated in
the History[3\6].

[Note 3\6: _Hist. Ind. Sc._ b. i. c. ii. sec. 2.]

This assumption of the derivation of the qualities of bodies
from similar qualities in the elements was, as we shall see,
altogether baseless and unphilosophical, yet it prevailed
long and universally. It was the foundation of medicine for
a long period, both in Europe and Asia; disorders being
divided into hot, cold, and the like; and remedies being
arranged according to similar distinctions. Many readers
will recollect, perhaps, the story[4\6] of the indignation
which the Persian physicians felt towards the European, when
he undertook to cure the ill effects of cucumber upon the
patient, by means of mercurial medicine: for cucumber, which
is cold, could not be counteracted, they maintained, by
mercury, which in their classification is cold also. Similar
views of the operation of medicines might {6} easily be
traced in our own country. A moment's reflection may
convince us that when drugs of any kind are subjected to the
chemistry of the human stomach and thus made to operate on
the human frame, it is utterly impossible to form the most
remote conjecture what the result will be, from any such
vague notions of their qualities as the common use of our
senses can give. And in like manner the common operations of
chemistry give rise, in almost every instance, to products
which bear no resemblance to the materials employed. The
results of the furnace, the alembic, the mixture, frequently
have no visible likeness to the ingredients operated upon.
Iron becomes steel by the addition of a little charcoal; but
what visible trace of the charcoal is presented by the metal
thus modified? The most beautiful colours are given to glass
and earthenware by minute portions of the ores of black or
dingy metals, as iron and manganese. The worker in metal,
the painter, the dyer, the vintner, the brewer, all the
artisans in short who deal with practical chemistry, are
able to teach the speculative chemist that it is an utter
mistake to expect that the qualities of the elements shall
be still discoverable, in an unaltered form, in the
compound. This first rude notion of an element, that it
determines the properties of bodies _by resemblance_, must
be utterly rejected and abandoned before we can make any
advance towards a true apprehension of the constitution of
bodies.

[Note 4\6: See _Hadji Baba_.]

4. This step accordingly was made, when the hypothesis of
the four elements was given up, and the doctrine of the
_three Principles_, Salt, Sulphur, and Mercury, was
substituted in its place. For in making this change, as I
have remarked in the History[5\6], the real advance was the
acknowledgment of the changes, produced by the chemist's
operations, as results to be accounted for by the union and
separation of substantial elements, however great the
changes, and however unlike the product might be to the
materials. And this step once made, chemists went on
constantly {7} advancing towards a truer view of the nature
of an element, and consequently, towards a more satisfactory
theory of chemical operations.

[Note 5\6: _Hist. Ind. Sc._ b. iv. c. 1.]

5. Yet we may, I think, note one instance, even in the works
of eminent modern chemists, in which this maxim, that we
have no right to expect any resemblance between the elements
and the compound, is lost sight of. I speak of certain
classifications of mineral substances. Berzelius, in his
System of Mineral Arrangement, places _sulphur_ next to the
_sulphurets_. But surely this is an errour, involving the
ancient assumption of the resemblance of elements and
compounds; as if we were to expect the sulphurets to bear a
resemblance to sulphur. All classifications are intended to
bring together things resembling each other: the sulphurets
of metals have certain general resemblances to each other
which make them a tolerably distinct, well determined, class
of bodies. But sulphur has no resemblances with these, and
no analogies with them, either in physical or even in
chemical properties. It is a simple body; and both its
resemblances and its analogies direct us to place it along
with other simple bodies, (selenium, and phosphorus,) which,
united with metals, produce compounds not very different
from the sulphurets. Sulphur cannot be, nor approach to
being, a sulphuret; we must not confound what it _is_ with
what it _makes_. Sulphur has its proper influence in
determining the properties of the compound into which it
enters; but it does not do this according to resemblance of
qualities, or according to any principle which properly
leads to propinquity in classification.

6. _Compounds assumed to be determined by the Figure of
Elements._--I pass over the fanciful modes of representing
chemical changes which were employed by the Alchemists; for
these strange inventions did little in leading men towards a
juster view of the relations of elements to compounds. I
proceed for an instant to the attempt to substitute another
obvious conception for the still obscure notion of
elementary composition. It was imagined that all the
properties of bodies and their mutual operations might be
{8} accounted for by supposing them constituted of
_particles_ of various _forms_, round or angular, pointed or
hooked, straight or spiral. This is a very ancient
hypothesis, and a favourite one with many casual speculators
in all ages. Thus Lucretius undertakes to explain why wine
passes rapidly through a sieve and oil slowly, by telling us
that the latter substance has its particles either larger
than those of the other, or more hooked and interwoven
together. And he accounts for the difference of sweet and
bitter by supposing the particles in the former case to be
round and smooth, in the latter sharp and jagged[6\6].
Similar assumptions prevailed in modern times on the revival
of the mechanical philosophy, and constitute a large part of
the physical schemes of Descartes and Gassendi. They were
also adopted to a considerable extent by the chemists. Acids
were without hesitation assumed to consist of sharp pointed
particles; which, 'I hope,' Lemery says[7\6], 'no one will
dispute, seeing every one's experience does demonstrate it:
he needs but taste an acid to be satisfied of it, for it
pricks the tongue like anything keen and finely cut.' Such
an assumption is not only altogether gratuitous and useless,
but appears to be founded in some degree upon a confusion in
the metaphorical and literal use of such words as _keen_ and
_sharp_. The assumption once made, it was easy to
accommodate it, in a manner equally arbitrary, to other
facts. 'A demonstrative and convincing proof that an acid
does consist of pointed parts is, that not only all acid
salts do crystallize into edges, but all dissolutions of
different things, caused by acid liquors, do assume this
figure in their crystallization. These crystals consist of
points differing both in length and bigness one from
another, and this diversity must be attributed to the keener
or blunter edges of the different sorts of acids: and so
likewise this difference of the points in subtilty is the
cause that one acid can penetrate and dissolve with one sort
of _mixt_, that another can't rarify at all: Thus _vinegar_
dissolves _lead_, {9} which _aqua fortis_ can't: _aqua
fortis_ dissolves _quicksilver_, which _vinegar_ will not
touch; _aqua regalis_ dissolves _gold_, whenas _aqua fortis_
cannot meddle with it; on the contrary, _aqua fortis_
dissolves _silver_, but can do nothing with gold, and so of
the rest.'

[Note 6\6: _De Rerum Natura_, ii. 390 sqq.]

[Note 7\6: _Chemistry_, p. 25.]

The leading fact of the vehement combination and complete
union of acid and alkali readily suggested a fit form for
the particles of the latter class of substances. 'This
effect,' Lemery adds, 'may make us reasonably conjecture
that an alkali is a terrestrious and solid matter whose
forms are figured after such a manner that the acid points
entering in do strike and divide whatever opposes their
motion.' And in a like spirit are the speculations in Dr.
Mead's _Mechanical Account of Poisons_ (1745). Thus he
explains the poisonous effect of _corrosive sublimate_ of
mercury by saying[8\6] that the particles of the salt are a
kind of lamellæ or blades to which the mercury gives an
additional weight. If resublimed with three-fourths the
quantity of mercury, it loses its corrosiveness, (becoming
_calomel_,) which arises from this, that in sublimation 'the
crystalline blades are divided every time more and more by
the force of the fire:' and 'the broken pieces of the
crystals uniting into little masses of differing figures
from their former make, those cutting points are now so much
smaller that they cannot make wounds deep enough to be
equally mischievous and deadly: and therefore do only
vellicate and twitch the sensible membranes of the stomach.'

[Note 8\6: P. 199.]

7. Among all this very fanciful and gratuitous assumption we
may notice one true principle clearly introduced, namely,
that the suppositions which we make respecting the forms of
the elementary particles of bodies and their mode of
combination must be such as to explain the facts of
crystallization, as well as of mere chemical change. This
principle we shall hereafter have occasion to insist upon
further.

I now proceed to consider a more refined form of assumption
respecting the constitution of bodies, yet {10} still one in
which a vain attempt is made to substitute for the peculiar
idea of chemical composition a more familiar mechanical
conception.

8. _Compounds assumed to be determined by the Mechanical
Attraction of the Elements._--When, in consequence of the
investigations and discoveries of Newton and his
predecessors, the conception of mechanical force had become
clear and familiar, so far as the action of external forces
upon a body was concerned, it was very natural that the
mathematicians who had pursued this train of speculation
should attempt to apply the same conception to that mutual
action of the internal parts of a body by which they are
held together. Newton himself had pointed the way to this
attempt. In the Preface to the _Principia_, after speaking
of what he has done in calculating the effects of forces
upon the planets, satellites, &e., he adds, 'Would it were
permitted us to deduce the other phenomena of nature from
mechanical principles by the same kind of reasoning. For
many things move me to suspect that all these phenomena
depend upon certain forces, by which the particles of
bodies, through causes not yet known, are either urged
towards each other, and cohere according to regular figures,
or are repelled and recede from each other; which forces
being unknown, philosophers have hitherto made their
attempts upon nature in vain.' The same thought is at a
later period followed out further in one of the Queries at
the end of the Opticks[9\6]. 'Have not the small particles
of bodies certain Powers, Virtues, or Forces, by which they
act at a distance, not only upon the rays of light for
reflecting, refracting and inflecting them, but also upon
one another for producing a great part of the phenomena of
nature?' And a little further on he proceeds to apply this
expressly to chemical changes. 'When Salt of Tartar runs
_per deliquium_ [or as we now express it, deliquesces] is
not this done by an _attraction_ between the particles of
the Salt of Tartar and the particles of the water which
float in the air in {11} the form of vapours? And why does
not common salt, or saltpetre, or vitriol, run _per
deliquium_, but for want of such an attraction? or why does
not Salt of Tartar draw more water out of the air than in a
certain proportion to its quantity, but for want of an
attractive force after it is saturated with water?' He goes
on to put a great number of similar cases, all tending to
the same point, that chemical combinations cannot be
conceived in any other way than as an attraction of
particles.

[Note 9\6: Query 31.]

9. Succeeding speculators in his school attempted to follow
out this view. Dr. Frend, of Christ Church, in 1710,
published his _Prælectiones Chymicæ, in quibus omne fere
Operationes Chymicæ ad vera Principia ex ipsius Naturæ
Legibus rediguntur. Oxonii habitæ_. This book is dedicated
to Newton, and in the dedication, the promise of advantage
to chemistry from the influence of the Newtonian discoveries
is spoken of somewhat largely,--much more largely, indeed,
than has yet been justified by the sequel. After declaring
in strong terms that the only prospect of improving science
consists in following the footsteps of Newton, the author
adds, 'That force of attraction, of which you first so
successfully traced the influence in the heavenly bodies,
operates in the most minute corpuscles, as you long ago
hinted in your _Principia_, and have lately plainly shown in
your _Opticks_; and this force we are only just beginning to
perceive and to study. Under these circumstances I have been
desirous of trying what is the result of this view in
chemistry.' The work opens formally enough, with a statement
of general mechanical principles, of which the most peculiar
are these:--'That there exists an attractive force by which
particles when at very small distances from each other, are
drawn together;--that this force is different, according to
the different figure and density of the particles;--that the
force may be greater on one side of a particle than on the
other;--that the force by which particles cohere together
arises from attraction, and is variously modified according
to the quantity of contacts.' But these principles are not
{12} applied in any definite manner to the explanation of
specific phenomena. He attempts, indeed, the question of
special solvents[10\6]. Why does _aqua fortis_ dissolve
silver and not gold, while _aqua regia_ dissolves gold and
not silver? which, he says, is the most difficult question
in chemistry, and which is certainly a fundamental question
in the formation of chemical theory. He solves it by certain
assumptions respecting the forces of attraction of the
particles, and also the diameter of the particles of the
acids and the pores of the metals, all which suppositions
are gratuitous.

[Note 10\6: P. 54.]

10. We may observe further, that by speaking, as I have
stated that he does, of the figure of particles, he mixes
together the assumption of the last section with the one
which we are considering in this. This combination is very
unphilosophical, or, to say the least, very insufficient,
since it makes a new hypothesis necessary. If a body be
composed of cubical particles, held together by their mutual
attraction, by what force are the parts of each cube held
together? In order to understand their structure, we are
obliged again to assume a cohesive force of the second
order, binding together the particles of each particle. And
therefore Newton himself says[11\6], very justly, 'The parts
of all homogeneal hard bodies which fully touch each other,
stick together very strongly: and for explaining how this
is, some have invented hooked atoms, _which is begging the
question_.' For (he means to imply,) how do the parts of the
hook stick together?

[Note 11\6: _Opticks_, p. 364.]

The same remark is applicable to all hypotheses in which
particles of a complex structure are assumed as the
constituents of bodies: for while we suppose bodies and
their known properties to result from the mutual actions of
these particles, we are compelled to suppose the parts of
each particle to be held together by forces still more
difficult to conceive, since they are disclosed only by the
properties of these particles, which as yet are unknown. Yet
Newton himself has not abstained from such hypotheses: thus
he says[12\6], 'A particle of {13} a salt may be compared to
a chaos, being dense, hard, dry, and earthy in the center,
and moist and watery in the circumference.'

[Note 12\6: _Opticks_, p. 362.]

Since Newton's time the use of the term _attraction_, as
expressing the cause of the union of the chemical elements
of bodies, has been familiarly continued; and has, no doubt,
been accompanied in the minds of many persons with an
obscure notion that chemical attraction is, in some way, a
kind of mechanical attraction of the particles of bodies.
Yet the doctrine that _chemical_ 'attraction' and
_mechanical_ attraction are forces of the same kind has
never, so far as I am aware, been worked out into a system
of chemical theory; nor even applied with any distinctness
as an explanation of any particular chemical phenomena. Any
such attempt, indeed, could only tend to bring more clearly
into view the entire inadequacy of such a mode of
explanation. For the leading phenomena of chemistry are all
of such a nature that no mechanical combination can serve to
express them, without an immense accumulation of additional
hypotheses. If we take as our problem the changes of colour,
transparency, texture, taste, odour, produced by small
changes in the ingredients, how can we expect to give a
mechanical account of these, till we can give a mechanical
account of colour, transparency, texture, taste, odour,
themselves? And if our mechanical hypothesis of the
elementary constitution of bodies does not explain _such_
phenomena as those changes, what can it explain, or what can
be the value of it? I do not here insist upon a remark which
will afterwards come before us, that even crystalline form,
a phenomenon of a far more obviously mechanical nature than
those just alluded to, has never yet been in any degree
explained by such assumptions as this, that bodies consist
of elementary particles exerting forces of the same nature
as the central forces which we contemplate in Mechanics.

When therefore Newton asks, 'When some stones, as spar of
lead, dissolved in proper menstruums, become salts, do not
these things show that salts are dry earth and watery acid
united by _attraction_?' we may {14} answer, that this mode
of expression appears to be intended to identify chemical
combination with mechanical attraction;--that there would be
no objection to any such identification, if we could, in
that way, explain, or even classify well, a collection of
chemical facts; but that this has never yet been done by the
help of such expressions. Till some advance of this kind can
be pointed out, we must necessarily consider the power which
produces chemical combination as a peculiar principle, a
special relation of the elements, not rightly expressed in
mechanical terms. And we now proceed to consider this
relation under the name by which it is most familiarly
known.

{{15}}
CHAPTER II.

ESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF CHEMICAL
AFFINITY.

1. THE earlier chemists did not commonly involve themselves
in the confusion into which the mechanical philosophers ran,
of comparing chemical to mechanical forces. Their attention
was engaged, and their ideas were moulded, by their own
pursuits. They saw that the connexion of elements and
compounds with which they had to deal, was a peculiar
relation which must be studied directly; and which must be
understood, if understood at all, in itself, and not by
comparison with a different class of relations. At different
periods of the progress of chemistry, the conception of this
relation, still vague and obscure, was expressed in various
manners; and at last this conception was clothed in
tolerably consistent phraseology, and the principles which
it involved were, by the united force of thought and
experiment, brought into view.

2. The power by which the elements of bodies combine
chemically, being, as we have seen, a peculiar agency,
different from mere mechanical connexion or attraction, it
is desirable to have it designated by a distinct and
peculiar name; and the term _Affinity_ has been employed for
that purpose by most modern chemists. The word 'affinity' in
common language means, sometimes resemblance, and sometimes
relationship and ties of family. It is from the latter sense
that the metaphor is borrowed when we speak of 'chemical
affinity.' By the employment of this term we do not indicate
a resemblance, but a disposition to unite. Using the word in
a common unscientific manner, we might say that chlorine,
bromine, and iodine, have a great {16} _natural affinity_
with each other, for there are considerable resemblances and
analogies among them; but these bodies have very little
_chemical_ Affinity for each other. The use of the word in
the _former_ sense, of resemblance, can be traced in earlier
chemists; but the word does not appear to have acquired its
peculiar chemical meaning till after Boerhaave's time.
Boerhaave, however, is the writer in whom we first find a
due apprehension of the peculiarity and importance of the
Idea which it now expresses. When we make a chemical
solution[13\6], he says, not only are the particles of the
dissolved body separated from each other, but they are
closely united to the particles of the solvent. When _aqua
regia_ dissolves gold, do you not see, he says to his
hearers, that there must be between each particle of the
solvent and of the metal, a mutual virtue by which each
loves, unites with, and holds the other (_amat_, _unit_,
_retinet_)? The opinion previously prevalent had been that
the solvent merely separates the parts of the body
dissolved: and most philosophers had conceived this
separation as performed by mechanical operations of the
particles, resembling, for instance, the operation of wedges
breaking up a block of timber. But Boerhaave forcibly and
earnestly points out the insufficiency of the conception.
This, he says, does not account for what we see. We have not
only a separation, but a new combination. There is a force
by which the particles of the solvent associate to
themselves the parts dissolved, not a force by which they
repel and dissever them. We are here to imagine not
mechanical action, not violent impulse, not antipathy, but
love, at least if love be the desire of uniting. (Non igitur
hic etiam actiones mechanicæ, non propulsiones violentæ, non
inimicitiæ cogitandæ, sed amicitiæ, si amor dicendus copulæ
cupido.) The novelty of this view is evidenced by the mode
in which he apologizes for introducing it. 'Fateor, paradoxa
hæc assertio.' To Boerhaave, therefore, (especially
considering his great influence as a teacher of chemistry,)
we may {17} assign the merit of first diffusing a proper
view of Chemical Affinity as a peculiar force, the origin of
almost all chemical changes and operations.

[Note 13\6: _Elementa Chemiæ_, Lugd. Bat. 1732, p. 677.]

3. To Boerhaave is usually assigned also the credit of
introducing the _word_ 'Affinity' among chemists; but I do
not find that the word is often used by him in this sense;
perhaps not at all[14\6]. But however this may be, the term
is, on many accounts, well worthy to be preserved, as I
shall endeavour to show. Other terms were used in the same
sense during the early part of the eighteenth century. Thus
when Geoffroy, in 1718, laid before the Academy of Paris his
Tables of Affinities, which perhaps did more than any other
event to fix the Idea of Affinity, he termed them 'Tables of
the Relations of Bodies;' '_Tables des Rapports_:' speaking
however, also, of their 'disposition to unite,' and using
other phrases of the same import.

[Note 14\6: See Dumas, _Leçons de Phil. Chim._ p. 364. Rees'
_Cyclopædia_, Art. Chemistry. In the passage of Boerhaave to
which I refer above, _affinitas_ is rather opposed to, than
identified with, chemical combination. When, he says, the
parts of the body to be dissolved are dissevered by the
solvent, why do they remain united to the particles of the
solvent, and why do not rather both the particles of the
solvent and of the dissolved body collect into homogeneous
bodies by their _affinity_? 'denuo se affinitate suæ naturæ
colligant in corpora homogenea?' And the answer is, because
they possess another force which counteracts this affinity
of homogeneous particles, and makes compounds of different
elements. Affinity, in chemistry, now means the tendency of
_different_ kinds of matter to unite: but it appears, as I
have said, to have acquired this sense since Boerhaave's time.]

The term _attraction_, having been recommended by Newton as
a fit word to designate the force which produces chemical
combination, continued in great favour in England, where the
Newtonian philosophy was looked upon as applicable to every
branch of science. In France, on the contrary, where
Descartes still reigned triumphant, 'attraction,' the
watch-word of the enemy, was a sound never uttered but with
dislike and suspicion. In 1718 (in the notice of Geoffroy's
Table,) the Secretary of the Academy, after pointing out
some of the peculiar circumstances of chemical {18}
combinations, says, 'Sympathies and attractions would suit
well here, if there were such things,' 'Les sympathies, les
attractions conviendroient bien ici, si elles étaient
quelque chose.' And at a later period, in 1731, having to
write the _éloge_ of Geoffroy after his death, he says, 'He
gave, in 1718, a singular system, and a Table of
_Affinities_, or Relations of the different substances in
chemistry. These affinities gave an easiness to some
persons, who feared that they were _attractions in
disguise_, and all the more dangerous in consequence of the
seductive forms which clever people have contrived to give
them. It was found in the sequel that this scruple might be
got over.'

This is the earliest published instance, so far as I am
aware, in which the word 'Affinity' is distinctly used for
the cause of chemical composition; and taking into account
the circumstances, the word appears to have been adopted in
France in order to avoid the word _attraction_, which had
the taint of Newtonianism. Accordingly we find the word
_affinité_ employed in the works of French chemists from
this time. Thus, in the _Transactions of the French Academy_
for 1746, in a paper of Macquer's upon Arsenic, he
says[15\6], 'On peut facilement rendre raison de ces
phenomènes par le moyen des affinités que les différens
substances qui entrent dans ces combinaisons, ont les uns
avec les autres:' and he proceeds to explain the facts by
reference to Geoffroy's Table. And in Macquer's _Elements of
Chemistry_, which appeared a few years later, the 'Affinity
of Composition' is treated of as a leading part of the
subject, much in the same way as has been practised in such
books up to the present time. From this period, the word
appears to have become familiar to all European chemists in
the sense of which we are now speaking. Thus, in the year
1758, the Academy of Sciences at Rouen offered a prize for
the best dissertation on Affinity. The prize was shared
between M. Limbourg of Theux, near Liege, and M. Le Sage
{19} of Geneva[16\6]. About the same time other persons
(Manherr[17\6], Nicolai[18\6], and others) wrote on the same
subject, employing the same name.

[Note 15\6: _A. P._ 1746, p. 201.]

[Note 16\6: Thomson's _Chemistry_, iii. 10. Limbourg's
Dissertation was published at Liege, in 1761; and Le Sage's
at Geneva.]

[Note 17\6: _Dissertatio de Affinitate Corporum_. Vindob. 1762.]

[Note 18\6: _Progr._ I. II. _de Affinitate Corporum Chimica_.
Jen. 1775, 1776.]

Nevertheless, in 1775, the Swedish chemist Bergman, pursuing
still further this subject of Chemical Affinities, and the
expression of them by means of Tables, returned again to the
old Newtonian term; and designated the disposition of a body
to combine with one rather than another of two others as
_Elective Attraction_. And as his work on _Elective
Attractions_ had great circulation and great influence, this
phrase has obtained a footing by the side of _Affinity_, and
both one and the other are now in common use among chemists.

4. I have said above that the term _Affinity_ is worthy of
being retained as a technical term. If we use the word
_attraction_ in this case, we identify or compare chemical
with mechanical attraction; from which identification and
comparison, as I have already remarked, no one has yet been
able to extract the means of expressing any single
scientific truth. If such an identification or comparison be
not intended, the use of the same word in two different
senses can only lead to confusion; and the proper course,
recommended by all the best analogies of scientific history,
is to adopt a peculiar term for that peculiar relation on
which chemical composition depends. The word _Affinity_,
even if it were not rigorously proper according to its
common meaning, still, being simple, familiar, and well
established in this very usage, is much to be preferred
before any other.

But further, there are some analogies drawn from the common
meaning of this word, which appear to recommend it as
suitable for the office which it has to discharge. For
common mechanical attractions and {20} repulsions, the
forces by which one body considered as a _whole_ acts upon
another external to it, are, as we have said, to be
distinguished from those more intimate ties by which the
_parts_ of each body are held together. Now this difference
is implied, if we compare the former relations, the
attractions and repulsions, to alliances and wars between
States, and the latter, the internal union of particles, to
those bonds of affinity which connect the citizens of the
same state with one another, and especially to the ties of
Family. We have seen that Boerhaave compares the union of
two elements of a compound to their marriage; 'we must
allow,' says an eminent chemist of our own time[19\6], 'that
there is some truth in this poetical comparison.' It
contains this truth,--that the two become one to most
intents and purposes, and that the Unit thus formed (the
Family) is not a mere juxtaposition of the component parts.
And thus the Idea of Affinity as the peculiar principle of
chemical composition, is established among chemists, and
designated by a familiar and appropriate name.

[Note 19\6: Dumas, _Leçons de Phil. Chim._ p. 363.]

5. _Analysis is possible._--We must, however, endeavour to
obtain a further insight into this Idea, thus fixed and
named. We must endeavour to extricate, if not from the Idea
itself, from the processes by which it has obtained
acceptation and currency among chemists, some principles
which may define its application, some additional
specialities in the relations which it implies. This we
shall proceed to do.

The Idea of Affinity, as already explained, implies a
disposition to combine. But this combination is to be
understood as admitting also of a possibility of separation.
Synthesis implies Analysis as conceivable: or to recur to
the image which we have already used, Divorce is possible
when the Marriage has taken place.

That there is this possibility, is a conviction implied in
all the researches of chemists, ever since the true notion
of composition began to predominate in their investigations.
One of the first persons who clearly {21} expressed this
conviction was Mayow, an English physician, who published
his _Medico-Physical Tracts_ in 1674. The first of them _De
Sale-Nitro et Spiritu Nitro-Aerio_, contains a clear
enunciation of this principle. After showing how, in the
combinations of opposite elements, as acid and alkali, their
properties entirely disappear, and a new substance is formed
not at all resembling either of the ingredients, he
adds[20\6], 'Although these salts thus mixed appear to be
destroyed it is still possible for them to be separated from
each other, with their powers still entire.' He proceeds to
exemplify this, and illustrates it by the same image which I
have already alluded to: 'Salia acida a salibus
volatilibus discedunt, ut cum sale fixo tartari, tanquam
_sponso_ magis idoneo, _conjugium_ strictius ineunt.' This
idea of a synthesis which left a complete analysis still
possible, was opposed to a notion previously current, that
when two heterogeneous bodies united together and formed a
third body, the two constituents were entirely destroyed,
and the result formed out of their ruins[21\6]. And this
conception of Synthesis and Analysis, as processes which are
possible successively and alternately, and each of which
supposes the possibility of the other, has been the
fundamental and regulative principle of the operations and
speculations of analytical chemistry from the time of Mayow
to the present day.

[Note 20\6: Cap. xiv. p. 233.]

[Note 21\6: Thomson's _Chemistry_, iii. 8.]

6. _Affinity is Elective._--When the idea of chemical
affinity, or disposition to unite, was brought into view by
the experiments and reasonings of chemists, they found it
necessary to consider this disposition as _elective_;--each
element _chose_ one rather than another of the elements
which were presented to it, and quitted its union with one
to unite with another which it preferred. This has already
appeared in the passage just quoted from Mayow. He adds in
the same strain, 'I have no doubt that fixed salts choose
one acid rather than another, in order that they may
coalesce with it {22} in a more intimate union.'--'Nullus
dubito salia fixa acidum unum præ aliis _eligere_, ut cum
eodem arctiore unione coalescant.' The same thought is
expressed and exemplified by other chemists: they notice
innumerable cases in which, when an ingredient is combined
with a liquid, if a new substance be immersed which has a
greater affinity for the liquid, the liquid combines with
the new substance by election, and the former **ingredient
is _precipitated_. Thus Stahl says[22\6], 'In spirit of
nitre dissolve silver; put in copper and the silver is
thrown down; put in iron and the copper goes down; put in
zinc, the iron precipitates; put in volatile alkali, the
zinc is separated; put in fixed alkali, the volatile quits
its hold.'--As may be seen in this example, we have in such
cases, not only a preference, but a long gradation of
preferences. The spirit of nitre will combine with silver,
but it prefers copper; prefers iron more; zinc still more;
volatile alkali yet more; fixed alkali the most.

[Note 22\6: _Zymotechnia_, 1697, p. 117.]

The same thing was proved to obtain with regard to each
element; and when this was ascertained, it became the object
of chemists to express these degrees of preference, by lists
in which substances were arranged according to their
disposition to unite with another substance. In this manner
was formed Geoffroy's Table of Affinities (1718), which we
have already mentioned. This Table was further improved by
other writers, as Gellert (1751) and Limbourg (1761).
Finally Bergman improved these Tables still further, taking
into account not only the order of affinities of each
element for others, but the _sum_ of the tendencies to unite
of each two elements, which sum, he held, determined the
resulting combination when several elements were in contact
with each other.

7. As we have stated in the History[23\6], when the doctrine
of elective affinities had assumed this very definite and
systematic form, it was assailed by Berthollet, who
maintained, in his _Essai de Statique_ {23} _Chimique_,
(1803,) that chemical affinities are _not_ elective:--that,
when various elements are brought together, their
combinations do not depend upon the kind of elements alone,
but upon the quantity of each which is present, that which
is most abundant always entering most largely into the
resulting compounds. It may seem strange that it should be
possible, at so late a period of the science, to throw doubt
upon a doctrine which had presided over and directed its
progress so long. Proust answered Berthollet, and again
maintained that chemical affinity is elective. I have, in
the History, given the judgment of Berzelius upon this
controversy. 'Berthollet,' he says, 'defended himself with
an acuteness which makes the reader hesitate in his
judgment; but the great mass of facts finally decided the
point in favour of Proust.' I may here add the opinion
pronounced upon this subject by Dr. Turner[24\6]: 'Bergman
erred in supposing the result of the chemical action to be
in every case owing to elective affinity [for this power is
modified in its effects by various circumstances]: but
Berthollet ran into the opposite extreme in declaring that
the effects formerly ascribed to that power are never
produced by it. That chemical attraction is exerted between
different bodies with different degrees of energy, is, I
apprehend, indisputable.' And he then proceeds to give many
instances of differences in affinity which cannot be
accounted for by the operation of any modifying causes.
Still more recently, M. Dumas has taken a review of this
controversy; and, speaking with enthusiasm of the work of
Berthollet, as one which had been of inestimable service to
himself in his early study of chemistry, he appears at first
disposed to award to him the victory in this dispute. But
his final verdict leaves undamaged the general principle now
under our consideration, that chemical affinity is elective.
'For my own part,' he says[25\6], 'I willingly admit the
notions of Berthollet when we have to do with acids or {24}
with bases, of which the energy is nearly equal: but when
bodies endued with very energetic affinities are in presence
of other bodies of which the affinities are very feeble, I
propose to adopt the following rule: In a solution,
everything remaining dissolved, the strong affinities
satisfy themselves, leaving the weak affinities to arrange
matters with one another. The strong acids take the strong
bases, and the weak acids can only unite with the weak
bases. The known facts are perfectly in accordance with this
practical rule.' It is obvious that this recognition of a
distinction between strong and weak affinities, which
operates to such an extent as to determine entirely the
result, is a complete acknowledgement of the Elective nature
of Affinity, as far as any person acquainted with chemical
operations could contend for it. For it must be allowed by
all, that solubility, and other collateral circumstances,
influence the course of chemical combinations, since they
determine whether or not there shall take place that contact
of elements without which affinity cannot possibly operate.

[Note 23\6: _Hist. Ind. Sc._ b. xiv. c. iii.]

[Note 24\6: _Chemistry_, p. 199. 6th edition.]

[Note 25\6: _Leçons de Philosophie Chimique_, p. 386.]

8. _Affinity is Definite as to quantity._--In proportion as
chemists obtained a clearer view of the products of the
laboratory as results of the composition of elements, they
saw more and more clearly that these results were definite;
that one element not only preferred to combine with another
of a certain kind, but also would combine with it to a
certain extent and no further, thus giving to the result not
an accidental and variable, but a fixed and constant
character. Thus salts being considered as the result of the
combination of two opposite principles, acid and alkali, and
being termed _neutral_ when these principles exactly
balanced each other, Rouelle (who was Royal Professor at
Paris in 1742) admits of neutral salts with excess of acid,
neutral salts with excess of base, and perfect neutral
salts. Beaume maintained[26\6] against him that there were
no salts except those perfectly neutral, the other classes
being the results of mixture and imperfect {25} combination.
But this question was not adequately treated till chemists
made every experiment with the balance in their hands. When
this was done, they soon discovered that, in each neutral
salt, the proportional weights of the ingredients which
composed it were always the same. This was ascertained by
Wenzel, whose _Doctrine of the Affinities of Bodies_
appeared in 1777. He not only ascertained that the
proportions of elements in neutral chemical compounds are
definite, but also that they are reciprocal; that is, (to
express his results in a manner now employed by chemists),
that if A, a certain weight of a certain acid, neutralize
_m_, a certain weight of a certain base, and B, a certain
weight of a certain other acid, neutralize _n_, a certain
weight of a certain other base; the compound of A and _n_
will also be neutral; as also that of B and _m_. The same
views were again presented by Richter in 1792, in his
_Principles of the Measure of Chemical Elements_. And along
with these facts, that of the combination of elements in
multiple proportions being also taken into account, the
foundations of the Atomic Theory were laid; and that Theory
was propounded in 1803 by Mr. Dalton. That theory, however,
rests upon the Idea of Substance, as well as upon that Idea
of Chemical Affinity which we are here considering; and the
discussion of its evidence and truth must be for the present
deferred.

[Note 26\6: Dumas, _Phil. Chim._ p. 198.]

9. The two principles just explained,--that Affinity is
Definite as to the Kind, and as to the Quantity of the
elements which it unites,--have here been stated as results
of experimental investigation. That they could never have
been clearly understood, and therefore never firmly
established, without laborious and exact experiments, is
certain; but yet we may venture to say that being once fully
known, they may seem to thoughtful men to possess an
evidence beyond that of mere experiment. For how, in fact,
can we conceive combinations, otherwise than as definite in
kind and quantity? If we were to suppose each element
ready to combine with any other indifferently, and
indifferently in any quantity, we should have a world in
{26} which all would be confusion and indefiniteness. There
would be no fixed kinds of bodies. Salts, and stones, and
ores, would approach to and graduate into each other by
insensible degrees. Instead of this, we know that the world
consists of bodies distinguishable from each other by
definite differences, capable of being classified and named,
and of having general propositions asserted concerning them.
And as we cannot conceive a world in which this should not
be the case, it would appear that we cannot conceive a state
of things in which the laws of the combination of elements
should not be of that definite and measured kind which we
have above asserted.

This will, perhaps, appear more clearly by stating our
fundamental convictions respecting chemical composition in
another form, which I shall, therefore, proceed to do.

10. _Chemical Composition determines Physical
Properties._--However obscure and incomplete may be our
conception of the internal powers by which the ultimate
particles of bodies are held together, it involves, at
least, this conviction:--that these powers are what
determine bodies to be bodies, and therefore contain the
reason of all the properties which, as bodies, they possess.
The forces by which the particles of a body are held
together, also cause it to be hard or soft, heavy or light,
opake or transparent, black or red; for if these forces are
not the cause of these peculiarities, what can be the cause?
By the very supposition which we make respecting these
forces, they include all the relations by which the parts
are combined into a whole, and therefore they, and they
only, must determine all the attributes of the whole. The
foundation of all our speculations respecting the intimate
constitution of bodies must be this principle, that their
composition determines their properties.

Accordingly we find our chemists reasoning from this
principle with great confidence, even in doubtful cases.
Thus Davy, in his researches concerning the diamond, says:
'That some chemical difference must exist between the
hardest and most beautiful of the {27} gems and charcoal,
between a non-conductor and a conductor of electricity, it
is scarcely possible to doubt: and it seems reasonable to
expect that a very refined or perfect chemistry will confirm
_the analogies of nature_; and show that bodies cannot be
the same in their composition or chemical nature, and yet
totally different in their chemical properties.' It is
obvious that the principle here assumed is so far from being
a mere result of experience, that it is here appealed to to
prove that all previous results of experience on this
subject must be incomplete and inaccurate; and that there
must be some chemical difference between charcoal and
diamond, though none had hitherto been detected.

11. In what manner, according to what rule, the chemical
composition shall determine the kind of the substance, we
cannot reasonably expect to determine by mere conjecture or
assumption, without a studious examination of natural bodies
and artificial compounds. Yet even in the most recent times,
and among men of science, we find that an assumption of the
most arbitrary character has in one case been mixed up with
this indisputable principle, that the elementary composition
determines the kind of the substance. In the classification
of minerals, one school of mineralogists have rightly taken
it as their fundamental principle that the chemical
composition shall decide the position of the mineral in the
system. But they have appended to this principle,
arbitrarily and unjustifiably, the maxim that the element
which is _largest in quantity_ shall fix the class of the
substance. To make such an assumption is to renounce, at
once, all hope of framing a system which shall be governed
by the resemblances of the things classified; for how can we
possibly know beforehand that fifty-five per cent, of iron
shall give a substance its predominant properties, and that
forty-five per cent, shall not? Accordingly, the systems of
mineralogical arrangement which have been attempted in this
way, (those of Haüy, Phillips, and others,) have been found
inconsistent with themselves, ambiguous, and incapable of
leading to any general truths. {28}

12. _Chemical Composition and Crystalline Form
correspond._--Thus the physical properties of bodies depend
upon their chemical composition, but in a manner which a
general examination of bodies with reference to their
properties and their composition can alone determine. We
may, however, venture to assert further, that the more
definite the properties are, the more distinct may we expect
to find this dependence. Now the most definite of the
properties of bodies are those constant properties which
involve relations of space; that is, their figure. We speak
not, however, of that external figure, derived from external
circumstances, which, so far from being constant and
definite, is altogether casual and arbitrary; but of that
figure which arises from their internal texture, and which
shows itself not only in the regular forms which they
spontaneously assume, but in the disposition of the parts to
separate in definite directions, and no others. In short,
the most definite of the properties of perfect chemical
compounds is their _crystalline structure_; and therefore it
is evident that the crystalline structure of each body, and
the forms which it affects, must be in a most intimate
dependence upon its chemical composition.

Here again we are led to the brink of another theory;--that
of crystalline structure, which has excited great interest
among philosophers ever since the time of Haüy. But this
theory involves, besides that idea of chemical composition
with which we are here concerned, other conceptions, which
enter into the relations of figure. These conceptions,
governed principally by the Idea of Symmetry, must be
unfolded and examined before we can venture to discuss any
theory of crystallization: and we shall proceed to do this
as soon as we have first duly considered the Idea of
Substance and its consequences.

{{29}}
CHAPTER III.

OF THE IDEA OF SUBSTANCE.

1. _Axiom of the Indestructibility of Substance._--WE now
come to an Idea of which the history is very different from
those of which we have lately been speaking. Instead of
being gradually and recently brought into a clear light, as
has been the case with the Ideas of Polarity and Affinity,
the Idea of Substance has been entertained in a distinct
form from the first periods of European speculation. That
this is so, is proved by our finding a principle depending
upon this Idea current as an axiom among the early
philosophers of Greece:--namely, that _nothing can be
produced out of nothing_. Such an axiom, more fully stated,
amounts to this: that the substance of which a body consists
is incapable of being diminished (and consequently incapable
of being augmented) in quantity, whatever apparent changes
it may undergo. Its forms, its distribution, its qualities,
may vary, but the substance itself is identically the same
under all these variations.

The axiom just spoken of was the great principle of the
physical philosophy of the Epicurean school, as it must be
of every merely material philosophy. The reader of Lucretius
will recollect the emphasis with which it is repeatedly
asserted in his poem:
E nilo nil gigni, in nilum nil posse reverti;
Nought comes of nought, nor ought returns to nought.

Those who engaged in these early attempts at physical
speculation were naturally much pleased with the clearness
which was given to their notions of change, composition, and
decomposition, by keeping steadily hold of the Idea of
Substance, as marked by this {30} fundamental axiom. Nor has
its authority ever ceased to be acknowledged. A philosopher
was asked[27\6], What is the weight of smoke? He answered,
'Subtract the weight of the ashes from the weight of the
wood which is burnt, and you have the weight of the smoke.'
This reply would be assented to by all; and it assumes as
incontestable that even under the action of fire, the
material, the substance, does not perish, but only changes
its form.

[Note 27\6: Kant, _Kritik der R. V._ p. 167.]

This principle of the indestructibility of substance might
easily be traced in many reasonings and researches, ancient
and modern. For instance, when the chemist works with the
_retort_, he places the body on which he operates in one
part of an inclosed cavity, which, by its bendings and
communications, separates at the same time that it confines,
the products which result from the action of fire: and he
assumes that this process is an analysis of the body into
its ingredients, not a creation of anything which did not
exist before, or a destruction of anything which previously
existed. And he assumes further, that the total quantity of
the substance thus analysed is the sum of the quantities of
its ingredients. This principle is the very basis of
chemical speculation, as we shall hereafter explain more fully.

2. _The Idea of Substance._--The axiom above spoken of
depends upon the Idea of Substance, which is involved in all
our views of external objects. We unavoidably assume that
the qualities and properties which we observe are properties
of _things_;--that the adjective implies a
substantive;--that there is, besides the external characters
of things, something _of which_ they are the characters. An
apple which is red, and round, and hard, is not merely
redness, and roundness, and hardness: these circumstances
may all alter while the apple remains the same apple. Behind
or under the appearances which we see, we conceive something
of which we think; or, to use the metaphor which obtained
currency among the ancient philosophers, the {31} attributes
and qualities which we observe are supported by and inherent
in something: and this something is hence called a
_substratum_ or _substance_,--that which stands _beneath_
the apparent qualities and supports them.

That we have such an _Idea_, using the term 'Idea' in the
sense in which I have employed it throughout these
disquisitions, is evident from what has been already said.
The Axiom of the Indestructibility of Substance proves the
existence of the Idea of Substance, just as the Axioms of
Geometry and Arithmetic prove the existence of the Ideas of
Space and Number. In the case of Substance, as of space or
number, the ideas cannot be said to be borrowed from
experience, for the axioms have an authority of a far more
comprehensive and demonstrative character than any which
experience can bestow. The axiom that nothing can be
produced from nothing and nothing destroyed, is so far from
being a result of experience, that it is apparently
contradicted by the most obvious observation. It has, at
first, the air of a paradox; and by those who refer to it,
it is familiarly employed to show how fallacious common
observation is. The assertion is usually made in this
form;--that nothing is created and nothing annihilated,
_notwithstanding_ that the common course of our experience
appears to show the contrary. The principle is not an
empirical, but a necessary and universal truth;--is
collected, not from the evidence of our senses, but from the
operation of our ideas. And thus the universal and
undisputed authority of the axiom proves the existence of
the Idea of Substance.

3. _Locke's Denial of the Idea of Substance._--I shall not
attempt to review the various opinions which have been
promulgated respecting this Idea: but it may be worth our
while to notice briefly the part which it played in the
great controversy concerning the origin of our ideas which
Locke's _Essay_ occasioned. Locke's object was to disprove
the existence of all ideas not derived from Sensation or
Reflection: and since the idea of substance as distinct from
external qualities, is {32} manifestly not derived directly
from sensation, nor by any very obvious or distinct process
from reflection, Locke was disposed to exclude the idea as
much as possible. Accordingly, in his argumentation against
Innate Ideas[28\6], he says plainly, 'the idea of substance,
which we neither have nor can have by sensation or
reflection.' And the inference which he draws is, 'that we
have no such clear idea at all.' What then, it may be asked,
do we mean by the word _substance_? This also he answers,
though somewhat strangely, 'We signify nothing by the word
_substance_, but only an uncertain supposition of we know
not what, _i. e._ of something whereof we have no particular
distinct positive idea, which we take to be the substratum,
or support, of those ideas we know.' That while he indulged
in this tautological assertion of our ignorance and
uncertainty, he should still have been compelled to
acknowledge that the word substance had some meaning, and
should have been driven to explain it by the identical
metaphors of 'substratum' and 'support,' is a curious proof
how impossible it is entirely to reject this idea.

[Note 28\6: _Essay_, b. i. c. iv. s. 18.]

But as we have already seen, the supposition of the
existence of substance is so far from being uncertain, that
it carries with it irresistible conviction, and substance is
necessarily conceived as something which cannot be produced
or destroyed. It may be easily supposed, therefore, that
when the controversy between Locke and his assailants came
to this point, he would be in some difficulty. And, indeed,
though with his accustomed skill in controversy, he managed
to retain a triumphant tone, he was driven from his main
points. Thus he repels the charge that he took the being of
substance to be doubtful[29\6]. He says, 'Having everywhere
affirmed and built upon it that man is a substance, I cannot
be supposed to question or doubt of the being of substance,
till I can question or doubt of my own being.' He attempts
to make a stand by saying that _being_ of things does not
depend upon our {33} _ideas_; but if he had been asked how,
without having an _idea_ of substance, he _knew_ substance
to _be_, it is difficult to conceive what answer he could
have made. Again, he had said that our idea of substance
arises from our 'accustoming ourselves to suppose' a
substratum of qualities. Upon this his adversary, Bishop
Stillingfleet, very properly asks, Is this custom grounded
upon true reason or no? To which Locke replies, that it is
grounded upon this: That we cannot conceive how simple ideas
of sensible qualities should subsist alone; and therefore we
suppose them to exist in, and to be supported by some common
subject, which support we denote by the name substance. Thus
he allows, not only that we necessarily assume the reality
of substance, but that we cannot conceive qualities without
substance; which are concessions so ample as almost to
include all that any advocate for the Idea of Substance need
desire.

[Note 29\6: _Essay_, b. ii. c. ii. and _First Letter to the
Bishop of Worcester_.]

Perhaps Locke, and the adherents of Locke, in denying that
we have an idea of substance in general, were latently
influenced by finding that they could not, by any effort of
mind, call up any _image_ which could be considered as an
image of substance in general. That in this sense we have no
idea of substance, is plain enough; but in the same sense we
have no idea of space in general, or of time, or number, or
cause, or resemblance. Yet we certainly have such a power of
representing to our minds space, time, number, cause,
resemblance, as to arrive at numerous truths by means of
such representations. These general representations I have
all along called Ideas, nor can I discover any more
appropriate word; and in this sense, we have also, as has
now been shown, an Idea of Substance.

4. _Is all Material Substance heavy?_--The principle that
the quantity of the substance of any body remains unchanged
by our operations upon it, is, as we have said, of universal
validity. But then the question occurs, how are we to
ascertain the quantity of substance, and thus, to apply the
principle in particular cases. In the case above mentioned,
where {34} smoke was to be weighed, it was manifestly
assumed that the quantity of the substance might be known by
its weight; and that the total quantity being unchanged, the
total weight also would remain the same. Now on what grounds
do we make this assumption? Is all material substance heavy?
and if we can assert this to be so, on what grounds does the
truth of the assertion rest? These are not idle questions of
barren curiosity; for in the history of that science
(Chemistry) to which the Idea of Substance is principally
applicable, nothing less than the fate of a comprehensive
and long established theory (the Phlogiston theory) depended
upon the decision of this question. When it was urged that
the reduction of a metal from a calcined to a metallic form
could not consist in the _addition_ of phlogiston, because
the metal was lighter than the calx had been; it was replied
by some, that this was not conclusive, for that phlogiston
was a principle of levity, diminishing the weight of the
body to which it was added. This reply was, however,
rejected by all the sounder philosophers, and the force of
the argument finally acknowledged. But why was this
suggestion of a substance having no weight, or having
absolute levity, repudiated by the most reflective
reasoners? It is assumed, it appears, that all matter must
be heavy; what is the ground of this assumption?

The ground of such an assumption appears to be the
following. Our idea of substance includes in it this:--that
substance is a quantity capable of addition; and thus
capable of making up, by composition, a sum equal to all its
parts. But substance, and the quantity of substance, can be
known to us only by its attributes and qualities. And the
qualities which are capable constantly and indefinitely of
increase and diminution by increase and diminution of the
parts, must be conceived inseparable from the substance. For
the qualities, if removable from the substance at all, must
be removable by some operation performed upon the substance;
and by the idea of substance, all such operations are only
equivalent to separation, junction, and union of parts.
Hence those characters {35} which thus universally increase
and diminish by addition and subtraction of the things
themselves, belong to the substance of the things. They are
measures of its quantity, and are not merely its separable
qualities.

The weight of bodies is such a character. However we
compound or divide bodies, we compound and divide their
weight in the same manner. We may dismember a body into the
minutest parts; but the sum of the weights of the parts is
always equal to the whole weight of the body. The weight of
a body can be in no way increased or diminished, except by
adding something to it or taking something from it. If we
bake a brick, we do not conceive that the change of colour
or of hardness, implies that anything has been created or
destroyed. It may easily be that the parts have only assumed
a new arrangement; but if the brick have lost weight, we
suppose that something (moisture for instance) has been
removed elsewhere.

Thus weight is apprehended as essential to matter. In
considering the dismemberment or analysis of bodies, we
assume that there must be some criterion of the quantity of
substance; and this criterion can possess no other
properties than their weight possesses. If we assume an
element which has no weight, or the weight of which is
negative, as some of the defenders of phlogiston attempted
to do, we put an end to all speculation on such subjects.
For if weight is not the criterion of the quantity of one
element, phlogiston for instance, why is weight the
criterion of the quantity of any other element? We may, by
the same right, assume any other real or imaginary element
to have levity instead of gravity; or to have a peculiar
intensity of gravity which makes its weight no index of its
quantity. In short, if we do this, we deprive of all
possibility of application our notions of element, analysis,
and composition; and violate the postulates on which the
questions are propounded which we thus attempt to decide.

We must, then, take a constant and quantitative property of
matter, such as weight is, to be an index {36} of the
quantity of matter or of substance to which it belongs. I do
not here speak of the question which has sometimes been
proposed, whether the _weight_ or the _inertia_ of bodies be
the more proper measure of the quantity of matter. For the
measure of inertia is regulated by the same assumption as
that of substance:--that the quantity of the whole must be
equal to the quantity of all the parts: and inertia is
measured by weight, for the same reason that substance is so.

Having thus established the certainty, and ascertained the
interpretation of the fundamental principle which the Idea
of Substance involves, we are prepared to consider its
application in the science upon which it has a peculiar
bearing.

{{37}}
NOTE TO CHAPTER III.

[3rd Ed.]--[THE doctrine here propounded, that All Matter is
Heavy, has been opposed by Sir William Hamilton of
Edinburgh. (_Works of Reid_, note, p. 853.) This writer is a
man of unquestionable acuteness and of very extensive
reading; but his acuteness shows itself in barren
ontological distinctions, which appear to me to be of the
same character as the speculations of the eminent Schoolmen
of the most sterile periods of the dark ages. That he should
have no conception of progressive or inductive science is
not wonderful, when we recollect that he holds, as an
important part of his philosophy, that the study of
mathematics perverts and obscures the mind. But it may be of
some interest to consider his objections to the doctrine
here maintained.

He says, 1st, that our reasoning assumes that we must
necessarily have it in our power to ascertain the Quantity
of Matter; whereas this may be a problem out of the reach of
human determination.

To this I reply, that my reasoning _does_ assume that there
is a science, or sciences, which make assertions concerning
the Quantity of Matter: Mechanics and Chemistry are such
sciences. My assertion is, that to make such sciences
possible, Quantity of Matter must be proportional to Weight.
If my opponent deny that Mechanics and Chemistry can exist
as sciences, he may invalidate my proof; but not otherwise.

2. He says that there are two conceivable ways of estimating
the Quantity of Matter: by the Space occupied, and by the
Weight or Inertia; and that I assume the second measure
gratuitously.

To which I reply, that the most elementary steps in
Mechanics and in Chemistry contradict the notion that {38}
the Quantity of Matter is proportionate to the Space. They
proceed necessarily on a distinction between Space and
Matter:--between mere Extension and material Substance.

3. He allows that we cannot make the Extension of a body the
measure of the Quantity of Matter, because, he says, we do
not know if 'the compressing force' is such as to produce
'the closest compression.' That is, he assumes a compressing
force, assumes a closest compression, assumes a peculiar
(and very improbable) atomic hypothesis; and all this to
supply a reason why we are not to believe the first simple
principle of Mechanics and Chemistry.

4. He speaks of 'a series of apparent fluids (as Light or
its vehicle, the Calorific, the Electro-galvanic, and
Magnetic agents) which we can neither denude of their
character of substance, nor clothe with the attribute of
weight.'

To which my reply is, that precisely because I cannot
'clothe' these agents with the attribute of Weight, I _do_
'denude them of the character of Substance.' They are not
substances, but agencies. These Imponderable Agents are not
properly called 'Imponderable Fluids.' This I conceive that
I have proved; and the proof is not shaken by denying the
conclusion without showing any defect in the reasoning.

5. Finally, my critic speaks about 'a logical canon,' and
about 'a criterion of truth, subjectively necessary and
objectively certain;' which matters I shall not waste the
reader's time by discussing.]

{{39}}
CHAPTER IV.

APPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY.

1. _A Body is Equal to the Sum of its Elements._--FROM the
earliest periods of chemistry the balance has been
familiarly used to determine the proportions of the
ingredients and of the compound; and soon after the middle
of the last century, this practice was so studiously
followed, that Wenzel and Richter were thereby led to the
doctrine of Definite Proportions. But yet the full value and
significance of the balance, as an indispensable instrument
in chemical researches, was not understood till the gaseous,
as well as solid and fluid ingredients were taken into the
account. When this was done, it was found that the
principle, that the whole is equal to the sum of its parts,
of which, as we have seen, the necessary truth, in such
cases, flows from the idea of substance, could be applied in
the most rigorous manner. And conversely, it was found that
by the use of the balance, the chemist could decide, in
doubtful cases, which was a whole, and which were parts.

For chemistry considers all the changes which belong to her
province as compositions and decompositions of elements; but
still the question may occur, whether an observed change be
the one or the other. How can we distinguish whether the
process which we contemplate be composition or
decomposition?--whether the new body be formed by addition
of a new, or subtraction of an old element? Again; in the
case of decomposition, we may inquire, What are the ultimate
limits of our analysis? If we decompound bodies into others
more and more simple, how far can we carry this succession
{40} of processes? How far can we proceed in the road of
analysis? And in our actual course, what evidence have we
that our progress, as far as it has gone, has carried us
from the more complex to the more simple?

To this we reply, that the criterion which enables us to
distinguish, decidedly and finally, whether our process have
been a mere analysis of the proposed body into its
ingredients, or a synthesis of some of them with some new
element, is the principle stated above, that the weight of
the whole is equal to the weight of all the parts. And no
process of chemical analysis or synthesis can be considered
complete till it has been verified by this fact;--by finding
that the weight of the compound is the weight of its
supposed ingredients; or, that if there be an element which
we think we have detached from the whole, its loss is
betrayed by a corresponding diminution of weight.

I have already noticed what an important part this principle
has played in the great chemical controversy which ended in
the establishment of the oxygen theory. The calcination of a
metal was decided to be the union of oxygen with the metal,
and not the separation of phlogiston from it, because it was
found that in the process of calcination, the weight of the
metal increased, and increased exactly as much as the weight
of ambient air diminished. When oxygen and hydrogen were
exploded together, and a small quantity of water was
produced, it was held that this was really a synthesis of
water, because, when very great care was taken with the
process, the weight of the water which resulted was equal to
the weight of the gases which disappeared.

2. _Lavoisier._--It was when gases came to be considered as
entering largely into the composition of liquid and solid
bodies, that extreme accuracy in weighing was seen to be so
necessary to the true understanding of chemical processes.
It was in this manner discovered by Lavoisier and his
contemporaries that oxygen constitutes a large ingredient of
calcined metals, of acids, and of water. A countryman of
Lavoisier[30\6] {41} has not only given most just praise to
that great philosopher for having constantly tested all his
processes by a careful and skilful use of the balance, but
has also claimed for him the merit of having introduced the
maxim, that in chemical operations nothing is created and
nothing lost. But I think it is impossible to deny that this
maxim is assumed in all the attempts at analysis made by his
contemporaries, as well as by him. This maxim is indeed
included in any clear notion of analysis: it could not be
the result of the researches of any one chemist, but was the
governing principle of the reasonings of all. Lavoisier,
however, employed this principle with peculiar assiduity and
skill. In applying it, he does not confine himself to mere
additions and subtractions of the quantities of ingredients;
but often obtains his results by more complex processes. In
one of his investigations he says, 'I may consider the
ingredients which are brought together, and the result which
is obtained as an algebraical equation; and if I
successively suppose each of the quantities of this equation
to be unknown, I can obtain its value from the rest: and
thus I can rectify the experiment by the calculation, and
the calculation by the experiment. I have often taken
advantage of this method, in order to correct the first
results of my experiments, and to direct me in repeating
them with proper precautions.'

[Note 30\6: M. Dumas, _Leçons de la Philosophie Chimique_.
1837. p. 157.]

The maxim, that the whole is equal to the sum of all its
parts, is thus capable of most important and varied
employment in chemistry. But it may be applied in another
form to the exclusion of a class of speculations which are
often put forwards.

3. _Maxim respecting Imponderable Elements._--Several of the
phenomena which belong to bodies, as heat, light,
electricity, magnetism, have been explained hypothetically
by assuming the existence of certain fluids; but these
fluids have never been shown to have weight. Hence such
hypothetical fluids have been termed _imponderable
elements_. It is however plain, that so long as these fluids
appear to be without weight, they are not _elements_ of
bodies in the same {42} sense as those elements of which we
have hitherto been speaking. Indeed we may with good reason
doubt whether those phenomena depend upon transferable
fluids at all. We have seen strong reason to believe that
light is not matter, but only motion; and the same thing
appears to be probable with regard to heat. Nor is it at all
inconceivable that a similar hypothesis respecting
electricity and magnetism should hereafter be found tenable.
Now if heat, light, and those other agents, be not matter,
they are not _elements_ in such a sense as to be included in
the principle referred to above, That the body is equal to
the sum of its elements. Consequently the maxim just stated,
that in chemical operations nothing is created, nothing
annihilated, does not apply to Light and Heat. They are not
_things_. And whether heat can be produced where there was
no heat before, and light struck out from darkness, the
ideas of which we are at present treating do not enable us
to say. In reasoning respecting chemical synthesis and
analysis therefore, we shall only make confusion by
attempting to include in our conception the Light and Heat
which are produced and destroyed. Such phenomena may be very
proper subjects of study, as indeed they undoubtedly are;
but they cannot be studied to advantage by considering them
as sharing the nature of composition and decomposition.

Again: in all attempts to explain the processes of nature,
the proper course is, first to measure the facts with
precision, and then to endeavour to understand their cause.
Now the facts of chemical composition and decomposition, the
weights of the ingredients and of the compounds, are facts
measurable with the utmost precision and certainty. But it
is far otherwise with the light and heat which accompany
chemical processes. When combustion, deflagration,
explosion, takes place, how can we measure the light or the
heat? Even in cases of more tranquil action, though we can
apply the thermometer, what does the thermometer tell us
respecting the _quantity_ of the heat? Since then we have no
measure which is of any value as {43} regards such
circumstances in chemical changes, if we attempt to account
for these phenomena _on chemical principles_, we introduce,
into investigations in themselves perfectly precise and
mathematically rigorous, another class of reasonings, vague
and insecure, of which the only possible effect is to
vitiate the whole reasoning, and to make our conclusions
inevitably erroneous.

We are led then to this maxim: that _imponderable fluids
are_ not _to be admitted as chemical elements of bodies_[31\6].

[Note 31\6: See the answer to Sir William Hamilton's
objections, at the end of the last chapter.

Since we are thus warned by a sound view of the nature of
science, from considering chemical affinity as having any
hold upon imponderable elements, we are manifestly still
more decisively prohibited from supposing mechanical impulse
or pressure to have any effect upon such elements. To make
this supposition, is to connect the most subtle and
incorporeal objects which we know in nature by the most
gross material ties. This remark seems to be applicable to
M. Poisson's hypothesis that the electric fluid is retained
at the surface of bodies by the pressure of the
atmosphere.]

4. It appears, I think, that our best and most philosophical
chemists have proceeded upon this principle in their
investigations. In reasoning concerning the constitution of
bodies and the interpretation of chemical changes, the
attempts to include in these interpretations the heat or
cold produced, by the addition or subtraction of a certain
hypothetical 'caloric,' have become more and more rare among
men of science. Such statements, and the explanations often
put forwards of the light and heat which appear under
various circumstances in the form of fire, must be
considered as unessential parts of any sound theory.
Accordingly we find Mr. Faraday gradually relinquishing such
views. In January, 1834, he speaks generally of an
hypothesis of this kind[32\6]: 'I cannot refrain from
recalling here the beautiful idea put forth, I believe by
Berzelius, in his development of his views of the
electro-chemical theory of affinity, that the heat and light
evolved during cases of powerful combination {44} are the
consequence of the electric discharge which is at that
moment taking place.' But in April of the same year[33\6],
he observes, that in the combination of oxygen and hydrogen
to produce water, electric powers to a most enormous amount
are for the time active, but that the flame which is
produced gives but feeble traces of such powers. 'Such
phenomena,' therefore, he adds, 'may not, cannot, be taken
as evidences of the nature of the action; but are merely
incidental results, incomparably small in relation to the
forces concerned, and supplying no information of the way in
which the particles are active on each other, or in which
their forces are finally arranged.'

[Note 32\6: _Researches_, 870.]

[Note 33\6: _Researches_, 960.]

In pursuance of this maxim, we must consider as an
unessential part of the oxygen theory that portion of it,
much insisted upon by its author at the time, in which when
sulphur, for instance, combined with oxygen to produce
sulphuric acid, the combustion was accounted for by means of
the _caloric_ which was supposed to be _liberated_ from its
combination with oxygen.

5. _Controversy of the Composition of Water._--There is
another controversy of our times to which we may with great
propriety apply the maxim now before us. After the glory of
having first given a true view of the composition of water
had long rested tranquilly upon the names of Cavendish and
Lavoisier, a claim was made in favour of James Watt as the
real author of this discovery by his son, (Mr J. Watt,) and
his eulogist, (M. Arago[34\6]). It is not to our purpose
here to discuss the various questions which have arisen on
this subject respecting priority of publication, and
respecting the translation of opinions published at one time
into the language of another period. But if we look at
Watt's own statement of his views, given soon after those of
Cavendish had been published, we shall perceive that it is
marked by a violation of this maxim: we shall find that he
does admit imponderable fluids {45} as chemical elements;
and thus shows a vagueness and confusion in his idea of
chemical composition. With such imperfection in his views,
it is not surprising that Watt, not only did not anticipate,
but did not apprehend quite precisely the discovery of
Cavendish and Lavoisier. Watt's statement of his views is as
follows[35\6]:--'Are we not authorized to conclude that
water is composed of dephlogisticated air and phlogiston
deprived of part of their latent or elementary heat; that
dephlogisticated or pure air is composed of water deprived
of its phlogiston and united to elementary heat and light;
and that the latter are contained in it in a latent state,
so as not to be sensible to the thermometer or to the eye;
and if light be only a modification of heat, or a
circumstance attending it, or a component part of the
inflammable air, then pure or dephlogisticated air is
composed of water deprived of its phlogiston and united to
elementary heat?'

[Note 34\6: Éloge de James Watt, _Annuaire du Bur. des
Long._ 1839.]

[Note 35\6: _Phil. Trans._ 1784, p. 332.]

When we compare this doubtful and hypothetical statement,
involving so much that is extraneous and heterogeneous, with
the conclusion of Cavendish, in which there is nothing
hypothetical or superfluous, we may confidently assent to
the decision which has been pronounced by one[36\6] of our
own time in favour of Cavendish. And we may with pleasure
recognize, in this enlightened umpire, a due appreciation of
the value of the maxim on which we are now insisting.
'Cavendish,' says Mr. Vernon Harcourt, 'pared off {46} from
the hypotheses their theories of combustion, and _affinities
of imponderable for ponderable matter_, as complicating
chemical with physical considerations.'

[Note 36\6: The Rev. W. Vernon Harcourt, Address to the
British Association, 1839.--Since the first edition of this
work was published, and also since the second edition of the
_History of the Inductive Sciences_, Mr. Watt's
correspondence bearing upon the question of the Composition
of Water has been published by Mr. Muirhead. I do not find,
in this publication, any reason for withdrawing what I have
stated in the text above: but with reference to the
statement in the _History_, it appears that Mr. Cavendish's
claim to the discovery was not uncontested in his own time.
Mr. Watt had looked at the composition of water, as a
problem to be solved, perhaps more distinctly than Mr.
Cavendish had done; and he conceived himself wronged by Mr.
Cavendish's putting forwards his experiment as the first
solution of this problem.]

6. _Relation of Heat to Chemistry._--But while we thus
condemn the attempts to explain the thermotical phenomena of
chemical processes by means of chemical considerations, it
may be asked if we are altogether to renounce the hope of
understanding such phenomena? It is plain, it may be said,
that heat generated in chemical changes is always a very
important circumstance, and can sometimes be measured, and
perhaps reduced to laws; are we prohibited from speculating
concerning the causes of such circumstances and such laws?
And to this we reply, that we may properly attempt to
connect chemical with thermotical processes, _so far as_ we
have obtained a clear and probable view of the nature of the
thermotical processes. When our theory of Thermotics is
tolerably complete and certain, we may with propriety
undertake to connect it with our theory of Chemistry. But at
present we are not far enough advanced in our knowledge of
heat to make this attempt with any hope of success. We can
hardly expect to understand the part which heat plays in the
union of two bodies, when we cannot as yet comprehend in
what manner it produces the liquefaction or vaporization of
one body. We cannot look to account for Gay Lussac and
Dalton's Law, that all gases expand equally by heat, till we
learn how heat causes a gas to expand. We cannot hope to see
the grounds of Dulong and Petit's Law, that the specific
heat of all atoms is the same, till we know much more, not
only about atoms, but about specific heat. We have as yet no
thermotical theory which even professes to account for all
the prominent facts of the subject[37\6]: and the theories
which have been proposed are of the most diverse kind.
Laplace assumes particles of bodies surrounded by
atmospheres of caloric[38\6]; Cauchy makes heat consist in
longitudinal vibrations of the ether of which transverse
vibrations {47} produce light: in Ampère's theory[39\6],
heat consists in the vibrations of the particles of bodies.
And so long as we have nothing more certain in our
conceptions of heat than the alternative of these and other
precarious hypotheses, how can we expect to arrive at any
real knowledge, by connecting the results of such hypotheses
with the speculations of Chemistry, of which science the
theory is at least equally obscure?

[Note 37\6: _Hist. Ind. Sci._ b. x. c. 4.]

[Note 38\6: _Ib._]

[Note 39\6: _Hist. Ind. Sci._ b. x. c. 4.]

The largest attempts at chemical theory have been made in
the form of the Atomic Theory, to which I have just had
occasion to allude. I must, therefore, before quitting the
subject, say a few words respecting this theory.

{{48}}
CHAPTER V.

THE ATOMIC THEORY.

1. _The Atomic Theory considered on Chemical Grounds._--WE
have already seen that the combinations which result from
chemical affinity are definite, a certain quantity of one
ingredient uniting, not with an uncertain, but with a
certain quantity of another ingredient. But it was found, in
addition to this principle, that one ingredient would often
unite with another in different proportions, and that, in
such cases, these proportions are multiples one of another.
In the three salts formed by potassa with oxalic acid, the
quantities of acid which combine with the same quantity of
alkali are exactly in the proportion of the numbers 1, 2, 4.
And the same rule of the existence of multiple proportions
is found to obtain in other cases.

It is obvious that such results will be accounted for, if we
suppose that the base and the acid consist each of numerous
definite equal particles, and that the formation of the
salts above mentioned consists in the combination of one
particle of the base with one particle of acid, with two
particles of acid, and with four particles of acid,
respectively. But further; as we have already stated,
chemical affinity is not only definite, but reciprocal. The
proportions of potassa and soda which form neutral salts
being 590 and 391 in one case, they are so in all cases.
These numbers represent _proportions_ of weight in which the
two bases, potassa and soda, enter into analogous
combinations; 590 of potassa is _equivalent_ to 391 of soda.
These facts with regard to combination are still expressed
by the above supposition of equal particles, assuming that
the weights of a {49} particle of potassa and of soda are in
the proportion of 590 to 391.

But we pursue our analysis further. We find that potassa is
a compound of a metallic base, potassium, and of oxygen, in
the proportion of 490 to 100; we suppose, then, that the
particle of potassa consists of a particle of potassium and
a particle of oxygen; and these latter particles, since we
see no present need to suppose them divided, potassium and
oxygen being simple bodies, we may call _atoms_, and assume to
be indivisible. And by supposing all simple bodies to
consist of such atoms, and compounds to be formed by the
union of two, or three, or more of such atoms, we explain
the occurrence of definite and multiple proportions, and we
construct the Atomic Theory.

2. _Hypothesis of Atoms._--So far as the assumption of such
atoms as we have spoken of serves to express those laws of
chemical composition which we have referred to, it is a
clear and useful generalization. But if the Atomic Theory be
put forwards (and its author, Dr. Dalton, appears to have
put it forwards with such an intention,) as asserting that
chemical elements are really composed of _atoms_, that is,
of such particles not further divisible, we cannot avoid
remarking, that for such a conclusion, chemical research has
not afforded, nor can afford, any satisfactory evidence
whatever. The smallest observable quantities of ingredients,
as well as the largest, combine according to the laws of
proportions and equivalence which have been cited above. How
are we to deduce from such facts any inference with regard
to the existence of certain smallest possible particles? The
Theory, when dogmatically taught as a physical truth,
asserts that all observable quantities of elements _are_
composed of proportional numbers of particles which can no
further be subdivided; but all which observation teaches us
is, that if there be such particles, they are smaller than
the smallest observable quantities. In chemical experiment,
at least, there is not the slightest positive evidence for
the existence of such atoms. The assumption of _indivisible_
particles, smaller than the smallest {50} observable, which
combine, particle with particle, will explain the phenomena;
but the assumption of particles bearing this proportion, but
_not_ possessing the property of indivisibility, will explain
the phenomena at least equally well. The decision of the
question, therefore, whether the Atomic Hypothesis be the
proper way of conceiving the chemical combinations of
substances, must depend, not upon chemical facts, but upon
our conception of Substance. In this sense the question is
an ancient and curious controversy, and we shall hereafter
have to make some remarks upon it.

3. _Chemical Difficulties of the Hypothesis._--But before
doing this, we may observe that there is no small difficulty
in reconciling this hypothesis with the facts of chemistry.
According to the theory, all salts, compounded of an acid
and a base, are analogous in their atomic constitution; and
the number of atoms in one such compound being known or
assumed, the number of atoms in other salts may be
determined. But when we proceed in this course of reasoning
to other bodies, as metals, we find ourselves involved in
difficulties. The protoxide of iron is a base which,
according to all analogy, must consist of one atom of iron
and one of oxygen: but the peroxide of iron is also a base,
and it appears by the analysis of this substance that it
must consist of _two-thirds_ of an atom of iron and one atom
of oxygen. Here, then, our indivisible atoms must be
divisible, even upon chemical grounds. And if we attempt to
evade this difficulty by making the peroxide of iron consist
of two atoms of iron and three of oxygen, we have to make a
corresponding alteration in the theoretical constitution of
all bodies analogous to the protoxide; and thus we overturn
the very foundation of the theory. Chemical facts,
therefore, not only do not prove the Atomic Theory as a
physical truth, but they are not, according to any
modification yet devised of the theory, reconcileable with
its scheme.

Nearly the same conclusions result from the attempts to
employ the Atomic Hypothesis in expressing another important
chemical law;--the law of the {51} combinations of gases
according to definite proportions of their volumes,
experimentally established by Gay Lussac[40\6]. In order to
account for this law, it has been very plausibly suggested
that all gases, under the same pressure, contain an equal
number of atoms in the same space; and that when they
combine, they unite atom to atom. Thus one volume of
chlorine unites with one volume of hydrogen, and forms
hydrochloric acid[41\6]. But then this hydrochloric acid
occupies the space of the two volumes; and therefore the
proper number of particles cannot be supplied, and the
uniform distribution of atoms in all gases maintained,
without dividing into two each of the compound particles,
constituted of an atom of chlorine and an atom of hydrogen.
And thus in this case, also, the Atomic Theory becomes
untenable if it be understood to imply the indivisibility of
the atoms.

[Note 40\6: _Hist. Ind. Sc._ b. xiv. c. 8.]

[Note 41\6: Dumas, _Phil. Chim._ 263.]

In all these attempts to obtain distinct physical conception
of chemical union by the aid of the Atomic Hypothesis, the
atoms are conceived to be associated by certain forces of
the nature of mechanical attractions. But we have already
seen[42\6] that no such mode of conception can at all
explain or express the facts of chemical combination; and
therefore it is not wonderful that when the Atomic Theory
attempts to give an account of chemical relations by
contemplating them under such an aspect, the facts on which
it grounds itself should be found not to authorize its
positive doctrines; and that when these doctrines are tried
upon the general range of chemical observation, they should
prove incapable of even expressing, without
self-contradiction, the laws of phenomena.

[Note 42\6: See Chapter I. of this book.]

4. _Grounds of the Atomic Doctrine._--Yet the doctrine of
atoms, or of substance as composed of indivisible particles,
has in all ages had great hold upon the minds of physical
speculators; nor would this doctrine ever have suggested
itself so readily, or have been maintained so tenaciously,
as the true mode of {52} conceiving chemical combinations,
if it had not been already familiar to the minds of those
who endeavour to obtain a general view of the constitution
of nature. The grounds of the assumption of the atomic
structure of substance are to be found rather in the idea of
substance itself, than in the experimental laws of chemical
affinity. And the question of the existence of atoms, thus
depending upon an idea which has been the subject of
contemplation from the very infancy of philosophy, has been
discussed in all ages with interest and ingenuity. On this
very account it is unlikely that the question, so far as it
bears upon chemistry, should admit of any clear and final
solution. Still it will be instructive to look back at some
of the opinions which have been delivered respecting this
doctrine.

5. _Ancient Prevalence of the Atomic Doctrine._--The
doctrine that matter consists of minute, simple,
indivisible, indestructible particles as its ultimate
elements, has been current in all ages and countries,
whenever the tendency of man to wide and subtle speculations
has been active. I need not attempt to trace the history of
this opinion in the schools of Greece and Italy. It was the
leading feature in the physical tenets of the Epicureans,
and was adopted by their Roman disciples, as the poem of
Lucretius copiously shows us. The same tenet had been held
at still earlier periods, in forms more or less definite, by
other philosophers. It is ascribed to Democritus, and is
said to have been by him derived from Leucippus. But this
doctrine is found also, we are told[43\6], among the
speculations of another intellectual and acute race, the
Hindoos. According to some of their philosophical writers,
the ultimate elements of matter are atoms, of which it is
proved by certain reasonings, that they are each one-sixth
of one of the motes that float in the sunbeam.

[Note 43\6: By Mr. Colebrook. _Asiatic Res._ 1824.]

This early prevalence of controversies of the widest and
deepest kind, which even in our day remain undecided, has in
it nothing which need surprize us; or, at least, it has in
it nothing which is not in conformity {53} with the general
course of the history of philosophy. As soon as any ideas
are clearly possessed by the human mind, its activity and
acuteness in reasoning upon them are such, that the
fundamental antitheses and ultimate difficulties which
belong to them are soon brought into view. The Greek and
Indian philosophers had mastered completely the Idea of
Space, and possessed the Idea of Substance in tolerable
distinctness. They were, therefore, quite ready, with their
lively and subtle minds, to discuss the question of the
finite and infinite divisibility of matter, so far as it
involved only the ideas of space and of substance, and this
accordingly they did with great ingenuity and perseverance.

But the ideas of Space and of Substance are far from being
sufficient to enable men to form a complete general view of
the constitution of matter. We must add to these ideas, that
of mechanical Force with its antagonist Resistance, and that
of the Affinity of one kind of matter for another. Now the
former of these ideas the ancients possessed in a very
obscure and confused manner; and of the latter they had no
apprehension whatever. They made vague assumptions
respecting the impact and pressure of atoms on each other;
but of their mutual attraction and repulsion they never had
any conception, except of the most dim and wavering kind;
and of an affinity different from mere local union they did
not even dream. Their speculations concerning atoms,
therefore, can have no value for us, except as a part of the
history of science. If their doctrines appear to us to
approach near to the conclusions of our modern philosophy,
it must be because our modern philosophy is that philosophy
which has not fully profited by the additional light which
the experiments and meditations of later times have thrown
upon the constitution of matter.

6. _Bacon._--Still, when modern philosophers look upon the
Atomic Theory of the ancients in a general point of view
merely, without considering the special conditions which
such a theory must fulfil, in order to represent the
discoveries of modern times, they are {54} disposed to
regard it with admiration. Accordingly we find Francis Bacon
strongly expressing such a feeling. The Atomic Theory is
selected and dwelt upon by him as the chain which connects
the best parts of the physical philosophy of the ancient and
the modern world. Among his works is a remarkable
dissertation _On the Philosophy of Democritus, Parmenides,
and Telesius_: the last mentioned of whom was one of the
revivers of physical science in modern times. In this work
he speaks of the atomic doctrine of Democritus as a
favourable example of the exertions of the undisciplined
intellect. 'Hæc ipsa placita, quamvis paulo emendatiora,
talia sunt qualia esse possunt illa quæ ab intellectu sibi
permisso, nec continenter et gradatim sublevato, profecta
videntur.'--'These doctrines, thus [in an ancient fable]
presented in a better form, are such glimpses of truth as
can be obtained by the intellect left to its own natural
impulses, and not ascending by successive and connected
steps,' [as the Baconian philosophy directs]. 'Accordingly,'
he adds, 'the doctrine of Atoms, from its going a step
beyond the period in which it was advanced, was ridiculed by
the vulgar, and severely handled in the disputations of the
learned, notwithstanding the profound acquaintance with
physical science by which its author was allowed to be
distinguished, and from which he acquired the character of a
magician.'

'However,' he continues, 'neither the hostility of
Aristotle, with all his skill and vigour in disputation,
(though, like the Ottoman sultans, he laboured to destroy
all his brother philosophers that he might rest undisputed
master of the throne of science,) nor the majestic and lofty
authority of Plato, could effect the subversion of the
doctrine of Democritus. And while the opinions of Plato and
Aristotle were rehearsed with loud declamation and
professorial pomp in the schools, this of Democritus was
always held in high honour by those of a deeper wisdom, who
followed in silence a severer path of contemplation. In the
days of Roman speculation it kept its ground and its favour;
Cicero everywhere speaks of its author with the {55}
greatest praise; and Juvenal, who, like poets in general,
probably expressed the prevailing judgment of his time,
proclaims his merit as a noble exception to the general
stupidity of his countrymen.
. . . . Cujus prudentia monstrat
Magnos posse viros et magna exempla daturos
Vervecum in patriâ crassoque sub aere nasci.

'The destruction of this philosophy was not effected by
Aristotle and Plato, but by Genseric and Attila, and their
barbarians. For then, when human knowledge had suffered
shipwreck, those fragments of the Aristotelian and Platonic
philosophy floated on the surface like things of some
lighter and emptier sort, and so were preserved; while more
solid matters went to the bottom, and were almost lost in
oblivion.'

7. _Modern Prevalence of the Atomic Doctrine._--It is our
business here to consider the doctrine of Atoms only in its
bearing upon existing physical sciences, and I must
therefore abstain from tracing the various manifestations of
it in the schemes of hypothetical cosmologists;--its place
among the _vortices_ of Descartes, its exhibition in the
_monads_ of Leibnitz. I will, however, quote a passage from
Newton to show the hold it had upon his mind.

At the close of his _Opticks_ he says, 'All these things
being considered, it seems probable to me that God, in the
beginning, formed matter in solid, massy, hard,
impenetrable, moveable particles, of such sizes and figures,
and with such other properties, and in such proportions to
space, as most conduced to the end for which He formed them;
and that the primitive particles, being solids, are
incomparably harder than any porous bodies compounded of
them, even so very hard as never to wear or break in pieces;
no ordinary power being able to divide what God had made one
in the first creation. While the particles continue entire,
they may compose bodies of one and the same nature and
texture in all ages: but should they wear away or break in
pieces, the nature of things depending on them would be
changed. Water and earth composed {56} of old worn particles
and fragments of particles would not be of the same nature
and texture now with water and earth composed of entire
particles in the beginning. And therefore that nature may be
lasting, the changes of corporeal things are to be placed
only in the various separations and new associations and
motions of these permanent particles; compounded bodies
being apt to break, not in the midst of solid particles, but
where those particles are laid together and only touch in a
few points.'

We shall hereafter see how extensively the atomic doctrine
has prevailed among still more recent philosophers. Not only
have the chemists assumed it as the fittest form for
exhibiting the principles of multiple proportions; but the
physical mathematicians, as Laplace and Poisson, have made
it the basis of their theories of heat, electricity,
capillary action; and the crystallographers have been
supposed to have established both the existence and the
arrangement of such ultimate molecules.

In the way in which it has been employed by such writers,
the hypothesis of ultimate particles has been of great use,
and is undoubtedly permissible. But when we would assert
this theory, not as a convenient hypothesis for the
expression or calculation of the laws of nature, but as a
philosophical truth respecting the constitution of the
universe, we find ourselves checked by difficulties of
reasoning which we cannot overcome, as well as by
conflicting phenomena which we cannot reconcile. I will
attempt to state briefly the opposing arguments on this
question.

8. _Arguments for and against Atoms._--The leading arguments
on the two sides of the question, in their most general
form, may be stated as follows:

_For_ the Atomic Doctrine.--The appearances which nature
presents are compounded of many parts, but if we go on
resolving the larger parts into smaller, and so on
successively, we must at last come to something simple. For
that which is compound can be so no otherwise than by
composition of what is simple; and if we suppose all
composition to be removed, which {57} hypothetically we may
do, there can remain nothing but a number of simple
substances, capable of composition, but themselves not
compounded. That is, matter being dissolved, resolves itself
into atoms.

_Against_ the Atomic Doctrine.--Space is divisible without
limit, as may be proved by Geometry; and matter occupies
space, therefore matter is divisible without limit, and no
portion of matter is indivisible, or an _atom_.

And to the argument on the other side just stated, it is
replied that we cannot even hypothetically divest a body of
composition, if by composition we mean the relation of point
to point in space. However small be a particle, it is
compounded of parts having relation in space.

The Atomists urge again, that if matter be infinitely
divisible, a finite body consists of an infinite number of
parts, which is a contradiction. To this it is replied, that
the finite body consists of an infinite number of parts in
the same sense in which the parts are infinitely small,
which is no contradiction.

But the opponents of the Atomists not only rebut, but retort
this argument drawn from the notion of infinity. Your atoms,
they say, are indivisible by any finite force; therefore
they are infinitely hard; and thus your finite particles
possess infinite properties. To this the Atomists are wont
to reply, that they do not mean the hardness of their
particles to be infinite, but only so great as to resist all
usual natural forces. But here it is plain that their
position becomes untenable; for, in the first place, their
assumption of this precise degree of hardness in the
particles is altogether gratuitous; and in the next place,
if it were granted, such particles are not atoms, since in
the next moment the forces of nature may be augmented so as
to divide the particle, though hitherto undivided.

Such are the arguments for and against the Atomic Theory in
its original form. But when these atoms are conceived, as
they have been by Newton, and commonly by his followers, to
be solid, hard particles exerting attractive and repulsive
forces, a new set of {58} arguments come into play. Of
these, the principal one may be thus stated: According to
the Atomic Theory thus modified, the properties of bodies
depend upon the attractions and repulsions of the particles.
Therefore, among other properties of bodies, their hardness
depends upon such forces. But if the hardness _of the
bodies_ depends upon the forces, the repulsion, for
instance, of the particles, upon what does the hardness _of
the particles_ depend? what progress do we make in
explaining the properties of bodies, when we assume the same
properties in our explanation? and to what purpose do we
assume that the particles are hard?

9. _Transition to Boscovich's Theory._--To this difficulty
it does not appear easy to offer any reply. But if the
hardness and solidity of the particles be given up as an
incongruous and untenable appendage to the Newtonian view of
the Atomic Theory, we are led to the theory of Boscovich,
according to which matter consists not of solid particles,
but of mere mathematical centers of force. According to this
theory, each body is composed of a number of geometrical
points from which emanate forces, following certain
mathematical laws in virtue of which the forces become, at
certain small distances attractive, at certain other
distances repulsive, and at greater distances attractive
again. From these forces of the points arise the cohesion of
the parts of the same body, the resistance which it exerts
against the pressure of another body, and finally the
attraction of gravitation which it exerts upon bodies at a
distance.

This theory is at least a homogeneous and consistent theory,
and it is probable that it may be used as an instrument for
investigating and expressing true laws of nature; although,
as we have already said, the attempt to identify the forces
by which the particles of bodies are bound together with
mechanical attraction, appears to be a confusion of two
separate ideas[44\6].

[Note 44\6: 'Boscovich's Theory,' that all bodies may be
considered as consisting of a mere collection of centers of
forces, may be so conceived as possibly to involve an
explanation of all the powers which their parts exert, (such
powers, namely, as those which produce optical, thermotical
and chemical phenomena;) but this theory cannot supply an
explanation of the mechanical properties of a body as a
whole, especially of its _inertia_. A collection of mere
centers of force can have no inertia. If two bodies are
considered as two collections of centers of force, the one
attracting the other, there is in this view nothing to limit
or determine the velocity with which the one body will
approach the other. A world composed of such bodies is not a
_material_ world: for matter (as we have already seen in
book iii. chapter v.) implies not only force, but something
which resists the action of force.]

{59} 10. _Use of the Molecular Hypothesis._--In this form,
representing matter as a collection of molecules or centers
of force, the Atomic Theory has been abundantly employed in
modern times as an hypothesis on which calculations
respecting the elementary forces of bodies might be
conducted. When thus employed it is to be considered as
expressing the principle that the properties of bodies
depend upon forces emanating from immovable points of their
mass. This view of the way in which the properties of bodies
are to be treated by the mechanical philosopher was
introduced by Newton, and was a natural sequel to the
success which he had obtained by reasoning concerning
central forces on a large scale. I have already quoted his
Preface to the _Principia_, in which he says, 'Many things
induce me to believe that the rest of the phenomena of
nature, as well as those of astronomy, may depend upon
certain forces by which the particles of bodies, in virtue
of causes not yet known, are urged towards each other and
cohere in regular figures, or are mutually repelled and
recede; and philosophers, knowing nothing of these forces,
have hitherto failed in their examination of nature.' Since
the time of Newton, this line of speculation has been
followed with great assiduity, and by some mathematicians
with great success. In particular Laplace has shown that the
hypothesis may, in many instances, be made a much closer
representation of nature, if we suppose the forces exerted
by the particles to decrease so rapidly with the increasing
distance from them, that {60} the force is finite only at
distances imperceptible to our senses, and vanishes at all
remoter points. He has taught the method of expressing and
calculating such forces, and he and other mathematicians of
his school have applied this method to many of the most
important questions of physics; as capillary action, the
elasticity of solids, the conduction and radiation of heat.
The explanation of many apparently unconnected and curious
observed facts by these mathematical theories gives a strong
assurance that its essential principles are true. But it
must be observed that the actual constitution of bodies as
composed of distinct and separate particles is by no means
proved by these coincidences. The assumption, in the
reasoning, of certain centers of force acting at a distance,
is to be considered as nothing more than a method of
reducing to calculation that view of the constitution of
bodies which supposes that they exert force at _every_
point. It is a mathematical artifice of the same kind as the
hypothetical division of a body into infinitesimal parts, in
order to find its center of gravity; and no more implies a
physical reality than that hypothesis does.

11. _Poisson's Inference._--When, therefore, M. Poisson, in
his views of Capillary Action, treats this hypothetical
distribution of centers of force as if it were a physical
fact, and blames Laplace for not taking account of their
different distribution at the surface of the fluid and below
it[45\6], he appears to push the claims of the molecular
hypothesis too far. The only ground for the assumption of
separate centers, is that we can thus explain the action of
the whole mass. The intervals between the centers nowhere
enter into this explanation: and therefore we can have no
reason for assuming these intervals different in one part of
the fluid and in the other. M. Poisson asserts that the
density of the fluid diminishes when we approach very near
the surface; but he allows that this diminution is not
detected by experiment, and that the formulæ on {61} his
supposition, so far as the results go, are identical with
those of Laplace. It is clear, then, that his doctrine
consists merely in the assertion of the necessary truth of a
part of the hypothesis which cannot be put to the test of
experiment. It is true, that so long as we have before us
the hypothesis of separate centers, the particles very near
the surface are not in a condition symmetrical with that of
the others: but it is also true that this hypothesis is only
a step of calculation. There results, at one period of the
process of deduction, a stratum of smaller density at the
surface of the fluid; but at a succeeding point of the
reasoning the thickness of this stratum vanishes; it has no
physical existence.

[Note 45\6: Poisson, _Théorie de l'Action Capillaire_.]

Thus the _molecular_ hypothesis, as used in such cases, does
not differ from the doctrine of forces acting at _every
point_ of the mass; and this principle, which is common to
both the opposite views, is the true part of each.

12. _Wollaston's Argument._--An attempt has been made in
another case, but depending on nearly the same arguments, to
bring the doctrine of ultimate atoms to the test of
observation. In the case of the air, we know that there _is_
a diminution of density in approaching the upper surface of
the atmosphere, if it have a surface: but it is held by some
that except we allow the doctrine of ultimate molecules, it
will not be bounded by any surface, but will extend to an
infinite distance. This is the reasoning of Wollaston[46\6].
'If air consists of any ultimate particles no longer
divisible, then must the expansion of the medium composed of
them cease at that distance where the force of gravity
downwards is equal to the resistance arising from the
repulsive force of the medium.' But if there be no such
ultimate particles, every stratum will require a stratum
beyond it to prevent by its weight a further expansion, and
thus the atmosphere {62} must extend to an infinite
distance. And Wollaston conceived that he could learn from
observation whether the atmosphere was thus diffused through
all space; for if so, it must, he argued, be accumulated
about the larger bodies of the system, as Jupiter and the
Sun, by the law of universal gravitation; and the existence
of an atmosphere about these bodies, might, he remarked, be
detected by its effects in producing refraction. His result
is, that 'all the phenomena accord entirely with the
supposition that the earth's atmosphere is of finite extent,
limited by the weight of ultimate atoms of definite
magnitude, no longer divisible by repulsion of their parts.'

[Note 46\6: _Phil. Trans._ 1822, p. 89.]

A very little reflection will show us that such a line of
reasoning cannot lead to any result. For we know nothing of
the law which connects the density with the compressing
force, in air so extremely rare as we must suppose it to be
near the boundary of the atmosphere. Now there are possible
laws of dependence of the density upon the compressing force
such that the atmosphere would terminate in virtue of the
law without any assumption of atoms. This may be proved by
mathematical reasoning. If we suppose the density of air to
be as the square root of the compressing force, it will
follow that at the very limits of the atmosphere, the strata
of equal thickness may observe in their densities such a law
of proportion as is expressed by the numbers 7, 5, 3,
1[47\6].

[Note 47\6: For the compressing force on each being as the
whole weight beyond it, it will be for the four highest
strata, 16, 9, 4 and 1, of which the square roots are as 4,
3, 2, 1, or, as 8, 6, 4, 2; and though these numbers are not
exactly as the densities 7, 5, 3, 1, those who are a little
acquainted with mathematical reasoning, will see that the
difference arises from taking so small a number of strata.
If we were to make the strata indefinitely thin, as to avoid
error we ought to do, the coincidence would be exact; and
thus, according to this law, the series of strata terminates
as we ascend, without any consideration of atoms.]

If it be asked how, on this hypothesis, the density of the
highest stratum can be as 1, since there is {63} nothing to
compress it, we answer that the upper part of the highest
stratum compresses the lower, and that the density
diminishes continually to the surface, so that the need of
compression and the compressing weight vanish together.

The fallacy of concluding that because the height of the
atmosphere is finite, the weight of the highest stratum must
be finite, is just the same as the fallacy of those who
conclude that when we project a body vertically upwards,
because it occupies only a finite time in ascending to the
highest point, the velocity at the last instant of the
ascent must be finite. For it might be said, if the last
velocity of ascent be not finite, how can the body describe
the last particle of space in a finite time? and the answer
is, that there is no last finite particle of space, and
therefore no last finite velocity.

13. _Permanence of Properties of Bodies._--We have already
seen that, in explaining the properties of matter as we find
them in nature, the assumption of solid, hard,
indestructible particles is of no use or value. But we may
remark, before quitting the subject, that Newton appears to
have had another reason for assuming such particles, and one
well worthy of notice. He wished to express, by means of
this hypothesis, the doctrine that the laws of nature do not
alter with the course of time. This we have already seen in
the quotation from Newton. 'The ultimate particles of matter
are indestructible, unalterable, impenetrable; for if they
could break or wear, the structure of material bodies now
would be different from that which it was when the particles
were new.' No philosopher will deny the truth which is thus
conveyed by the assertion of atoms; but it is obviously
equally easy for a person who rejects the atomic view, to
state this truth by saying that the forces which matter
exerts do not vary with time, but however modified by the
new modifications of its form, are always unimpaired in
quantity, and capable of being restored to their former mode
of action. {64}

We now proceed to speculations in which the fundamental
conceptions may, perhaps, be expressed, at least in some
cases, by means of the arrangement of atoms; but in which
the philosophy of the subject appears to require a reference
to a new Fundamental Idea.

{{65}}
BOOK VII.

THE
PHILOSOPHY
OF
MORPHOLOGY,
INCLUDING
CRYSTALLOGRAPHY.

CRYSTALLIZATION exhibits to us the effects of the natural
arrangement of the ultimate particles of various compound
bodies; but we are scarcely yet sufficiently acquainted with
chemical synthesis and analysis to understand the rationale
of this process. The rhomboidal form may arise from the
proper position of 4, 6, 8 or 9 globular particles, the
cubic form from 8 particles, the triangular form from 3, 6
or 10 particles, the hexahedral prism from 7 particles, &c.
Perhaps, in due time we may be enabled to ascertain the
number and order of elementary particles, constituting any
given compound element, and from that determine the figure
which it will prefer on crystallization, and _vice versâ_.

JOHN DALTON, _Chemical Philosophy_ (1808), p. 210.

{{67}}
BOOK VII.

THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.

CHAPTER I.

EXPLICATION OF THE IDEA OF SYMMETRY.

1. WE have seen in the History of the Sciences, that the
principle which I have there termed[1\7] the Principle of
Developed and Metamorphosed Symmetry, has been extensively
applied in botany and physiology, and has given rise to a
province of science termed Morphology. In order to
understand clearly this principle, it is necessary to obtain
a clear idea of the Symmetry of which we thus speak. But
this Idea of Symmetry is applicable in the inorganic, as
well as in the organic kingdoms of nature; it is presented
to our eyes in the forms of minerals, as well as of flowers
and animals; we must, therefore, take it under our
consideration here, in order that we may complete our view
of Mineralogy, which, as I have repeatedly said, is an
essential part of Chemical science. I shall accordingly
endeavour to unfold the Idea of Symmetry with which we here
have to do.

[Note 1\7: _Hist. Ind. Sc._ b. xvii. c. vi.]

It will of course be understood that by the term _Symmetry_
I here intend, not that more indefinite attribute of form
which belongs to the domain of the fine arts, as when we
speak of the 'symmetry' of an edifice {68} or of a
sculptured figure, but a certain definite relation or
property, no less rigorous and precise than other relations
of number and position, which is thus one of the sure guides
of the scientific faculty, and one of the bases of our exact
science.

2. In order to explain what Symmetry is in this sense, let
the reader recollect that the bodies of animals consist of
_two_ equal and similar sets of members, the right and the
left side;--that some flowers consist of three or of five
equal sets of organs, similarly and regularly disposed, as
the iris has _three_ straight petals, and three reflexed
ones, alternately disposed, the rose has _five_ equal and
similar sepals of the calyx, and alternate with these, as
many petals of the corolla. This orderly and exactly similar
distribution of two, or three, or five, or any other number
of parts, is Symmetry; and according to its various
modifications, the forms thus determined are said to be
_symmetrical_ with various numbers of members. The
classification of these different kinds of symmetry has been
most attended to in Crystallography, in which science it is
the highest and most general principle by which the classes
of forms are governed. Without entering far into the
technicalities of the subject, we may point out some of the
features of such classes.

[Illustration] The first of the figures (1) in the margin
may represent the summit of a crystal as it appears to an
eye looking directly down upon it; the center of the figure
represents the summit of a pyramid, and the spaces of
various forms which diverge from this point represent
sloping sides of the pyramid. Now it will be observed that
the figure consists of three portions exactly similar to one
another, and that each part or member is repeated in each of
these portions. The faces, or pairs of faces, are repeated
in _threes_, with exactly similar forms and angles. This
figure is said to be _three-membered_, or to have
_triangular_ symmetry. The same kind of {69} symmetry may
exist in a flower, as presented in the accompanying figure,
and does, in fact, occur in a large class of flowers, as for
example, all the lily tribe. The next pair of figures (2)
have four equal and similar portions, and have their members
or pairs of members four times repeated. Such figures are
termed _four-membered_, and are said to have _square_ or
_tetragonal_ symmetry. The _pentagonal_ symmetry, formed by
_five_ similar _members_, is represented in the next figures
(3). It occurs abundantly in the vegetable world, but never
among crystals; for the pentagonal figures which crystals
sometimes assume, are never exactly regular. But there is
still another kind of symmetry (4) in which the opposite
ends are exactly similar to each other and also the opposite
sides; this is _oblong_, or _two-and-two-membered_ symmetry.
And finally, we have the case of _simple_ symmetry (5) in
which the two sides of the object are exactly alike (in
opposite positions) without any further repetition.
[Illustration]

3. These different kinds of symmetry occur in various ways
in the animal, vegetable, and mineral kingdom. Vertebrate
animals have a right and a {70} left side exactly alike, and
thus possess _simple_ symmetry. The same kind of symmetry
(simple symmetry) occurs very largely in the forms of
vegetables, as in most leaves, in _papilionaceous_,
_personate_, and _labiate_ flowers. Among minerals, crystals
which possess this symmetry are called _oblique-prismatic_,
and are of very frequent occurrence. The _oblong_, or
_two-and-two-membered_ symmetry belongs to _right-prismatic_
crystals; and may be seen in _cruciferous_ flowers, for
though these are cross-shaped, the cross has two longer and
two shorter arms, or pairs of arms. The _square_ or
_tetragonal_ symmetry occurs in crystals abundantly; to the
vegetable world it appears to be less congenial; for though
there are flowers with four exactly similar and
regularly-disposed petals, as the herb Paris (_Paris
quadrifolia_), these flowers appear, from various
circumstances, to be deviations from the usual type of
vegetable forms. The _trigonal_, or _three-membered_
symmetry is found abundantly both in plants and in crystals,
while the _pentagonal_ symmetry, on the other hand, though
by far the most common among flowers, nowhere occurs in
minerals, and does not appear to be a possible form of
crystals. This pentagonal form further occurs in the animal
kingdom, which the oblong, triangular, and square forms do
not. Many of Cuvier's _radiate_ animals appear in this
pentagonal form, as _echini_ and _pentacrinites_, which
latter have hence their name.

4. The regular, or as they may be called, the _normal_ types
of the vegetable world appear to be the forms which possess
triangular and pentagonal symmetry; from these the others
may be conceived to be derived, by transformations resulting
from the expansion of one or more parts. Thus it is manifest
that if in a three-membered or five-membered flower, one of
the petals be expanded more than the other, it is
immediately reduced from pentagonal or trigonal, to simple
symmetry. And the oblong or two-and-two-membered symmetry of
the flowers of cruciferous plants, (in which the stamens are
four large and two small ones, arranged in regular
opposition,) is held by botanists to result {71} from a
normal form with ten stamens; Meinecke explaining this by
adhesion, and Sprengel by the metamorphosis of the stamens
into petals[2\7].

[Note 2\7: Sprengel, _Gesch. d. Bot._ ii. 304.]

It is easy to see that these various kinds of symmetry
include relations both of form and of number, but more
especially of the latter kind; and as this symmetry is often
an important character in various classes of natural
objects, such classes have often curious numerical
properties. One of the most remarkable and extensive of
these is the distinction which prevails between
monocotyledonous and dicotyledonous plants; the number
_three_ being the ground of the symmetry of the former, and
the number _five_, of the latter. Thus liliaceous and
bulbous plants, and the like, have flowers of three or six
petals, and the other organs follow the same numbers: while
the vast majority of plants are pentandrous, and with their
five stamens have also their other parts in fives. This
great numerical distinction corresponding to a leading
difference of physiological structure cannot but be
considered as a highly curious fact in phytology. Such
properties of numbers, thus connected in an incomprehensible
manner with fundamental and extensive laws of nature, give
to numbers an appearance of mysterious importance and
efficacy. We learn from history how strongly the study of
such properties, as they are exhibited by the phenomena of
the heavens, took possession of the mind of Kepler; perhaps
it was this which, at an earlier period, contributed in no
small degree to the numerical mysticism of the Pythagoreans
in antiquity, and of the Arabians and others in the middle
ages. In crystallography, numbers are the primary characters
in which the properties of substances are expressed;--they
appear, first, in that classification of forms which depends
on the degree of symmetry, that is, upon the number of
correspondencies; and next, in the laws of derivation,
which, for the most part, appear to be common in their
occurrence in proportion to the numerical simplicity of
their expression. But the manifestation {72} of a governing
numerical relation in the organic world strikes us as more
unexpected; and the selection of the number _five_ as the
index of the symmetry of dicotyledonous plants and radiated
animals, (a number which is nowhere symmetrically produced
in inorganic bodies,) makes this a new and remarkable
illustration of the constancy of numerical relations. We may
observe, however, that the moment one of these radiate
animals has one of its five members expanded, or in any way
peculiarly modified, (as happens among the echini), it is
reduced to the common type of animals simply symmetrical,
with a right and left side.

5. It is not necessary to attempt to enumerate all the kinds
of Symmetry, since our object is only to explain what
Symmetry is, and for this purpose enough has probably been
said already. It will be seen, as soon as the notion of
Symmetry in general is well apprehended, that it is or
includes a peculiar Fundamental Idea, not capable of being
resolved into any of the ideas hitherto examined. It may be
said, perhaps, that the Idea of Symmetry is a modification
or derivative of our ideas of space and number;--that a
symmetrical shape is one which consists of parts exactly
similar, repeated a certain number of times, and placed so
as to correspond with each other. But on further reflection
it will be seen that this repetition and correspondence of
parts in symmetrical figures are something peculiar; for it
is not _any_ repetition or any correspondence of parts to
which we should give the name of symmetry, in the manner in
which we are now using the term. Symmetrical arrangements
may, no doubt, be concerned with space and position, time
and number; but there appears to be implied in them a
Fundamental Idea of regularity, of completeness, of complex
simplicity, which is not a mere modification of other ideas.

6. It is, however, not necessary, in this and in similar
cases, to determine whether the idea which we have before us
be a peculiar and independent Fundamental Idea or a
modification of other ideas, provided we clearly perceive
the evidence of those Axioms by {73} means of which the Idea
is applied in scientific reasonings. Now in the application
of the Idea of Symmetry to crystallography, phytology and
zoology, we must have this idea embodied in some principle
which asserts more than a mere geometrical or numerical
accordance of members. We must have it involved in some
vital or productive action, in order that it may connect and
explain the facts of the organic world. Nor is it difficult
to enunciate such a principle. We may state it in this
manner. _All the symmetrical members of a natural product
are, under like circumstances, alike affected by the natural
formative power._ The parts which we have termed
_symmetrical_, resemble each other, not only in their form
and position, but also in the manner in which they are
produced and modified by natural causes. And this principle
we assume to be necessarily true, however unknown and
inconceivable may be the causes which determine the
phenomena. Thus it has not yet been found possible to
discover or represent to ourselves, in any intelligible
manner, the forces by which the various faces of a crystal
are consequent upon its primary form: for the hypothesis of
their being built up of integrant molecules, as Haüy held,
cannot be made satisfactory. But though the mechanism of
crystals is still obscure, there is no doubt as to the
principle which regulates their modifications. The whole of
crystallography rests upon this principle, that if one of
the primary planes or axes be modified in any manner, all
the symmetrical planes and axes must be modified in the same
manner. And though accidental mechanical or other causes may
interfere with the actual exhibition of such faces, we do
not the less assume their crystallographical reality, as
inevitably implied in the law of symmetry of the
crystal[3\7]. And we apply similar considerations to
organized beings. We assume that in a regular flower, each
of the similar {74} members has the same organization and
similar powers of developement; and hence if among these
similar parts some are much less developed than others, we
consider them as _abortive_; and if we wish to remove doubts
as to what are symmetrical members in such a case, we make
the inquiry by tracing the anatomy of these members, or by
following them in their earlier states of developement, or
in cases where their capabilities are magnified by
monstrosity or otherwise. The power of developement may be
modified by external causes, and thus we may pass from one
kind of symmetry to another; as we have already remarked.
Thus a regular flower with pentagonal symmetry, growing on a
lateral branch, has one petal nearest to the axis of the
plant: if this petal be more or less expanded than the
others, the pentagonal symmetry is interfered with, and the
flower may change to a symmetry of another kind. But it is
easy to see that all such conceptions of expansion,
abortion, and any other kind of metamorphosis, go upon the
supposition of identical faculties and tendencies in each
similar member, in so far as such tendencies have any
relation to the symmetry. And thus the principle we have
stated above is the basis of that which, in the History, we
termed the Principle of Developed and Metamorphosed
Symmetry.

[Note 3\7: Some crystalline forms, instead of being
_holohedral_ (provided with their whole number of faces),
are _hemihedral_ (provided with only half their number of
faces). But in these hemihedral forms the half of the faces
are still _symmetrically_ suppressed.]

We shall not at present pursue the other applications of
this Idea of Symmetry, but we shall consider some of the
results of its introduction into Crystallography.

{{75}}
CHAPTER II.

APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS.

1. MINERALS and other bodies of definite chemical
composition often exhibit that marked regularity of form and
structure which we designate by terming them _Crystals_; and
in such crystals, when we duly study them, we perceive the
various kinds of symmetry of which we have spoken in the
previous chapter. And the different kinds of symmetry which
we have there described are now usually distinguished from
each other, by writers on crystallography. Indeed it is
mainly to such writers that we are indebted for a sound and
consistent classification of the kinds and degrees of
symmetry of which forms are capable. But this classification
was by no means invented as soon as mineralogists applied
themselves to the study of crystals. These first attempts to
arrange crystalline forms were very imperfect; those, for
example, of Linnæus, Werner, Romé de Lisle, and Haüy. The
essays of these writers implied a classification at once
defective and superfluous. They reduced all crystals to one
or other of certain _fundamental forms_; and this procedure
might have been a perfectly good method of dividing
crystalline forms into classes, if the fundamental forms had
been selected so as to exemplify the different kinds of
symmetry. But this was not the case. Haüy's fundamental or
'primitive' forms, were, for instance, the following: the
_parallelepiped_, the _octahedron_, the _tetrahedron_, the
_regular hexagonal prism_, the _rhombic dodecahedron_, and
the _double hexagonal pyramid_. Of these, the _octahedron_,
the _tetrahedron_, the _rhombic dodecahedron_, all belong to
the {76} same kind of symmetry (the TESSULAR systems); also
the _hexagonal prism_ and the _hexagonal pyramid_ both
belong to the RHOMBIC system; while the _parallelepiped_ is
so employed as to include all kinds of symmetry.

It is, however, to be recollected that Haüy, in his
selection of primitive forms, not only had an eye to the
external form of the crystal and to its degree and kind of
regularity, but also made his classification with an
especial reference to the _cleavage_ of the mineral, which
he considered as a primary element in crystalline analysis.
There can be no doubt that the cleavage of a crystal is one
of its most important characters: it is a relation of form
belonging to the interior, which is to be attended to no
less than the form of the exterior. But still, the cleavage
is to be regarded only as determining the degree of
geometrical symmetry of the body, and not as defining a
special geometrical figure to which the body _must_ be
referred. To have looked upon it in the latter light, was a
mistake of the earlier crystallographic speculators, on
which we shall shortly have to remark.

2. I have said that the reference of crystals to Primitive
Forms might have been well employed as a mode of expressing
a just classification of them. This follows as a consequence
from the application of the Principle stated in the last
chapter, that _all symmetrical members are alike affected_.
Thus we may take an upright triangular prism as the
representative of the rhombic system, and if we then suppose
one of the upper edges to be cut off, or truncated, we must,
by the Principle of Symmetry, suppose the other two upper
edges to be truncated in precisely the same manner. By this
truncation we may obtain the upper part of a rhombohedron;
and by truncations of the same kind, symmetrically affecting
all the analogous parts of the figure, we may obtain any
other form possessing three-membered symmetry. And the same
is true of any of the other kinds of symmetry, provided we
make a proper selection of a fundamental form. And this was
really the method employed by Demeste, Werner, and Romé de
Lisle. They {77} assumed a Primitive Form, and then
conceived other forms, such as they found in nature, to be
derived from the Primitive Form by truncation of the edges,
acumination of the corners, and the like processes. This
mode of conception was a perfectly just and legitimate
expression of the general Idea of Symmetry.

3. The true view of the degrees of symmetry was, as I have
already said, impeded by the attempts which Haüy and others
made to arrive at primitive forms by the light which
cleavage was supposed to throw upon the structure of
minerals. At last, however, in Germany, as I have narrated
in the History of Mineralogy[4\7], Weiss and Mohs introduced
a classification of forms implying a more philosophical
principle, dividing the forms into Systems; which, employing
the terms of the latter writer, we shall call the
_tessular_, the _pyramidal_ or _square pyramidal_, the
_prismatic_ or _oblong_, and the _rhombohedral_ systems.

[Note 4\7: _Hist. Ind. Sc._ b. xv. c. iv.]

Of these forms, the three latter may be at once referred to
those kinds of symmetry of which we have spoken in the last
chapter. The _rhombohedral_ system has _triangular_
symmetry, or is three-membered: the _pyramidal_ has _square_
symmetry, or is four-membered: the _prismatic_ has _oblong_
symmetry, and is two-and-two-membered. But the kinds of
symmetry which were spoken of in the former chapter, do not
exhaust the idea when applied to minerals. For the symmetry
which was there explained was such only as can be exhibited
on a surface, whereas the forms of crystals are solid. Not
only have the right and left parts of the upper surface of a
crystal relations to each other; but the upper surface and
the lateral faces of the crystal have also their relations;
they may be different, or they may be alike. If we take a
cube, and hold it so that four of its faces are vertical,
not only are all these four sides exactly similar, so as to
give square symmetry; but also we may turn the cube, so that
any one of these four sides shall become the top, and still
the four sides which are thus made vertical, though {78} not
the same which were vertical before, are still perfectly
symmetrical. Thus this cubical figure possesses more than
square symmetry. It possesses square symmetry in a vertical
as well as in a horizontal sense. It possesses a symmetry
which has the same relation to a _cube_ which four-membered
symmetry has to a _square_. And this kind of symmetry is
termed the _cubical_ or _tessular_ symmetry. All the other
kinds of symmetry have reference to an axis, about which the
corresponding parts are disposed; but in tessular symmetry
the horizontal and vertical axes are also symmetrical, or
interchangeable; and thus the figure may be said to have no
axis at all.

4. It has already been repeatedly stated that, by the very
idea of symmetry, all the incidents of form must affect
alike all the corresponding parts. Now in crystals we have,
among these incidents, not only external figure, but
_cleavage_, which may be considered as internal figure.
Cleavage, then, must conform to the degree of symmetry of
the figure. Accordingly cleavage, no less than form, is to
be attended to in determining to what system a mineral
belongs. If a crystal were to occur as a square prism or
pyramid, it would not on that account necessarily belong to
the square pyramidal system. If it were found that it was
cleavable parallel to one side of the prism, but not in the
transverse direction, it has only oblong symmetry; and the
equality of the sides which makes it square is only
accidental.

Thus no cleavage is admissible in any system of
crystallization which does not agree with the degree of
symmetry of the system. On the other hand, _any_ cleavage
which _is_ consistent with the symmetry of the system, is
(hypothetically at least) allowable. Thus in the oblong
prismatic system we may have a cleavage parallel to one side
only of the prism; or parallel to both, but of different
distinctness; or parallel to the two diagonals of the prism
but of the same distinctness; or we may have both these
cleavages together. In the rhombohedral system, the cleavage
may be parallel to the sides of the rhombohedron, as in Calc
{79} Spar: or, in the same system, the cleavage, instead of
being thus oblique to the axis, may be along the axis in
those directions which make equal angles with each other:
this cleavage easily gives either a triangular or a
hexagonal prism. Again, in the tessular system, the cleavage
may be parallel to the surface of the cube, which is thus
readily separable into other cubes, as in Galena; or the
cleavage may be such as to cut off the solid angle of the
cube, and since there are eight of these, such cleavage
gives us an octahedron, which, however, may be reduced to a
tetrahedron, by rejecting all parallel faces, as being mere
repetitions of the same cleavage; this is the case with
Fluor Spar: or the cube of the tessular system may be
cleavable in planes which truncate all the edges of the
cube; and as these are twelve, we thus obtain the
dodecahedron with rhombic faces: this occurs in Zinc Blende.
And thus we see the origin of Haüy's various primitive
forms, the tetrahedron, octahedron, and rhombic
dodecahedron, all belonging to the tessular system:--they
are, in fact, different cleavage forms of that system.

5. I do not dwell upon other incidents of crystals which
have reference to form, nor upon the lustre, smoothness, and
striation of the surfaces. To all such incidents the general
principle applies, that similar parts are similarly
affected; and hence, if any parts are found to be constantly
and definitely different from other parts of the same sort,
they are not similar parts; and the symmetry is to be
interpreted with reference to this difference.

We have now to consider the inferences which have been drawn
from these incidents of crystallization, with regard to the
intimate structure of bodies.

{{80}}
CHAPTER III.

SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS.

1. WHEN a crystal, as, for instance, a crystal of Galena,
(sulphuret of lead,) is readily divisible into smaller
cubes, and these into smaller ones, and so on without limit,
it is very natural to represent to ourselves the original
cube as really consisting of small cubical elements; and to
imagine that it is a philosophical account of the physical
structure of such a substance to say that it is made up of
cubical molecules. And when the Galena crystal has
externally the form of a cube, there is no difficulty in
such a conception; for the surface of the crystal is also
conceived as made up of the surfaces of its cubical
molecules. We conceive the crystal so constituted, as we
conceive a wall built of bricks.

But if, as often happens, the Galena crystal be an
octahedron, a further consideration is requisite in order to
understand its structure, pursuing still the same
hypothesis. The mineral is still, as in the other case,
readily cleavable into small cubes, having their corners
turned to the faces of the octahedron. Therefore these faces
can no longer be conceived as made up of the faces of
cubical elements of which the whole is constituted. If we
suppose a pile of such small cubes to be closely built
together, but with decreasing width above, so as to form a
pyramid, the face of such a pyramid will no longer be plane;
it will consist of a great number of the corners or edges of
the small elementary cubes. It would appear at first sight,
therefore, that such a face cannot represent the smooth
polished surface of a crystal. {81}

But when we come to look more closely, this difficulty
disappears. For how large are these elementary cubes? We
cannot tell, even supposing they really have any size. But
we know that they must be, at any rate, very small; so small
as to be inappreciable by our senses, for our senses find no
limit to the divisibility of minerals by cleavage. Hence the
surface of the pyramid above described would not consist of
visible corners or edges, but would be roughened by specks
of imperceptible size; or rather, by supposing these specks
to become still smaller, the roughness becomes smoothness.
And thus we may have a crystal with a smooth surface, made
up of small cubes in such a manner that their surfaces are
all oblique to the surface of the crystal.

Haüy, struck by some instances in which the supposition of
such a structure of crystals appeared to account happily for
several of their relations and properties, adopted and
propounded it as a general theory. The small elements, of
which he supposed crystals to be thus built up, he termed
_integrant molecules_. The form of these molecules might or
might not be the same as the _primitive form_ with which his
construction was supposed to begin; but there was, at any
rate, a close connexion between these forms, since both of
them were founded on the cleavage of the mineral. The tenet
that crystals are constituted in the manner which I have
been describing, I shall call the _Theory of Integrant
Molecules_, and I have now to make some remarks on the
grounds of this theory.

2. In the case of which I have spoken, the mineral used as
the example, Galena, readily splits into cubes, and cubes
are easily placed together so as to fit each other, and fill
the space which they occupy. The same is the case in the
mineral which suggested to Haüy his theory, namely, Calc
Spar. The crystals of this substance are readily divisible
into rhombohedrons, a form like a brick with oblique angles;
and such bricks can be built together so as to produce
crystals of all the immense varieties of form which Calc
Spar presents. This kind of masonry is equally possible in
many other {82} minerals; but as we go through the mineral
kingdom in our survey, we soon find cases which offer
difficulties. Some minerals cleave only in two directions,
some in one only; in such cases we cannot by cleavage obtain
an integrant molecule of definite form; one of its
dimensions, at least, must remain indeterminate and
arbitrary. Again, in some instances, we have more than three
different planes of cleavage, as in Fluor Spar, where we
have four. The solid, bounded by four planes, is a
tetrahedron; or if we take four _pairs_ of parallel faces,
an octahedron. But if we attempt to take either of these
forms for our integrant molecule, we are met by this
difficulty: that a collection of such forms will not fill
space. Perhaps this difficulty will be more readily
conceived by the general reader if it be contemplated with
reference to plane figures. It will readily be seen that a
number of equal squares may be put together so as to fill
the space which they occupy; but if we take a number of
equal regular octagons, we may easily convince ourselves
that no possible arrangement can make them cover a flat
space without leaving blank spots between. In like manner
octahedrons or tetrahedrons cannot be arranged in solid
space so as to fill it. They necessarily leave vacancies.
Hence the structure of Fluor Spar, and similar crystals, was
a serious obstacle in the way of the theory of integrant
molecules. That theory had been adopted in the first
instance because portions of the crystal, obtained by
cleavage, could be built up into a solid mass; but this
ground of the theory failed altogether in such instances as
I have described, and hence the theory, even upon the
representations of its adherents, had no longer any claim to
assent.

The doctrine of Integral Molecules, however, was by no means
given up at once, even in such instances. In this and in
other subjects, we may observe that a theory, once
constructed and carried into detail, has such a hold upon
the minds of those who have been in the habit of applying
it, that they will attempt to uphold it by introducing
suppositions inconsistent with {83} the original foundations
of the theory. Thus those who assert the Atomic Theory,
reconcile it with facts by taking the _halves of atoms_; and
thus the Theory of Integrant Molecules was maintained for
Fluor Spar, by representing the elementary octahedrons of
which crystals are built up, as touching each other only by
the _edges_. The contact of surface with surface amongst
integrant molecules had been the first basis of the theory;
but this supposition being here inapplicable, was replaced
by one which made the theory no longer a representation of
the facts (the cleavages), but a mere geometrical
construction. Although, however, the inapplicability of the
theory to such cases was thus, in some degree, disguised to
the disciples of Haüy, it was plain that, in the face of
such difficulties, the Theory of Integrant Molecules could
not hold its place as a philosophical truth. But it still
answered the purpose (a very valuable one, and one to which
crystallography is much indebted,) of an instrument for
calculating the geometrical relations of the parts of
crystals to each other: for the integrant molecules were
supposed to be placed layer above layer, each layer as we
ascend, _decreasing_ by a certain number of molecules and
rows of molecules; and the calculation of these _laws of
decrement_ was, in fact, the best mode then known of
determining the positions of the faces. The Theory of
Decrements served to express and to determine, in a great
number of the most obvious cases, _the laws of phenomena_ in
crystalline forms, though the Theory of Integrant Molecules
could not be maintained as a just view of the structure of
crystals.

3. The Theory of Integrant Molecules, however, involved this
just and important principle: that a true view of the
intimate structure of crystals must include and explain the
facts of crystallization, that is, crystalline form and
cleavage; and that it must take these into account,
according to their degree of _Symmetry_. So far all theories
concerning the elements of crystals must agree. And it was
soon seen that this was, in reality, all that had been
established by the investigations of Haüy and his school. I
have already, in the {84} _History_, quoted Weiss's
reflections on making this step. 'When in 1809,' he
says[5\7], 'I published my Dissertation, I shared the common
opinion as to the necessity of the assumption, and the
reality of the existence of a primitive form, at least in a
sense not very different from the usual sense of the
expression.' He then proceeds to relate that he sought a
ground for such an opinion, independent of the doctrine of
_Atoms_, which he, in common with a great number of
philosophers of that time in his own country, was disposed
to reject, inclining to believe that the properties of
bodies were determined by _Forces_ which acted in them, and
not by _Molecules_ of which they were composed. He adds,
that in pursuing this train of thought, he found, 'that out
of his Primitive Forms there was gradually unfolded to his
hands that which really governs them, and is not affected by
their casual fluctuations; namely, the Fundamental Relations
of their Dimensions,' or as we now may call them, _Axes of
Symmetry_. With reference to these Axes, he found, as he
goes on to say, that 'a multiplicity of internal
Oppositions, necessarily and mutually interdependent, are
developed in the crystalline mass, each Relation having its
own Polarity; so that the Crystalline Character is
co-extensive with these Polarities.' The character of these
polarities, whether manifested in crystalline faces,
cleavage, or any other incidents of crystallization, is
necessarily displayed in the degree and kind of Symmetry
which the crystal possesses: and thus this Symmetry, in all
our speculations concerning the structure of crystals,
necessarily takes the place of that enumeration of Primitive
Forms which were rejected as inconsistent with observed
facts, and destitute of sound scientific principle.

[Note 5\7: _Acad. Berlin._ 1816, p. 307.]

I may just notice here what I have stated in the History of
Mineralogy[6\7], that the distinction of systems of
crystallization, as introduced by Weiss and Mohs, was
strikingly confirmed by Sir David Brewster's discoveries
respecting the optical properties of minerals. {85} The
splendid phenomena which were produced by passing polarized
light through crystals, were found to vary according as the
crystals were of the Rhombohedral, Square Pyramidal, Oblong
Prismatic, or Tessular System. The Optical Symmetry exactly
corresponded with the Geometrical Symmetry. In the two
former Systems were crystals _uniaxal_ in respect of their
optical properties; the oblong prismatic, was _biaxal_;
while in the tessular, the want of a predominant axis
prevented the phenomena here spoken of from occurring at
all. The optical experiments must have led, and would have
led, to a classification of crystals into the above systems
or something nearly equivalent, even had they not been
already so arranged by attention to their forms.

[Note 6\7: _Hist. Ind. Sc._ b. xv. c. v.]

4. While in Germany Weiss and Mohs with their disciples,
were gradually rejecting what was superfluous in the
previous crystallographical hypotheses, philosophers in
England were also trying to represent to themselves the
constitution of crystals in a manner which should be free
from the obviously arbitrary and untenable fictions of the
Haüyian school. These attempts, however, were not crowned
with much success. One mode of representing the structure of
crystals which suggested itself, was to reject the
polyhedral forms which Haüy gave to his integrant molecules,
and to conceive the elements of crystals as _spheres_, the
properties of the crystal being determined not by the
_surfaces_, but by the _position_ of the elements. This was
done by Wollaston, in the _Philosophical Transactions_ for
1813. He applied this view to the tessular system, in which,
indeed, the application is not difficult; and he showed that
octahedral and tetrahedral figures may be deduced from
symmetrical arrangements of equal spherules. But though in
doing this, he manifested a perception of the conditions of
the problem, he appeared to lose his hold on the real
question when he tried to pass on to other systems of
crystallization. For he accounted for the rhombohedral
system by supposing the spheres changed into _spheroids_.
Such a procedure involved him in a gratuitous and useless
hypothesis: for to what purpose do we introduce the {86}
arrangement of atoms (instead of their figure,) as a mode of
explaining the symmetry of the crystallization, when at the
next step we ascribe to the atom, by an arbitrary fiction, a
symmetry of figure of the same kind as that which we have to
explain? It is just as easy, and as allowable, to assume an
elementary rhombohedron, as to assume elementary spheroids,
of which the rhombohedrons are constructed.

5. Many hypotheses of the same kind might be adduced,
devised both by mineralogists and chemists. But almost all
such speculations have been pursued with a most surprising
neglect of the principle which obviously is the only sound
basis on which they can proceed. The principle is
this:--that _All hypotheses concerning the arrangement of
the elementary atoms of bodies in space must be constructed
with reference to the general facts of crystallization_. The
truth and importance of this principle can admit of no
doubt. For if we make any hypothesis concerning the mode of
connexion of the elementary particles of bodies, this must
be done with the view of representing to ourselves the
forces which connect them, and the results of these forces
as manifested in the properties of the bodies. Now the
forces which connect the particles of bodies so as to make
them crystalline, are manifestly chemical forces. It is only
definite chemical compounds which crystallize; and in
crystals the force of cohesion by which the particles are
held together cannot in any way be distinguished or
separated from the chemical force by which their elements
are combined. The elements are understood to be combined,
precisely because the result is a definite, apparently
homogeneous substance. The properties of the compound bodies
depend upon the elements and their mode of combination; for,
in fact, these include everything on which they can depend.
There are no other circumstances than these which can affect
the properties of a body. Therefore all those properties
which have reference to space, namely, the crystalline
properties, cannot depend upon anything else than the
arrangement of the elementary molecules in space. These {87}
properties are the facts which any hypothesis of the
arrangement of molecules must explain, or at least render
conceivable; and all such hypotheses, all constructions of
bodies by supposed arrangements of molecules, can have no
other philosophical object than to account for facts of this
kind. If they do not do this, they are mere arbitrary
geometrical fictions, which cannot be in any degree
confirmed or authorised by an examination of nature, and are
therefore not deserving of any regard.

6. Those philosophers who have endeavoured to represent the
mode in which bodies are constructed by the combination of
their chemical atoms, have often undertaken to show, not
only that the atoms are combined, but also in what positions
and configurations they are combined. And it is truly
remarkable, as I have already said, that they have done
this, almost in every instance, without any consideration of
the crystalline character of the resulting combinations;
from which alone we receive any light as to the relation of
their elements in space. Thus Dr. Dalton, in his _Elements
of Chemistry_, in which he gave to the world the Atomic
Theory as a representation of the doctrine of definite and
multiple proportions, also published a large collection of
Diagrams, exhibiting what he conceived to be the
configuration of the atoms in a great number of the most
common combinations of chemical elements. Now these
hypothetical diagrams do not in any way correspond, as to
the nature of their symmetry, with the compounds, as we find
them displaying their symmetry when they occur crystallized.
Carbonate of lime has in reality a triangular symmetry,
since it belongs to the rhombohedral system; Dr. Dalton's
carbonate of lime would be an oblique rhombic prism or
pyramid. Sulphate of baryta is really two-and-two membered;
Dr. Dalton's diagram makes it two-and-one membered. Alum is
really octahedral or tessular; but according to the diagram
it could not be so, since the two ends of the atom are not
symmetrical. And the same want of correspondence between the
facts and the hypothesis runs through the whole {88} system.
It need not surprise us that the theoretical arrangement of
atoms does not explain the facts of _crystallization_; for
to produce such an explanation would be a second step in
science quite as great as the first, the discovery of the
atomic theory in its _chemical_ sense. But we may allow
ourselves to be surprised that an utter discrepance between
all the facts of crystallization and the figures assumed in
the theory, did not suggest any doubt as to the soundness of
the mode of philosophizing by which this part of the theory
was constructed.

7. Some little accordance between the hypothetical
arrangements of chemical atoms and the facts of
crystallization, does appear to have been arrived at by some
of the theorists to whom we here refer, although by no means
enough to show a due conviction of the importance of the
principle stated above. Thus Wollaston, in the Essay above
noticed, after showing that a symmetrical arrangement of
equal spherules would give rise to octahedral and other
tessular figures, remarks, very properly, that the metals,
which are simple bodies, crystallize in such forms. M.
Ampère[7\7] also, in 1814, published a brief account of an
hypothesis of a somewhat similar nature, and stated himself
to have developed this speculation in a Memoir which has not
yet, so far as I am aware, been published. In this notice he
conceives bodies to be compounded of _molecules_, which,
arranged in a polyhedral form, constitute _particles_. These
_representative forms_ of the particles depend on chemical
laws. Thus the particles of oxygen, of hydrogen, and of
azote, are composed each of four molecules. Hence it is
collected that the particles of nitrous gas are composed of
two molecules of oxygen and two of azote; and similar
conclusions are drawn respecting other substances. These
conclusions, though expressed by means of the polyhedrons
thus introduced, are supported by chemical, rather than by
crystallographical comparisons. The author does, indeed,
appeal to the crystallization of sal {89} ammoniac as an
argument[8\7]; but as _all_ the forms which he introduces
appear to belong to the _tessular_ system of
crystallization, there is, in his reasonings, nothing
distinctive; and therefore nothing, crystallographically
speaking, of any weight on the side of this theory.

[Note 7\7: _Ann. de Chimie_, tom. xc. p. 43.]

[Note 8\7: _Ann. de Chimie_, tom. xc. p. 83.]

8. Any hypothesis which should introduce any principle of
chemical order among the actual forms of minerals, would
well deserve attention. At first sight, nothing can appear
more anomalous than the forms which occur. We have, indeed,
one broad fact, which has an encouraging aspect, the
tessular forms in which the pure metals crystallize. The
highest degree of chemical and of geometrical simplicity
coincide: irregularity disappears precisely where it is
excluded by the consideration above stated, that the
symmetry of chemical composition must determine the symmetry
of crystalline form[9\7].

[Note 9\7: Inasmuch as this law, that the simple metals
crystallize in tessular forms, is the most signal example of
that connexion between the chemical nature of a body and its
crystalline form, I in the former Edition stated it with as
much generality as I could find any ground for, and I should
have been glad if I could have added confirmation of the
law, derived from later observations. But the most recent
investigations of crystallographers appear to have afforded
exceptions rather than examples of the rule. Arsenic and
Tellurium are said to be _rhombohedral_. Antimony, stated by
Haüy to be octahedral (and therefore tessular), has been
found by more modern observers to be _rhombohedral_. Tin has
been obtained by Professor Miller in beautiful crystals
belonging to the _pyramidal_ system. Professor Nöggerath has
observed in Zinc, after cooling from fusion, hexagonal
cleavage, rendering it probable that the mineral
crystallized in _rhombohedrons_ having their axes vertical,
like ice. G. Rose conceives it highly probable that Osmium
and Iridium are _rhombohedral_. (Poggendorf. Bd. liv.)

But all the more perfect metals are tessular; namely, Gold,
Silver, Mercury, Platinum, Iron, Copper; also Bismuth [?]
Perhaps the observation in which the crystallization of Zinc
is affected by its position is, on that very account, no
sufficient evidence of its free crystallization. We can
hardly conceive a collection of perfectly simple, similar
particles to crystallize so as to have one pre-eminent axis,
without some extraneous action affecting them.]

But if we go on to any other class of crystalline forms, we
soon find ourselves lost in our attempts to {90} follow any
thread of order. We have indeed many large groups connected
by obvious analogies; as the rhombohedral carbonates of
lime, magnesia, iron, manganese;--the prismatic carbonates
and sulphates of lime, baryta, strontia, lead. But even in
these, we cannot form any plausible hypothesis of the
arrangement of the elements; and in other cases to which we
naturally turn, we can find nothing but confusion. For
instance, if we examine the oxides of metals:--those of iron
are rhombohedral and tessular; those of copper, tessular;
those of tin, of titanium, of manganese, square pyramidal;
those of antimony, prismatic; and we have other forms for
other substances.

It may be added, that if we take account of the optical
properties which, as we have already stated, have constant
relations to the crystalline forms, the confusion is still
further increased; for the optical dimensions vary in
amount, though not in symmetry, where chemistry can trace no
difference of composition.

9. We will not quit the subject, however, without noticing
the much more promising aspect which it has assumed by the
detection of such groups as are referred to in the last
article; or in other words, by Mitscherlich's discovery of
_Isomorphism_. According to that discovery, there are
various elements which may take the place of each other in
crystalline bodies, either without any alteration of the
crystalline form, or at most with only a slight alteration
of its dimensions. Such a group of elements we have in the
earths lime and magnesia, the protoxides of iron and
manganese: for the carbonates of all these bases occur
crystallized in forms of the rhombohedral system, the
characteristic angle being nearly the same in all. Now lime
and magnesia, by the discoveries of modern chemistry, are
really oxides of metals; and therefore all these carbonates
have a similar chemical constitution, while they have also a
similar crystalline form. Whether or no we can devise any
arrangement of molecules by which this connexion of the
chemical and the geometrical property can be represented, we
cannot help {91} considering the connexion as an extremely
important fact in the constitution of bodies; and such facts
are more likely than any other to give us some intelligible
view of the relations of the ultimate parts of bodies. The
same may be said of all the other isomorphous or
plesiomorphous groups[10\7]. For instance, we have a number
of minerals which belong to the same system of
crystallization, but in which the chemical composition
appears at first sight to be very various: namely, spinelle,
pleonaste, gahnite, franklinite, chromic iron oxide,
magnetic iron oxide: but Abich has shown that all these may
be reduced to a common chemical formula;--they are bioxides
of one set of bases, combined with trioxides of another set.
Perhaps some mathematician may be able to devise some
geometrical arrangement of such a group of elements which
may possess the properties of the tessular system.
Hypothetical arrangements of atoms, thus expressing both the
chemical and the crystalline symmetry which we know to
belong to the substance, would be valuable steps in
analytical science; and when they had been duly verified,
the hypotheses might easily be divested of their atomic
character.

[Note 10\7: See _Hist. Ind. Sc._ b. xv. c. vi.]

Thus, as we have already said, mineralogy, understood in its
wider sense, as the counterpart of chemistry, has for one of
its main objects to discover those Relations of the Elements
of bodies which have reference to Space. In this research,
the foundation of all sound speculation is the kind and
degree of Symmetry of form which we find in definite
chemical compounds: and the problem at present before the
inquirer is, to devise such arrangements of molecules as
shall answer the conditions alike of Chemistry and of
Crystallography.

We now proceed to the Classificatory Sciences, of which
Mineralogy is one, though hitherto by far the least
successful.

{{93}}
BOOK VIII.

THE
PHILOSOPHY
OF THE
CLASSIFICATORY SCIENCES.

WHERE a certain apparent difference between things (although
perhaps in itself of little moment) answers to we know not
what number of other differences, pervading not only their
known properties but properties yet undiscovered, it is not
optional but imperative to recognise this difference as the
foundation of a specific distinction.

JOHN S. MILL, _System of Logic_, b. 1, ch. vii. § 4.

{{95}}
BOOK VIII.

THE PHILOSOPHY OF THE CLASSIFICATORY SCIENCES.

CHAPTER I.

THE IDEA OF LIKENESS AS GOVERNING THE USE OF COMMON NAMES.

1. _Object of the Chapter._--NOT only the Classificatory
Sciences, but the application of names to things in the
rudest and most unscientific manner, depends upon our
apprehending them as _like_ each other. We must therefore
endeavour to trace the influence and operation of the Idea
of Likeness in the common use of language, before we speak
of the conditions under which it acquires its utmost
exactness and efficacy.

It will be my object to show in this, as in previous cases,
that the impressions of sense are apprehended by acts of the
mind; and that these mental acts necessarily imply certain
relations which may be made the subjects of speculative
reasoning. We shall have, if we can, to seize and bring into
clear view the principles which the relation of _like_ and
_unlike_ involves, and the mode in which these principles
have been developed.

2. _Unity of the Individual._--But before we can attend to
several things as like or unlike, we must be able to
apprehend each of these by itself as _one thing_. {96} It
may at first sight perhaps appear that this apprehension
results immediately from the impressions on our senses,
without any act of our thoughts. A very little attention,
however, enables us to see that thus to single out special
objects requires a mental operation as well as a sensation.
How, for example, without an exertion of mental activity,
can we see one tree, in a forest where there are many? We
have, spread before us, a collection of colours and forms,
green and brown, dark and light, irregular and straight:
this is all that sensation gives or can give. But we
associate one brown trunk with one portion of the green
mass, excluding the rest, although the neighbouring leaves
are both nearer in contiguity and more similar in appearance
than is the stem. We thus have before us one tree; but this
unity is given by the mind itself. We see the green and the
brown, but we must _make_ the tree before we can see _it_.

That this composition of our sensations so as to form _one
thing_ implies an act of our own, will perhaps be more
readily allowed, if we once more turn our attention to the
manner in which we sometimes attempt to imitate and record
the objects of sight, by drawing. When we do this, as we
have already observed, we mark this unity of each object, by
drawing a line to separate the parts which we include from
those which we exclude;--an _Outline_. This line corresponds
to nothing which we see; the beginner in drawing has great
difficulty in discerning it; he has in fact to make it. It
is, as has been said by a painter of our own time[1\8], a
fiction: but it is a fiction employed to mark a real act of
the mind; to designate the singleness of the object in our
conception. As we have said elsewhere, we see lines, but
especially outlines, by mentally drawing them ourselves.

[Note 1\8: Phillips _On Painting_,--Design.]

The same act of conception which the outline thus represents
and commemorates in visible objects,--the same combination
of sensible impressions into a unit,--is exercised also with
regard to the objects of all {97} our senses: and the
singleness thus given to each object, is a necessary
preliminary to its being named or represented in any other
way.

But it may be said, Is it then by an arbitrary act of our
own that we put together the branches of the same tree, or
the limbs of the same animal? Have we equally the power and
the right to make the branch of the fir a part of the
neighbouring oak? Can we include in the outline of a man any
object with which he happens to be in contact?

Such suppositions are manifestly absurd. And the answer is,
that though we give unity to objects by an act of thought,
it is not by an _arbitrary_ act; but by a process subject to
certain conditions;--to conditions which exclude such
incongruous combinations as have just been spoken of.

What are these conditions which regulate our apprehension of
an object as one?--which determine what portion of our
impressions does, and what portion does not belong to the
same thing?

3. _Condition of Unity._--I reply, that the primary and
fundamental condition is, that we must be able to make
intelligible assertions respecting the object, and to
entertain that belief of which assertions are the
exposition. A tree _grows_, _sheds_ its leaves in autumn,
and _buds_ again in the spring, _waves_ in the wind, or
_falls_ before the storm. And to the tree belong all those
parts which must be included in order that such
declarations, and the thought which they convey, shall have
a coherent and permanent meaning. Those are _its_ branches
which wave and fall with _its_ trunk; those are _its_ leaves
which grow on _its_ branches. The permanent connexions which
we observe,--permanent, among unconnected changes which
affect the surrounding appearances,--are what we bind
together as belonging to one object. This permanence is the
condition of our conceiving the object _as_ one. The
connected changes may always be described by means of
assertions; and the connexion is seen in the identity of the
subject of successive predications; in the possibility of
applying many verbs to one substantive. We may {98}
therefore express the condition of the unity of an object to
be this: that _assertions concerning the object shall be
possible_: or rather we should say, that the acts of belief
which such assertions enunciate shall be possible.

It may seem to be superfluous to put in a form so abstract
and remote, the grounds of a process apparently so simple as
our conceiving an object to be one. But the same condition
to which we have thus been led, as the essential principle
of the unity of objects, namely, that propositions shall be
possible, will repeatedly occur in the present chapter; and
it may serve to illustrate our views, to show that this
condition pervades even the simplest cases.

4. _Kinds._--The mental synthesis of which we have thus
spoken, gives us our knowledge of _individual_ things; it
enables me to apprehend that particular tree or man which I
now see, or, by the help of memory, the tree or the man I
saw yesterday. But the knowledge with which we have mainly
here to do is not a knowledge of individuals but of kinds;
of such classes as are indicated by common names. We have to
make assertions concerning a tree or a man in general,
without regarding what is peculiar to this man or that tree.

Now it is clear that certain individual objects are all
called _man_, or all called _tree_, in virtue of some
resemblance which they have. If we had not the power of
perceiving in the appearances around us, likeness and
unlikeness, we could not consider objects as distributed
into kinds at all. The impressions of sense would throng
upon us, but being uncompared with each other, they would
flow away like the waves of the sea, and each vanish from
our contemplation when the sensation faded. That we do
apprehend surrounding objects as belonging to permanent
kinds, as being men and horses, oaks and roses, arises from
our having the idea of likeness, and from our applying it
habitually, and so far as such a classification requires.

Not only can we employ the idea of likeness in this manner,
but we apply it incessantly and universally to {99} the
whole mass and train of our sensations. For we have no
external sensations to which we cannot apply some language
or other; and all language necessarily implies recognition
of resemblances. We cannot call an object _green_ or _round_
without comparing in our thoughts its colour or its shape,
with a shape and a colour seen in other objects. All our
sensations, therefore, without any exception of kind or
time, are subject to this constant process of
classification; and the idea of likeness is perpetually
operating to distribute them into kinds, at least so far as
the use of language requires.

We come then again to the question, Upon what principle,
under what conditions, is the Idea of Likeness thus
operative? What are the limits of the classes thus formed?
Where does that similarity end, which induces and entitles
us to call a thing a _tree_? What universal rule is there
for the application of common names, so that we may not
apply them wrongly?

5. _Not made by Definitions._--Perhaps some one might expect
in answer to these inquiries a definition or a series of
definitions;--might imagine that some description of a tree
might be given which might show when the term was applicable
and when it was not; and that we might construct a body of
rules to which such descriptions must conform. But on
consideration it will be clear that the real solution of our
difficulty cannot be obtained in such a manner. For _first_;
such descriptions must be given in words, and must therefore
suppose that we have already satisfied ourselves how words
are to be used. If we define a tree to be 'a living thing
without the power of voluntary motion,' we shall be called
upon to define 'a living thing;' and it is manifest that
this renewal of the demand for definition might be repeated
indefinitely; and, therefore, we cannot in this way come to
a final principle. And in the _next_ place, most of those
who use language, even with great precision and consistency,
would find it difficult or impossible to give good
definitions even of a few of the general names which they
use; and therefore their practice cannot be regulated by any
{100} tacit reference to such definitions. That definitions
of terms are of great use and importance in their right
place, we shall soon see; but their place is not to regulate
the use of common language.

What then, once more, is this regulative principle? What
rules do men follow in the use of words, so as commonly to
avoid confusion and ambiguity? How do they come to
understand each other so well as they ordinarily do,
respecting the limits of classes never defined, and which
they cannot define? What is the common Convention, or
Condition to which they conform?

6. _Condition of the Use of Terms._--To this we reply, that
the Condition which regulates the use of language, is, that
it shall be capable of being used;--that is, that general
assertions shall be possible. The term _tree_ is applicable
as far as it is useful in expressing our knowledge
concerning trees:--thus we know that trees are fixed in the
ground, have a solid stem, branches, leaves, and many other
properties. With regard to all the objects which surround
us, we have an immense store of knowledge of such
properties, and we employ the names of the objects in such a
manner as enables us to express these properties.

But the connexion of such properties is variable and
indefinite. Some properties are constantly combined, others
occasionally only. The leaves of different oaks resemble
each other, the branches resemble far less, and may differ
very widely. The term _oak_ does not enable us to say that all
oaks have straight branches or all crooked. Terms can only
express properties as far as they are constant. Not only,
therefore, the accumulation of a vast mass of knowledge of
the properties and attributes of objects, but also an
observation of the habitual _connexion_ of such properties
is needed, to direct us to the consistent application of
terms:--to enable us to apply them so as to express truths.
But here again we are largely provided with the requisite
knowledge and observation by the common course of our
existence. The unintermitting stream of experience supplies
us with an incalculable {101} amount of such observed
connexions. All men have observed that the associations of
the same form of leaves are more constant than of the same
form of branches;--that though persons walk in different
attitudes, none go on all fours; and thus the term _oak_ is
so applied as to include those cases in which the leaves are
alike in form though the branches be unlike; and though we
should refuse to apply the term _man_ to a class of
creatures which habitually and without compulsion used four
legs, we make no scruple of affixing it to persons of very
different figures. The whole of human experience being
composed of such observed connexions, we have thus materials
even for the immense multiplicity of names which human
language contains; all which names are, as we have said,
regulated in their application by the condition of their
expressing such experience.

Thus amid the countless combinations of properties and
divisions of classes which the structure of language
implies, scarcely any are arbitrary or capricious. A word
which expressed a mere wanton collection of unconnected
attributes could hardly be called a _word_; for of such a
collection of properties no truth could be asserted, and the
word would disappear, for want of some occasion on which it
could be used. Though much of the fabric of language
appears, not unnaturally, fantastical and purely
conventional, it is in fact otherwise. The associations and
distinctions of phraseology are not more fanciful than is
requisite to make them correspond to the apparent caprices
of nature or of thought; and though much in language may be
called conventional, the conventions exist for the sake of
expressing some truth or opinion, and not for their own
sake. The principle, that _the condition of the use of terms
is the possibility of general, intelligible, consistent
assertions_, is true in the most complete and extensive sense.

7. _Terms may have different Uses._--The Terms with which we
are here most concerned are Names of Classes of natural
objects; and when we say that the principle and the limit of
such Names are their use in expressing propositions
concerning the classes, it is {102} clear that much will
depend on the kind of propositions which we mainly have to
express: and that the same name may have different limits,
according to the purpose we have in view. For example, is
the _whale_ properly included in the general term _fish_?
When men are concerned in catching marine animals, the main
features of the process are the same however the animals may
differ; hence whales are classed with fishes, and we speak
of the _whale-fishery_. But if we look at the analogies of
organization, we find that, according to these, the whale is
clearly not a fish, but a _beast_, (confining this term, for
the sake of distinctness, to suckling beasts or _mammals_).
In Natural History, therefore, the whale is not included
among fish. The indefinite and miscellaneous propositions
which language is employed to enunciate in the course of
common practical life, are replaced by a more coherent and
systematic collection of properties, when we come to aim at
scientific knowledge. But we shall hereafter consider the
principle of the classifications of Natural History; our
present subject is the application of the Idea of Likeness
in common practice and common language.

8. _Gradation of Kinds._--Common names, then, include many
individuals associated in virtue of resemblances, and of
permanently connected properties; and such names are
applicable as far as they serve to express such properties.
These collections of individuals are termed _Kinds_,
_Sorts_, _Classes_.

But this association of particulars is capable of degrees.
As individuals by their resemblances form Kinds, so kinds of
things, though different, may resemble each other so as to
be again associated in a higher Class; and there may be
several successive steps of such classification. _Man_,
_horse_, _tree_, _stone_, are each a name of a Kind; but
_animal_ includes the two first and excludes the others;
_living thing_ is a term which includes _animal_ and _tree_
but not _stone_; _body_ includes all the four. And such a
subordination of kinds may be traced very widely in the
arrangements of language. {103}

The condition of the use of the wider is the same as that of
the narrower Names of Classes;--they are good as far as they
serve to express true propositions. In common language,
though such an order of generality may in a variety of
instances be easily discerned, it is not systematically and
extensively referred to; but this subordination and
graduated comprehensiveness is the essence of the methods
and nomenclatures of Natural History, as we shall soon have
to show.

But such subordination is not without its use, even in
common cases, and when it is expressed in the terms of
common language. Thus _organized body_ is a term which
includes plants and animals; _animal_ includes beasts,
birds, fishes; _beast_ includes horses and dogs; _dogs_,
again, are greyhounds, spaniels, terriers.

9. _Characters of Kinds._--Now when we have such a Series of
Names and Classes, we find that we take for granted
irresistibly that each class has some _Character_ which
distinguishes it from other classes included in the superior
division. We ask what kind of beast a dog is; what kind of
animal a beast is; and we assume that such questions admit
of answer;--that each kind has some mark or marks by which
it may be described. And such descriptions may be given: an
animal is an organized body _having sensation and volition_;
man is a _reasonable_ animal. Whether or no we assent to the
exactness of these definitions, we allow the propriety of
their form. If we maintain these definitions to be wrong, we
must believe some others to be right, however difficult it
may be to hit upon them. We entertain a conviction that
there must be, among things so classed and named, a
possibility of defining each.

Now what is the foundation of this postulate? What is the
ground of this assumption, that there must exist a
definition which we have never seen, and which perhaps no
one has seen in a satisfactory form? The knowledge of this
definition is by no means necessary to our using the word
with propriety; for any one can make true assertions about
dogs, but who can define a {104} dog? And yet if the
definition be not necessary to enable us to use the word,
why is it necessary at all? I allow that we possess an
indestructible conviction that there must be such a
character of each kind as will supply a definition; but I
ask, on what this conviction rests.

I reply, that our persuasion that there must needs be
characteristic marks by which things can be defined in
words, is founded on the assumption of _the necessary
possibility of reasoning_.

The reference of any object or conception to its class
without definition, may give us a persuasion that it shares
the properties of its class, but such classing does not
enable us to reason upon those properties. When we consider
man as an animal, we ascribe to him in thought the
appetites, desires, affections, which we habitually include
in our notion of animal: but except we have expressed these
in some definition or acknowledged description of the term
_animal_, we can make no use of the persuasion in
ratiocination. But if we have described animals as 'being
impelled to action by appetites and passions,' we can not
only think, but say, 'man is an animal, and therefore he is
impelled to act by appetites and passions.' And if we add a
further definition, that 'man is a reasonable animal,' and
if it appear that 'reason implies conformity to a rule of
action,' we can then further infer that man's nature is to
conform the results of animal appetite and passion to a rule
of action.

The possibility of pursuing any such train of reasoning as
this, depends on the definitions, of _animal_ and of _man_,
which we have introduced; and the possibility of reasoning
concerning the objects around us being inevitably assumed by
us from the constitution of our nature, we assume
consequently the possibility of such definitions as may thus
form part of our deduction, and the existence of such
defining characters.

10. _Difficulty of Definitions._--But though men are, on
such grounds, led to make constant and importunate _demands_
for definitions of the terms which they employ in their
speculations, they are, in fact, far {105} from being able
to carry into complete effect the postulate on which they
proceed, that they must be able to find definitions which by
logical consequence shall lead to the truths they seek. The
postulate overlooks the process by which our classes of
things are formed and our names applied. This process
consisting, as we have already said, in observing permanent
connexions of properties, and in fixing them by the
attribution of names, is of the nature of the process of
Induction, of which we shall afterwards have to speak. And
the postulate is so far true, that this process of induction
being once performed, its result may usually be expressed by
means of a few definitions, and may thus lead by a deduction
to a train of real truths.

But in the subjects where we principally find such a
subordination of classes as we have spoken of, this process
of deduction is rarely of much prominence: for example, in
the branches of natural history. Yet it is in these subjects
that the existence and importance of these characteristic
marks, which we have spoken of, principally comes into view.
In treating of these marks, however, we enter upon methods
which are technical and scientific, not popular and common.
And before we make this transition, we have a remark to make
on the manner in which writers, without reference to physics
or natural history, have spoken of kinds, their
subordination, and their marks.

11. '_The Five Words._'--These things,--the Nature and
Relations of Classes,--were, in fact, the subjects of minute
and technical treatment by the logicians of the school of
Aristotle. Porphyry wrote an Introduction to the
_Categories_ of that philosopher, which is entitled _On the
Five Words_. The 'Five Words' are _Genus_, _Species_,
_Difference_, _Property_, _Accident_. Genus and Species are
superior and inferior classes, and are stated[2\8] to be
capable of repeated subordination. The 'most {106} general
Genus' is the widest class; the 'most special Species' the
narrowest. Between these are intermediate classes, which are
Genera with regard to those below, and Species with regard
to those above them. Thus Being is the most general Genus;
under this is Body; under Body is Living Body; under this
again Animal; under Animal is Rational Animal, or Man; under
Man are Socrates and Plato, and other individual men.

[Note 2\8: Porphyr. _Isagog._ c. 23.]

The _Difference_ is that which is added to the genus to make
the species; thus Rational is the Difference by which the
genus Animal is made the species Man; the Difference in this
Technical sense is the 'Specific,' or species-making
Difference[3\8]. It forms the Definition for the purposes of
logic, and corresponds to the 'Character' (specific or
generic) of the Natural Historians. Indeed several of them,
as, for instance, Linnæus, in his _Philosophia Botanica_,
always call these Characters the _Difference_, by a
traditional application of the Peripatetic terms of art.

[Note 3\8: εἰδοποιός.]

Of the other two words, the Property is that which though
not employed in defining the class, belongs to every part of
it[4\8]: it is, 'What happens to all the class, to it alone,
and at all times; as _to be capable of laughing_ is a
Property of man.'

[Note 4\8: _Isagog._ c. 4]

The Accident is that which may be present and absent without
the destruction of the subject, as to sleep is an Accident
(a thing which happens) to man.

I need not dwell further on this system of technicalities.
The most remarkable points in it are those which I have
already noticed; the doctrine of the successive
Subordination of genera, and the fixing attention upon the
Specific Difference. These doctrines, though invented in
order to make reasoning more systematic, and at a period
anterior to the existence of any Classificatory Science,
have, by a curious contrast with the intentions of their
founders, been of scarcely {107} any use in sciences of
_Reasoning_, but have been amply applied and developed in
the _Natural History_ which arose in later times.

We must now treat of the principles on which this science
(Natural History) proceeds, and explain what peculiar and
technical processes it employs in addition to those of
common thought and common language.

{{108}}
CHAPTER II.

THE METHODS OF NATURAL HISTORY, AS REGULATED BY THE IDEA OF
LIKENESS.

SECT. I.--_Natural History in general._

1. _Idea of Likeness in Natural History._--THE various
branches of Natural History, in so far as they are
classificatory sciences merely, and do not depend upon
physiological views, rest upon the same Idea of Likeness
which is the ground of the application of the names, more or
less general, of common language. But the nature of science
requires that, for her purposes, this Idea should be applied
in a more exact and rigourous manner than in its common and
popular employment; just as occurs with regard to the other
Ideas on which science is founded;--for instance, as the
idea of space gives rise, in popular use, to the relations
implied in the prepositions and adjectives which refer to
position and form, and in its scientific development gives
rise to the more precise relations of geometry.

The way in which the Idea of Likeness has been applied, so
as to lead to the construction of a science, is best seen in
Botany: for, in the Classification of Animals, we are
inevitably guided by a consideration of the _function_ of
parts; that is, by an idea of _purpose_, and not of likeness
merely: and in Mineralogy, the attempts at classification on
the principles of Natural History have been hitherto very
imperfectly successful. But in Botany we have an example of
a branch of knowledge in which systematic classification has
been effected with great beauty and advantage; and in which
the peculiarities and principles on which such {109}
classification must depend have been carefully studied. Many
of the principal botanists, as Linnæus, Adanson, Decandolle,
have not only practically applied, but have theoretically
enunciated, what they held to be the sound maxims of
classificatory science: and have thus enabled us to place
before the reader with confidence the philosophy of this
kind of science.

2. _Condition of its Use._--We may begin by remarking that
the Idea of Likeness, in its systematic employment, is
governed by the same principle which we have already spoken
of as regulating the distribution of things into kinds, and
the assignment of names in unsystematic thought and speech;
namely, the condition that _general propositions shall be
possible_. But as in this case the propositions are to be of
a scientific form and exactness, the likeness must be
treated with a corresponding precision; and its consequences
traced by steady and distinct processes. Naturalists must,
for their purposes, employ the resemblances of objects in a
technical manner. This technical process may be considered
as consisting of three steps;--The fixation of the
resemblances; The use of them in making a classification;
The means of applying the classification. These three steps
may be spoken of as the _Terminology_, the _Plan of the
System_, and the _Scheme of the Characters_.

SECT. II.--_Terminology._[5\8]

[Note 5\8: Decandolle and others use the term _Glossology_
instead of Terminology, to avoid the blemish of a word
compounded of two parts taken from different languages. The
convenience of treating the termination _ology_ (and a few
other parts of compounds) as not restricted to Greek
combinations, is so great, that I shall venture, in these
cases, to disregard this philological scruple.]

3. _Terminology_ signifies the collection of _terms_, or
technical words, which belong to the science. But in fixing
the meaning of the terms, at least of the descriptive terms,
we necessarily fix, at the same time, the perceptions and
notions which the terms are to {110} convey; and thus the
Terminology of a classificatory science exhibits the
elements of its substance as well as of its language. A
large but indispensable part of the study of botany (and of
mineralogy and zoology also,) consists in the acquisition of
the peculiar vocabulary of the science.

The meaning of technical terms can be fixed in the first
instance only by convention, and can be made intelligible
only by presenting to the senses that which the terms are to
signify. The knowledge of a colour by its name can only be
taught through the eye. No description can convey to a
hearer what we mean by _apple-green_ or _French grey_. It
might, perhaps, be supposed that, in the first example, the
term _apple_, referring to so familiar an object,
sufficiently suggests the colour intended. But it may easily
be seen that this is not true; for apples are of many
different hues of green, and it is only by a conventional
selection that we can appropriate the term to one special
shade. When this appropriation is once made, the term refers
to the sensation, and not to the parts of this term; for
these enter into the compound merely as a help to the
memory, whether the suggestion be a natural connexion as in
'apple-green,' or a casual one as in 'French grey.' In order
to derive due advantage from technical terms of this kind,
they must be associated _immediately_ with the perception to
which they belong; and not connected with it through the
vague usages of common language. The memory must retain the
sensation; and the technical word must be understood as
directly as the most familiar word, and more distinctly.
When we find such terms as _tin-white_ or _pinchbeck-brown_,
the metallic colour so denoted ought to start up in our
memory without delay or search.

This, which it is most important to recollect with respect
to the simpler properties of bodies, as colour and form, is
no less true with respect to more compound notions. In all
cases the term is fixed to a peculiar meaning by convention;
and the student, in order to use the word, must be
completely familiar with the convention, so that he has no
need to frame {111} conjectures from the word itself. Such
conjectures would always be insecure, and often erroneous.
Thus the term _papilionaceous_, applied to a flower, is
employed to indicate, not only a resemblance to a butterfly,
but a resemblance arising from five petals of a certain
peculiar shape and arrangement; and even if the resemblance
to a butterfly were much stronger than it is in such cases,
yet if it were produced in a different way, as, for example,
by one petal, or two only, instead of a 'standard,' two
'wings,' and a 'keel' consisting of two parts more or less
united into one, we should no longer be justified in
speaking of it as a 'papilionaceous' flower.

The formation of an exact and extensive descriptive language
for botany has been executed with a degree of skill and
felicity, which, before it was attained, could hardly have
been dreamt of as attainable. Every part of a plant has been
named; and the form of every part, even the most minute, has
had a large assemblage of descriptive terms appropriated to
it, by means of which the botanist can convey and receive
knowledge of form and structure, as exactly as if each
minute part were presented to him vastly magnified. This
acquisition was part of the Linnæan Reform, of which we have
spoken in the _History_. 'Tournefort,' says Decandolle[6\8],
'appears to have been the first who really perceived the
utility of fixing the sense of terms in such a way as always
to employ the same word in the same sense, and always to
express the same idea by the same word; but it was Linnæus
who really created and fixed this botanical language, and
this is his fairest claim to glory, for by this fixation of
language he has shed clearness and precision over all parts
of the science.'

[Note 6\8: _Theor. Elem._ p. 327.]

It is not necessary here to give any detailed account of the
terms of botany. The fundamental ones have been gradually
introduced, as the parts of plants were more carefully and
minutely examined. Thus the flower was successively
distinguished into the _calyx_, {112} the _corolla_, the
_stamens_, and the _pistils_: the sections of the corolla
were termed _petals_ by Columna; those of the calyx were
called _sepals_ by Necker[7\8]. Sometimes terms of greater
generality were devised; as _perianth_ to include the calyx
and corolla, whether one or both of these were present[8\8];
_pericarp_ for the part inclosing the grain, of whatever
kind it be, fruit, nut, pod, &c. And it may easily be
imagined that descriptive terms may, by definition and
combination, become very numerous and distinct. Thus leaves
may be called _pinnatifid_[9\8], _pinnatipartite_,
_pinnatisect_, _pinnatilobate_, _palmatifid_,
_palmatipartite_, &c., and each of these words designates
different combinations of the modes and extent of the
divisions of the leaf with the divisions of its outline. In
some cases arbitrary numerical relations are introduced into
the definition: thus a leaf is called _bilobate_[10\8] when
it is divided into two parts by a notch; but if the notch go
to the middle of its length, it is _bifid_; if it go near
the base of the leaf, it is _bipartite_; if to the base, it
is _bisect_. Thus, too, a pod of a cruciferous plant is a
_silica_[11\8] if it be four times as long as it is broad,
but if it be shorter than this it is a _silicula_. Such
terms being established, the form of the very complex leaf
or frond of a fern is exactly conveyed by the following
phrase: 'fronds rigid pinnate, pinnæ recurved subunilateral
pinnatifid, the segments linear undivided or bifid
spinuloso-serrate[12\8].'

[Note 7\8: Decandolle, 329]

[Note 8\8: For this Erhart and Decandolle use _Perigone_.]

[Note 9\8: Dec. 318.]

[Note 10\8: _Ib._ 493.]

[Note 11\8: _Ib._ 422.]

[Note 12\8: Hooker, _Brit. Flo._ p. 457. _Hymenophyllum
Wilsoni_, Scottish filmy-fern, abundant in the highlands of
Scotland and about Killarney.]

Other characters, as well as form, are conveyed with the
like precision: Colour by means of a classified scale of
colours, as we have seen in speaking of the Measures of
Secondary Qualities; to which, however, we must add, that
the naturalist employs arbitrary names, (such as we have
already quoted,) and not mere numerical exponents, to
indicate a certain number of {113} selected colours. This
was done with most precision by Werner, and his scale of
colours is still the most usual standard of naturalists.
Werner also introduced a more exact terminology with regard
to other characters which are important in mineralogy, as
lustre, hardness. But Mohs improved upon this step by giving
a numerical scale of hardness, in which _talc_ is 1,
_gypsum_ 2, _calc spar_ 3, and so on, as we have already
explained in the History of Mineralogy. Some properties, as
specific gravity, by their definition give at once a
numerical measure; and others, as crystalline form, require
a very considerable array of mathematical calculation and
reasoning, to point out their relations and gradations. In
all cases the features of likeness in the objects must be
rightly apprehended, in order to their being expressed by a
distinct terminology. Thus no terms could describe crystals
for any purpose of natural history, till it was discovered
that in a class of minerals the proportion of the faces
might vary, while the angle remained the same. Nor could
crystals be described so as to distinguish species, till it
was found that the derived and primitive forms are connected
by very simple relations of space and number. The discovery
of the mode in which characters must be apprehended so that
they may be considered as _fixed_ for a class, is an
important step in the progress of each branch of Natural
History; and hence we have had, in the History of Mineralogy
and Botany, to distinguish as important and eminent persons
those who made such discoveries, Romé de Lisle and Haüy,
Cesalpinus and Gesner.

By the continued progress of that knowledge of minerals,
plants, and other natural objects, in which such persons
made the most distinct and marked steps, but which has been
constantly advancing in a more gradual and imperceptible
manner, the most important and essential features of
similarity and dissimilarity in such objects have been
selected, arranged, and fitted with names; and we have thus
in such departments, systems of Terminology which fix our
attention upon the resemblances which it is proper to
consider, and {114} enable us to convey them in words. We
have now to speak of the mode in which such resemblances
have been employed in the construction of a Systematic
Classification.

SECT. III. _The Plan of the System._

4. The collection of sound views and maxims by which the
resemblances of natural objects are applied so as to form a
scientific classification, is a department of the philosophy
of natural history which has been termed by some writers (as
Decandolle), _Taxonomy_, as containing the _Laws_ of the
_Taxis_ (_arrangement_). By some Germans this has been
denominated _Systematik_; if we could now form a new
substantive after the analogy of the words _Logick_,
_Rhetorick_, and the like, we might call it _Systematick_.
But though our English writers commonly use the expression
_Systematical Botany_ for the Botany of Classification, they
appear to prefer the term _Diataxis_ for the method of
constructing the classification. The rules of such a branch
of science are curious and instructive.

In framing a Classification of objects we must attend to
their resemblances and differences. But here the question
occurs, to _what_ resemblances and differences? for a
different selection of the points of resemblance would give
different results: a plant frequently agrees in leaves with
one group of plants, in flowers with another. Which set of
characters are we to take as our guide?

The view already given of the regulative principle of all
classification, namely, that it must enable us to assert
true and general propositions, will obviously occur as
applicable here. The object of a scientific Classification
is to enable us to enunciate scientific truths: we must
therefore classify according to those resemblances of
objects (plants or any others) which bring to light such
truths.

But this reply to the inquiry, 'On what characters of
resemblance we are to found our system,' is still too
general and vague to be satisfactory. It carries us, {115}
however, as far as this;--that since the truths we are to
attend to are scientific truths, governed by precise and
homogeneous relations, we must not found our scientific
Classification on casual, indefinite, and unconnected
considerations. We must not, for instance, be satisfied with
dividing plants, as Dioscorides does, into _aromatic_,
_esculent_, _medicinal_ and _vinous_; or even with the long
prevalent distribution into _trees_, _shrubs_, and _herbs_;
since in these subdivisions there is no consistent
principle.

5. _Latent Reference to Natural Affinity._--But there may be
several kinds of truths, all exact and coherent, which may
be discovered concerning plants or any other natural
objects; and if this should be the case, our rule leaves us
still at a loss in what manner our classification is to be
constructed. And, historically speaking, a much more serious
inconvenience has been this;--that the task of
classification of plants was necessarily performed when the
general laws of their form and nature were very little
known; or rather, when the existence of such laws was only
just beginning to be discerned. Even up to the present day,
the general propositions which botanists are able to assert
concerning the structure and properties of plants, are
extremely imperfect and obscure.

We are thus led to this conclusion:--that the Idea of
Likeness could not be applied so as to give rise to a
scientific Classification of plants, till considerable
progress was made in studying the general relations of
vegetable form and life; and that the selection of the
resemblances which should be taken into account, must depend
upon the nature of the relations which were then brought
into view.

But this amounts to saying that, in the consideration of the
Classification of vegetables, other Ideas must be called
into action as well as the Idea of Likeness. The additional
general views to which the more intimate study of plants
leads, must depend, like all general truths, upon some
regulating Idea which gives unity to scattered facts. No
progress could be made in botanical knowledge without the
{116} operation of such principles: and such additional
Ideas must be employed, besides those of mere likeness and
unlikeness, in order to point out that Classification which
has a real scientific value.

Accordingly, in the classificatory sciences, Ideas other
than Likeness do make their appearance. Such Ideas in botany
have influenced the progress of the science, even before
they have been clearly brought into view. We have especially
the Idea of Affinity, which is the basis of all Natural
Systems of Classification, and which we shall consider in a
succeeding chapter. The assumption that there _is_ a Natural
System, an assumption made by all philosophical botanists,
implies a belief in the existence of Natural Affinity, and
is carried into effect by means of principles which are
involved in that Idea. But as the formation of all systems
of classification must involve, in a great degree, the Idea
of Resemblance and Difference, I shall first consider the
effect of that Idea, before I treat specially of Natural
Affinity.

6. _Natural Classes._--Many attempts were made to classify
vegetables before the rules which govern a natural system
were clearly apprehended. Botanists agree in esteeming some
characters as of more value than others, before they had
agreed upon any general rules or principles for estimating
the relative importance of the characters. They were
convinced of the necessity of adding other considerations to
that of Resemblance, without seeing clearly what these
others ought to be. They aimed at a Natural Classification,
without knowing distinctly in what manner it was to be
Natural.

The attempts to form _Natural Classes_, therefore, in the
first part of their history, belong to the Idea of Likeness,
though obscurely modified, even from an early period, by the
Ideas of Affinity, and even of Function and of Development.
Hence Natural Classes may, to a certain extent, be treated
of in this place.

Natural Classes are opposed to Artificial Classes which are
understood to be regulated by an _assumed_ {117} character.
Yet no classes can be so absolutely Artificial in this
sense, as to be framed upon characters _arbitrarily_
assumed; for instance, no one would speak of a class of
shrubs defined by the circumstance of each having a hundred
leaves: for of such a class no assertion could be made, and
therefore the class could never come under our notice. In
what sense then are Artificial Classes to be understood, as
opposed to Natural?

7. _Artificial Classes._--To this question, the following is
the answer. When Natural Classes of a certain small extent
have been formed, a system may be devised which shall be
regulated by a few selected characters, and which shall not
dissever these small Natural Classes, but conform to them as
far as they go. If these selected characters be then made
absolute and imperative, and if we abandon all attempt to
obtain Natural Classes of any higher order and wider extent,
we form an Artificial System.

Thus in the Linnæan System of Botanical Classification, it
is assumed that certain natural groups, namely, Species and
Genera, are established; it is conceived, moreover, that the
division of Classes according to the number of stamens and
of pistils does not violate the natural connexions of
Species and Genera. This arrangement, according to the
number of stamens and pistils, (further modified in certain
cases by other considerations,) is then made the ground of
all the higher divisions of plants, and thus we have an
Artificial System.

It has been objected to this view, that the Linnæan
Artificial System does not in all cases respect the
boundaries of genera, but would, if rigorously applied,
distribute the species of the same genus into different
artificial classes; it would divide, for instance, the
genera _Valeriana_, _Geranium_[13\8], &c. To this we must
reply, that so far as the Linnæan System does this, it is an
imperfect Artificial System. Its great merit is in its
making such a disjunction in comparatively so {118} few
cases; and in the artificial characters being, for the most
part, obvious and easily applied.

[Note 13\8: Decand. _Theor. Elem._ p. 45.]

8. _Are Genera Natural_?--It has been objected also that
Genera are not Natural groups. Linnæus asserts in the most
positive manner that they are[14\8]. On which Adanson
observes[15\8], 'I know not how any Botanist can maintain
such a thesis: that which is certain is, that up to the
present time no one has been able to prove it, nor to give
an exact definition of a natural genus, but only of an
artificial.' He then brings several arguments to confirm
this view.

[Note 14\8: _Phil. Bot._ Art. 165.]

[Note 15\8: _Famille de Ph._ Pref. cv.]

But we are to observe, in answer to this, that Adanson
improperly confounds the recognition of the existence of a
natural group with the invention of a technical mark or
definition of it. Genera are groups of species associated in
virtue of natural affinity, of general resemblance, of real
propinquity: of such groups, certain selected characters,
one or few, may usually be discovered, by which the species
may be referred to their groups. These Artificial characters
do not constitute, but indicate the genus: they are the
_Diagnosis_, not the basis of the _Diataxis_: and they are
always subject to be rejected, and to have others
substituted for them, when they violate the natural
connexion of species which a minute and enlarged study
discovers.

It is, therefore, no proof that Genera are not Natural, to
say that their artificial characters are different in
different systems. Such characters are only different
attempts to confine the variety of nature within the limits
of definition. Nor is it sufficient to say that these groups
themselves are different in different writers; that some
botanists make genera what others make only species; as
_Pedicularis_, _Rhinanthus_, _Euphrasia_,
_Antirrhinum_[16\8]. This discrepancy shows only that the
natural arrangement is not yet completely known, even in the
smaller groups; a conclusion to which we need not refuse our
assent. But in {119} opposition to these negatives, the
manner in which Genera have been established proves that
they are regulated by the principle of being natural, and by
that alone. For they are not formed according to any _à
priori_ rule. The Botanist does not take any selected or
arbitrary part or parts of the plants, and marshal his
genera according to the differences of this part. On the
contrary, the divisions of genera are sometimes made by
means of the flower; sometimes by means of the fruit: the
anthers, the stamens, the seeds, the pericarp, and the most
varied features of these parts, are used in the most
miscellaneous and unsystematic manner. Linnæus has indeed
laid down a maxim that the characteristic differences of
genera must reside in the fructification[17\8]: but Adanson
has justly remarked[18\8], that an arbitrary restriction
like this makes the groups artificial: and that in some
families other characters are more essential than those of
the fructification; as the leaves in the families of
_Aparineæ_ and _Leguminosæ_, and the disposition of the
flowers in _Labiatæ_. And Naturalists are so far from
thinking it sufficient to distribute species into genera by
_arbitrary_ marks, that we find them in many cases lamenting
the absence of good _natural_ marks: as in the families of
_Umbelliferæ_, where Linnæus declared that any one who could
find good characters of genera would deserve great
admiration, and where it is only of late that good
characters have been discovered and the arrangement
settled[19\8] by means principally of the ribs of the
fruit[20\8].

[Note 16\8: Adanson, p. cvi.]

[Note 17\8: _Phil. Bot._ Art. 162.]

[Note 18\8: Adanson, Pref. p. cxx.]

[Note 19\8: Lindley, _Nat. Syst._ p. 5.]

[Note 20\8: In like manner we find Cuvier saying of Rondelet
that he has 'un _sentiment_ très vrai des genres.' _Hist.
Ichth._ p. 39.]

It is thus clear that Genera are not established on any
assumed or preconceived basis. What, then, is the principle
which regulates botanists when they try to fix genera? What
is the arrangement which they thus wish for, without being
able to hit upon it? What is the tendency which thus drives
them from the corolla to the anthers, from the flower to the
fruit, {120} from the fructification to the leaves? It is
plain that they seek something, not of their own devising
and creating;--not anything merely conventional and
systematic; but something which they conceive to exist in
the relations of the plants themselves;--something which is
without the mind, not within;--in nature, not in art;--in
short, a Natural Order.

Thus the regulative principle of a Genus, or of any other
natural group is, that it is, or is supposed to be, natural.
And by reference to this principle as our guide, we shall be
able to understand the meaning of that indefiniteness and
indecision which we frequently find in the descriptions of
such groups, and which must appear so strange and
inconsistent to any one who does not suppose these
descriptions to assume any deeper ground of connexion than
an arbitrary choice of the botanist. Thus in the family of
the Rose-tree, we are told that the _ovules_ are _very
rarely_ erect[21\8], the _stigmata_ are _usually_ simple. Of
what use, it might be asked, can such loose accounts be? To
which the answer is, that they are not inserted in order to
distinguish the species, but in order to describe the
family, and the total relations of the ovules and of the
stigmata of the family are better known by this general
statement. A similar observation may be made with regard to
the Anomalies of each group, which occur so commonly, that
Mr. Lindley, in his _Introduction to the Natural System of
Botany_, makes the 'Anomalies' an article in each Family.
Thus, part of the character of the Rosaceæ is that they have
alternate _stipulate_ leaves, and that the _albumen_ is
_obliterated_: but yet in _Lowea_, one of the genera of this
family, the stipulæ are _absent_; and the albumen is
_present_ in another, _Neillia_. This implies, as we have
already seen, that the artificial character (or _diagnosis_
as Mr. Lindley calls it) is imperfect. It is, though very
nearly, yet not exactly, commensurate with the natural
group: and hence, in certain cases, this character is made
to yield to the general weight of natural affinities.

[Note 21\8: Lindley, _Nat. Syst._ p. 81.]

{121} 9. _Difference of Natural History and
Mathematics._--These views,--of classes determined by
characters which cannot be expressed in words,--of
propositions which state, not what happens in all cases, but
only usually,--of particulars which are included in a class
though they transgress the definition of it, may very
probably surprise the reader. They are so contrary to many
of the received opinions respecting the use of definitions
and the nature of scientific propositions, that they will
probably appear to many persons highly illogical and
unphilosophical. But a disposition to such a judgment arises
in a great measure from this;--that the mathematical and
mathematico-physical sciences have, in a great degree,
determined men's views of the general nature and form of
scientific truth; while Natural History has not yet had time
or opportunity to exert its due influence upon the current
habits of philosophizing. The apparent indefiniteness and
inconsistency of the classifications and definitions of
Natural History belongs, in a far higher degree, to all
other except mathematical speculations: and the modes in
which approximations to exact distinctions and general
truths have been made in Natural History, may be worthy our
attention, even for the light they throw upon the best modes
of pursuing truth of all kinds.

10. _Natural Groups given by Type not by Definition._--The
further development of this suggestion must be considered
hereafter. But we may here observe, that though in a Natural
Group of objects a definition can no longer be of any use as
a regulative principle, classes are not, therefore, left
quite loose, without any certain standard or guide. The
class is steadily fixed, though not precisely limited; it is
given, though not circumscribed; it is determined, not by a
boundary line without, but by a central point within; not by
what it strictly excludes, but by what it eminently
includes; by an example, not by a precept; in short, instead
of Definition we have a _Type_ for our director.

A Type is an example of any class, for instance, a species
of a genus, which is considered as eminently {122}
possessing the characters of the class. All the species
which have a greater affinity with this Type-species than
with any others, form the genus, and are ranged about it,
deviating from it in various directions and different
degrees. Thus a genus may consist of several species, which
approach very near the type, and of which the claim to a
place with it is obvious; while there may be other species
which straggle further from this central knot, and which yet
are clearly more connected with it than with any other. And
even if there should be some species of which the place is
dubious, and which appear to be equally bound by two generic
types, it is easily seen that this would not destroy the
reality of the generic groups, any more than the scattered
trees of the intervening plain prevent our speaking
intelligibly of the distinct forests of two separate hills.

The Type-species of every genus, the Type-genus of every
family, is, then, one which possesses all the characters and
properties of the genus in a marked and prominent manner.
The Type of the Rose family has alternate stipulate leaves,
wants the albumen, has the ovules not erect, has the
stigmata simple, and besides these features, which
distinguish it from the exceptions or varieties of its
class, it has the features which make it prominent in its
class. It is one of those which possess clearly several
leading attributes; and thus, though we cannot say of any
one genus that it _must_ be the Type of the family, or of
any one species that it _must_ be the Type of the genus, we
are still not wholly to seek: the Type must be connected by
many affinities with most of the others of its group; it
must be near the center of the crowd, and not one of the
stragglers.

11. It has already been repeatedly stated, as the great rule
of all classification, that the classification must serve to
assert general propositions. It may be asked _what_
propositions we are able to enunciate by means of such
classifications as we are now treating of. And the answer
is, that the collected knowledge of the characters, habits,
properties, organization, and {123} functions of these
groups and families, as it is found in the best botanical
works, and as it exists in the minds of the best botanists,
exhibits to us the propositions which constitute the
science, and to the expression of which the classification
is to serve. All that is not strictly definition, that is,
all that is not artificial character, in the descriptions of
such classes, is a statement of truths, more or less
general, more or less precise, but making up, together, the
positive knowledge which constitutes the science. As we have
said, the consideration of the properties of plants in order
to form a system of classification, has been termed
Taxonomy, or the Systematick of Botany; all the parts of the
descriptions, which, taking the system for granted, convey
additional information, are termed the _Physiography_ of the
science; and the same terms may be applied in the other
branches of Natural History.

12. _Artificial and Natural Systems._--If I have succeeded
in making it apparent that an artificial system of
characters necessarily implies natural classes which are not
severed by the artificial marks, we shall now be able to
compare the nature and objects of the Artificial and Natural
Systems; points on which much has been written in recent times.

The Artificial System is one which is, or professes to be,
entirely founded upon marks selected according to the
condition which has been stated, of not violating certain
narrow natural groups; namely in the Linnæan system, the
natural genera of plants. The marks which form the basis of
the system, being thus selected, are applied rigorously and
universally without any further regard to any other
characters or indications of affinity. Thus in the Linnæan
system, which depends mainly on the number of male organs or
stamens, and on the number of female organs or styles, the
largest divisions, or the Classes, are arranged according to
the number of the stamens, and are _monandria_, _diandria_,
_triandria_, _tetrandria_, _pentandria_, _hexandria_, and so
on: the names being formed of the Greek numerical words, and
of the word which implies _male_. And the Orders of each of
these Classes are {124} distinguished by the number of
styles, and are called _monogynia_, _digynia_, _trigynia_,
and so on, the termination of these words meaning _female_.
And so far as this numerical division and subdivision go on,
the system is a rigorous system, and strictly artificial.

But the condition that the artificial system shall leave
certain natural affinities untouched, makes it impossible to
go through the vegetable kingdom by a method of mere
numeration of stamens and styles. The distinction of flowers
with twenty and with thirty stamens is not a fixed
distinction: flowers of one and the same kind, as roses,
have, some fewer than the former, some more than the latter
number. The Artificial System, therefore, must be modified.
And there are various relations of connexion and proportion
among the stamina which are more permanent and important
than their mere number. Thus flowers with two longer and two
shorter stamens are not placed in the class _tetrandria_,
but are made a separate class _didynamia_; those with four
longer and two shorter are in like manner _tetradynamia_,
not _hexandria_; those in **which the filaments are bound
into two bundles are _diadelphia_. All these and other
classes are deviations from the plan of the earlier Classes,
and are so far defects of the artificial system; but they
are deviations requisite in order that the system may leave
a basis of natural groups, without which it would not be a
System of _Vegetables_. And as the division is still founded
on some properties of the stamens, it combines not ill with
that part of the system which depends on the number of them.
The Classes framed in virtue of these various considerations
make up an Artificial System which is tolerably coherent.

'But since the Artificial System thus regards natural
groups, in what does it differ from a Natural System?' It
differs in this:--That though it allows certain subordinate
natural groups, it merely allows _these_, and does not
endeavour to ascend to any wider natural groups. It takes
all the _higher_ divisions of its scheme from its artificial
characters, its stamens and pistils, without looking to any
natural affinities. It {125} accepts natural _Genera_, but
it does not seek natural _Families_, or Orders, or Classes.
It _assumes_ natural groups, but does not _investigate_ any;
it forms wider and higher groups, but professes to frame
them arbitrarily.

But then, on the other hand, the question occurs, 'This
being the case, what can be the use of the Artificial
System?' If its characters, in the higher stages of
classification, be arbitrary, how can it lead us to the
natural relations of plants? And the answer is, that it does
so in virtue of the original condition, that there shall be
certain natural relations which the artificial system shall
not transgress; and that its use arises from the facility
with which we can follow the artificial arrangement as far
as it goes. We can count the stamens and pistils, and thus
we know the Class and Order of our plant; and we have then
to discover its Genus and Species by means less symmetrical
but more natural. The Artificial System, though arbitrary in
a certain degree, brings us to a Class in which the whole of
each Genus is contained, and there we can find the proper
Genus by a suitable method of seeking. No Artificial System
can conduct us into the extreme of detail, but it can place
us in a situation where the detail is within our reach. We
cannot find the house of a foreign friend by its latitude
and longitude; but we may be enabled, by a knowledge of the
latitude and longitude, to find the city in which he dwells,
or at least the island; and we then can reach his abode by
following the road or exploring the locality. The Artificial
System is such a method of travelling by latitude and
longitude; the Natural System is that which is guided by a
knowledge of the country.

The Natural System, then, is that which endeavours to
arrange by the natural affinities of objects; and more
especially, which attempts to ascend from the lower natural
groups to the higher; as for example from genera to natural
families, orders, and classes. But as we have already
hinted, these expressions of natural affinities, natural
groups, and the like, when {126} considered in reference to
the idea of resemblance alone, without studying analogy or
function, are very vague and obscure. We must notice some of
the attempts which were made under the operation of this
imperfect view of the subject.

SECT. IV.--_Modes of framing Natural Systems._

13. Decandolle[22\8] distinguishes the attempts at Natural
Classifications into three sorts: those of _blind trial_
(_tâtonnement_), those of _general comparison_, and those of
_subordination of characters_. The two former do not depend
distinctly upon any principle, except resemblance; the third
refers us to other views, and must be considered in a future
chapter.

[Note 22\8: _Theor. Elem._ art 41.]

_Method of Blind Trial._--The notion of the existence of
natural classes dependent on the general resemblance of
plants,--of an affinity showing itself in different parts
and various ways,--though necessarily somewhat vague and
obscure, was acted upon at an early period, as we have seen
in the formation of genera; and was enunciated in general
terms soon after. Thus Magnolius[23\8] says that he discerns
in plants an affinity, by means of which they may be
arranged in families: 'Yet it is impossible to obtain from
the fructification alone the Characters of these families;
and I have therefore chosen those parts of plants in which
the principal characteristic marks are found, as the root,
the stem, the flower, the seed. In some plants there is even
a certain resemblance; an affinity which does not consist in
the parts considered separately, but in their totality; an
affinity which may be felt but not expressed; as we see in
the families of agrimonies and cinquefoils, which every
botanist will judge to be related, though they differ by
their roots, their leaves, their flowers, and their seeds.'

[Note 23\8: Dec. _Theor. Elem._ art. 42. Petri Magnoli,
_Prodromus Hist. Gen. Plant._ 1689.]

{127} This obscure feeling of a resemblance on the whole, an
affinity of an indefinite kind, appears fifty years later in
Linnæus's attempts. 'In the Natural Classification,' he
says[24\8], 'no _à priori_ rule can be admitted, no part of
the fructification can be taken exclusively into
consideration; but only the simple symmetry of all its
parts.' Hence though he proposed Natural Families, and even
stated the formation of such Families to be the first and
last object of all Methods, he never gave the Characters of
those groups, or connected them by any method. He even
declared it to be impossible to lay down such a system of
characters. This persuasion was the result of his having
refused to admit into his mind any Idea more profound than
that notion of Resemblance of which he had made so much and
such successful use; he would not attempt to unravel the
Ideas of Symmetry and of Function on which the clear
establishment of natural relations must depend. He even
despised the study of the inner organization of plants; and
reckoned[25\8] the _Anatomici_, who studied the anatomy and
physiology of plants and the laws of vegetation, among the
_Botanophili_, the mere amateurs of his science.

[Note 24\8: Dec. _Theor. Elem._ art 42.]

[Note 25\8: _Phil. Bot._ s. 44.]

The same notion of general resemblance and affinity,
accompanied with the same vagueness, is to be found in the
writer who least participated in the general admiration of
Linnæus, Buffon. Though it was in a great measure his love
of higher views which made him dislike what he considered
the pedantry of the Swedish school, he does not seem to have
obtained a clearer sight of the principle of the natural
method than his rival, except that he did not restrict his
Characters to the fructification. Things must be arranged by
their resemblances and differences, (he says in 1750[26\8],)
'but the resemblances and differences must be taken not from
one part but from the whole; and we must attend to the form,
the size, the habit, the number and position of the parts,
even the substance {128} of the part; and we must make use
of these elements in greater or smaller number, as we have need.'

[Note 26\8: Adanson, p. clvi. Buffon, _Hist. Nat._ t. i. p. 21.]

14. _Method of General Comparison._--A countryman of Buffon,
who shared with him his depreciating estimate of the Linnæan
system, and his wish to found a natural system upon a
broader basis, was Adanson; and he invented an ingenious
method of apparently avoiding the vagueness of the practice
of following the general feeling of resemblance. This method
consisted in making many Artificial Systems, in each of
which plants were arranged by some one part; and then
collecting those plants which came near each other in the
greatest number of those Artificial Systems, as plants
naturally the most related. Adanson gives an account[27\8]
of the manner in which this system arose in his mind. He had
gone to Senegal, animated by an intense zeal for natural
history; and there, amid the luxuriant vegetation of the
torrid zone, he found that the methods of Linnæus and
Tournefort failed him altogether as means of arranging his
new botanical treasures. He was driven to seek a new system.
'For this purpose,' he says, 'I examined plants in all their
parts, without omitting any, from the roots to the embryo,
the folding of the leaves in the bud, their mode of
sheathing[28\8], the situation and folding of the embryo and
of its radicle in the seed, relatively to the fruit; in
short, a number of particulars which few botanists notice. I
made in the first place a complete description of each
plant, putting each of its parts in separate articles, in
all its details; when new species occurred I put down the
points in which they differed, omitting those in which they
agreed. By means of the aggregate of these comparative
descriptions, I perceived that plants arranged themselves
into classes or families which could not be artificial or
arbitrary, not being founded upon one or two parts, which
might change at certain limits, but on all the parts; so
that the disproportion of one of these parts was corrected
and balanced by the introduction of another.' Thus the
principle of Resemblance {129} was to suffice for the
general arrangement, not by means of a new principle, as
Symmetry or Organization, which should regulate its
application, but by a numeration of the peculiarities in
which the resemblance consisted.

[Note 27\8: Pref. p. clvii.]

[Note 28\8: 'Leur manière de s'engainer.']

The labour which Adanson underwent in the execution of this
thought was immense. By taking each Organ, and considering
its situation, figure, number, &c., he framed sixty-five
Artificial Systems; and collected his Natural Families by a
numerical combination of these. For example, his
_sixty-fifth_ Artificial System[29\8] is that which depends
upon the situation of the Ovary with regard to the Flower;
according to this system he frames _ten_ Artificial Classes,
including _ninety-three_ Sections: and of these Sections the
resulting Natural Arrangement retains _thirty-five_, above
one-third: the same estimate is applied in other cases.

[Note 29\8: Adanson, Pref. p. cccxii.]

But this attempt to make Number supply the defects which the
vague notion of Resemblance introduces, however ingenious,
must end in failure. For, as Decandolle observes[30\8], it
supposes that we know, not only all the Organs of plants,
but all the points of view in which it is possible to
consider them; and even if this assumption were true, which
it is not, and must long be very far from being, the
principle is altogether vicious; for it supposes that all
these points of view, and all the resulting artificial
systems are of equal importance:--a supposition manifestly
erroneous. We are thus led back to the consideration of the
_Relative Importance_ of Organs and their qualities, as a
basis for the classification of plants, which no Artificial
Method can supersede; and thus we find the necessity of
attending to something besides mere external and detached
Resemblance. The method of General Comparison cannot, any
more than the method of Blind Trial, lead us, with any
certainty or clearness, to the Natural Method. Adanson's
Families are held by the best botanists to be, for the
greater part, Natural; but his hypotheses are unfounded; and
his success is {130} probably more due to the dim feeling of
Affinity, by which he was unconsciously guided, than to the
help he derived from his numerical processes.

[Note 30\8: Dec. _Theor. Elem._ p. 67.]

In a succeeding chapter I shall treat of that Natural
Affinity on which a Natural System must really be founded.
But before proceeding to this higher subject, we must say a
few words on some of the other parts of the philosophy of
Natural History,--the Gradation of Groups, the Nomenclature,
the Diagnosis, and the application of the methods to other
subjects.

SECT. V.--_Gradation of Groups._

15. It has been already noticed (last chapter,) that even
that vague application of the idea of resemblance which
gives rise to the terms of common language, introduces a
subordination of classes, as _man_, _animal_, _body_,
_substance_. Such a subordination appears in a more precise
form when we employ this idea in a scientific manner as we
do in Natural History. We have then a series of divisions,
each inclusive of the lower ones, which are expressed by
various metaphors in different writers. Thus some have gone
as far as eight terms of the series[31\8], and have taken,
for the most part, military names for them; as _Hosts_,
_Legions_, _Phalanxes_, _Centuries_, _Cohorts_, _Sections_,
_Genera_, _Species_. But the most received series is
_Classes_, _Orders_, _Genera_, and _Species_; in which,
however, we often have other terms interpolated, as
_Sub-genera_, or Sections of genera. The expressions
_Family_ and _Tribe_, are commonly appropriated to natural
groups; and we speak of the Vegetable, Animal, Mineral
_Kingdom_; but the other metaphors of Provinces, Districts,
&c., which this suggests, have not been commonly used[32\8].

[Note 31\8: Adanson, p. cvi.]

[Note 32\8: _Sub-Kingdom_ has recently been employed by
some naturalists.]

It will of course be understood that each ascending step of
classification is deduced by the same process from the one
below. A Genus is a collection of Species which resemble
each other more than they {131} resemble other species; an
Order is a collection of Genera having, in like manner, the
first degree of resemblance, and so on. How close or how
wide the Degrees of Resemblance are, must depend upon the
nature of the objects compared, and cannot possibly be
prescribed beforehand. Hence the same term, _Class_ and
_Order_ for instance, may imply, in different provinces of
nature, very different degrees of resemblance. The Classes
of Animals are Insects, Birds, Fish, Beasts, &c. The Orders
of Beasts are _Ruminants_, _Tardigrades_, _Plantigrades_,
&c. The two Classes of Plants (according to the Natural
Order[33\8]) are _Vascular_ and _Cellular_, the latter
having neither sexes, flowers, nor spiral vessels. The
Vascular Plants are divided into Orders, as _Umbelliferæ_,
_Ranunculaceæ_, &c.; but between this Class and its Orders
are interposed two other steps:--two Sub-classes,
_Dicotyledonous_ and _Monocotyledonous_, and two Tribes of
each: _Angiospermiæ_, _Gymnospermiæ_ of the first; and
_Petaloideæ_, _Glumaciæ_ of the second. Such interpolations
are modifications of the general formula of subordination,
for the purpose of accommodating it to the most prominent
natural affinities.

[Note 33\8: Lindley.]

16. _Species._--As we have already seen in tracing the
principles of the Natural Method, when by the intimate study
of plants we seek to give fixity and definiteness to the
notion of resemblance and affinity on which all these
divisions depend, we are led to the study of Organization
and Analogy. But we make a reference to physiological
conditions even from the first, with regard to the lowest
step of our arrangement, the _Species_; for we consider it a
proof of the impropriety of separating two Species, if it be
shown that they can by any course of propagation, culture,
and treatment, the one pass into the other. It is in this
way, for example, that it has been supposed to be
established that the common Primrose, Oxlip, Polyanthus, and
Cowslip, are all the same species. Plants which thus, in
virtue of external circumstances, as soil, {132} exposure,
climate, exhibit differences which may disappear by changing
the circumstances, are called _Varieties_ of the species.
And thus we cannot say that a Species is a collection of
individuals which possess the First Degree of Resemblance;
for it is clear that a primrose resembles another primrose
more than it does a cowslip; but this resemblance only
constitutes a Variety. And we find that we must necessarily
include in our conception of Species, the notion of
propagation from the same stock. And thus a Species has been
well defined[34\8]: 'The collection of the individuals
descended from one another, or from common parents, and of
those which resemble these as much as these resemble each
other.' And thus the sexual doctrine of plants, or rather
the consideration of them as things which propagate their
kind, (whether by seed, shoot, or in any other way,) is at
the basis of our classifications.

[Note 34\8: Cuv. _Règne Animal_, p. 19.]

17. The First permanent Degree of Resemblance among
organized beings is thus that which depends on this relation
of generation, and we might expect that the groups which are
connected by this relation would derive their names from the
notion of generation. It is curious that both in Greek and
Latin languages and in our own, the words which have this
origin (γένος, _genus_, _kind_,) do not, in the phraseology
of science at least, denote the nearest degree of
relationship, but have other terms subordinate to them,
which appear etymologically to indicate a mere resemblance
of appearance (εἶδος, _species_, _sort_); and these latter
terms are appropriated to the groups resulting from
propagation. Probably the reason of this is, that the former
terms (_genus_, &c.) had been applied so widely and loosely
before the scientific fixation of terms, that to confine
them to what we call _species_ would have been to restrict
them in a manner too unusual to be convenient.

18. _Varieties. Races._--The Species, as we have said, is
the collection of individuals which resemble each other as
much as do the offspring of a common {133} stock. But within
the limits of this boundary, there are often observable
differences permanent enough to attract our notice, though
capable of being obliterated by mixture in the course of
generation. Such different groups are called _Varieties_.
Thus the Primrose and Cowslip, as has been stated above, are
found to be varieties of the same plant; the Poodle and the
Greyhound are well marked varieties of the species _dog_.
Such differences are hereditary, and it may be long doubtful
whether such hereditary differences are varieties only, or
different species. In such cases the term _Race_ has been
applied.

SECT. VI.--_Nomenclature._

19. The Nomenclature of any branch of Natural History is the
collection of names of all its species; which, when they
become extremely numerous, requires some artifice to make it
possible to recollect or apply them. The known species of
plants, for example, were 10,000 at the time of Linnæus, and
are now probably 60,000. It would be useless to endeavour to
frame and employ separate names for each of these species.

The division of the objects into a subordinated system of
classification enables us to introduce a Nomenclature which
does not require this enormous number of names. The artifice
employed to avoid this inconvenience is to name a Species by
means of two (or it might be more) steps of the successive
division. Thus in Botany, each of the genera has its name,
and the species are marked by the addition of some epithet
to the name of the genus. In this manner about 1,700 generic
names, with a moderate number of specific names, were found
by Linnæus sufficient to designate with precision all the
species of vegetables known at his time. And this _Binary
Method_ of Nomenclature has been found so convenient that it
has been universally adopted in every other department of
the Natural History of organized beings.

Many other modes of Nomenclature have been tried, but no
other has at all taken root. Linnæus himself {134} appears
at first to have intended marking each species by the
Generic Name accompanied by a characteristic Descriptive
Phrase; and to have proposed the employment of a _trivial_
Specific Name, as he termed it, only as a method of
occasional convenience. The use of these _trivial names_,
has, however, become universal, as we have said, and is by
many persons considered the greatest improvement introduced
at the Linnæan reform.

Both Linnæus and other writers (as Adanson) have given many
maxims with a view of regulating the selection of generic
and specific names. The maxims of Linnæus were intended as
much as possible to exclude barbarism and confusion, and
have, upon the whole, been generally adopted; though many of
them were objected to by his contemporaries (Adanson and
others[35\8]), as capricious or unnecessary innovations.
Many of the names, introduced by Linnæus, certainly appear
fanciful enough: thus he gives the name of _Bauhinia_ to a
plant with leaves in pairs, because the Bauhins were a pair
of brothers; _Banisteria_ is the name of a climbing plant,
in honour of Banister, who travelled among mountains. But
such names, once established by adequate authority, lose all
their inconvenience, and easily become permanent; and hence
the reasonableness of the Linnæan rule[36\8], that as such a
perpetuation of the names of persons by the names of plants
is the only honour botanists have to bestow, it ought to be
used with care and caution.

[Note 35\8: Pp. cxxix. clxxii.]

[Note 36\8: _Phil Bot._ s. 239.]

The generic name must, as Linnæus says, be fixed[37\8]
before we attempt to form a specific name; 'the latter
without the former is like the clapper without the bell.'
The name of the genus being established, the species may be
marked by adding to it 'a single word taken at will from any
quarter;' that is, not involving a description or any
essential property of the plant, but a casual or arbitrary
appellation[38\8]. Thus the {135} various species of
_Hieracium_[39\8] are _Hieracium Alpinum_, _H. Halleri_, _H.
Pilosella_, _H. dubium_, _H. murorum_, &c. where we see how
different may be the kind of origin of the words.

[Note 37\8: _Ib._ s. 222.]

[Note 38\8: _Ib._ s. 260.]

[Note 39\8: Hooker, _Fl. Scot._ 228.]

Attempts have been made at various times to form the name of
species from those of genera in some more symmetrical
manner. Thus some have numbered the species of genus, 1, 2,
3, &c.; but this method is liable to the inconveniences,
first, that it offers nothing for the memory to take hold
of; and second, that if a new species intermediate between 1
and 2, 2 and 3, &c., be discovered, it cannot be put in its
place. It has also been proposed to mark the species by
altering the termination of the genus. Thus Adanson[40\8],
denoting a genus by the name _Fonna_ (_Lychnidea_),
conceived he might mark five of its species by altering the
last vowel, _Fonna_, _Fonna-e_, _Fonna-i_, _Fonna-o_,
_Fonna-u_; then others by _Fonna-ha_, _Fonna-ka_, and so on.
This course would be liable to the same evils which have
been noticed as belonging to the numerical method.

[Note 40\8: Pref. clxxvi.]

The names of plants (and the same is true of animals) have
in common practice been binary only, consisting of a generic
and a specific name. The Class and Order have not been
admitted to form part of the appellation of the species.
Indeed it is easy to see that a name which must be identical
in so many instances as that of an Order would be, would be
felt as superfluous and burdensome. Accordingly, Linnæus
makes it a precept[41\8], that the name of the Class and the
Order must not be expressed but understood: and hence, he
says, Royen, who took _Lilium_ for the name of a Class,
rightly rejected it as a generic name, and substituted
_Lirium_, with the Greek termination.

[Note 41\8: _Phil. Bot._ s. 215.]

Yet we must not too peremptorily assume such maxims as these
to be universal for all classificatory sciences. It is very
possible that it may be found advisable to use _three_
terms, that of order, genus and {136} species, in
designating minerals, as is done in Mohs's nomenclature; for
example, _Rhombohedral Calc Haloide_, _Paratomous Hal
Baryte_.

It is possible also that it may be found useful in the same
science to mark some of the steps of classification by the
termination. Thus it has been proposed to confine the
termination _ite_ to the Order _Silicides_ of Naumann, as
Apophyll_ite_, Stilb_ite_, Leuc_ite_, &c., and to use names
of different form in other orders, as Talc _Spar_ for
Brennerite, Pyramidal Titanium _Oxide_ for Octahedrite. Some
such method appears to be the most likely to give us a
tolerable mineralogical nomenclature.

SECT. VII.--_Diagnosis._

20. German Naturalists speak of a part of the general method
which they call the _Characteristik_ of Natural History, and
which is distinguished from the _Systematik_ of the science.
The _Systematick_ arranges the objects by means of all their
resemblances, the _Characteristick_ enables us to detect
their place in the arrangement by means of a few of their
characters. What these characters are to be, must be
discovered by observation of the groups and divisions of the
system when they are formed. To construct a collection of
such characters as shall be clear and fixed, is a useful,
and generally a difficult task; for there is usually no
apparent connexion between the marks which are used in
discriminating the groups, and the nature of the groups
themselves. They are assumed only because the naturalist,
extensively and exactly acquainted with the groups and the
properties of the objects which compose them, sees, by a
survey of the field, that these marks divide it properly.

The Characteristick has been termed by some English
Botanists the _Diagnosis_ of plants; a word which we may
conveniently adopt. The Diagnosis of any genus or species is
different according to the system we follow. Thus in the
Linnæan System the Diagnosis of the Rose is in the first
place given by its Class and Order: it is {137} Icosandrous,
and Polygynous; and then the Generic Distinction is that the
calyx is five-cleft, the tube urceolate, including many
hairy achenia, the receptacle villous[42\8]. In the Natural
System the Rose-Tribe are distinguished as being[43\8]
'Polypetalous dicotyledons, with lateral styles, superior
simple ovaria, regular perigynous stamens, exalbuminous
definite seeds, and alternate stipulate leaves.' And the
true Roses are further distinguished by having 'Nuts,
numerous, hairy, terminated by the persistent lateral style
and inclosed within the fleshy tube of the calyx,' &c.

[Note 42\8: Lindley, _Nat. Syst._ p. 149.]

[Note 43\8: _Ib._ pp. 81, 3.]

It will be observed that in a rigorous Artificial System the
_Systematick_ coincides with the _Characteristick_; the
_Diataxis_ with the _Diagnosis_; the reason why a plant is
put in a division is identical with the mode by which it is
known to be in the division. The Rose is in the class
_icosandria_, because it has many stamens inserted in the
calyx; and when we see such a set of stamens we immediately
know the class. But this is not the case with the Diagnosis
of Natural Families. Thus the genera _Lamium_ and
_Galeopsis_ (Dead Nettle and Hemp Nettle) are each formed
into a separate group in virtue of their general
resemblances and differences, and not because the former has
one tooth on each side of the lower lip, and the latter a
notch in its upper lip, though they are distinguished by
these marks.

Thus so far as our Systems are natural, (which, as we have
shown, all systems to a certain extent must be), the
Characteristick is distinct both from a Natural and an
Artificial System; and is, in fact, an Artificial Key to a
Natural System. As being Artificial, it takes as few
characters as possible; as being Natural, its characters are
not selected by any general or prescribed rule, but follow
the natural affinities. The Botanists who have made any
steps in the formation of a natural method of plants since
Linnæus, have all attempted to give a Diagnosis
corresponding to the Diataxis of their method.

{{138}}
CHAPTER III.

APPLICATION OF THE NATURAL HISTORY METHOD TO MINERALOGY.

1. THE philosophy of the Sciences of Classification has had
great light thrown upon it by discussions concerning the
methods which are used in Botany: for that science is one of
the most complete examples which can be conceived of the
consistent and successful application of the principles and
ideas of Classification; and this application has been made
in general without giving rise to any very startling
paradoxes, or disclosing any insurmountable difficulties.
But the discussions concerning methods of Mineralogical
Classification have been instructive for quite a different
reason: they have brought into view the boundaries and the
difficulties of the process of Classification; and have
presented examples in which every possible mode of
classifying appeared to involve inextricable contradictions.
I will notice some of the points of this kind which demand
our attention, referring to the works published recently by
several mineralogists.

In the History of Mineralogy we noticed the attempt made by
Mohs and other Germans to apply to minerals a method of
arrangement similar to that which has been so successfully
employed for plants. The survey which we have now taken of
the grounds of that method will point out some of the
reasons of the very imperfect success of this attempt. We
have already said that the _Terminology_ of Mineralogy was
materially reformed by Werner; and including in this branch
of the subject (as we must do) the Crystallography of later
writers, it may be considered as to a great extent complete.
Of the attempts at a Natural arrangement, that of Mohs
appears to proceed by the {139} method of _blind trial_, the
undefinable perception of relationship, by which the
earliest attempts at a Natural Arrangement of plants were
made. Breithaupt however, has made (though I do not know
that he has published) an essay in a mode which corresponds
very nearly to Adanson's process of _multiplied
comparisons_. Having ascertained the specific gravity and
hardness of all the species of minerals, he arranged them in
a table, representing by two lines at right angles to each
other these two numerical quantities. Thus all minerals were
distributed according to two co-ordinates representing
specific gravity and hardness. He conceived that the groups
which were thus brought together were natural groups. On
both these methods, and on all similar ones, we might
observe, that in minerals as in plants, the mere general
notion of Likeness cannot lead us to a real arrangement:
this notion requires to have precision and aim given it by
some other relation;--by the relation of Chemical
Composition in minerals, as by the relation of Organic
Function in vegetables. The physical and crystallographical
properties of minerals must be studied with reference to
their constitution; and they must be arranged into Groups
which have some common Chemical Character, before we can
consider any advance as made towards a Natural Arrangement.

In reality, it happens in Mineralogy as it happened in
Botany, that those speculators are regulated by an obscure
perception of this ulterior relation, who do not profess to
be regulated by it. Several of the Orders of Mohs have
really great unity of chemical character, and thus have good
evidence of their being really Natural Orders.

2. Supposing the Diataxis of minerals thus obtained, Mohs
attempted the Diagnosis; and his _Characteristick of the
Mineral Kingdom_, published in Dresden, in 1820, was the
first public indication of his having constructed a system.
From the nature of a Characteristick, it is necessarily
brief, and without any ostensible principle; but its
importance was duly appreciated by the author's countrymen.
Since that {140} time, many attempts have been made at
improved arrangements of minerals, but none, I think,
(except perhaps that of Breithaupt,) professing to proceed
rigorously on the principles of Natural History;--to arrange
by means of external characters, neglecting altogether, or
rather postponing, the consideration of chemical properties.
By relaxing from this rigour, however, and by combining
physical and chemical considerations, arrangements have been
obtained (for example, that of Naumann,) which appear more
likely than the one of Mohs to be approximations to an
ultimate really natural system. Naumann's Classes are
_Hydrolytes_, _Haloides_, _Silicides_, _Metal Oxides_,
_Metals_, _Sulphurides_, _Anthracides_, with subdivisions of
Orders, as _Anhydrous unmetallic Silicides_. It may be
remarked that the designations of these are mostly chemical.
As we have observed already, Chemistry, and Mineralogy in
its largest sense, are each the necessary supplement of the
other. If Chemistry furnish the Nomenclature, Mineralogy
must supply the Physiography: if the Arrangement be founded
on External Characters and the Names be independent of
Chemistry, the chemical composition of each species is an
important scientific Truth respecting it.

3. The inquiry may actually occur, whether any subordination
of groups in the mineral kingdom has really been made out.
The ancient chemical arrangements, for instance, that of
Haüy, though professing to distribute minerals according to
Classes, Orders, Genera, and Species, were not only
arbitrary, but inapplicable; for the first postulate of any
method, that the species should have constant characters of
unity and difference, was not satisfied. It was not
ascertained that carbonate of lime was really
distinguishable in all cases from carbonate of magnesia, or
of iron; yet these species were placed in remote parts of
the system: and the above carbonates made just so many
species; although, if they were distinct from one another at
all, they were further distinguishable into additional
species. Even now, we may, perhaps, say that the limits of
mineralogical species, and their laws of fixity, are {141}
not yet clearly seen. For the discoveries of the isomorphous
relations and of the optical properties of minerals have
rather shown us in what direction the object lies, than led
us to the goal. It is clear that, in the mineral kingdom,
the Definition of Species, borrowed from the laws of the
continuation of the kind, which holds throughout the organic
world, fails us altogether, and must be replaced by some
other condition: nor is it difficult to see that the
definite atomic relations of the chemical constituents, and
the definite crystalline angle, must supply the principles
of the _Specific_ Identity for minerals. Yet the exact
limits of definiteness in both these cases (when we admit
the effect of mechanical mixtures, &c.) have not yet been
completely disentangled. Moreover, any _arbitrary_
assumption (as the allowance of a certain per-centage of
mixture, or a certain small deviation in the angle,) is
altogether contrary to the philosophy of the Natural System,
and can lead to no stable views. It is only by laborious,
extensive, and minute research, that we can hope to attain
to any solid basis of arrangement.

4. Still, though there are many doubts respecting
mineralogical species, a large number of such species are so
far fixed that they may be supposed capable of being united
under the higher divisions of a system with approximate
truth. Of these higher divisions, those which have been
termed _Orders_ appear to tend to something like a fixed
chemical character. Thus the _Haloids_ of Naumann, and
mostly those of Mohs, are combinations of an oxide with an
acid, and thus resemble Salts, whence their name. The
Silicides contain most of Mohs's _Spaths_: and the Orders
_Pyrites_, _Glance_, and _Blende_, are common to Naumann and
Mohs; being established by the latter on a difference of
external character, which difference is, indeed, very
manifest; and being included by the former in one chemical
_Class_, _Sulphurides_. The distinctions of _Hydrous_ and
_Anhydrous_, _Metallic_ and _Unmetallic_, are, of course,
chemical distinctions, but occur as the differences of
Orders in Naumann's mixed system. {142}

We may observe that some French writers, following Haüy's
last edition, use, instead of _metallic_ and _unmetallic_,
_autopside metallic_ and _heteropside metallic_; meaning by
this phraseology to acknowledge the discovery that earths,
etc., _are_ metallic, though they do not _appear_ to be so,
while metals both are and appear metallic. But this seems to
be a refinement not only useless but absurd. For what is
gained by adding the word _metallic_, which is common to
all, and therefore makes no distinction? If certain metals
are distinguished by their _appearing_ to be metals, this
appearance is a reason for giving them the peculiar name,
_metals_. Nothing is gained by first bringing earths and
metals together, and then immediately separating them again
by new and inconvenient names. No proposition can be
expressed better by calling _earths_, _heteropside metallic
substances_, and therefore such nomenclature is to be
rejected.

Granting, then, that the Orders of the best recent
mineralogical systems approximate to natural groups, we are
led to ask whether the same can be said of the Genera of the
Natural History systems, such as those of Mohs and
Breithaupt. And here I must confess that I see no principle
in these Genera; I have failed to apprehend the conceptions
by the application of which they have been constructed: I
shall therefore not pass any further judgment upon them. The
subordination of Mineralogical Species to Orders is a
manifest gain to science: in the interposition of Genera I
see nothing but a source of confusion.

5. In Mineralogy, as in other branches of natural history, a
reformed arrangement ought to give rise to a reformed
Nomenclature; and for this, there is more occasion at
present in Mineralogy than there was in Botany at the worst
period, at least as far as the extent of the subject allows.
The characters of minerals are much more dimly and
unfrequently developed than those of plants; hence arbitrary
chemical arrangements, which could not lead to any natural
groups, and therefore not to any good names, prevailed till
recently; and this state of things produced an anarchy {143}
in which every man did what seemed right in his own
eyes,--proposed species without any ascertained distinction,
and without a thought of subordination, and gave them
arbitrary names; and thus with only about two or three
hundred known species, we have thousands upon thousands of
names, of anomalous form and uncertain application.

Mohs has attempted to reform the Nomenclature of the subject
in a mode consistent with his attempt to reform the System.
In doing this, he has fatally transgressed a rule always
insisted upon by the legislators of Botany, of altering
usual names as little as possible; and his names are both so
novel and so cumbrous, that they appear to have little
chance of permanent currency. They are, perhaps, more
unwieldy than they need to be, by referring, as we have
said, to three of the steps of his classification, the
Species, Genus, and Order. We may, however, assert
confidently, from the whole analogy of natural history, that
no good names can be found which do not refer to at least
_two_ terms of the arrangement. This rule has been
practically adopted to a great extent by Naumann, who gives
to most of his Haloids the name _Spar_, as Calc spar, Iron
spar, &c.; to all his Oxides the terminal word _Erz_
(_Ore_); and to the species of the orders _Kies_
(_Pyrites_), _Glance_, and _Blende_, these names. It has
also been theoretically assented to by Beudant, who proposes
that we should say _silicate stilbite_, _silicate chabasie_;
_carbonate calcaire_, _carbonate witherite_; _sulphate
couperose_, &c. One great difficulty in this case would
arise from the great number of _silicides_; it is not likely
that any names would obtain a footing which tacked the term
_silicide_ to another word for each of these species. The
artifice which I have proposed, in order to obviate this
difficulty, is that we should make the names of the
silicides, and those alone, end in _ite_ or _lite_, which a
large proportion of them do already.

By this and a few similar contrivances, we might, I
conceive, without any inconvenient change, introduce into
Mineralogy a systematic nomenclature. {144}

6. I shall now proceed to make a few remarks on a work on
Mineralogy more recent than those which I have above
noticed, and written with express reference to such
difficulties as I have been discussing. I allude to the
treatise of M. Necker, _Le Règne Mineral ramené aux Methods
d'Histoire Naturelle_[44\8], which also contains various
dissertations on the Philosophy of Classification in
general, and its application to Mineralogy in particular.

[Note 44\8: Paris, 1835.]

M. Necker remarks very justly, that Mineralogy, as it has
hitherto been treated, differs from all other branches of
Natural History in this:--that while it is invested with all
the forms of the sciences of classification,--Classes,
Divisions, Genera, and the like,--the properties of those
bodies to which the mineralogical student's attention is
directed have no bearing whatever on the classification. A
person, he remarks[45\8], might be perfectly well acquainted
with all the characters of minerals which Werner or Haüy
examined so carefully, and might yet be quite unable to
assign to any mineral its place in the divisions of their
methods. There is[46\8] a complete separation between the
study of mineralogical characters and the recognition of the
name and systematic place of a mineral. Those who know
_mineralogy_ well, may know _minerals_ ill, or hardly at
all; the systematist may be in such knowledge vastly
inferior to the mineral-dealer or the miner. In this respect
there is a complete contrast between this science and other
classificatory sciences.

[Note 45\8: _Règne Mineral_, p. 3.]

[Note 46\8: _Ib._ p. 8.]

Again, in the best-known systems of Mineralogy, (as those of
Werner and Haüy,). the bodies which are grouped together as
belonging to the same division, have not, as they have in
other classificatory sciences, any resemblance. The
different members of the larger classes are united by the
common possession of some abstract property,--as, that they
all contain iron. This is a property to which no common
circumstance in the bodies themselves corresponds. What is
there common to the minerals named oxidulous iron, sulphuret
{145} of iron, carbonate of iron, sulphate of iron, except
that they all contain iron? And when we have classed these
bodies together, what general assertion can we make
concerning them, except that which is the ground of our
classification, that they contain iron? They have nothing in
common with iron or with each other in any other way.

Again, as these classes have no general properties, all the
properties are particular to the species; and the
descriptions of these necessarily become both tediously
long, and inconveniently insulated.

7. These inconveniences arise from making Chemical
Composition the basis of Mineralogical Classification
without giving Chemical Analysis the first place among
Mineral Properties. Shall we, then, correct this omission,
so far as it has affected mineralogical systems? Shall we
teach the student the chemical analysis of minerals, and
then direct him to classify them according to the results of
his analysis[47\8]?

[Note 47\8: _Règne Mineral_, p. 18.]

But why should we do this? To what purpose, or on what
ground, do we arrange the results of chemical analysis
according to the forms and subordination of natural history?
Is not Chemistry a science distinct from Natural History?
Are not the sciences opposed? Is not natural history
confined to organic bodies? Can mere chemical elements and
their combinations be, with any propriety or consistency,
arranged into Species, Genera, and Families? What is the
principle on which genera and species depend? Do not Species
imply Individuals? What is an Individual in the case of a
chemical substance?

8. We thus find some of the widest and deepest questions of
the philosophy of classification brought under our
consideration when we would provide a method for the
classification of minerals. The answers to these questions
are given by M. Necker; and I shall state some of his
opinions; taking the liberty of adding such remarks as are
suggested by referring the subject {146} to those principles
which have already been established in this work.

M. Necker asserts[48\8] that the distinctions of different
Sciences depend, not on the objects they consider, but on
the different and independent points of view on which they
proceed. Each science has its logic, that is, its mode of
applying the general rules of human reason to its own
special case. It has been said by some[49\8], that in
minerals, natural history and chemistry contemplate common
objects, and thus form a single science. But do chemistry
and natural history consider minerals in the same point of view?

[Note 48\8: _Règne Mineral_, p. 23.]

[Note 49\8: _Ib._ p. 27.]

The answer is, that they do not. Physics and Chemistry
consider the properties of bodies in an abstract manner; as,
their composition, their elements, their mutual actions,
with the laws of these; their forces, as attraction,
affinity; all which objects are abstract ideas. In these
cases we have nothing to do with bodies themselves, but as
the vehicles of the powers and properties which we
contemplate.

Natural History, on the other hand, has to do with natural
bodies: their properties are not considered abstractedly,
but only as characters. If the properties are abstracted, it
is but for a moment. Natural history has to describe and
class bodies as they are. All which cannot be perceived by
the senses, belongs not to its domain, as molecules, atoms,
elements.

Natural history[50\8] may have recourse to physics or
chemistry in order to recognize those properties of bodies
which serve as characters; but natural history is not, on
that account, physics or chemistry. Classification is the
essential business of the natural historian[51\8], to which
task chemistry and physics are only instrumental, and the
further account of properties only complementary.

[Note 50\8: _Ib._ p. 37.]

[Note 51\8: _Ib._ p. 41.]

It has been said, in support of the doctrine that chemistry
and mineralogy are identical, that chemistry does not
neglect external characters. 'The chemist in {147}
describing sulphur, mentions its colour, taste, odour,
hardness, transparence, crystalline form, specific gravity;
how does he then differ from the mineralogist?' But to this
it is replied, that these notices of the external characters
of this or any substance are introduced in chemistry merely
as convenient marks of recognition; whereas they are
essential in mineralogy. If we had taken the account given
of several substances instead of one, we should have seen
that the chemist and the naturalist consider them in ways
altogether different. The chemist will make it his business
to discover the mutual action of the substances; he will
combine them, form new products, determine the proportions
of the elements. The mineralogist will divide the substances
into groups according to their properties, and then
subdivide these groups, till he refers each substance to its
species. Exterior and physical characters are merely
accessory and subordinate for the chemist; chemistry is
merely instrumental for the mineralogist.

This view agrees with that to which we have been led by our
previous reasonings; and may, according to our principles,
be expressed briefly by saying, that the Idea which
Chemistry has to apply is the Idea of Elementary
Composition, while Natural History applies the Idea of
Graduated Resemblances, and thus performs the task of
classification.

9. The question occurs[52\8], whether Natural History can be
applied to Inorganic Substances? And the answer to this
question is, that it can be applied, if there are such
things as inorganic individuals, since the resemblances and
differences with which natural history has to do are the
resemblances and differences of individuals.

[Note 52\8: _Règne Mineral_, p. 46.]

What is an Individual? It certainly is not that which is so
simple that it cannot be divided. Individual animals are
composed of many parts. But if we examine, we shall find
that our Idea of an Individual is, that it is a whole
composed of parts, which {148} are not similar to the whole,
and have not an independent existence, while the whole has
an independent existence and a definite form[53\8].

[Note 53\8: _Règne Mineral_, p. 52.]

What then is the Mineralogical Individual? At first, while
minerals were studied for their use, the most precious of
the substances which they contained was looked upon as the
characteristic of the mineral. The smallest trace of silver
made a mineral an _ore of silver_. Thus forms and properties
were disregarded, and _substance_ was considered as
identical with _mineral_. And hence[54\8] Daubenton refused
to recognize _species_ in the mineral kingdom, because he
recognized no individuals. He proposed to call _sorts_ what
we call species. In this way of considering minerals, there
are no individuals.

[Note 54\8: _Ib._ p. 54.]

10. But still this is not satisfactory: for if we take a
well-formed and distinct crystal, this clearly _is_ an
individual[55\8].

[Note 55\8: _Ib._ p. 56.]

It may be objected, that the crystal is divisible (according
to the theory of crystallography) into smaller solids; that
these small solids are really the simple objects; and that
actual crystals are formed by combinations of these
molecules according to certain laws.

But, as we have already said, an individual is such, not
because it cannot be divided, but because it cannot be
divided into parts similar to the whole. As to the division
of the form into its component _laws_, this is an abstract
proceeding, foreign to natural history[56\8]. Therefore
there is so far nothing to prevent a crystal from being an
individual.

[Note 56\8: _Ib._ p. 58.]

11. We cannot (M. Necker goes on to remark) consider the
_Integrant Molecules_ as individuals. These are useful
abstractions, but abstractions only, which we must not deal
with as real objects. Haüy himself warns us[57\8] that his
doctrine of increments is a purely abstract conception, and
that nature, in fact, follows a different process.
Accordingly, Weiss and Mohs express laws identical with
those of Haüy, without even {149} speaking of molecules; and
Wollaston and Davy have deemed it probable that the
molecules are not polyhedrons, but spheres or spheroids.
Such mere creations of the mind can never be treated as
individuals. If the maxim of natural history,--that the
Species is a collection of Individuals--be applied so as to
make those individuals mere abstractions; or if, instead of
Individuals, we take such an abstraction as Substance or
Matter, the course of natural history is altogether
violated. And yet this errour has hitherto generally
prevailed; and mineralogists have classified, not things,
but abstract ideas[58\8].

[Note 57\8: _Ib._ p. 61.]

[Note 58\8: _Règne Mineral_, p. 67.]

12. But it may be said[59\8], will not the small solids
obtained by Cleavage better answer the idea of individuals?
To this it is replied, that these small solids have no
independent existence. They are only the result of a mode of
division. They are never found separate and independent. The
secondary forms which they compose are determined by various
circumstances (the nature of the solution, &c.); and the
cleavage which produces these small solids is only one
result among many, from the crystalline forces[60\8].

[Note 59\8: _Ib._ p. 69.]

[Note 60\8: _Ib._ p. 71.]

Thus neither Integrant Molecules, nor Solids obtained by
Cleavage, can be such mineralogical Individuals as the
spirit of natural history requires. Hence it appears that we
must take the real Crystals for Individuals[61\8].

[Note 61\8: _Ib._ p. 73.]

13. We must, however, reject crystals (generally large ones)
which are obviously formed of several smaller ones of a
similar form (as occurs so often in quartz and calc spar).
We must also distinguish cases in which a large regular form
is composed of smaller but different regular forms (as
octahedrons of fluor spar made up of cubes). Here the small
component forms are the individuals. Also we must notice the
cases[62\8] in which we have a natural crystal, similar to
the primary form. Here the face will show whether {150} the
body is a result obtained by cleavage or a natural individual.

[Note 62\8: _Ib._ p. 75.]

14. It will be objected[63\8], that the crystalline form
ought not to be made the dominant character in mineralogy,
since it rarely occurs perfect. To this it is replied, that
even if the application of the principle be difficult, still
it has been shown to be the only true principle, and
therefore we have no alternative. But further[64\8], it is
not true that amorphous substances are more numerous than
crystals. In Leonhard's _Manual of Oryctognosy_, there are
377 mineral substances. Of these, 281 have a crystalline
structure, and 96 only have not been found in a regular form.

[Note 63\8: _Règne Mineral_, p. 79.]

[Note 64\8: _Ib._ p. 82.]

Again, the 281 crystalline forms have each its varieties,
some of which are crystalline, and some are not so. Now the
crystalline varieties amount to 1453, and the uncrystalline
to 186 only. Thus mineralogy, according to the view of it
here presented, has a sufficiently wide field[65\8].

[Note 65\8: _Ib._ p. 84.]

15. It will be objected[66\8], that according to this mode
of proceeding, we must reject from our system all
non-crystalline minerals. But we reply, that if the mass be
composed of crystals, the size of the crystals makes no
difference. Now lamellar and other compact masses are very
generally groups of crystals in various positions.
Individuals mutilated and mixed together are not the less
individuals; and therefore such masses may be treated as
objects of natural history.

[Note 66\8: _Ib._ p. 86.]

If we cannot refer all rocks to crystalline species, those
which elude our method may appear as an appendix,
corresponding to those plants which botanists call _genera
incertæ sedis_[67\8].

[Note 67\8: _Ib._ p. 91.]

But these genera and species will often be afterwards
removed into the crystalline part of the system, by being
identified with crystalline species. Thus _pyrope_, &c.,
have been referred to _garnet_, and _basalt_, {151} _wacke_,
&c., to compound rocks. Thus veins of _Dolerite_, visibly
composed of two or three elements, pass to an apparently
simple state by becoming fine-grained[68\8].

[Note 68\8: _Règne Mineral_, p. 93.]

16. Finally[69\8], we have to ask, are artificial crystals
to enter into our classification? M. Necker answers, No;
because they are the result of art, like mules, mestizos,
hybrids, and the like.

[Note 69\8: _Ib._ p. 95.]

17. Upon these opinions, we may observe, that they appear to
be, in the main, consistent with the soundest philosophy.
That each natural crystal is an individual, is a doctrine
which is the only basis of Mineralogy as a Natural
Historical Science; yet the imperfections and confused
unions of crystals make this principle difficult to apply.
Perhaps it may be expressed in a more precise manner by
referring to the crystalline forces, and to the axes by
which their operation is determined, rather than to the
external form. _That_ portion of a mineral substance is a
mineralogical _individual_ which is determined by
crystalline forces acting to the _same axes_. In this way we
avoid the difficulty arising from the absence of faces, and
enable ourselves to use either cleavage, or optical
properties, or any others, as indications of the identity of
the individual. The individual extends so far as the polar
forces extend by which crystalline form is determined,
whether or not those forces produce their full effect,
namely, a perfectly circumscribed polyhedron.

18. There is only one material point on which our principles
lead us to differ from M. Necker;--the propriety of
including _artificial crystals_ in our mineralogical
classification. To exclude them, as he does, is a conclusion
so entirely at variance with the whole course of his own
reasonings, that it is difficult to conceive that he would
persist in his conclusion, if his attention were drawn to
the question more steadily. For, as he justly says[70\8],
each science has its appropriate domain, determined by its
peculiar point of view. Now artificial and natural crystals
are considered in the same point of view, (namely, with
reference to {152} crystalline, physical, and optical
properties, as subservient to classification,) and ought,
therefore, to belong to the same science. Again, he
says[71\8], that Chemistry would reject as useless all
notice of the physical properties and external characters of
substances, if a _special science_ were to take charge of
the description and classification of these products. But
such a special science must be Mineralogy; for we cannot
well make one science of the classification of natural, and
another of that of artificial substances: or if we do, the
two sciences will be identical in method and principles, and
will extend over each other's boundaries, so that it will be
neither useful nor possible to distinguish them. Again, M.
Necker's own reasonings on the selection of the individual
in mineralogy are supported by well chosen examples[72\8];
but these examples are taken from artificial salts; as, for
instance, common salt crystallizing in different mixtures.
Again, the analogy of mules and mestizos, as products of
art, with chemical compounds, is not just. Chemical
compounds correspond rather to natural species, propagated
by man under the most natural circumstances, in order that
he may study the laws of their production[73\8].

[Note 70\8: _Ib._ p. 23.]

[Note 71\8: _Règne Mineral_, p. 36.]

[Note 72\8: _Ib._ p. 71.]

[Note 73\8: We may remark that M. Necker, in his own
arrangement of minerals, inserts among his species Iron and
Lead, which do not occur Native.]

19. But the decisive argument against the separation of
natural and artificial crystals in our schemes of
classification is, that we _cannot_ make such a separation.
Substances which were long known only as the products of the
laboratory, are often discovered, after a time, in natural
deposits. Are the crystals which are found in a forgotten
retort or solution to be considered as belonging to a
different science from those which occur in a deserted mine?
And are the crystals which are produced where man has turned
a stream of water or air out of its course, to be separated
from natural crystals, when the composition, growth, and
properties, are exactly the same in both? And again: How
many natural crystals can we already produce by {153}
synthesis! How many more may we hope to imitate hereafter!
M. Necker himself states[74\8], that Mitscherlich found, in
the scoriæ of the mines of Sweden and Germany, artificial
minerals having the same composition and the same
crystalline form with natural minerals: as silicates of
iron, lime, and magnesia, agreeing with Peridot; bisilicate
of iron, lime, and magnesia, agreeing with Pyroxene; red
oxide of copper; oxide of zinc; protoxide of iron (_fer
oxydulé_); sulphurets of iron, zinc, lead; arseniuret of
nickel; black mica. These were accidental results of fusion.
But M. Berthier, by bringing together the elements in proper
quantities, has succeeded in composing similar minerals, and
has thus obtained artificial silicates, with the same forms
and the same characters as natural silicates. Other chemists
(M. Haldat, M. Becquerel) have, in like manner, obtained, by
artificial processes, other crystals, known previously as
occurring naturally. How are these crystals, thus identical
with natural minerals, to be removed out of the domain of
mineralogy, and transferred to a science which shall
classify artificial crystals only? If this be done, the
mineralogist will not be able to classify any specimen till
he has human testimony whether it was found naturally
occurring or produced by chemical art. Or is the other
alternative to be taken, and are these crystals to be given
up to mineralogy because they occur naturally also? But what
can be more unphilosophical than to refer to separate
sciences the results of chemical processes closely allied,
and all but identical? The chemist constructs bisilicates,
and these are classified by the mineralogist: but if he
constructs a trisilicate, it belongs to another science. All
these intolerable incongruities are avoided by acknowledging
that artificial, as well as natural, crystals belong to the
domain of mineralogy. It is, in fact, the _name_ only of
_Mineralogy_ which appears to discover any inconsistency in
this mode of proceeding. Mineralogy is the {154}
representative of a science which has a wider office than
mineralogists first contemplated; but which must exist, in
order that the body of science may be complete. There must,
as we have already said, be a Science, the object of which
is to classify bodies by their physical characters, in order
that we may have some means of asserting chemical truths
concerning bodies; some language in which we may express the
propositions which chemical analysis discovers. And this
Science will have its object prescribed, not by any
accidental or arbitrary difference of the story belonging to
each specimen;--not by knowing whether the specimen was
found in the mine or in the laboratory; produced by
attempting to imitate nature, or to do violence to her:--but
will have its course determined by its own character. The
range and boundaries of this Science will be regulated by
the Ideas with which it deals. Like all other sciences, it
must extend to everything to which its principles apply. The
limits of the province which it includes are fixed by the
consideration that it must be a connected whole. No previous
definition, no historical accident, no casual phrase, can at
all stand in the way of philosophical consistency;--can make
this Science exclude what that includes, or oblige it to
admit what that rejects. And thus, whatever we call our
Science;--whether we term it External Chemistry, Mineralogy,
the Natural History of Inorganic Bodies;--since it can be
nothing but the Science of the Classification of Inorganic
Bodies of definite forms and properties, it must classify
all such bodies, whether or not they be minerals, and
whether or not they be natural.

[Note 74\8: _Règne Mineral_, p. 151.]

20. In the application of the principles of classification
to minerals, the question occurs, What are to be considered
as mineral _Species_? By Species we are to understand,
according to the usage of other parts of natural history,
the lowest step of our subordinate divisions;--the most
limited of the groups which have definite distinctions. What
definite distinctions of groups of objects of any kind
really occur in nature, is to be learnt from an examination
of nature: and the {155} result of our inquiries will be
some general principle which connects the members of each
group, and distinguishes the members of groups which, though
contiguous, are different. In the classification of
organized bodies, the rule which thus presides over the
formation of Species is the principle of _reproduction_.
Those animals and those plants are of the same Species which
are produced from a common stock, or which resemble each
other as much as the progeny of a common stock. Accordingly
in practice, if any questions arise whether two varieties of
form in organic things be of the same or different species,
it is settled by reference to the fact of reproduction; and
when it is ascertained that the two forms come within the
habitual and regular limits of a common circle of
reproduction, they are held to be of the same species. Now
in crystals, this principle of reproduction disappears
altogether, and the basis of the formation of species must
be sought elsewhere. We must have some other principle to
replace the reproduction which belongs only to organic life.
This principle will be, we may expect, one which secures the
permanence and regularity of mineral forms, as the
reproductive power does of animal and vegetable. Such a
principle is the _Power of Crystallization_. The forces of
which solidity, cohesion, and crystallization are the
result, are those which give to minerals their permanent
existence and their physical properties; and ever since the
discovery of the distinctions of Crystalline Forms and
Crystalline Systems, it is certain that this force
distinguishes groups of crystals in the most precise and
definite manner. The rhombohedral carbonates of lime and of
iron, for instance, are distinguished exactly by the angles
of their rhombohedrons. And if, in the case of any proposed
crystal, we should doubt to which kind the specimen belongs,
the measurement of the angles of cleavage would at once
decide the question. The principle of Crystallization
therefore appears, from analogy, to be exactly fitted to
take the place of the principle of organic Generation. The
forces which make the individual permanent and its
properties definite, here stand in the place of the forces
{156} which preserve the race, while individuals are
generated and die.

21. According to this view, the different Modifications of
the _same_ crystalline form would be _Varieties_ only of the
same Species. All the various solids, for example, which are
produced by the different laws of derivation of rhombohedral
carbonate of lime, would fall within the same Species. And
this appears to be required by the general analogy of
Natural History. For these differences of form, produced by
the laws of crystalline derivation, are not _definite_. The
faces which are added to one form in order to produce
another, may be of any size, small or large, and thus the
crystal which represents one modification passes by
insensible degrees to another. The forms of calc spar, which
we call _dog-tooth spar_, _cannon spar_, _nail-head spar_,
and the like, appear at first, no doubt, distinct enough;
but so do the races of dogs. And we find, in the mineral as
in the animal, that the distinction is obliterated by taking
such intermediate steps as really occur. And if a _fragment_
of any of these crystals is given us, we can determine that
it is rhombohedral carbonate of lime; but it is not
possible, in general, to determine to which of the kinds of
crystals it has belonged.

22. Notwithstanding these considerations, M. Necker has
taken for his basis of mineral species[75\8] the _Secondary_
Modifications, and not the Primary Forms. Thus _cubical
galena_, _octahedral galena_, and _triform galena_, are,
with him, three _species_ of crystals.

[Note 75\8: _Règne Mineral_, p. 396.]

On this I have to observe, as I have already done, that on
this principle we have no _definite_ distinction of species;
for these forms may and do pass into each other: among
cubo-octahedrons of galena occur cubes and octahedrons, as
one face or another vanishes, and the transition is
insensible. We shall, on this principle, find almost always
three or four species in the same tuft of crystals; for
almost every individual in such assemblages may exhibit a
different combination of {157} secondary faces. Again, in
cases where the secondary laws are numerous, it would be
impracticable to enumerate all their combinations, and
impossible therefore to give a list of species. Accordingly
M. Necker[76\8] gives seventy-one Species of _spath
calcaire_, and then says, 'Nous n'avons pas énumeré la
dixième partie des espèces connues de ce genre, qui se
montent à plus de huit cents.' Again, in many substances, of
which few crystals are found, every new specimen would be a
new species; if indeed it were perfect enough to be referred
to a species at all. But from a specimen without perfect
external form, however perfect in crystalline character,
although everything else might be known,--angles, optical
properties, physical properties, and chemical
constitution,--the species could not be determined. Thus M.
Necker says[77\8] of the micas, 'Quant aux espèces propre à
chaque genre, la lacune sera presque complète; car jusqu'ici
les cristaux entiers de Mica et de Talc n'ont pas été fort communs.'

[Note 76\8: _Règne Mineral_, p. 364.]

[Note 77\8: _Ib._ ii. 414.]

These inconveniences arise from neglecting the leading rule
of natural history, that the _predominant principle_ of the
existence of an object must determine the Species; whether
this principle be Reproduction operating for Development, or
Crystallization operating for Permanence of form. We may add
to the above statement of inconveniences this;--that if M.
Necker's view of mineralogical species be adopted, the
distinction of Species is vague and indefinite, while that
of Genera is perfectly precise and rigorous;--an aspect of
the system entirely at variance with other parts of Natural
History; for in all these the Species is a more definite
group than the Genus.

This result follows, as has already been said, from M.
Necker's wish to have individuals marked by external form.
If, instead of this, we are contented to take for an
individual that portion of a mass, of whatever form, which
is connected by the continuous influence of the same
crystalline forces, by whatever incidents these forces may
be manifested, (as cleavage, {158} physical and optical
properties, and the like,) our mode of proceeding avoids all
the above inconveniences, applies alike to the most perfect
and most imperfect specimens, and gives a result agreeable
to the general analogy of natural history, and the rules of
its methods[78\8].

[Note 78\8: I will not again enter into the subject of
Nomenclature; but I may remark that M. Necker has adopted
(i. 415) the Nomenclature of Beudant, latinizing the names,
and thus converting each into a single word. He has also
introduced, besides the names of Genera, names of Families
taken from the _typical_ Genus. Thus the Family of
_Carbonidiens_ contains the following genera:
_Calcispathum_, _Magnesispathum_, _Dolomispathum_,
_Ferrispathum_, _&c._, _Malachita_, _Azuria_, _Gaylusacia_.]

I now quit the subject of mere Resemblance, and proceed to
treat of that natural affinity which Natural Systems of
Classification for organic bodies must involve.

{{159}}
CHAPTER IV.

OF THE IDEA OF NATURAL AFFINITY.

1. IN the Second Chapter of this Book it was shown that
although the Classificatory Sciences proceed ostensibly upon
the Idea of Resemblance as their main foundation, they
necessarily take for granted in the course of their progress
a further Idea of Natural Affinity. This appeared[79\8] by a
general consideration of the nature of Science, by the
recognition of natural species and genera, even in
Artificial Systems of Classification[80\8], and by the
**attempts of botanists to form a Natural System. It further
appeared that among the processes by which endeavours have
been made to frame a Natural System, some, as the method of
_Blind Trial_ and the method of _General Comparison_, have
been altogether unsuccessful, being founded only upon a
collection of resemblances, casual in the one case and
arbitrary in the other. In neither of these processes is
there employed any general principle by which we may be
definitely directed as to what resemblances we should
employ, or by which the result at which we arrive may be
verified and confirmed. Our object in the present chapter is
to show that the Idea of Natural Affinity supplies us with a
principle which may answer such purposes.

[Note 79\8: Art. 5.]

[Note 80\8: Art. 7.]

I shall first consider the Idea of Affinity as exemplified
in organized beings. In doing this, we may appear to take
for granted Ideas which have not yet come under our
discussion, as the Ideas of Organization, and Vital
Function; but it will be found that the principle to which
we are led is independent of these additional Ideas. {160}

2. We have already seen that the attempts to discover the
divisions which result from this Natural Affinity have led
to the consideration of the _Subordination of Characters_.
It is easy to see that some organs are more essential than
others to the existence of an organized being; the organs of
nutrition, for example, more essential than those of
locomotion. But at the same time it is clear that any
_arbitrary_ assumption of a certain scale of relative values
of different kinds of characters will lead only to an
Artificial System. This will happen, if, for example, we
begin by declaring the nutritive to be superior in
importance to the reproductive functions. It is clear that
this relation of importance of organs and functions must be
collected by the study of the organized beings; and cannot
be determined _à priori_, without depriving us of all right
to expect a general accordance between our system and the
arrangement of nature. We see, therefore, that our notion of
Natural Affinity involves in it this consequence;--that it
is not to be made out by an arbitrary subordination of characters.

3. The functions and actions of living things which we
separate from each other in our consideration, cannot be
severed in nature. Each function is essential; Life implies
a collection of movements, and ceases when any of these
movements is stopped. A change in the organization
subservient to one set of functions may lead necessarily to
a change in the organization belonging to others. We can
often see this necessary connexion; and from a comparison of
the forms of organized beings,--from the way in which their
structure changes in passing from one class to another, we
are led to the conviction that there is some general
principle which connects and graduates all such changes.
When the circulatory system changes, the nervous system
changes also: when the mode of locomotion changes, the
respiration is also modified.

4. These corresponding changes may be considered as ways in
which the living thing is fitted to its mode of life; as
marks of _adaptation to a purpose_; or, as it has been
otherwise expressed, as results of the {161} _conditions of
existence_. But at the present moment, we put forward these
correspondencies in a different light. We adduce them as
illustrations of what we mean by Affinity, and what we
consider as the tendency of a Natural Classification. It has
sometimes been asserted that if we were to classify any of
the departments of organized nature by means of one
function, and then by means of another, the two
classifications, if each strictly consistent with itself,
would be consistent with each other. Such an assertion is
perhaps more than we are entitled to make with confidence;
but it shows very well what is meant by Affinity. The
disposition to believe such a general identity of all
partial natural classifications, shows how readily we fix
upon the notion of Affinity, as a general result of the
causes which determine the forms of living things. When
these causes or principles, of whatever nature they are
conceived to be, vary so as to modify one part of the
organization of the being, they also modify another: and
thus the groups which exhibit this variation of the
fundamental principles of form, are the same, whether the
manifestation of the change be sought in one part or in
another of the organized structure. The groups thus formed
are related by Affinity; and in proportion as we find the
evidence of more functions and more organs to the propriety
of our groups, we are more and more satisfied that they are
Natural Classes. It appears, then, that our Idea of Affinity
involves the conviction of the _Coincidence of natural
arrangements formed on different functions_; and this,
rather than the principle of the Subordination of some
characters to others, is the true ground of the natural
method of Classification.

5. For example, Cuvier, after speaking of the Subordination
of Characters as the guide which he intends to follow in his
arrangement of animals, interprets this principle in such a
manner[81\8] as to make it agree nearly with the one just
stated: 'In pursuance of what has been said on methods in
general, we now require to {162} know what characters in
animals are the most influential, and therefore those which
must be made the grounds of the primary divisions.' 'These,'
he says, 'it is clear must be those which are taken from the
animal functions;--sensation and motion:'--But how does he
confirm this? Not by showing that the animal functions are
independent of, or predominant over, the vegetative, but by
observing that they follow the same gradations.
'Observation,' he continues, 'confirms this view, by showing
that the degrees of development and complication of the
animal functions agree with those of the vegetative. The
heart and the organs of the circulation are a sort of center
for the vegetative functions, as the brain and the trunk of
the nervous system are for the animal functions. Now we see
these two systems descend in the scale, and disappear the
one with the other. In the lowest animals, when there are no
longer any distinct nerves, there are also no longer
distinct fibres, and the organs of digestion are simply
hollowed out in the homogeneous mass of the body. The
muscular system disappears even before the nervous, in
insects; but in general the distribution of the medullary
masses corresponds to that of the muscular instruments; a
spinal cord, on which knots or ganglions represent so many
brains, corresponds to a body divided into numerous rings
and supported on pairs of members placed at different points
of the length, and so on.

[Note 81\8: _Règne Animal_, p. 55.]

'This _correspondence_ of the general forms which result
from the arrangement of the motive organs, from the
distribution of the nervous masses, and from the energy of
the circulatory system, must therefore form the ground of
the first great sections by which we divide the animal kingdom.'

6. Decandolle takes the same view. There must be, he says,
_an equilibrium_ of the different functions[82\8]. And he
exemplifies this by the case of the distinction of
monocotyledonous and dicotyledonous plants, which being at
first established by means of the organs of {163}
reproduction, was afterwards found to coincide with the
distinction of endogenous and exogenous, which depends on
the process of nutrition. 'Thus,' he adds, '_the natural
classes founded on one of the great functions of the
vegetable are necessarily the same as those which are
founded upon the other function_; and I find here a very
useful criterion to ascertain whether a class is natural:
namely, in order to announce that it is so, it must be
arrived at by the two roads which vegetable organization
presents. Thus I affirm,' he says, 'that the division of
monocotyledons from dicotyledons, and the distinction of
Gramineæ from Cyperaceæ, are real, because in these cases, I
arrive at the same result by the reproductive and the
nutritive organs; while the distinction of monopetalous and
polypetalous, of Rhodoraceæ and Ericineæ, appears to me
artificial, because I can arrive at it only by the
reproductive organs.'

[Note 82\8: _Theor. Elem._ p. 79.]

Thus the Correspondence of the indications of different
functions is the criterion of Natural Classes; and this
correspondence may be considered as one of the best and most
characteristic marks of the fundamental Idea of Affinity.
And the Maxim by which all Systems professing to be natural
must be tested is this:--that the _arrangement obtained from
one set of characters coincides with the arrangement
obtained from another set_.

This Idea of Affinity, as a natural connexion among various
species, of which connexion all particular resemblances are
indications, has principally influenced the attempts at
classifying the animal kingdom. The reason why the
classification in this branch of Natural History has been
more easy and certain than that of the vegetable world is,
as Decandolle says[83\8], that besides the functions of
nutrition and reproduction, which animals have in common
with plants, they have also in addition the function of
sensation; and thus have a new means of verification and
concordance. But we may add, as a further reason, that the
functions of {164} animals are necessarily much more obvious
and intelligible to us than those of vegetables, from their
clear resemblance to the operations which take place in our
own bodies, to which our attention has necessarily been
strongly directed.

[Note 83\8: _Theor. Elem._ p. 80.]

7. The question here offers itself, whether this Idea of
Natural Affinity is applicable to inorganic as well as to
organic bodies;--whether there be Natural Affinities among
Minerals. And to this we are now enabled to reply by
considering whether or not the principle just stated is
applicable in such cases. And the conclusion to which our
principle leads us is,--that there are such Natural
Affinities among Minerals, since there are different sets of
characters which may be taken, (and have by different
writers been taken,) as the basis of classification. The
hardness, specific gravity, colour, lustre, crystallization,
and other _external_ characters, as they are termed, form
one body of properties according to which minerals may be
classified; as has in fact been done by Mohs, Breithaupt,
and others. The _chemical_ constitution of the substances,
on the other hand, may be made the principle of their
arrangement, as was done by Haüy, and more recently, and on
a different scheme, by Berzelius. Which of these is the true
and natural classification? To this we answer, that _each_
of these arrangements is true and natural, then, and then
only, when it coincides with the other. An arrangement by
external characters which gives us classes possessing a
common chemical character;--a chemical order which brings
together like and separates unlike minerals;--such
classifications have the evidence of truth in their
agreement with one another. Every classification of minerals
which does not aim at and tend to such a result, is so far
merely arbitrary; and cannot be subservient to the
expression of general chemical and mineralogical truths,
which is the proper purpose of such a classification.

8. In the History of Mineralogy I have related the advances
which have been made among mineralogists and chemists in
modern times towards a System {165} possessing this
character of truth. I have there described the mixed systems
of Werner and Haüy;--the attempt made by Mohs to form a pure
Natural History system;--the first and second attempt of
Berzelius to form a pure chemical system; and the failure of
both these attempts. But the distinct separation of the two
elements of which science requires the coincidence threw a
very useful light upon the subject; and the succeeding mixed
systems, such as that of Naumann, approached much nearer to
the true conditions of the problem than any of the preceding
ones had done. Thus, as I have stated, several of Naumann's
groups have both a common chemical character and great
external resemblances. Such are his _Anhydrous Unmetallic
Haloids_--his _Anhydrous Metallic Haloids_--_Hydrous
Metallic Haloids_--_Oxides_ of metals--_Pyrites_--_Glances_--
Blendes_. The existence of such groups shows that we may hope
ultimately to obtain a classification of minerals which shall
be both chemically significant, and agreeable to the methods
of Natural History: although when we consider how very imperfect
as yet our knowledge of the chemical composition of minerals is,
we can hardly flatter ourselves that we shall arrive at such a
result very soon.

We have thus seen that in Mineralogy, as well as in the
sciences which treat of organized bodies, we may apply the
Idea of Natural Affinity; of which the fundamental maxim is,
that _arrangements obtained from different sets of
characters must coincide_.

Since the notion of Affinity is thus applicable to inorganic
as well as to organic bodies, it is plain that it is not a
mere modification of the Idea of Organization or Function,
although it may in some of its aspects appear to approach
near to these other Ideas. But these Ideas, or others which
are the foundation of them, necessarily enter in a very
prominent and fundamental manner into all the other parts of
Natural History. To the consideration of these, therefore,
we shall now proceed.

{{167}}
BOOK IX.

THE
PHILOSOPHY
OF
BIOLOGY.

LA vie est donc un TOURBILLON plus ou moins rapide, plus ou
moins compliqué, dont la direction est constante, et qui
entraine toujours des molecules de mêmes sorts, mais où les
molecules individuelles entrent et d'où elles sortent
continuellement, de manière que la _Forme_ du corps vivant
lui est plus essentielle que sa _Matière_.

Tant que ce mouvement subsiste, le corps où il s'exerce est
_vivant_; _il vit_. Lorsque le mouvement s'arrête sans
retour, le corps _meurt_.

CUVIER, _Règne Animal_, s. 12.

I REMEMBER, upon asking our famous Harvey, what induced him
to think of a circulation of the blood, he said, that
observing the valves in the veins of many parts of the body,
so placed as to give a free passage to the blood towards the
heart, but to oppose the passage of the venal blood the
contrary way, he imagined that so provident a cause as
nature had not thus placed so many valves without design;
and as no design seemed more probable than that the blood
could not well, because of the interposing valves, be sent
by the veins to the limbs, it should be sent through the
arteries and return through the veins when valves did not
oppose its course that way.

BOYLE, _On the Final Causes of Natural Things_. On the
Proposition: _'Tis often allowable for a naturalist, from the
manifest and apposite uses of the parts of animal bodies, to
collect some of the particular ends for which the Creator
designed them: and in some cases we may, from the known
nature and structure of the parts, draw particular
conjectures about the particular offices of them._

{{169}}
BOOK IX.

THE PHILOSOPHY OF BIOLOGY.

CHAPTER I.

ANALOGY OF BIOLOGY WITH OTHER SCIENCES.

1. IN the History of the Sciences, after treating of the
Sciences of Classification, we proceeded to what are there
termed the Organical Sciences, including in this term
Physiology and Comparative Anatomy. A peculiar feature in
this group of sciences is that they involve the notion of
_living_ things. The notion of _Life_, however vague and
obscure it may be in men's minds, is apprehended as a
peculiar Idea, not resolvable into any other Ideas, such,
for instance, as Matter and Motion. The separation between
living creatures and inert matter, between organized and
unorganized beings, is conceived as a positive and
insurmountable barrier. The two classes of objects are
considered as of a distinct kind, produced and preserved by
different forces. Whether the Idea of Life is really thus
original and fundamental, and whether, if so, it be one Idea
only, or involve several, it must be the province of true
philosophy to determine. What we shall here offer may be
considered as an attempt to contribute something to the
determination of these questions; but we shall perhaps be
able to make it appear that science is at present only in
the course of its progress towards a complete solution of
such problems.

Since the main feature of those sciences of which we have
now to examine the philosophy is, that they {170} involve
the Idea of Life, it would be desirable to have them
designated by a name expressive of that circumstance. The
word _Physiology_, by which they have most commonly been
described, means _the Science of Nature_; and though it
would be easy to explain, by reference to history, the train
of thought by which the word was latterly restricted to
_Living Nature_, it is plain that the name is,
etymologically speaking, loose and improper. The term
_Biology_, which means exactly what we wish to express, _the
Science of Life_, has often been used, and has of late
become not uncommon among good winters. I shall therefore
venture to employ it, in most cases, rather than the word
_Physiology_.

2. As I have already intimated, one main inquiry belonging
to the Philosophy of Biology, is concerning the Fundamental
Idea or Ideas which the science involves. If we look back at
the course and the results of our disquisitions respecting
other sciences in this work, and assume, as we may
philosophically do, that there will be some general analogy
between those sciences and this, in their development and
progress, we shall be enabled to anticipate in some measure
the nature of the view which we shall now have to take. We
have seen that in other subjects the Fundamental Ideas on
which science depended, and the Conceptions derived from
these, were at first vague, obscure, and confused;--that by
gradual steps, by a constant union of thought and
observation, these conceptions become more and more clear,
more and more definite;--and that when they approached
complete distinctness and precision, there were made great
positive discoveries into which these conceptions entered;
and thus the new precision of thought was fixed and
perpetuated in some conspicuous and lasting truths. Thus we
have seen how the first confused mechanical conceptions
(Force, and the like,) were, from time to time, growing
clearer, down to the epoch of Newton;--how true conceptions
of Genera and of wider classes, gradually unfolded
themselves among the botanists of the sixteenth and
seventeenth centuries;--how the idea of Substance became
steady enough to govern the {171} theories of chemists only
at the epoch of Lavoisier;--how the Idea of Polarity,
although often used by physicists and chemists, is even now
somewhat vague and indistinct in the minds of the greater
part of speculators. In like manner we may expect to find
that the Idea of Life, if indeed _that_ be the governing
Idea of the Science which treats of Living Things, will be
found to have been gradually approaching towards a distinct
and definite form among the physiologists of all ages up to
the present day. And if this be the case, it may not be
considered superfluous, with reference to so interesting a
subject, if we employ some space in tracing historically the
steps of this progress;--the changes by which the originally
loose notion of Life, or of Vital Powers, became more nearly
an Idea suited to the purposes of science.

3. But we may safely carry this analogy between Biology and
other sciences somewhat further. We have seen, in other
sciences, that while men in their speculations were thus
tending towards a certain peculiar Idea, but before they as
yet saw clearly that it was peculiar and independent, they
naturally and inevitably clothed their speculations in
conceptions borrowed from some other extraneous idea. And
the unsatisfactoriness of all such attempts, and the
necessary consequence of this, a constant alteration and
succession of such inappropriate hypotheses, were
indications and aids of the progress which was going on
towards a more genuine form of the science. For instance, we
have seen that in chemistry, so long as men refused to
recognize a peculiar and distinct kind of power in the
_Affinity_ which binds together the elements of bodies, they
framed to themselves a series of hypotheses, each
constructed according to the prevalent ideas of the time, by
which they tried to represent the relation of the compound
to the ingredients:--first, supposing that the elements
bestowed upon the whole qualities _resembling_ their
own:--then giving up this supposition, and imagining that
the properties of the body depended upon the _shape_ of the
component particles;--then, as their view expanded, assuming
that it was {172} not the shape, but the mechanical _forces_
of the particles which gave the body its attributes;--and
finally acquiescing in, or rather reluctantly admitting, the
idea of _Affinity_, conceived as a peculiar power, different
not only from material contact, but from any mechanical or
dynamical attraction.

Now we cannot but think it very natural, if we find that the
history of Biology offers a series of occurrences of the
same nature. The notions of Life in general, or of any Vital
Functions or Vital Forces in particular, are obviously very
loose and vague as they exist in the minds of most men. The
discrepancies and controversies respecting the definitions
of all such terms, which are found in all works on
physiology, afford us abundant evidence that these notions
are not, at least not generally, apprehended with complete
clearness and steadiness. We shall therefore find approaches
and advances, intermediate steps, gradually leading up to
the greatest degree of distinctness which has yet been
attained. And in those stages of imperfect apprehension in
which the notions of Life and of Vital Powers are still too
loose and unformed to be applied independently, we may
expect to find them supported and embodied by means of
hypotheses borrowed from other subjects, and thus, made so
distinct and substantial as to supply at least a temporary
possibility of scientific reasoning upon the laws of life.

4. For example, if we suppose that men begin to speculate
upon the properties of living things, not acknowledging a
peculiar Vital Power, but making use successively of the
knowledge supplied by the study of other subjects, we may
easily imagine a series of hypotheses along which they would pass.

They would probably, first, in this as in other sciences,
have their thoughts occupied by vague and _mystical_ notions
in which material and spiritual agency, natural and
supernatural events, were mixed together without
discrimination, and without any clear notion at all. But as
they acquired a more genuine perception of the nature of
**knowledge, they would naturally try to explain vital
motions and processes by means of {173} such forces as they
had learnt the existence of from other sciences. They might
first have a _mechanical_ hypothesis, in which the
mechanical _Forces_ of the solids and fluids which compose
organized bodies should be referred to, as the most
important influences in the process of life. They might then
attend to the actions which the fluids exercise in virtue of
their _Affinity_, and might thus form a _chemical_ theory.
When they had proved the insufficience of these hypotheses,
borrowed from the powers which matter exhibits in other
cases, they might think themselves authorized to assume some
peculiar power or agency, still material, and thus they
would have the hypothesis of a _Vital Fluid_. And if they
were driven to reject this, they might think that there was
no resource but to assume an immaterial principle of life,
and thus they would arrive at the doctrine of an _Animal Soul_.

Now, through the cycle of hypotheses which we have thus
supposed, physiology has actually passed. The conclusions to
which the most philosophical minds have been led by a survey
of this progress is, that by the failure of all these
theories, men have exhausted this path of inquiry, and shown
that scientific truth is to be sought in some other manner.
But before I proceed further to illustrate this result, it
will be proper, as I have already stated, to exhibit
historically the various hypotheses which I have described.
In doing this I shall principally follow the _History of
Medicine_ of Sprengel. It is only by taking for my guide a
physiologist of acknowledged science and judgment, that I
can hope, on such a subject, to avoid errours of detail. I
proceed now to give in succession an account of the
Mystical, the Iatrochemical, the Iatromathematical, and the
Vital-Fluid Schools; and finally of the Psychical School,
who hold the Vital Powers to be derived from the Soul
(_Psyche_).

{{174}}
CHAPTER II.

SUCCESSIVE BIOLOGICAL HYPOTHESES.

SECT. I.--_The Mystical School._

IN order to abbreviate as much as can conveniently be done
the historical view which I have now to take, I shall
altogether pass over the physiological speculations of the
ancients, and begin my survey with the general revival of
science in modern times.

We need not dwell long on the fantastical and unsubstantial
doctrines concerning physiology which prevailed in the
sixteenth century, and which flowed in a great measure from
the fertile but ill-regulated imaginations of the
cultivators of Alchemy and Magic. One of the prominent
doctors of this school is the celebrated Paracelsus, whose
doctrines contained a combination of biblical
interpretations, visionary religious notions, fanciful
analogies, and bold experiments in practical medicine. The
opinion of a close but mystical resemblance of parts between
the universe and the human body,--the _Macrocosm_ and the
_Microcosm_,--as these two things, thus compared, were
termed, had probably come down from the Neoplatonists; it
was adopted by the Paracelsists[1\9], and connected with
various astrological dreams and cabbalistic riddles. A
succession of later Paracelsists[2\9], Rosicrucians, and
other fanatics of the same kind, continued into the
seventeenth century. Upon their notions was founded the
pretension of curing wounds by a sympathetic powder, which
Sir Kenelm Digby, among others, asserted; while animal
magnetism, and the transfer of diseases from one person to
another[3\9], were maintained by others of this {175}
school. They held, too, the doctrines of _astral bodies_
corresponding to each terrestrial body; and of the
_signatures_ of plants, that is, certain features in their
external form by which their virtues might be known. How
little advantage or progress real physiology could derive
from speculations of this kind may be seen from this, that
their tendency was to obliterate the distinction between
living and lifeless things: according to Paracelsus, all
things are alive, eat, drink, and excrete; even minerals and
fluids[4\9]. According to him and his school, besides
material and immaterial beings, there are _elementary
Spirit_s which hold an intermediate place, _Sylvans_,
_Nymphs_, _Gnomes_, _Salamanders_, &c. by whose agency
various processes of enchantment may be achieved, and things
apparently supernatural explained. Thus this spiritualist
scheme dealt with a world of its own by means of fanciful
inventions and mystical visions, instead of making any step
in the study of nature.

[Note 1\9: Spr. iii. 456.]

[Note 2\9: _Ib._ iv. 270.]

[Note 3\9: _Ib._ iv. 276.]

[Note 4\9: Spr. iii. 458. Parac. _De Vita Rerum Naturalium_, p. 889.]

Perhaps, however, one of the most fantastical of the
inventions of Paracelsus may be considered as indicating a
perception of a peculiar character in the vital powers.
According to him, the business of digestion is performed by
a certain demon whom he calls _Archæus_, who has his abode
in the stomach, and who, by means of his alchemical
processes, separates the nutritive from the harmful part of
our food, and makes it capable of assimilation[5\9]. This
fanciful notion was afterwards adopted and expanded by Van
Helmont[6\9]. According to him the stomach and spleen are
both under the direction of this Master-spirit, and these
two organs form a sort of _Duumvirate_ in the body.

[Note 5\9: _Ib._ iii. 468.]

[Note 6\9: _Ib._ iv. 302.]

But though we may see in such writers occasional gleams of
physiological thought, the absence of definite physical
relations in the speculations thus promulgated was
necessarily intolerable to men of sound understanding and
scientific tendencies. Such men naturally took hold of that
part of the phenomena of life which could be most distinctly
conceived, and {176} which could be apparently explained by
means of the sciences then cultivated; and this was the part
which appeared to be reducible to chemical conceptions and
doctrines. It will readily be supposed that the processes of
chemistry have a considerable bearing upon physiological
processes, and might, till their range was limited by a
sound investigation, be supposed to have still more than
they really had; and thus a Physiology was formed which
depended mainly upon Chemistry, and the school which held
this doctrine has been called the _Iatrochemical_ School.

SECT. II.--_The Iatrochemical School._

That all physical properties, and therefore chemical
relations, have a material influence on physiological
results, was already recognized, though dimly, in the
Galenic doctrine of the 'four elementary qualities.' But at
the time of Paracelsus, chemical action was more distinctly
than before separated from other kinds of physical action;
and therefore a physiological doctrine, founded upon
chemistry, and freed from the extravagance and mysticism of
the Paracelsists, was a very promising path of speculation.
Andrew Libavius[7\9] of Halle, in Saxony, Physician and
Teacher in the Gymnasium at Koberg, is pointed out by
Sprengel as the person who began to cultivate chemistry, as
distinct from the theosophic fantasies of his predecessors;
and Angelus Sala of Vienna[8\9], as his successor. The
latter has the laudable distinction of having rejected the
prevalent conceits about a potable gold, a universal
medicine, and the like[9\9]. In Germany already at the
beginning of the seventeenth century a peculiar chair of
_Chymiatria_ was already created at Marpurg: and many in
various places pursued the same studies, till, in the middle
of the seventeenth century, we come to Lemery[10\9], the
principal reformer of pharmaceutical chemistry. But we are
not here so much concerned {177} with the practical as with
the theoretical parts of Iatrochemistry; and hence we pass
on to Sylvius[11\9] and his system.

[Note 7\9: Spr. iii. 550.]

[Note 8\9: _Ib._ iv. 281.]

[Note 9\9: _Ib._ iv. 283.]

[Note 10\9: _Ib._ iv. 291.]

[Note 11\9: Spr. iv. 336.]

The opinion that chemistry had an important bearing upon
physiology did not, however, begin with Sylvius. Paracelsus,
among his extravagant absurdities, did some service to
medicine by drawing attention to this important truth. He
used[12\9] chemical principles for the explanation of
particular diseases: most or all diseases according to him,
arise from the effervescence of salts, from the combustion
of sulphur, or from the coagulation of mercury. His
medicines were chemical preparations; and it was[13\9] an
undeniable advantage of the Paracelsian doctrine that
chemistry thus became indispensable to the physician. We
still retain a remnant of the chemical nomenclature of
Paracelsus in the term _tartar_, denoting the stony
concretion which forms on the teeth[14\9]. According to him
there is a certain substance, the basis of all diseases
which arise from a thickening of the juices and a collection
of earthy matter; and this substance he calls _Tartarus_,
because 'it burns like the fire of hell.' Helmont, the
successor of Paracelsus in many absurdities, also followed
him in the attempt to give a chemical account, however loose
and wild, of the functions of the human body; and is by
Sprengel considered, with all his extravagancies, as a
meritorious and important discoverer. The notion of the
fermentation of fluids[15\9], and of the aërial product
thence resulting, to which he gave the name of _Gas_, forms
an important part of his doctrines; and of the six
digestions which he assumes, the _first_ prepares an acid,
which is neutralized by the gall when it reaches the
duodenum, and this constitutes the _second_ digestion.

[Note 12\9: _Ib._ iii. 472.]

[Note 13\9: _Ib._ iii. 482.]

[Note 14\9: _Ib._ iii. 475.]

[Note 15\9: Vol. v. 315.]

I have already, in the History of Chemistry[16\9], stated,
that the doctrine of the opposition of acid and alkali, the
great step which theoretical chemistry owes to Sylvius, was
first brought into view as a physiological {178} tenet,
although we had then to trace its consequences in another
science. The explanation of all the functions of the animal
system, both healthy and morbid, by means of this and other
chemical doctrines, and the prescription of methods of cure
founded upon such explanations, form the scheme of the
_iatrochemical_ school; a school which almost engrossed the
favour of European physicians during the greater part of the
seventeenth century.

[Note 16\9: _Hist. Ind. Sc._ b. xiii. c. 2.]

Sylvius taught medicine at Leyden, from the year 1658, with
so much success, that Boerhaave alone surpassed him[17\9].
His notions, although he piqued himself on their
originality, were manifestly suggested in no small degree
(as all such supposed novelties are) by the speculations of
his predecessors, and the spirit of the times. Like
Helmont[18\9], he considers digestion as consisting in a
fermentation; but he states it more definitely as the
effervescence of an acid, supplied by the saliva and the
pancreatic juice, with the alkali of the gall. By various
other hypothetical processes, all of a chemical nature, the
blood becomes a collection of various juices, which are the
subjects of the speculations of the iatrochemists, to the
entire neglect of the solid parts of the body. Diseases were
accounted for by a supposed prevalence of one or the other
of the acrid principles, the acid or the alkaline: and
Sylvius[19\9] was bold enough to found upon these hypotheses
practical methods of cure, which were in the highest degree
mischievous.

[Note 17\9: Spr. iv. 336.]

[Note 18\9: _Ib._ 338.]

[Note 19\9: _Ib._ iv. 345.]

The Sylvian doctrine was often combined with some of the
notions of the Cartesian system of philosophy; but this
mixture I shall not notice, since my present object is to
trace the history of a mere chemical physiology as one of
the unsuccessful attempts at a philosophy of life. With
various modifications, this doctrine was diffused over
Europe. It gave rise to several controversies, which turned
upon the questions of the novelty of the doctrine, and the
use of chemical remedies to which it pointed, as well as
upon its {179} theoretical truth. We need not dwell long
upon these controversies, although they were carried on with
no small vehemence in their time. Thus the school of Paris
opposed all innovation, remained true to the Galenic
dogmatism, and declared itself earnestly against all
combination of chemistry with medicine; and even against the
chemical preparation of medicaments. Guy Patin, a celebrated
and learned professor of that day, declares[20\9] that the
chemists are no better than forgers, and ought to be
punished as such. The use of antimonial medicines was a main
point of dispute between the iatrochemists and their
opponents; Patin maintained that more men had been destroyed
by antimony than by the thirty years' war of Germany; and
endeavoured to substantiate this assertion by collecting all
such cases in his _Martyrologium Antimonii_. It must have
been a severe blow to Patin when[21\9] in 1666, the Doctors
of the Faculty of Paris, assembled by command of the
parliament, declared, by a majority of ninety-two voices,
that the use of antimonial medicines was allowable and
laudable, and when all attempts to set aside this decision failed.

[Note 20\9: Spr. 349.]

[Note 21\9: _Ib._ iv. 350.]

Florentius Schuyl of Leyden sought to recommend the
iatrochemical doctrines, by maintaining that they were to be
found in the Hippocratic writings; nor was it difficult to
give a chemical interpretation of the humoral pathology of
the ancients. The Italian[22\9] physicians also, for the
most part, took this line, and attempted to show the
agreement of the principles of the ancient school of
medicine with the new chemical notions. This, indeed, is the
usual manner in which the diffusion of new theoretical ideas
becomes universal.

[Note 22\9: _Ib._ 368.]

The progress of the chemical school of medicine in
England[23\9] requires our more especial notice. Willis was
the most celebrated champion of this sect. He assumed, but
with modifications of his own, the three Paracelsian
principles, Salt, Sulphur, and Mercury; considered digestion
as the effect of an acid, and {180} explained other parts of
the animal economy by distillation, fermentation, and the
like. All diseases arise from the want of the requisite
_ferment_; and the physician, he says[24\9], may be compared
to a vintner, since both the one and the other have to take
care that the necessary fermentations go on, that no foreign
matter mixes itself with the wine of life, to interrupt or
derange those operations. In the middle of the seventeenth
century, medicine had reached a point in which the life of
the animal body was considered as merely a chemical process;
the wish to explain everything on known principles left no
recognized difference between organized and unorganized
bodies, and diseases were treated according to this delusive
notion. The condition of chemistry itself during this
period, though not one of brilliant progress, was
sufficiently stable and flourishing to give a plausibility
to any speculation which was founded on chemical principles;
and the real influence of these principles in the animal
frame could not be denied.

[Note 23\9: _Ib._ 353.]

[Note 24\9: Spr. 354.]

The iatrochemists were at first resisted, as we have seen,
by the adherents of the ancient schools; they were attacked
on various grounds, and finally deposed from them ascendancy
by another sect, which we have to speak of, as the
iatromathematical, or mechanical school. This sect was no
less unsatisfactory and erroneous in its positive doctrines
than the chemists had been; for the animal frame is no more
a mere machine than a mere laboratory: but it promoted the
cause of truth, by detecting and exposing the insufficient
explanations and unproved assertions of the reigning theory.

Boyle was one of the persons who first raised doubts against
the current chemical doctrines of his time, as we have
elsewhere noted; but his objections had no peculiar
physiological import. Herman Coming[25\9], the most learned
physician of his time, a contemporary with Sylvius, took a
view more pertinent to our present object; for he not only
rejected the alchemical {181} and hermetical medicines, but
taught expressly that chemistry, in its then existing
condition, was better fitted to be of use in the practice of
pharmacy, than in the theories of physiology and pathology.
He made the important assertion, also, that chemical
principles do not pre-exist _as such_ in the animal body;
and that there are higher powers which operate in the
organic world, and which do not depend on the form and
mixture of matter.

[Note 25\9: _Ib._ iv. 361.]

Attempts were made to prove the acid and alkaline nature of
the fluids of the human body by means of experiments, as by
John Viridet of Geneva[26\9], and by Raimond
Vieussens[27\9], the latter of whom maintained that he had
extracted an acid from the blood, and detected a ferment in
the stomach. In opposition to him, Hecquet, a disciple of
the iatromathematical school, endeavoured to prove that
digestion was performed, not by means of fermentation, but
by trituration. Hecquet's own opinions cannot be defended;
but his objections to the chemical doctrines, and his
assertion of the difference of chemical and organical
processes, are evidences of just thought[28\9].

[Note 26\9: Spr. iv. 329.]

[Note 27\9: _Ib._ 350, (1715).]

[Note 28\9: _Ib._ 401.]

The most important opponents of the iatrochemical school
were Pitcairn in England, Bohn and Hoffman in Germany, and
Boerhaave in Holland. These eminent physicians, about the
end of the seventeenth century, argued on the same grounds
of observation, that digestion is not fermentation, and that
the Sylvian accounts of the origin of diseases by means of
acid and alkali are false. The arguments and authority of
these and other persons finally gained an ascendancy in the
medical world, and soon after this period we may consider
the reign of the chemical school of physiology as past. In
fact, the attempts to prove its assertions experimentally
were of the feeblest kind, and it had no solid basis on
which it could rest, so as to resist the shock of the next
hypothesis which the progress of the physical sciences might
impel against it. We may, therefore, now consider the
opinion of the mere {182} chemical nature of the vital
processes as disproved, and we proceed next to notice the
history of another unsuccessful essay to reduce vital
actions to known actions of another kind.

SECT. III.--_The Iatromathematical School._

In the first Section of this chapter, we enumerated the
biological hypotheses which at first present themselves, as
the mystical, the mechanical, the chemical. We might have
expected that they should occur to men's minds in the order
thus stated: and in fact they did so; for the physiology of
the ancient materialists, as Democritus and Lucretius, is
mechanical so far as it is at all distinct in its views, and
thus the mechanical preceded the chemical doctrine. But in
modern times, the fluid or chemical physiology was developed
before the solid or mechanical: of which the reason appears
to have been this;--that Mechanics and Chemistry began to
assume a scientific character about the same time; and that
of the two, Chemistry not only appeared at first sight more
applicable to the functions of the body, because all the
more rapid changes appear to be connected with modifications
of the fluids of the animal system, but also, by its wider
range of facts and more indefinite principles, afforded a
better temporary refuge for the mind when perplexed by the
difficulties and mysteries which spring out of the
speculations concerning life. But if Chemistry was thus at
first a more inviting field for the physiologist, Mechanics
soon became more attractive in virtue of the splendid
results obtained by the schools of Galileo and Newton. And
when the insufficiency of chemical physiology was discovered
by trial, as we have seen it was, the hope naturally arose,
that the mechanical principles which had explained so many
of the phenomena of the external universe might also be
found, applicable to the smaller world of material
life;--that the _microcosm_ as well as the _macrocosm_ might
have its mechanical principles. From this hope sprung the
{183} Iatromathematical School, or school of Mechanical
Physiologists.

We may, however, divide this school into two parts, the
Italian, and the Cartesio-Newtonian sect. The former
employed themselves in calculating and analysing a number of
the properties of the animal frame which are undoubtedly
mechanical; the latter, somewhat intoxicated by the supposed
triumphs of the corpuscular philosophy, endeavoured to
extend these to physiology, and for this purpose introduced
into the subject many arbitrary and baseless hypotheses. I
will very briefly mention some of the writers of both these sects.

The main points to which the Italian or genuine Mechanical
Physiologists attended, were the application of mechanical
calculations to the force of the muscles, and of hydraulical
reasonings to the motion of the fluids of the animal system.
The success with which Galileo and his disciples had pursued
these branches of mechanical philosophy, and the ascendancy
which they had obtained, first in Italy, and then in other
lands, made such speculations highly interesting. Borelli
may be considered as the first great name in his line, and
his book, _De Motu Animalium_, (_Opus Posthumum_, Romæ,
1680,) is even now a very instructive treatise on the forces
and action of the bones and muscles. This, certainly one of
the most valuable portions of mechanical physiology, has not
even yet been so fully developed as it deserves, although
John Bernoulli[29\9] and his son Daniel[30\9] applied to it
the resources of analysis, and Pemberton[31\9] in England,
pursued the same subject. Other of these mechanico-physiological
problems consisted in referring the pressure of the blood
and of the breath to hydrostatical principles. In this
manner Borelli was led to assert that the muscles of the
heart exert a force of 180,000 pounds[32\9]. But a little
later, Keill reduced this force {184} to a few ounces[33\9].
Keill and others attempted to determine, on similar
principles, the velocity of the blood; we need not notice
the controversies which thus arose, since there is not
involved in them any peculiar physiological principle.

[Note 29\9: _De Motu Musculorum_.]

[Note 30\9: _Act. Acad. Petrop._]

[Note 31\9: _Course of Physiology_, 1773.]

[Note 32\9: Spr. iv. 110.]

[Note 33\9: Spr. iv. 443.]

The peculiar character of the iatromathematical school, as
an attempt at physiological theory, is more manifest in its
other section, which we have called the Cartesio-Newtonian.
The Cartesian system pretended to account for the
appearances and changes of bodies by means of the size,
figure, and motion of their minute particles. And though
this system in its progress towards the intellectual empire
of Europe was suddenly overturned by the rise of the
Newtonian philosophy, these corpuscular doctrines rather
gained than lost by the revolution; for the Newtonian
philosophy enlarged the powers of the corpuscular
hypothesis, by adding the effects of the attractive and
repulsive forces of particles to those of their form and
motion. By this means, although Newton's discoveries did not
in fact augment the probability of the corpuscular
hypothesis, they so far increased its plausibility, that
this hypothesis found favour both with Newton himself and
his contemporaries, no less than it had done with the
Cartesians.

The attempt to apply this corpuscular hypothesis to
physiology was made by Des Cartes himself. The general
character of such speculations may easily be guessed[34\9].
The secretions are effected by the organs operating after
the manner of sieves. Bound particles pass through
cylindrical tubes, pyramidal ones through triangular pores,
cubical particles through square apertures, and thus
different kinds of matter are separated. Similar
speculations were pursued by other mathematicians: the
various diameter of the vessels[35\9], their curvatures,
folds, and angles, were made subjects of calculation.
Bellini, Donzellini, Gulielmini, in Italy; Perrault, Dodart,
in France; Cole, Keill, Jurin, in England, were the
principal cultivators of such studies. {185} In the earlier
part of the eighteenth century, physiological theorists
considered it as almost self-evident that their science
required them to reason concerning the size and shape of the
particles of the fluids, the diameter and form of the
invisible vessels. Such was, for instance, the opinion of
Cheyne[36\9], who held that acute fevers arise from the
obstruction of the glands, which occasions a more vehement
motion of the blood. Mead, the physician of the King, and
the friend of Newton, in like manner explained the effects
of poisons by hypotheses concerning the form of their
particles[37\9], as we have already seen in speaking of chemistry.

[Note 34\9: _Ib._ 329.]

[Note 35\9: _Ib._ 432.]

[Note 36\9: Spr. iv. 223.]

[Note 37\9: _ Mechanical Account of Poisons_, 1702.]

It is not necessary for us to dwell longer on this subject,
or to point out the total insufficiency of the mere
mechanical physiology. The iatrochemists had neglected the
effect of the solids of the living frame; the
iatromathematicians attended only to these[38\9]. And even
these were considered only as canals, as cords, as levers,
as lifeless machines. These reasoners never looked for any
powers of a higher order than the cohesion, the resistance,
the gravity, the attraction, which operate in inert matter.
If the chemical school assimilated the physician to a
vintner or brewer, the mechanical physiologists made him an
hydraulic engineer; and, in fact, several of the
iatromathematicians were at the same time teachers of
engineering and of medicine.

[Note 38\9: Spr. iv. 419.]

Several of the reasoners of this school combined chemical
with their mechanical principles; but it would throw no
additional light upon the subject to give any account of
these, and I shall therefore go on to speak of the next form
of the attempt to explain the processes of life.

SECT. IV.--_The Vital-Fluid School._

I speak here, not of that opinion which assumes some kind of
fluid or ether as the means of {186} communication along the
_nerves_ in particular, but of the hypothesis that _all_ the
peculiar functions of _life_ depend upon some subtile
ethereal substance diffused through the frame;--not of a
_Nervous_ Fluid, but of a _Vital_ Fluid. Again, I
distinguish this opinion from the doctrine of an
_immaterial_ vital power or principle, an Animal Soul, which
will be the subject of the next Section: nor is this
distinction insignificant; for a material element, however
subtile, however much spiritualized, must still act
everywhere according to the same laws; whereas we do not
conceive an immaterial spirit or soul to be subject to this
necessity.

The iatromathematical school could explain to their own
satisfaction how motions, once begun, were transferred and
modified; but in many organs of the living frame there
seemed to be a power of beginning motion, which is beyond
all mere mechanical action. This led to the assumption of a
Principle of a higher kind, though still material. Such a
Principle was asserted by Frederick Hoffmann, who was born
at Halle, in 1660[39\9], and became Professor of Medicine at
the newly established University there in 1694. According to
him[40\9], the reason of the greater activity of organized
bodies lies in the influence of a material substance of
extreme subtilty, volatility, and energy. This is, he holds,
no other than the Ether, which, diffused through all nature,
produces in plants the bud, the secretion and motion of the
juices, and is separated from the blood and lodged in the
brain of animals[41\9]. From this, acting through the
nerves, must be derived all the actions of the organs in the
animal frame; for when the influence of the nerve upon the
muscle ceases, muscular motion ceases also.

[Note 39\9: Spr. v. 254.]

[Note 40\9: _Ib._ v. 257.]

[Note 41\9: _De Differentiâ Organismi et Mechanismi_, pp. 48, 67.]

The mode of operation of this vital fluid was, however, by
no means steadily apprehended by Hoffmann and his followers.
Its operations are so far mechanical[42\9] that all effects
are reduced to motion, yet they {187} cannot be explained
according to known mechanical laws. At one time the effects
are said to take place according to laws of a Higher
Mechanics which are still to be discovered[43\9]. At another
time, in complete contradiction of the general spirit of the
system, metaphysical conceptions are introduced: each
particle of the vital fluid is said to have a determined
_idea_ of the whole mechanism and organism[44\9], and
according to this, it forms the body and preserves it by its
motion. By means of this fluid the soul operates upon the
body, and the instincts and the passions have their source
in this material sensitive soul. This attribution of ideas
to the particles of the fluid is less unaccountable when we
recollect that something of the same kind is admitted into
Leibnitz's system, whose Monads have also ideas.

[Note 42\9: Spr. v. 262, 3.]

[Note 43\9: Hoffmann, _Opp._ Vol. v. p. 123.]

[Note 44\9: _De Diff. Organ. et Mechan._ p. 81.]

Notwithstanding its inconsistencies, Hoffmann's system was
received with very general favour both in Germany and in the
rest of Europe; the more so, inasmuch as it fell in very
well with the philosophy both of Leibnitz and of Newton. The
Newtonians were generally inclined to identify the Vital
Fluid with the Ether, of which their master was so strongly
disposed to assume the existence: and indeed he himself
suggested this identification.

When the discoveries made respecting Electricity in the
course of the eighteenth century had familiarized men with
the notion of a pervading subtile agent, invisible,
intangible, yet producing very powerful effects in every
part of nature, physiologists also caught at the suggestion
of such an agent, and tried, by borrowing or imitating it,
to aid the imperfection of their notions of the vital
powers. The Vital Principle[45\9] was imagined to be a
substance of the same kind, by some to be the same
substance, with the Electric Fluid. By its agency all these
processes in organized bodies were accounted for which
cannot be {188} explained by mechanical or chemical laws, as
the secretion of various matters (tears, milk, bile, &c.)
from an homogeneous fluid, the blood; the production of
animal heat, digestion, and the like. According to John
Hunter, this attenuated substance pervaded the blood itself,
as well as the solid organic frame; and the changes which
take place in the blood which has flowed out of the veins
into a basin are explained by saying that it is, for a time,
till this vital fluid evaporates, truly alive.

[Note 45\9: Prichard, _On the Doctrine of a Vital
Principle_, p. 12.]

The notion of a Vital Fluid appears also to be favourably
looked upon by Cuvier; although with him this doctrine is
mainly put forwards in the form of a Nervous Fluid. Yet in
the following passage he extends the operation of such an
agent to all the vital functions[46\9]: 'We have only to
suppose that all the medullary and nervous parts produce the
Nervous Agent, and that they alone conduct it; that is, that
it can only be transmitted by them, and that it is changed
or consumed by their actions. Then everything appears
simple. A detached portion of muscle preserves for some time
its irritability, on account of the portion of nerve which
always adheres to it. The sensibility and the irritability
reciprocally exhaust each other by their exercise, because
they change or consume the same agent. All the interior
motions of digestion, secretion, excretion, participate in
this exhaustion, or may produce it. All local excitation of
the nerves brings thither more blood by augmenting the
irritability of the arteries, and the afflux of blood
augments the real sensibility by augmenting the production
of the nervous agent. Hence the pleasures of titillations,
the pains of inflammation. The particular sensations
increase in the same manner and by the same causes; and the
imagination exercises, (still by means of the nerves,) upon
the internal fibres of the arteries or other parts, and
through them on the sensations, an action analogous to that
of the will upon the voluntary motions. As each exterior
sense is exclusively disposed {189} to admit the substances
which it is to perceive, so each interior organ, secretory
or other, is also more excitable by some one agent than by
another: and hence arises what has been called the _proper
sensibility_ or _proper life of the organs_; and the
influence of specifics which, introduced into the general
circulation, affect only certain parts. In fine, if the
nervous agent cannot become sensible to us, the reason is
that all sensation requires that this agent should be
altered in some way or other; and it cannot alter itself.

[Note 46\9: _Hist. Sc. Nat. depuis_ 1789, i. 214.]

'Such is the summary idea which we may at present form of
the mutual and general working of the vital powers in
animals.'

Against the doctrine of a Vital Fluid as one uniform
material agent pervading the organic frame, an argument has
been stated which points out extremely well the
philosophical objection to such an hypothesis[47\9]. If the
Vital Principle be the _same_ in all parts of the body, how
does it happen, it is asked, that the secretions are so
_different_? How do the particles in the blood, separated
from their old compounds and united into new ones, under the
same influence, give origin to all the different fluids
which are produced by the glands? The liver secretes bile,
the lacrymal gland, tears, and so on. Is the Vital Principle
different in all these organs? To assert this, is to
multiply nominal principles without limit, and without any
advance in the explanation of facts. Is the Vital Principle
the same, but its operation modified by the structure of the
organ? We have then two unknown causes, the Vital Principle
and the Organic Structure, to account, for the effect. By
such a multiplication of hypotheses nothing is gained. We
may as well say at once, that the structure of the organ,
acting by laws yet unknown, is the cause of the peculiar
secretion. It is as easy to imagine this structure acting to
produce the whole effect, as it is to imagine it modifying
the activity of another agent. Thus the hypothesis of the
Vital Fluid in this form explains nothing, and does not in
any {190} way help onwards the progress of real biological
knowledge.

[Note 47\9: Prichard, _On a Vital Principle_, p. 98.]

The hypothesis of an _immaterial_ vital principle must now be
considered.

SECT. V.--_The Psychical School._

The doctrine of an Animal Soul as the principle which makes
the operations of organic different from those of inorganic
matter, is quite distinct from, and we may say independent
of, the doctrine of the soul as the intelligent, moral,
responsible part of man's nature. It is the former doctrine
alone of which we have here to speak, and those who thus
hold the existence of an immaterial agent as the cause of
the phenomena of life, I term the _Psychical School_.

Such a view of the constitution of living things is very
ancient. For instance, Aristotle's Treatise '_On the Soul_,'
goes entirely upon the supposition that the Soul is the
cause of motion, and he arrives at the conclusion that there
are different _parts_ in the Soul; the _nutritive_ or
_vegetative_, the _sensitive_, and the _rational_[48\9].

[Note 48\9: Aristotle. Περὶ Ψυχῆς, ii. 2.]

But this doctrine is more instructive to us, when it appears
as the antagonist of other opinions concerning the nature of
life. In this form it comes before us as promulgated by
Stahl, whom we have already noticed as one of the great
discoverers in chemistry. Born in the same year as Hoffmann,
and appointed at his suggestion professor at the same time
in the same new university of Halle, he soon published a
rival physiological theory. In a letter to Lucas Schröck,
the president of the Academy of Naturalists, he describes
the manner in which he was led to form a system for
himself[49\9]. Educated in the tenets of Sylvius and Willis,
according to which all diseases are derived from the acidity
of the fluids, Stahl, when a young student, often wondered
how these fluids, so liable to be polluted and corrupted,
are so wonderfully preserved through innumerable external
influences, and seem to {191} be far less affected by these
than by age, constitution, passion. No material cause could,
he thought, produce such effects. No attention to mechanism
or chemistry alone could teach us the true nature and laws
of organization.

[Note 49\9: Spr. v. 303.]

So far as Stahl recognized the influence, in living bodies,
of something beyond the range of mechanics and chemistry,
there can be no doubt of the sound philosophy of his views;
but when he proceeds to found a positive system of
physiology, his tenets become more precarious. The basis of
his theory is this[50\9]: the body has, as body, no power to
move itself, and must always be put in motion by immaterial
substances. All motion is a spiritual act[51\9]. The source
of all activity in the organic body, from which its
preservation, the permanency of its composition, and all its
other functions proceed, is an immaterial being, which Stahl
calls the _Soul_; because, as he says, when the effects are
so similar, he will not multiply powers without necessity.
Of this principle, he says, as the Hippocratians said of
Nature, that 'it does without teaching what it ought to
do[52\9],' and does it 'without consideration[53\9].' These
ancient tenets Stahl interprets in such a manner that even
the involuntary motions proceed from the soul, though
without reflection or clear consciousness. It is indeed
evident, that there are many customary motions and
sensations which are perfectly rational, yet not the objects
of distinct consciousness: and thus instinctive motions, and
those of which we are quite unconscious, may still be
connected with reason. The questions which in this view
offer themselves, as, how the soul passes from the mother to
the child, he dismisses as unprofitable[54\9]. He considers
nutrition and secretion as the work of the soul. The
corpuscular theory and the doctrine of animal spirits {192}
are, he rightly observes, mere hypotheses, which are
arbitrary in their character, and only shift the difficulty.
For, if the animal spirits are not matter, how can they
explain the action of an immaterial substance on the body;
and if they are matter, how are they themselves acted on?

[Note 50\9: Spr. v. 308]

[Note 51\9: _Ib._ v. 314.]

[Note 52\9: Stahl, περὶ φύσεως ἀπαίδευτου.]

[Note 53\9: οὐκ ἐκ διανοίης.]

[Note 54\9: This was of course an obvious problem. Harvey,
_On Generation_ Exercise 27, p. 148, teaches, 'That the egg
is not the production of the womb, but of the soul.']

This doctrine of the action of the soul on the body, was
accepted by many persons, especially by the
iatromathematicians, who could not but feel the
insufficiency of their system without some such supplement:
such were Cheyne and Mead. In Germany, Stahl's disciples in
physiology were for the most part inconsiderable
persons[55\9]. Several Englishmen who speculated concerning
the metaphysics as well as the physiology of Sensation and
Motion, inclined to this psychical view, as Porterfield and
Whytt. Among the French, Boissier de Sauvages was the most
zealous defender of the Stahlian system. Actions, he
says[56\9], which belong to the preservation of life are
determined by a moral not a mechanical necessity. They
proceed from the soul, but cannot be controlled by it, as
the starting from fear, or the trembling at danger. Unzer, a
physician at Altona[57\9], was also a philosophical
Stahlian[58\9].

[Note 55\9: Spr. v. 339, &c.]

[Note 56\9: _Ib._ 358.]

[Note 57\9: A.D. 1799]

[Note 58\9: Spr. v. 360.]

We need not dwell on the opposition which was offered to
this theory, first by Hoffmann, and afterwards by Haller.
The former of these had promulgated, as we have seen, the
rival theory of a Nervous Fluid, the latter was the
principal assertor of the doctrine of Irritability, an
important theory on which we may afterwards have to touch.
Haller's animosity against the Stahlian hypothesis is a
remarkable feature in one who is in general so tolerant in
his judgment of opinions. His arguments are taken from the
absence of the control of the will over the vital actions,
from the want of consciousness accompanying these actions,
from the uniformity of them in different conditions of the
mind, and from the small sensibility of {193} the heart
which is the source of the vital actions. These objections,
and the too decided distinction which Haller made between
voluntary and involuntary muscles, were very satisfactorily
answered by Whytt and Platner. In particular it was urged
that the instinctive actions of brutes are inexplicable by
means of mechanism, and may be compared with the necessary
vital actions of the human body. Neither kind are
accidental, neither kind are voluntary, both are performed
without reflection.

Without tracing further the progress of the Psychical
Doctrine, I shall borrow a few reflections upon it from
Sprengel[59\9]:--

'When the opponents of the Stahlian system repeat
incessantly that the assumption of a psychical cause in
corporeal effects is a metaphysical speculation which does
not belong to medicine, they talk to no purpose. The states
of the soul are objects of our internal experience, and
interest the physician too nearly to allow him to neglect
them. The innumerable unconscious efforts of the soul, the
powerful and daily effects of the passions upon the body,
too often put to confusion those who would expel into the
region of metaphysics the dispositions of the mind. The
connexion of our knowledge of the soul, as gathered from
experience, with our knowledge of the human body, is far
closer than the mechanical and chemical physiologists
suspect.

[Note 59\9: Spr. v. 383.]

'The strongest objection against the psychical system, and
one which has never been sufficiently answered by any of its
advocates, is the universality of organic effects in the
_vegetable_ kingdom. The comparison of the physiology of
plants with the physiology of animals puts the latter in its
true light. Without absolutely trifling with the word
_soul_, we cannot possibly derive from a soul the organic
operations of vegetables. But just as little can we, as some
Stahlians have done, draw a sharp line between plants and
animals, and ascribe the processes of the former to mere
mechanism, while {194} we derive the operations of the
latter from an intellectual principle. Not to mention that
such a line is not possible, the rise of the sap and the
alteration of the fluids of plants cannot be derived
entirely from material causes as their highest origin.'

Thus, I may add, this psychical theory, however difficult to
defend in its detail, does in its generalities express some
important truths respecting the vital powers. It not only,
like the last theory, gives unity to the living body, but it
marks, more clearly than any other theory, the wide interval
which separates mechanical and chemical from vital action,
and fixes our attention upon the new powers which the
consideration of life compels us to assume. It not only
reminds us that these powers are elevated above the known
laws of the material world, but also that they are closely
connected with the world of thought and feeling, of will and
reason; and thus it carries us, in a manner in which none of
the preceding theories have done, to a true conception of a
living, conscious, sentient, active individual.

At the same time we cannot but allow that the life of
plants and of the lower orders of animals shows us very
clearly that, in order to arrive at any sound and consistent
knowledge respecting life, we must form some conception of
it from which all the higher attributes which the term
'soul' involves, are utterly and carefully excluded; and
therefore we cannot but come to the conclusion that the
psychical school are right mainly in this; that in ascribing
the functions of life to a _soul_, they mark strongly and
justly the impossibility of ascribing them to any known
attributes of _body_.

{{195}}
CHAPTER III.

ATTEMPTS TO ANALYSE THE IDEA OF LIFE.

1. _Definitions of Life._--WE have seen in the preceding
chapter that all attempts to obtain a distinct conception of
the nature of Life in general have ended in failure, and
produced nothing beyond a negative result. And the
conjecture may now naturally occur, that the cause of this
failure resides in an erroneous mode of propounding to
ourselves the problem. Instead of contemplating Life as a
single Idea, it may perhaps be proper to separate it into
several component notions: instead of seeking for one cause
of all vital operations, it may be well to look at the
separate vital functions, and to seek their causes. When the
view of this possibility opens upon us, how shall we
endeavour to verify it, and to take advantage of it?

Let us, as one obvious course, take some of the attempts
which have been made to _define_ Life, and let us see
whether they appear to offer to us any analysis of the idea
into component parts. Such definitions, when they proceed
from men of philosophical minds, are the ultimate result of
a long course of thought and observation; and by no means
deserve to be slighted as arbitrary selections of
conditions, or empty forms of words.

2. Life has been defined by Stahl[60\9], 'The condition by
which a body resists a natural tendency to chemical changes,
such as putrefaction.' In like manner, M. von Humboldt[61\9]
defines living bodies to be 'those which, notwithstanding
the constant operation {196} of causes tending to change
their form, are hindered by a certain inward power from
undergoing such change.' The first of these definitions
amounts only to the assertion, that vital processes are not
chemical; a negative result, which we may accept as true,
but which is, as we have seen, a barren truth. The second
appears to be, in its import, identical with the first. An
_inward_ principle can only be understood as distinguished
from known external powers, such as mechanical and chemical
agencies. Or if, by an internal principle, we mean such a
principle as that of which we are _conscious_ within
ourselves, we ascribe a soul to all living things: an
hypothesis which we have seen is not more effective than the
former in promoting the progress of biological science.
Nearly the same criticism applies to such definitions as
that of Kant: that 'Life is an internal faculty producing
change, motion, and action.'

[Note 60\9: Treviranus, _Biologie_, p. 19. Stahlii, _**Theor.
Med._ p. 254.]

[Note 61\9: _Aphorismen aus d. Chem. Physiol. der Pflanzen_, s. 1.]

Other definitions refer us, not to some property residing in
the whole of an organized mass, but to the connexion and
relation of its parts. Thus M. von Humboldt[62\9] has given
another definition of a living body: that 'it is a whole
whose parts, arbitrarily separated, no longer resist
chemical changes.' But this additional assertion concerning
the parts, adds nothing of any value to the definition of
the whole. And in some of the lower kinds of plants and
animals it is hardly true as a fact.

[Note 62\9: _Versuche über die gereitzte Muskel und
Nervenfüser_, b. ii. p. 433.]

3. Another definition[63\9] places the character of Life in
'motions serviceable to the body moved.' To this it has been
objected[64\9], that, on this definition, the earth and the
planets are living bodies. Perhaps it would be more
philosophical to object to the introduction of so loose a
notion as that of a property being _serviceable_ to a body.
We might also add, that if we speak of all vital functions
as _motions_, we make an assumption quite unauthorized, and
probably false.

[Note 63\9: Erhard, Röschlaub's _Magazin der Heilkunde_, b.
i. st. 1. p. 69.]

[Note 64\9: Treviranus, _Biologie_, p. 41.]

{197} Other definitions refer the idea of Life to the idea
of Organization. 'Life is the activity of matter according
to laws of organization[65\9].' We are then naturally led to
ask, What is Organization? In reply to this is given us the
Kantian definition of Organization, which I have already
quoted elsewhere[66\9], 'An organized product of nature is
that in which all the parts are mutually ends and
means[67\9].' That this definition involves exact
fundamental ideas, and is capable of being made the basis of
sound knowledge, I shall hereafter endeavour to show. But I
may observe that such a definition leads us somewhat
further. If the parts of organized bodies are known to be
means to certain ends, this must be known because they
fulfil these ends, and produce certain effects by the
operation of a certain cause or causes. The question then
recurs, what is _the cause_ which produces such effects as
take place in organized or living bodies? and this is
identical with the problem of which in the last chapter we
traced the history, and related the failure of physiologists
in all attempts at its solution.

[Note 65\9: Schmid, _Physiologie_, b. ii. p. 274.]

[Note 66\9: _Hist. Ind. Sc._ b. xvii. c. viii. s. 2.]

[Note 67\9: Kant, _Urtheilskraft_, p. 296.]

4. But what has been just said suggests to us that it may be
an improvement to put our problem in another shape:--not to
take for granted that the cause of all vital processes is
one, but to suppose that there may be several separate
causes at work in a living body. If this be so, life is no
longer one kind of activity, but several. We have a number
of operations which are somehow bound together, and life is
the totality of all these: in short, life is not one
Function, but a System of Functions.

5. We are thus brought very near to the celebrated
definition of life given by Bichat[68\9]: 'Life is the sum
of the functions by which death is resisted.' But upon the
definition thus stated, we may venture to observe;--first,
that the introduction of the notion of {198} _death_ in
order to define the notion of _life_ appears to be
unphilosophical. We may more naturally define death with
reference to life, as the cessation of life; or at least we
may consider life and death as correlative and
interdependent notions. Again, the word 'sum,' used in the
way in which it here occurs, appears to be likely to convey
an erroneous conception, as if the functions here spoken of
were simply added to each other, and connected by
co-existence. It is plain that our idea of life involves
more than this: the functions are all clearly connected, and
mutually depend on each other; nutrition, circulation,
locomotion, reproduction,--each has its influence upon all
the others. These functions not merely co-exist, but exist
with many mutual relations and connexions; they are
continued so as to form, not merely a _sum_, but a _system_.
And thus we are led to modify Bichat's definition, and to
say that _Life is the system of vital functions_.

[Note 68\9: _Physiological Researches on Life and Death_.]

6. But it will be objected that by such a definition we
explain nothing: the notion of _vital functions_, it may be
said, involves the idea of _life_, and thus brings us round
again to our starting-point. Or if not, at least it is as
necessary to define Vital Functions as to define Life
itself, so that we have made little progress in our task.

To this we reply, that if any one seeks, upon such subjects,
some ultimate and independent definition from which he can,
by mere reasoning, deduce a series of conclusions, he seeks
that which cannot be found. In the Inductive Sciences, a
Definition does not form the basis of reasoning, _but points
out the course of investigation_. The definition must
include words; and the meaning of these words must be sought
in the progress and results of observations, as I have
elsewhere said[69\9]. 'The meaning of words is to be sought
in the progress of thought; the history of science is our
dictionary; the steps of scientific induction are our
definitions.' It will appear, I think, that it is more easy
for us to form an idea of a separate Function of the {199}
animal frame, as Nutrition or Reproduction, than to
comprehend Life in general under any single idea. And when
we say that Life is a system of Vital Functions, we are of
course directed to study these functions separately, and (as
in all other subjects of scientific research) to endeavour
to form of them such clear and definite ideas as may enable
us to discover their laws.

[Note 69\9: _Hist. Ind. Sc._ b. xiii. c. ix.]

7. The view to which we are thus led, of the most promising
mode of conducting the researches of Biology, is one which
the greatest and most philosophical physiologists of modern
times have adopted. Thus Cuvier considers this as the true
office of physiology at present. 'It belongs to modern
times,' he says, 'to form a just classification of the vital
phenomena; the task of the present time is to analyse the
forces which belong to each organic element, and upon the
zeal and activity which are given to this task, depends,
according to my judgment, the fortune of physiology[70\9].'
This classification of the phenomena of life involves, of
course, a distinction and arrangement of the vital
functions; and the investigation of the powers by which
these functions are carried on, is a natural sequel to such
a classification.

[Note 70\9: _Hist. Sc. Nat. dep._ 1789, i. 218.]

8. _Classification of Functions._--Attempts to classify the
Vital Functions of man were made at an early period, and
have been repeated in great number up to modern times. The
task of classification is exposed to the same difficulties,
and governed by the same conditions, in this as in other
subjects. Here, as in the case of other things, there may be
many classifications which are moderately good and natural,
but there is only one which is the best and the true natural
system. Here, as in other cases, one classification brings
into view one set of relations; another, another; and each
may be valuable for its special purpose. Here, as in other
cases, the classes may be well constituted, though the
boundary lines which divide them be somewhat indistinct, and
the order doubtful. Here, {200} as in other cases, we may
have approached to the natural classification without having
attained it; and here, as in other cases, to _define_ our
classes is the last and hardest of our problems.

9. The most ancient classification of the Functions of
living things[71\9], is the division of them into _Vital_,
_Natural_, and _Animal_. The Vital Functions are those which
cannot be interrupted without loss of life, as
_Circulation_, _Respiration_, and _Nervous Communication_.
The _Natural Functions_ are those which without the
intervention of the will operate on their proper occasions
to preserve the bodies of animals; they are _Digestion_,
_Absorption_, _Nutrition_; to which was added _Generation_.
The _Animal_ Functions are those which involve perception
and will, by which the animal is distinguished from the
vegetable; they are _Sensibility_, _Locomotion_, and _Voice_.

[Note 71\9: _Dict. des Sciences Nat._ art. _Fonctions_.]

The two great grounds of this division, the distinction of
functions which operate continually, and those which operate
occasionally; and again, the distinction of functions which
involve sensation and voluntary motion from those which do
not; are truly of fundamental importance, and gave a real
value to this classification. It was, however, liable to
obvious objections: namely, _First_, that the names of the
classes were ill chosen; for all the functions are natural,
all are vital: _Second_, that the lines of demarcation
between the classes are indefinite and ambiguous;
Respiration is a _vital_ function, as being continually
necessary to life; but it is also a _natural_ function,
since it occurs in the formation of the nutritive fluid, and
an _animal_ function, since it depends in part on the will.
But these objections were not fatal, for a classification
may be really sound and philosophical, though its boundary
lines are vague, and its nomenclature ill selected. The
division of the functions we have mentioned kept its ground
long; or was employed with a subdivision of one class, so as
to make them four; the _vital_, _natural_, _animal_ and
_sexual_ functions. {201}

10. I pass over many intermediate attempts to classify the
functions, and proceed to that of Bichat as that which is, I
believe, the one most generally assented to in modern times.
The leading principle in the scheme of this celebrated
physiologist is the distinction between _organic_ and
_animal_ life. This separation is nearly identical with the
one just noticed between the vital and animal functions; but
Bichat, by the contrasts which he pointed out between these
classes of functions, gave a decided prominence and
permanence to the distinction. The Organic Life, which in
animals is analogous to the life of vegetables, and the
Animal Life, which implies sensation and voluntary motion,
have each its system of organs. The center of the animal
life is the brain, of the organic life, the heart. The
former is carried on by a symmetrical, the latter, by an
unsymmetrical system of organs: the former produces
intermitting, the latter continuous actions: and, in
addition to these, other differences are pointed out. This
distinction of the two lives, being thus established, each
is subdivided into two orders of Functions. The Animal
Functions are passive, as _Sensation_: or active, as
_Locomotion_ and _Voice_; again, the Organic Functions are
those of Composition, which are concerned in taking matter
into the system; _Digestion_, _Absorption_, _Respiration_,
_Circulation_, _Assimilation_; and those of Decomposition,
which reject the materials when they have discharged their
office in the system; and these are again, _Absorption_,
_Circulation_, and _Secretion_. To these are added
_Calorification_, or the production of animal heat. It
appears, from what has been said, that _Absorption_ and
_Circulation_ (and we may add _Assimilation_ and
_Secretion_, which are difficult to separate,) belong alike
to the processes of composition and decomposition; nor in
truth, can we, with any rigour, separate the centripetal and
centrifugal movements in that vortex which, as we shall see,
is an apt image of organic life.

Several objections have been made to this classification:
and in particular, to the terms thus employed. It has been
asserted to be a perversion of language to {202} ascribe to
animals _two lives_, and to call the higher faculties in
man, perception and volition, the _animal_ functions. But,
as we have already said, when a classification is really
good, such objections, which bear only upon the mode in
which it is presented, are by no means fatal: and it is
generally acknowledged by all the most philosophical
cultivators of biology, that this arrangement of the
functions is better suited to the purposes of the science
than those which preceded it.

11. But according to the principles which we have already
laid down, the solidity of such a classification is to be
verified by its serving as a useful guide in biological
researches. If the arrangement which we have explained be
really founded in natural relations, it will be found that
in proportion as physiologists have studied the separate
functions above enumerated, their ideas of these functions,
and of the powers by which they are carried on, have become
more and more clear;--have tended more and more to the
character of exact and rigorous science.

To examine how far this has been the case with regard to all
the separate functions, would be to attempt to estimate the
value of all the principal physiological speculations of
modern times; a task far too vast and too arduous for any
one to undertake who has not devoted his life to such
studies. But it may properly come within the compass of our
present plan to show how, with regard to the broader lines
of the above classification, there has been such a progress
as we have above described, from more loose and inaccurate
notions of some of the vital functions to more definite and
precise ideas. This I shall attempt to point out in one or
two instances.

{{203}}
CHAPTER IV.

ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES, AND FIRST
OF ASSIMILATION AND SECRETION.

SECT. I.--_Course of Biological Research._

1. IT is to be observed that at present I do not speak of
the progress of our knowledge with regard to the detail of
the processes which take place in the human body, but of the
approach made to some distinct Idea of the specially vital
part of each process. In the History of Physiology, it has
been seen[72\9] that all the great discoveries made respecting
the organs and motions of the animal frame have been
followed by speculations and hypotheses connected with such
discoveries. The discovery of the circulation of the blood
led to theories of animal heat; the discovery of the motion
of the chyle led to theories of digestion; the close
examination of the process of reproduction in plants and
animals led to theories of generation. In all these cases,
the discovery brought to light some portion of the process
which was mechanical or chemical, but it also, in each
instance, served to show that the process was something more
than mechanical or chemical. The theory attempted to explain
the process by the application of known causes; but there
always remained some part of it which must unavoidably be
referred to an unknown cause. But though unknown, such a
cause was not a hopeless object of study. As the vital
functions became better and better understood, it was seen
more and more clearly at what precise points of the process
it was necessary to assume a peculiar vital energy, and what
sort of properties {204} this energy must be conceived to
possess. It was perceived where, in what manner, in what
degree, mechanical and chemical agencies were modified,
over-ruled, or counteracted, by agencies which must be
hypermechanical and hyperchemical. And thus the discoveries
made in anatomy by a laborious examination of facts, pointed
out the necessity of introducing new ideas, in order that
the facts might be intelligible. Observation taught much;
and among other things, she taught that there was something
which could not be observed, but which must, if possible, be
conceived. I shall notice a few instances of this.

[Note 72\9: _Hist. Ind. Sc._ b. xvii.]

SECT. II.--_Attempts to form a distinct Conception of
Assimilation and Secretion._

2. _The Ancients._--That plants and animals grow by taking
into their substance matter previously extraneous, is
obvious to all: but as soon as we attempt to conceive this
process distinctly in detail, we find that it involves no
inconsiderable mystery. How does the same food become blood
and flesh, bone and hair? Perhaps the earliest attempt to
explain this mystery, is that recorded by Lucretius[73\9] as
the opinion of Anaxagoras, that food contains some bony,
some fleshy particles, some of blood, and so on. We might,
on this supposition, conceive that the mechanism of the body
appropriates each kind of particle to its suitable place.

[Note 73\9: Lucr. i. 855. Nunc et Anaxagoræ scrutemur
ὁμοιομέρειαν.]

But it is easy to refute this essay at philosophizing (as
Lucretius refutes it) by remarking that we do not find milk
in grass, or blood in fruit, though such food gives such
products in cattle and in men. In opposition to this
'Homoiomereia,' the opinion that is forced upon us by the
facts is, that the process of nutrition is not a selection
merely, but an _assimilation_; the organized system does not
_find_, but _make_, the additions to its structure. {205}

3. _Buffon._--This notion of _assimilation_ may be variously
expressed and illustrated; and all that we can do here, in
order to show the progress of thought, is to adduce the
speculations of those writers who have been most successful
in seizing and marking its peculiar character. Buffon may be
taken as an example of the philosophy of his time on this
subject. 'The body of the animal,' says he[74\9], 'is a kind
of _interior mould_, in which the matter subservient to its
increase is modelled and assimilated to the whole, in such a
way that, without occasioning any change in the order and
proportion of the parts, there results an augmentation in
each part taken separately. This increase, this development,
if we would have a _clear idea_ of it, how can we obtain it,
except by considering the body of the animal, and each of
the parts which is to be developed, as so many interior
moulds which only receive the accessory matter in the order
which results from the position of all their parts? This
development cannot take place, as persons sometimes persuade
themselves, by an addition to the outside; on the contrary,
it goes on by an intimate susception which penetrates the
mass; for, in the part thus developed, the size increases in
all parts proportionally, so that the new matter must
penetrate it in all its dimensions: and it is quite
necessary that this penetration of substance must take place
in a certain order, and according to a certain measure; for
if this were not so, some parts would develope themselves
more than others. Now what can there be which shall
prescribe such a rule to the accessory matter except the
_interior mould_?'

[Note 74\9: _Hist. Nat._ b. i. c. iii.]

To speak of a _mould_ simply, would convey a coarse
mechanical notion, which could not be received as any useful
contribution to physiological speculation. But this
_interior_ mould is, of course, to be understood
figuratively, not as an assemblage of cavities, but as a
collection of laws, shaping, directing, and modifying the
new matter; giving it not only form, but motion {206} and
activity, such as belong to the parts of an organic being.

4. It must be allowed, however, that even with this
explanation, the comparison is very loose and insufficient.
A _mould_ may be permitted to mean a collection of laws, but
still it can convey no conception except that of laws
regulated by relations of space; and such a conception is
very plainly quite inadequate to the purpose. What can we
conceive of the interior mould by which chyle is separated
from the aliments at the pores of the lacteals, or tears
secreted in the lacrymatory gland?

An additional objection to this mode of expression of Buffon
is, that it suggests to us only a single marked change in
the assimilated matter, not a continuous series of changes.
Yet the animal fluids and other substances are, in fact,
undergoing a constant series of changes. Food becomes chyme,
and chyme becomes chyle; chyle is poured into the blood;
from the blood secretions take place, as the bile; the bile
is poured into the digestive canal, and a portion of the
matter previously introduced is rejected out of the system.
Here we must have a series of 'interior moulds;' and these
must impress matter at its ejection from the organic system
as well as at its reception. But, moreover, it is probable
that none of the above transformations are quite abrupt.
Change is going on between the beginning and the end of each
stage of the nutritive circulation. To express the laws of
this continuous change, the image of an interior mould is
quite unsuited. We must seek a better mode of conception.

5. Vegetable and animal nutrition is, as we have said, a
constant circulation. The matter so assumed is not all
retained: a perpetual subtraction accompanies a perpetual
addition. There is an excretion as well as an
intussusception. The matter which is assumed by the living
creature is retained only for a while, and is then parted
with. The individual is the same, but its parts are in a
perpetual flux: they come and go. For a time the matter
which belongs to the organic body is bound to it by certain
laws: but before it is thus bound, and {207} after it is
loose, this matter may circulate about the universe in any
other form. Life consists in a permanent influence over a
perpetually changing set of particles.

_Cuvier._--This condition also has been happily expressed,
by means of a comparison, by another great naturalist. 'If,'
says Cuvier[75\9], 'if, in order to obtain a just idea of
the essence of life, we consider it in the beings where its
effects are most simple, we shall soon perceive that it
consists in the faculty which belongs to certain bodily
combinations to continue during a determinate time under a
determinate form; constantly attracting into their
composition a part of the surrounding substances, and giving
up in return some part of their own substance.

[Note 75\9: _Règne Animal_, i. 11.]

'Life is thus a _vortex_, more or less rapid, more or less
complex, which has a constant direction, and which always
carries along its stream particles of the same kinds; but in
which the individual particles are constantly entering in
and departing out; so that the _form_ of the living body is
more essential to it than its matter.

'So long as this motion subsists, the body in which it takes
place is _alive_; it _lives_. When the motion stops finally,
the body _dies_. After death, the elements which compose the
body, given up to the ordinary chemical affinities, soon
separate, and the body which was alive is dissolved.'

This notion of a vortex[76\9] which is permanent while the
matter which composes it constantly changes,--of peculiar
forces which act in this vortex so long as it exists, and
which give place to chemical forces when {208} the
circulatory motion ceases,--appears to express some of the
leading conditions of the assimilative power of living
things in a simple and general manner, and thus tends to
give distinctness to the notion of this vital function.

[Note 76\9: The definition of life given by M. de Blainville
appears to me not to differ essentially from that of Cuvier:
'Un corps vivant est une sorte de foyer chimique où il-y-a à
tous momens apport de nouvelles molecules et départ de
molecules anciennes; où la composition n'est jamais fixe (si
ce n'est d'un certain nombre de parties veritablement mortes
ou en depôt), mais toujours pour ainsi dire _in nisu_, d'où
mouvement plus ou moins lent et quelquefois
chaleur.'--_Principes d'Anat._ 1822, t. i. p. 16.]

6. But we may observe that this notion of a Vortex is still
insufficient. Particles are not only taken into the system
and circulated through it for a time, but, as we have seen,
they are altered in character in a manner to us
unintelligible, both at their first admission into the
system and at every period of their progress through it. In
the vortex each particle is constantly _transformed_ while
it whirls.

It may be said, perhaps, that this transformation of the
kinds of matter may be conceived to be merely a new
arrangement of their particles, and that thus all the
changes which take place in the circulating substances are
merely so many additional windings in the course of the
whirling current. But to say this, is to take for granted
the atomic hypothesis in its rudest form. What right have we
to assume that blood and tears, bile and milk, consist of
like particles of matter differently arranged? What can
arrangement, a mere relation of space, do towards explaining
such differences? Is not the insufficiency, the absurdity of
such an assumption proved by the whole course of science?
Are not even chemical changes, according to the best views
hitherto obtained, something more than a mere new
arrangement of particles? And are not vital as much beyond
chemical, as chemical are beyond geometrical modifications?
It is not enough, then, to conceive life as a vortex. The
particles which are taken into the organic frame do more
than circulate there. They are, at every point of their
circulation, acted upon by laws of an unknown kind, changing
the nature of the substance which they compose. Life is a
vortex in which vital forces act at every point of the
stream: it is not only a current of whirling _matter_, but a
cycle of recurring _powers_.

7. _Matter and Form._--This image of a vortex is closely
connected with the representation of life offered {209} us
by writers of a very different school. In Schelling's
_Lectures on Academic Study_, he takes a survey of the
various branches of human knowledge, determining according
to his own principles the shape which each science must
necessarily assume. The peculiar character of organization,
according to him[77\9], is that the matter is only an
accident of the thing itself, and the organization consists
in Form alone. But this Form, by its very opposition to
Matter, ceases to be independent of it, and is only ideally
separable. In organization, therefore, substance and
accident, matter and form, are completely identical[78\9].
This notion, that in organization the Form is essential and
the Matter accidental, or, in other words, that the Form is
permanent and the Matter fluctuating and transitory, agrees,
if taken in the grossest sense of matter and form, with
Cuvier's image of a Vortex. In a whirlpool, or in a
waterfall, the form remains, the matter constantly passes
away and is renewed. But we have already seen[79\9] that in
metaphysical speculations in which matter and form are
opposed, the word form is used in a far more extensive sense
than that which denotes a relation of space. It may indeed
designate any change which matter can undergo; and we may
very allowably say that food and blood are the same matter
under different _forms_. Hence if we assert that _Life is a
constant Form of a circulating Matter_, we express Cuvier's
notion in a mode free from the false suggestion which
'Vortex' conveys.

[Note 77\9: Lect. xiii. p. 288.]

[Note 78\9: I have not translated Schelling's words, but
given their import as far as I could.]

[Note 79\9: Book i.]

8. We may, however, still add something to this account of
life. The circulating parts of the system not only
circulate, but they form the non-circulating parts. Or
rather, there are no non-circulating parts: all portions of
the frame circulate more or less rapidly. The food which we
take circulates rapidly in the fluids, more slowly in the
flesh, still more slowly in the bones; but in all these
parts it is taken into the system, {210} retained there for
some time, and finally replaced by other matter. But while
it remains in the body, it exercises upon the other
circulating parts the powers by which their motion is
produced. Nutriment forms and supports the organs, and the
organs carry fresh nutriment to its destination. The
peculiar forces of the living body, and its peculiar
structure, are thus connected in an indescribable manner.
The forces produce the structure; the structure, again, is
requisite for the exertion of the forces. The Idea of an
Organic or Living Being includes this peculiar
condition--that its construction and powers are such, that
it constantly appropriates to itself new portions of
substance which, so appropriated, become indistinguishable
parts of the whole, and serve to carry on subsequently the
same functions by which they were assimilated. And thus
_Organic Life is a constant Form of a circulating Matter, in
which the Matter and the Form determine each other by
peculiar laws_ (_that is, by Vital Forces_).

SECT. III.--_Attempts to conceive the forces of Assimilation
and Secretion._

9. I have already stated that in our attempts to obtain
clear and scientific Ideas of Vital Forces, we have, in the
first place, to seek to understand the course of change and
motion in each function, so as to see at what points of the
process peculiar causes come into play; and next, to
endeavour to obtain some insight into the peculiar character
and attributes of these causes. Having spoken of the first
part of this mode of investigation in regard to the general
nutrition of organic bodies, I must now say a few words on
the second part.

The Forces here spoken of are _Vital_ Forces. From what has
been said, we may see in some measure the distinction
between forces of this kind and mechanical or chemical
forces; the latter tend constantly to produce a final
condition, after which there is no further cause of change:
mechanical forces tend to produce equilibrium; chemical
forces tend to produce {211} composition or decomposition;
and this point once reached, the matter in which these
forces reside is altogether inert. But an organic body tends
to a constant motion, and the highest activity of organic
forces shows itself in continuous change. Again, in
mechanical and chemical forces, the force of any aggregate
is the sum of the forces of all the parts: the sum of the
forces corresponds to the sum of the matter. But in organic
bodies, the amount of effect does not depend on the matter,
but on the form: the particles lose their separate energy,
in order to share in that of the system; they are not added,
they are _assimilated_.

10. It is difficult to say whether anything has been gained
to science by the various attempts to assign a fixed _name_
to the vital force which is thus the immediate cause of
Assimilation. It has been called _Organic Attraction_ or
_Vital Attraction_, _Organic Affinity_ or _Vital Affinity_,
being thus compared with mechanical Attraction or chemical
Affinity. But, perhaps, as the process is certainly neither
mechanical nor chemical, it is desirable to appropriate to
it a peculiar name; and the name _Assimilation_, or _Organic
Assimilation_, by the usage of good biological writers, is
generally employed for this purpose, and may be taken as the
standard name of this Vital Force. To illustrate this, I
will quote a passage from the excellent _Elements of
Physiology_ of Professor Müller. 'In the process of
nutrition is exemplified the fundamental principle of
_organic assimilation_. Each elementary particle of an organ
attracts similar particles from the blood, and by the
changes it produces in them, causes them to participate in
the vital principle of the organ itself. Nerves take up
nervous substance, muscles, muscular substance: even morbid
structures have the assimilating power; warts in the skin
grow with their own peculiar structure; in an ulcer, the
base and border are nourished in a way conformable to the
mode of action and secretion determined by the disease.'

11. The Force of Organic Assimilation spoken of in the last
paragraph denotes peculiarly the force by which each organ
appropriates to itself a part of the {212} nutriment
received into the system, and thus is maintained and
augmented with the growth of the whole. But the growth of
the solid parts is only one portion of the function of
nutrition; besides this, we must consider the motion and
changes of the fluids, and must ask what kind of forces may
be conceived to produce these. What are the powers by which
chyle is _absorbed_ from the food, by which bile is
_secreted_ from the blood, by which the circulating _motion_
of these and all other fluids of the body are constantly
maintained? To the questions,--What are the forces by which
_absorption_, _secretion_, and the _vital motions_, of
fluids are produced?--no satisfactory answer has been
returned. Yet still some steps have been made, which it may
be instructive to point out.

12. In _Absorption_ it would appear that a part of the
agency is inorganic; for not only dead membranes, but
inorganic substances, absorb fluids, and even absorb them
with elective forces, according to the ingredients, of the
fluid. A force which is of this kind, and which has been
termed _Endosmose_, has been found to produce very curious
effects. When a membrane separates two fluids, holding in
solution different ingredients, the fluids pass through the
membrane in an imperceptible manner, and mix or exchange
their elements. The force which produces these effects is
capable of balancing a very considerable pressure. It
appears, moreover, to depend, at least among other causes,
upon attractions operating between the elements of the
solids and the fluids, as well as between the different
fluids; and this force, though thus apparently of a
mechanical and chemical nature, probably has considerable
influence in vital phenomena.

13. But still, though Endosmose may account in part for
absorption in some cases, it is certain that there is some
other vital force at work in this process. There must be, as
Müller says[80\9], 'an organic attraction of a kind hitherto
unknown.' 'If absorption,' he adds[81\9], is to be explained
in a manner analogous to {213} the laws of endosmose, it
must be supposed that a chemical affinity, resulting from
the vital process itself, is exerted between the chyme in
the intestines and the chyle in the lacteals, by which the
chyle is enabled to attract the chyme without being itself
attracted by it. But such affinity or attraction would be of
a vital nature, since it does not exist after death.'

[Note 80\9: _Physiology_, p. 299.]

[Note 81\9: _Ib._ p. 301.]

14. If the force of absorption be thus mysterious in its
nature, the force of _Secretion_ is still more so. In this
case we have an organ filled with a fine net-work of
blood-vessels, and in the cavities of some _gland_, or open
part, we have a new fluid formed, of a kind altogether
different from the blood itself. It is easily shown that
this cannot be explained by any action of pores or capillary
tubes. But what conception can we form of the forces by
which such a change is produced? Here, again, I shall borrow
the expressions of Müller, as presenting the last result of
modern physiology. He says[82\9], 'The more probable
supposition is, that by virtue of imbibition, or the general
organic porosity, the fluid portion of the blood becomes
diffused through the tissue of the secreting organ; that the
external surface of the glandular canals exerts a chemical
attraction on the elements of the fluid, infusing into them
at the same time a tendency to unite in new combinations;
and then repels them in a manner which is certainly quite
inexplicable, towards the inner surface of the secreting
membrane, or glandular canals.' 'Although quite unsupported
by facts,' he adds, 'this theory of attraction and repulsion
is not without its analogy in physical phenomena; and it
would appear that very similar powers effect the elimination
of the fluid in secretion, and cause it to be taken up by
the lymphatics in absorption.' He elsewhere says[83\9],
'Absorption seems to depend on an attraction the nature of
which is unknown, but of which the very counterpart, as it
were, takes place in secretion; the fluids altered by the
secreting action being repelled towards the free side or
open surface only of the {214} secreting membranes, and then
pressed forwards by the successive portions of the fluids
secreted.'

[Note 82\9: _Physiology_, p. 464.]

[Note 83\9: _Ib._ p. 301.]

15. With regard to the forces which produce the _Motion_ of
absorbed or secreted fluids along their destined course, it
may be seen, from the last quoted sentence, that the same
vital force which changes the nature, also produces the
movement of the substance. The fluids are pressed forwards
by the successive portions absorbed or secreted. That this
is the sole cause, or at least a very powerful cause, of the
motion of the nutritive fluids in organic bodies, is easily
shown by experience. It is found[84\9] that the organs which
effect the ascent of the sap in trees during the spring are
the terminal parts of the roots; that the whole force by
which the sap is impelled upwards is the _vis a tergo_, as
it has been called, the force pushing from behind, exerted
in the roots. And thus the force which produces this motion
is exerted exactly at those points where the organic body
selects from the contiguous mass those particles which it
absorbs and appropriates. And the same may most probably be
taken for the cause of the motion of the lymph and chyle; at
least, Müller says[85\9] that no other motive power has been
detected which impels those fluids in their course.

[Note 84\9: Müller, p. 300.]

[Note 85\9: _Ib._ p. 254.]

Thus, though we must confess the Vital Force concerned in
Assimilation and Secretion to be unknown in its nature, we
still obtain a view of some of the attributes which it
involves. It has mechanical efficacy, producing motions,
often such as would require great mechanical force. But it
exerts at the same point both an attraction and a repulsion,
attracting matter on one side, and repelling it on the
other; and in this circumstance it differs entirely from
mechanical forces. Again, it is not only mechanical but
chemical, producing a complete change in the nature of the
substance on which it acts; to which we must add that the
changes produced by the vital forces are such as, for the
most part, our artificial chemistry {215} cannot imitate.
But, again, by the action of the vital force at any point of
an organ, not only are fluids made to pass, and changed as
they pass, but the organ itself is maintained and
strengthened, so as to continue or to increase its
operation: and thus the vital energy supports its activity
by its action, and is augmented by being exerted.

We have thus endeavoured to obtain a view of some of the
peculiar characters which belong to the Force of Organic
Assimilation;--the Force by which life is kept up, conceived
in the most elementary form to which we can reduce it by
observation and contemplation. It appears that it is a force
which not only produces motion and chemical change, but also
_vitalizes_ the matter on which it acts, giving to it the
power of producing like changes on other matter, and so on
indefinitely. It not only circulates the particles of
matter, but puts them in a stream of which the flow is
development as well as movement.

The force of Organic Assimilation being thus conceived, it
becomes instructive to compare it with the force concerned
in Generation, which we shall therefore endeavour to do.

SECT. IV.--_Attempts to conceive the Process of Generation._

16. At first sight the function of Nutrition appears very
different from the function of Generation. In the former
case we have merely the existing organs maintained or
enlarged, and their action continued; in the latter, we have
a new individual produced and extricated from the parent.
The term _Reproduction_ has, no doubt, been applied, by
different writers, to both these functions;--to the
processes by which an organ when mutilated, is restored by
the forces of the living body, and to the process by which a
new generation of individuals is produced which may be
considered as taking the place of the old generation, as
these are gradually removed by death. But these are
obviously different senses of the word. In the latter case,
the {216} term _Reproduction_ is figuratively used; for the
_same_ individuals are not reproduced; but the species is
kept up by the propagation of new individuals, as in
nutrition the organ is kept up by the assimilation of new
matter. To escape ambiguity, I shall avoid using the term
_Reproduction_ in the sense of _Propagation_.

17. In Nutrition, as we have seen, the matter, which from
being at first extraneous, is appropriated by the living
system, and directed to the sustentation of the organs,
undergoes a series of changes of which the detail eludes our
observation and apprehension. The nutriment which we receive
contributes to the growth of flesh and bone, viscera and
organs of sense. But we cannot trace in its gradual changes
a visible preparation for its final office. The portion of
matter which is destined to repair the waste of the eye or
the skin, is not found assuming a likeness to the parts of
the eye or the structure of the skin, as it comes near the
place where it is moulded into its ultimate form. The new
parts are insinuated among the old ones, in an obscure and
imperceptible matter. We can trace their progress only by
their effects. The organs _are_ nourished, and that is
almost all we can learn: we cannot discover _how_ this is
done. We cannot follow nature through a series of manifest
preparations and processes to this result.

18. In Generation the case is quite different. The young
being is formed gradually and by a series of distinguishable
processes. It is included within the parent before it is
extruded, and approaches more or less to the likeness of the
parent before it is detached. While it is still an embryo,
it shares in the nutriment which circulates through the
system of the mother; but its destination is already clear.
While the new and the old parts, in every other portion of
the mother, are undistinguishably mixed together, this new
part, the fœtus, is clearly distinct from the rest of the
system, and becomes rapidly more and more so, as the time
goes on. And thus there is formed, not a new part, but a new
whole; it is not an organ which is kept up, but an offspring
which is prepared. The progeny is {217} included in the
parent, and is gradually fitted to be separated from it. The
young is at first only the development of a part of the
organization of the mother;--of a germ, an ovule. But it is
not developed like other organs, retaining its general form.
It does not become merely a larger bud, a larger ovule; it
is entirely changed; it becomes--from a bud--a blossom, a
flower, a fruit, a seed; from an ovule it becomes an egg, a
chick, a bird; or it may be, a fœtus, a child. The original
rudiment is not merely nourished, but unfolded and
transformed through the most marked and remote changes,
gradually tending to the form of the new individual.

19. But this is not all. The fœtus is, as we have said, a
development of a portion of the mother's organization. But
the fœtus (supposing it female) is a likeness of the mother.
The mother, even before conception, contains within herself
the germs of her progeny; the female fœtus, therefore, at a
certain stage of development, will contain also the germs of
possible progeny; and thus we may have the germs of future
generations, pre-existing and included successively within
one another. And this state of things, which thus suggests
itself to us as possible, is found to be the case in facts
which observation supplies. Anatomists have traced ovules in
the unborn fœtus, and thus we have three generations
included one within another.

20. Supposing we were to stop here, the process of
propagation might appear to be altogether different from
that of nutrition. The latter, as we have seen, may be in
some measure illustrated by the image of a _vortex_; the
former has been represented by the image of a series of
germs, _sheathed_ one within another successively, and this
without any limit. This view of the subject has been termed
the doctrine of the _Pre-existence of germs_; and has been
designated by German writers by a term 'Einschachtelungs-theorie'
descriptive of the successive sheathing of which I have
spoken. Imitating this term, we may call it _the Theory of
successive inclusion_. It has always had many {218}
adherents; and has been, perhaps, up to the present time,
the most current opinion on the subject of generation.
Cuvier inclines to this opinion[86\9]. 'Fixed forms
perpetuating themselves by generation distinguish the
species of living things. These forms do not produce
themselves, do not change themselves. Life supposes them to
exist already; its flame can be lighted only in organization
previously prepared; and the most profound meditations and
the most delicate researches terminate alike in the mystery
of the _pre-existence of germs_.'

[Note 86\9: _Règne Animal_, p. 20.]

21. Yet this doctrine is full of difficulty. It is, as
Cuvier says, a mysterious view of the subject;--so
mysterious, that it can hardly be accepted by us, who seek
distinct conceptions as the basis of our philosophy. Can it
be true, not only that the germ of the offspring is
originally included in the parent, but also the germs of
_its_ progeny, and so on without limit:--so that each
fruitful individual contains in itself an infinite
collection of future possible individuals;--a reserve of
infinite succeeding generations? This is hard to admit. Have
we no alternative? What is the opposite doctrine?

22. The opposite doctrine deserves at least some notice. It
extends, to the production of a new individual, the
conception of growth by nutrition. According to this view,
we suppose propagation to take place, not as in the view
just spoken of, by inclusion and extrusion, but by
assimilation and development;--not by the material
pre-existence of germs, but by the communication of vital
forces to new matter. This opinion appears to be entertained
by some of the most eminent physiologists of the present
time. Thus, Müller says, 'The organic force is also
creative. The organic force which resides in the whole, and
on which the existence of each part depends, has also the
property of generating, from organic matter, the parts
necessary to the whole.' Life, he adds, is not merely a
harmony of the {219} parts. On the contrary, the harmonious
action of the parts subsists only by the influence of a
force pervading all parts of the body. 'This force exists
before the harmonizing parts, which are in fact formed by it
during the development of the embryo.' And again; 'The
creative force exists in the germ, and creates in it the
essential force of the future animal. The germ is
_potentially_ the whole animal: during the development of
the germ the parts which constitute the actual whole are
produced.'

23. In this view, we extend to the reproduction of an
individual the same conception of organic assimilation which
we have already arrived at, as the best notion we can form
of the force by which the reproduction and sustentation of
parts takes place. And is not such an extension really very
consistent? If a living thing can appropriate to itself
extraneous matter, invest it with its own functions, and
thus put it in the stream of constant development, may we
not conceive the development of a new _whole_ to take place
in this way as well as of a _part_? If the organized being
can infuse into new matter its vital forces, is there any
contradiction in supposing this infusion to take place in
the full measure which is requisite for the production of a
new individual? The force of organic assimilation is
transferred to the very matter on which it acts; it may be
transferred so that the operation of the forces produces not
only an organ, but a system of organs.

24. This identification of the forces which operate in
Nutrition and Generation may at first seem forced and
obscure, in consequence of the very strong apparent
differences of the two processes which we have already
noticed. But this defect in the doctrine is remedied by the
consideration of what may be considered as intermediate
cases. It is not true that, in the nutrition of special
organs, the matter is always conveyed to its ultimate
destination without being on its way moulded into the form
which it is finally to bear, as the embryo is moulded into
the form of the {220} future individual. On the contrary,
there are cases in which the waste of the organs is supplied
by the growth of new ones, which are prepared and formed
before they are used, just as the offspring is prepared and
formed before it is separated from the parent. This is the
case with the teeth of many animals, and especially with the
teeth of animals of the crocodile kind. Young teeth grow
near the root of the old ones, like buds on the stem of a
plant; and as these become fully developed, they take the
place of the parent tooth when that dies and is cast away.
And these new teeth in their turn are succeeded by others
which germinate from them. Several generations of such
teeth, it is said as many as four, have been detected by
anatomists, visibly existing at the same time; just as
several generations of germs of individuals have been, as we
already stated, observed included in one another. But this
case of the teeth appears to show very strikingly how
insufficient such observations are to establish the doctrine
of successive inclusion, or of the pre-existence of germs.
Are we to suppose that every crocodile's tooth includes in
itself the germs of an infinite number of possible teeth, as
in the theory of pre-existing germs every individual
includes an infinite number of individuals? If this be true
of teeth, we must suppose that organ to follow laws entirely
different from almost every other organ; for no one would
apply to the other organs in general such a theory of
reproduction. But if such a theory be not maintained
respecting the teeth, how can we maintain the theory of the
pre-existing germs of individuals, which has no
recommendation except that of accounting for exactly the
same phenomena?

It would seem, then, that we are, by the closest
consideration of the subject, led to conceive the forces by
which generation is produced, as forces which vitalize
certain portions of matter, and thus prepare them for
development according to organic forms; and thus the
conception of this Generative Force is identified with the
conception of the Force of Organic Assimilation, to {221}
which we were led by the consideration of the process of
nutrition.

I shall not attempt to give further distinctness and fixity
to this conception of one of the vital forces; but I shall
proceed to exemplify the same analysis of life by some
remarks upon another Vital Process, and the Forces of which
it exhibits the operation.

{{222}}
CHAPTER V.

ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES,
_continued_.--VOLUNTARY MOTION.

1. WE formerly noticed the distinctions of _organic_ and
_animal_ functions, organic and animal forces, as one of the
most marked distinctions to which physiologists have been
led in their analysis of the vital powers. I have now taken
one of the former, the _organic_ class of functions, namely,
Nutrition; and have endeavoured to point out in some measure
the peculiar nature of the vital forces by which this
function is carried on. It may serve to show the extent and
the difficulty of this subject, if, before quitting it, I
offer a few remarks suggested by a function belonging to the
other class, the _animal_ functions. This I shall briefly do
with respect to _Voluntary Motion_.

2. In the History of Physiology, I have already related the
progress of the researches by which the organs employed in
voluntary motion became known to anatomists. It was
ascertained to the satisfaction of all physiologists, that
the immediate agents in such motion are the muscles; that
the muscles are in some way contracted, when the nerves
convey to them the agency of the will; and that thus the
limbs are moved. It was ascertained, also, that the nerves
convey sensations from the organs of sense inwards, so as to
make these sensations the object of the animal's
consciousness. In man and the higher animals, these
impressions upon the nerves are all conveyed to one internal
organ, the brain; and from this organ all impressions of the
will appear to proceed; and thus the brain is {223} the
center of animal life, towards which sensations converge,
and from which volitions diverge.

But this being the process, we are led to inquire how far we
can obtain any knowledge, or form any conception, of the
vital forces by means of which the process is carried on.
And here I have further stated in the History[87\9], that
the transfer of sensations and volitions along the nerves
was often represented as consisting in the motion of a
Nervous Fluid. I have related that the hypothesis of such a
fluid, conveying its impressions either by motions of
translation or of vibration, was countenanced by many great
names, as Newton, Haller, and even Cuvier. But I have
ventured to express my doubt whether this hypothesis can
have much value: 'for,' I have said, 'this principle cannot
be mechanical, chemical, or physical, and therefore cannot
be better understood by embodying it in a fluid. The
difficulty we have in conceiving what the force _is_, is not
got rid of by explaining the machinery by which it is
_transferred_.'

[Note 87\9: _Hist. Ind. Sc._ b. xvii. c. v. s. 2.]

3. I may add, that no succeeding biological researches
appear to have diminished the force of these considerations.
In modern times, attempts have repeatedly been made to
identify the nervous fluid with electricity or galvanism.
But these attempts have not been satisfactory or conclusive
of the truth of such an identity: and Professor Müller
probably speaks the judgment of the most judicious
physiologists, when he states it as his opinion, after
examining the evidence[88\9], 'That the vital actions of the
nerves are not attended with the development of any galvanic
currents which our instruments can detect; and that the laws
of action of the nervous principle are totally different
from those of electricity.'

[Note 88\9: _Elem. Phys._ p. 640.]

That the powers by which the nerves are the instruments of
sensation, and the muscles of motion, are vital endowments,
incapable of being expressed or explained by any comparison
with mechanical, chemical, and electrical forces, is the
result which we should {224} expect to find, judging from
the whole analogy of science; and which thus is confirmed by
the history of physiology up to the present time. We
naturally, then, turn to inquire whether such peculiar vital
powers have been brought into view with any distinctness and
clearness.

4. The property by which muscles, under proper stimulation,
contract and produce motion, has been termed _Irritability_
or _Contractility_; the property by which nerves are
susceptible of their appropriate impressions has been termed
_Sensibility_. A very few words on each of these subjects
must suffice.

_Irritability._--I have, in the History of Physiology[89\9],
noticed that Glisson, a Cambridge professor, distinguished
the Irritation of muscles as a peculiar property, different
from any merely mechanical or physical action. I have
mentioned, also, that he divides Irritation into _natural_,
_vital_, and _animal_; and points out, though briefly, the
graduated differences of Irritability in different organs.
Although these opinions did not at first attract much
notice, about seventy years afterwards attention was
powerfully called to this vital force, _Irritability_, by
Haller. I shall borrow Sprengel's reflections on this subject.

[Note 89\9: _Hist. Ind. Sc._ b. xvii. c. v.]

'Hitherto men had been led to see more and more clearly that
the cause of the bodily functions, the fundamental power of
the animal frame, is not to be sought in the mechanism, and
still less in the mixture of the parts. In this conviction,
they had had recourse partly to the quite supersensuous
principle of the Soul, partly to the half-material principle
of the Animal Spirits, in order to explain the bodily
motions. Glisson alone saw the necessity of assuming an
Original Power in the fibres, which, independent of the
influence of the animal spirits, should produce contraction
in them. And Gorter first held that this Original Power was
not to be confined to the muscles, but to be extended to all
parts of the living body. {225}

'But as yet the laws of this Power were not known, nor had
men come to an understanding whether it were fully distinct
from the elasticity of the parts, or by what causes it was
put in action. They had neither instituted observations nor
experiments which established its relation to other assumed
forces of the body. There was still wanting a determination
of the peculiar seat of this power, and experiments to trace
its gradual differences in different parts of the body. In
addition to other causes, the necessity of the assumption of
such a power was felt the more, in consequence of the
prevalence of Leibnitz's doctrine of the activity of matter;
but it was an occult quality, and remained so till Haller,
by numerous experiments and solid observations, placed in a
clear light the peculiarities of the powers of the animal body.'

5. Perhaps, however, Haller did more in the way of
determining experimentally the limits and details of the
application of this idea of Irritability as a peculiar
attribute, than in developing the Idea itself. In that way
his merits were great. As early as the year 1739, he
published his opinion upon Irritability as the cause of
muscular motion, which he promulgated again in 1743. But
from the year 1747 he was more attentive to the
peculiarities of Irritability, and its difference from the
effect of the nerves. In the first edition of his
_Physiology_, which appeared in 1747, he distinguished three
kinds of Force in muscles,--the Dead Force, the Innate
Force, and the Nervous Power. The first is identical with
the elastic force of dead matter, and remains even after
death. The _innate force_ continues only a short time after
death, and discloses itself especially by alternate
oscillations; the motions which arise from this are much
more lively than those which arise from mere elasticity:
they are not excited by tension, nor by pressure, nor by any
mechanical alteration, but only by _irritation_. The
_nervous force_ of the muscle is imparted to it from without
by the nerves; it preserves the _irritability_, which cannot
long subsist without the influence of the nervous force, but
is not identical with it. {226}

In the year 1752, Haller laid before the Society of
Göttingen the result of one hundred and ninety experiments;
from which it appears to what parts of the animal system
Irritability and Nervous Power belong. These I need not
enumerate. He also investigated with care its gradations in
those parts which do possess it. Thus the heart possesses it
in the highest degree, and other organs follow in their
order.

6. Haller's doctrine was, that there resides in the muscles
a peculiar vital power by which they contract, and that this
power is distinct from the attributes of the nerves. And
this doctrine has been accepted by the best physiologists of
modern times. But this distinction of the _irritability_ of
the muscles from the _sensibility_ of the nerves became
somewhat clearer by giving to the former attribute the name
of _Contractility_. This accordingly was done; it is, for
example, the phraseology used by Bichat. By speaking of
_animal sensibility_ and _animal contractility_, the passive
and the active element of the processes of animal life are
clearly separated and opposed to each other. The sensations
which we feel, and the muscular action which we exert, may
be closely and inseparably connected, yet still they are
clearly distinguishable. We can easily in our apprehension
separate the titillation felt in the nose on taking snuff,
from the action of the muscles in sneezing; or the
perception of an object falling towards the eye, from the
exertion which shuts the eye-lid; although in these cases
the passive and active part of the process are almost or
quite inseparable in fact. And this clear separation of the
active from the passive power is something, it would seem,
peculiar to the Animal Vital Powers; it is a character by
which they differ, not only from mechanical, chemical, and
all other merely physical forces, but even from Organic
Vital Powers.

7. But this difference between the Animal and the Organic
Vital Powers requires to be further insisted upon, for it
appears to have been overlooked or denied by very eminent
physiologists. For instance, Bichat classifies the Vital
Powers as Animal Sensibility, {227} Animal Contractility,
Organic Sensibility, Organic Contractility.

Now the view which suggests itself to us, in agreement with
what has been said, is this:--that though Animal Sensibility
and Animal Contractility are clearly and certainly distinct,
Organic Sensibility and Organic Contractility are neither
separable in fact nor in our conception, but together make
up a single Vital Power. That they are not separable in fact
is, indeed, acknowledged by Bichat himself. 'The organic
contractility,' he says[90\9], 'can never be separated from
the sensibility of the same kind; the reaction of the
excreting tubes is immediately connected with the action
which the secreted fluids exercise upon them: the
contraction of the heart must necessarily succeed the influx
of the blood into it.' It is not wonderful, therefore, that
it should have happened, as he complains, that 'authors have
by no means separated these two things, either in their
consideration or in language.' We cannot avoid asking, Are
Organic Sensibility and Organic Contractility really
anything more than two different aspects of the same thing,
like action and reaction in mechanics, which are only two
ways of considering the action which takes place at a point;
or like the positive and negative electricities, which, as
we have seen, always co-exist and correspond to each other?

[Note 90\9: _Life and Death_, p. 94.]

8. But we may observe, moreover, that Bichat, by his use of
the term Contractility, includes in it powers to which it
cannot with any propriety be applied. Why should we suppose
that the vital powers of absorption, secretion,
assimilation, are of such a nature that the name
_contractility_ may be employed to describe them? We have
seen, in the last chapter, that the most careful study of
these powers leads us to conceive them in a manner
altogether removed from any notion of contraction. Is it not
then an abuse of language which cannot possibly lead to
anything but {228} confusion, to write thus[91\9]: 'The
insensible organic contractility is that, by virtue of which
the excreting tubes react upon their respective fluids, the
secreting organs upon the blood which flows into them, the
parts where nutrition is performed upon the nutritive
juices, and the lymphatics upon the substances which excite
their open extremities'? In the same manner he
ascribes[92\9] to the peculiar sensibility of each organ the
peculiarity of its products and operations. An increased
absorption is produced by an increased susceptibility of the
'absorbent orifices.' And thus, in this view, each organic
power may be contemplated either as sensibility or as
contractility, and may be supposed to be rendered more
intense by magnifying either of these its aspects; although,
in fact, neither can be conceived to be increased without an
exactly commensurate increase of the other.

[Note 91\9: _Life and Death_, p. 95.]

[Note 92\9: _Ib._ p. 90.]

9. This opinion, unfounded as it thus appears to be, that
all the different organic vital powers are merely different
kinds of Contractility or Excitability, was connected with
the doctrines of Brown and his followers, which were so
celebrated in the last century, that all diseases arise from
increase or from diminution of the Vital Force. The
considerations which have already offered themselves would
lead us to assent to the judgment which Cuvier has
pronounced upon this system. 'The theory of excitation,' he
says, 'so celebrated in these later times by its influence
upon pathology and therapeutick, is at bottom only a
modification of that, in which, including under a common
name Sensibility and Irritability,' and we may add, applying
this name to all the Vital Powers, 'the speculator takes
refuge in an abstraction so wide, that if, by it, he
simplifies medicine, he by it annihilates all positive
physiology[93\9].'

[Note 93\9: _Hist. des Sc. Nat. depuis_ 1789, i. 219.]

10. The separation of the nervous influence and the muscular
irritability, although it has led to many highly instructive
speculations, is not without its {229} difficulties, when
viewed with reference to the Idea of Vital Power. If the
irritability of each muscle reside in the muscle itself, how
does it differ from a mere mechanical force, as elasticity?
But, in point of fact, it is certain that the muscular
irritability of the animal body is not an attribute of the
muscle itself independent of its connexion with the system.
No muscle, or other part, removed from the body, _long_
preserves its irritability. This power cannot subsist
permanently, except in connexion with an organic whole. This
condition peculiarly constitutes irritability a _living_
force: and this condition would be satisfied by considering
the force as derived from the nervous system; but it appears
that though the nervous system has the most important
influence upon all vital actions, the muscular irritability
must needs be considered as something distinct. And thus the
Irritability or Contractility of the muscle is a peculiar
endowment of the texture, but it is at the same time an
endowment which can only co-exist with life; it is, in
short, a peculiar Vital Power.

11. This necessity of the union of the muscle with the whole
nervous system, in order that it may possess irritability,
was the meaning of the true part of Stahl's psychical
doctrine; and the reason why he and his adherents persisted
in asserting the power of the soul even over involuntary
motions. This doctrine was the source of much controversy in
later times.

'But,' says Cuvier[94\9], 'this opposition of opinion may be
reconciled by the intimate union of the nervous substance
with the fibre and the other contractile organic elements,
and by their reciprocal action;--doctrines which had been
presented with so much probability by physiologists of the
Scotch school, but which were elevated above the rank of
hypotheses only by the observations of more recent times.

[Note 94\9: _Hist. des Sc. Nat. depuis_ 1789, i. 213.]

'The fibre does not contract by itself, but by the influence
of the nervous filaments, which are always united with it.
The change which produces the {230} contraction cannot take
place without the concurrence of both these substances; and
it is further necessary that it should be occasioned each
time by an exterior cause, by a stimulant.

'The Will is one of these stimulants; but it only excites
the Irritability, it does not constitute it; for in the case
of persons paralytic from apoplexy, the Irritability
remains, though the power of the Will over it is gone. Thus
_irritability_ depends in part on the _nerve_, but not on
the _sensibility_: this last is another property, still more
admirable and occult than the irritability; but it is only
one among several functions of the nervous system. It would
be an abuse of words to extend this denomination to
functions unaccompanied by perception.'

12. Supposing, then, that Contractility is established as a
peculiar Vital Power residing in the muscles, we may ask
whether we can trace with any further exactness the seat and
nature of this power. It would be unsuitable to the nature
of the present work to dwell upon the anatomical discussions
bearing upon this point. I will only remark that some
anatomists maintain[95\9] that muscles are contracted by
those fibres assuming a zigzag form, which at first were
straight. Others (Professor Owen and Dr. A. Thompson) doubt
the accuracy of this observation; and conceive that the
muscular fibre becomes shorter and thicker, but does not
deviate from a right line. We may remark that the latter
kind of action appears to be more elementary in its nature.
We can, as a matter of geometry, conceive a straight line
thrown into a zigzag shape by muscular contractions taking
place between remote parts of it; but it is difficult to
conceive by what _elementary_ mode of action a straight
fibre could bend itself at certain points, and at certain
points only; since the elementary force must act at every
point of the fibre, and not at certain selected points.

[Note 95\9: Müller, _Elem. Phys._ p. 887.]

13. A circumstance which remarkably marks the difference
between the vital force of Contractility, {231} inherent in
muscles, and any merely dead or mechanical force, is this;
that in assuming their contractile state, muscles exert a
tension which they could not themselves support or convey if
not strengthened by their vital irritability. They are
capable of raising weights by their exertion, which will
tear them asunder when the power of contraction is lost by
death. This has induced Cuvier and other physiologists[96\9]
to believe 'that in the moment of action, the particles that
compose a fibre, not only approach towards each other
longitudinally, but that their cohesive attraction becomes
instantaneously much greater than it was before: for without
such an increase of cohesive force, the tendency to shorten
could not, as it would appear, prevent the fibre from being
torn.' We see here the difficulty, or rather the
impossibility, of conceiving muscular contractility as a
mere mechanical force; and perhaps there is little hope of
any advantage by calling in the aid of chemical hypothesis
to solve the mechanical difficulty. Cuvier conjectures that
a sudden change in the chemical composition may thus so
quickly and powerfully augment the cohesion. But we may ask,
are not a chemical synthesis and analysis, suddenly
performed by a mere act of the will, as difficult to
conceive as a sudden increase and decrease of mechanical
power directly produced by the same cause?

[Note 96\9: Prichard, _Vital Prin._ p. 126.]

14. _Sensibility._ The nerves are the organs and channels of
Sensibility. By means of them we receive our sensations,
whether of mere pleasure and pain, or of qualities which we
ascribe to external objects, as a bitter taste, a sweet
odour, a shrill sound, a red colour, a hard or a hot feeling
of touch. Some of these sensations are but obscurely the
objects of our consciousness; as for example the feeling
which our feet have of the ground, or the sight which our
eyes have of neighbouring objects, when we walk in a
reverie. In these cases the sensations, though obscure,
exist; for they {232} serve to balance and guide us as we
walk. In other cases, our sensations are distinctly and
directly the objects of our attention.

But our Sensations, as we have already said, we ascribe as
Qualities to external objects. By our senses we perceive
objects, and thus our _sensations_ become _perceptions_. We
have not only the sensation of _round_, _purple_, and
_green_, repeated and varied, but the perception of a _bunch
of grapes_ partly ripe and partly unripe. We have not only
sensations of noise and of variously-coloured specks rapidly
changing their places, but we have perceptions, by sound and
sight, of a stone rolling down the hill and crushing the
shrubs in its path. We scarcely ever dwell upon our
Sensations; our thoughts are employed upon Objects. We
regard the impressions upon our nerves, not for what they
_are_, but for what they _tell_ us.

But in what Language do the impressions upon the nerves thus
speak to us of an external world,--of the forms and
qualities and actions of objects? How is it that by the aid
of our nervous system we become acquainted not only with
impressions but with _things_; that we learn not only the
relation of objects to us, but to one another?

15. It has been shown at some length in the previous Books,
that the mode in which Sensations are connected in our minds
so as to convey to us the knowledge of Objects and their
Relations, is by being contemplated with reference to
_Ideas_. Our Sensations, connected by the Idea of Space,
become Figures; connected by the Idea of Time, they become
Causes and Effects; connected by the Idea of Resemblance,
they become Individuals and Kinds; connected by the Idea of
Organization, they become Living Things. It has been shown
that without these Ideas there can be no connexion among our
sensations, and therefore no perception of Figure, Action,
Kind, or in short, of bodies under any aspect whatever.
Sensations are the rude _Matter_ of our perceptions; and are
nothing, except so far as they have _Form_ given them by
Ideas. {233} But thus moulded by our Ideas, Sensation
becomes the source of an endless store of important
Knowledge of every possible kind.

16. But one of the most obvious uses of our perceptions and
our knowledge is to direct our Actions. It is suitable to
the condition of our being that when we perceive a bunch of
grapes, we should be able to pluck and eat the ripe ones;
that when we perceive a stone rushing down the side of a
hill, we should be able to move so as to avoid it. And this
must be done by moving our limbs; in short, by the use of
our muscles. And thus Sensation leads, not directly, but
through the medium of Ideas, to muscular Contraction. I say
that sensation and Muscular action are in such cases
connected through the medium of Ideas. For when we proceed
to pluck the grape which we see, the _sensation_ does not
determine the motion of the hand by any necessary
geometrical or mechanical conditions, as an impression made
upon a machine determines its motions; but the _perception_
leads us to stretch forth the hand to that part of space,
wherever it is, where we _know_ that the grape is; and this,
not in any determinate path, but, it may be, avoiding or
removing intervening obstacles, which we also _perceive_.
There is in every such case a connexion between the
sensation and the resulting action, not of a material but of
a mental kind. The cause and the effect are bound together,
not by physical but by intellectual ties.

17. And thus in such cases, between the two _vital_
operations, Sensation and Muscular Action, there intervenes,
as an intermediate step, Perception or Knowledge, which is
not merely vital but _ideal_. But this is not all; there is
still another mental part of the process which may be
readily distinguished from that which we have described. An
act of the _Will_, a Volition, is that, in the Mind, which
immediately determines the action of the Muscles of the
Body. And thus Will intervenes between Knowledge and Action;
and the cycle of operations which take place when animals
act with reference to external objects is {234}
this:--Sensation, Perception, Volition, Muscular
Contraction.

18. To attempt further to analyse the mental part of this
cycle does not belong to the present part of our work. But
we may remark here, as we have already remarked in the
History[97\9], how irresistibly we are led by physiological
researches into the domain of thought and mind. We pass from
the body to the soul, from physics to metaphysics; from
biology to psychology; from things to persons; from nouns to
pronouns. I have there noticed the manner in which Cuvier
expresses this transition by the introduction of the
pronoun: 'The impression of external objects upon the ME,
the production of a sensation, of an image, is a mystery
impenetrable to our thoughts.'

[Note 97\9: _Hist. Ind. Sc._ b. xvii. c. v. s. 2.]

19. But to return to the merely biological part of our
speculations. We have arrived, it will be perceived, at this
result: that in animal actions there intervenes between the
two terms of Sensation and Muscular Contraction, an
intermediate process; which may be described as a
communication to and from a Center. The Center is the seat
of the sentient and volent faculties, and is of a
_hyperphysical_ nature. But the existence of such a Center
as a necessary element in the functions of the _animal_ life
is a truth which is important in biology. This indeed may be
taken as the peculiar character of animal, as distinguished
from merely _organic_ powers. Accordingly, it is so stated
by Bichat. For although he superfluously, as I have tried to
show, introduces into his list of vital powers an organic
sensibility, he still draws the distinction of which I have
spoken; 'in the animal life, Sensibility is the faculty of
receiving an Impression _plus_ that of referring it to a
common Center[98\9].'

[Note 98\9: _Life and Death_, p. 84.]

20. But since Sensibility and Contractility are thus
connected by reference to a common Center, we may ask,
before quitting the subject, what are the different forms
which this reference assumes? Is the connexion {235} always
attended by the distinct steps of Knowledge and Will,--by a
clear act of consciousness, as in the case which we have
taken, of plucking a grape; or may these steps become
obscure, or vanish altogether?

We need not further illustrate the _conscious_ connexion.
Such actions as we have described are called _voluntary_
actions. In extreme cases, the mental part of the process is
obvious enough. But we may gradually pass from these to
cases in which the mental operation is more and more obscure.

In walking, in speaking, in eating, in breathing, our
muscular exertions are directed by our sensations and
perceptions: yet in such processes, how dimly are we
conscious of perceptive and directive power! How the mind
should be able to exercise such a power, and yet should be
scarcely or not at all conscious of its exercise, is a very
curious problem. But in all or in most of the instances just
mentioned, the solution of this problem appears to depend
upon psychological rather than biological principles, and
therefore does not belong to this place.

21. But in cases at the other extreme (unconscious actions)
the mental part of the operation vanishes altogether. In
many animals, even after decapitation, the limbs shrink when
irritated. The motions of the iris are determined by the
influence of light on our eyes, without our being aware of
the motions. Here Sensations produce Motions, but with no
trace of intervening Perception or Will. The Sensation
appears to be _reflected_ back from the central element of
animal life, in the form of a Muscular Contraction; but in
this case the Sensation is not modified or regulated by any
_Idea_. These reflected motions have no reference to
relations of space or force among surrounding objects. They
are blind and involuntary, like the movements of convulsion,
depending for direction and amount only on the position and
circumstances of the limb itself with its muscles. Here the
Centre from which the reflection takes place is merely
_animal_, not intellectual.

In this case some physiologists have doubted whether the
reflection of the sensation in the form of a muscular {236}
contraction does really take place from the Center; and have
conceived that sensorial impressions might affect motor
nerves without any communication with the nervous Center.
But on this subject we may, I conceive, with safety adopt
the decision of Professor Müller, deliberately given after a
careful examination of the subject: 'When impressions made
by the action of external stimuli on sensitive nerves give
rise to motions in other parts, these motions are never the
result of the _direct_ reaction of the sensitive and motor
fibres of the nerves on each other; the irritation is
conveyed by the sensitive fibres to the brain and spinal
cord, and is by these communicated to the motor fibres.'

22. Thus we have two extreme cases of the connexion of
sensation with muscular action; in one of which the
connexion clearly _is_, and in the other it as clearly _is
not_, determined by relations of Ideas, in its transit
through the nervous Center. There is another highly curious
case standing intermediate between these two, and extremely
difficult to refer to either. I speak of the case of _Instinct_.

Instinct leads to actions which are _such as if they were
determined by Ideas_. The lamb follows its mother by
instinct; but the motions by which it does this, the special
muscular exertions, depend entirely upon the geometrical and
mechanical relations of external bodies, as the form of the
ground, and the force of the wind. The contractions of the
muscles which are requisite in order that the creature may
obey its instinct, vary with every variation of these
external conditions;--are not determined by any rule or
necessity, but by properties of Space and Force. Thus the
action is not governed by Sensations directly, but by
sensations moulded by Ideas. And the same is the case with
other cases of instinct. The dog hunts by instinct; but he
hunts certain kinds of animals merely, thus showing that his
instinct acts according to Resemblances and Differences; he
crosses the field repeatedly to find the track of his prey
by scent; thus recognizing the relations of Space with
reference to the track; he leaps, adjusting his Force to
{237} the distance and height of the leap with mechanical
precision; and thus he practically recognizes the Ideas of
Resemblance, Space, and Force.

But have animals such Ideas? In any proper sense in which we
can speak of possessing Ideas, it appears plain that they
have not. Animals cannot, at any time, be said properly to
possess ideas, for ideas imply the possibility of
_speculative_ knowledge.

23. But even if we allow to animals only the _practical_
possession of Ideas, we have still a great difficulty
remaining. In the case of man, his ideas are unfolded
gradually by his intercourse with the external world. The
child learns to distinguish forms and positions by a
repeated and incessant use of his hands and eyes; he learns
to walk, to run, to leap, by slow and laborious degrees; he
distinguishes one man from another, and one animal from
another, only after repeated mistakes. Nor can we conceive
this to be otherwise. How should the child know at once what
muscles he is to exert in order to touch with his hand a
certain visible object? How should he know what muscles to
exert that he may stand and not fall, till he has tried
often? How should he learn to direct his attention to the
differences of different faces and persons, till he is
roused by some memory, or hope which implies memory? It
seems to us as if the sensations could not, without
considerable practice, be rightly referred to Ideas of
Space, Force, Resemblance, and the like.

Yet that which thus appears impossible, is in fact done by
animals. The lamb almost immediately after its birth follows
its mother, accommodating the actions of its muscles to the
form of the ground. The chick, just escaped from the shell,
picks up a minute insect, directing its beak with the
greatest accuracy. Even the human infant seeks the breast
and exerts its muscles in sucking, almost as soon as it is
born. Hence, then, we see that Instinct produces at once
actions regulated by Ideas, or, at least, which take place
_as if_ they were regulated by Ideas; although the Ideas
cannot have been developed by exercise, and only appear to
exist so far as such actions are concerned. {238}

24. The term _Instinct_ may properly be opposed to
_Insight_. The former implies an inward principle of action,
implanted within a creature and practically impelling it,
but not capable of being developed into a subject of
contemplation. While the instinctive actions of animals are
directed by such a principle, the deliberate actions of man
are governed by insight: he can contemplate the ideal
relations on which the result of his action depends. He can
in his mind map the path he will follow, and estimate the
force he will exert, and class the objects he has to deal
with, and determine his actions by the relations which he
thus has present to his mind. He thus possesses Ideas not
only practically, but speculatively. And knowing that the
Ideas by which he commonly directs his actions, Space,
Cause, Resemblance, and the like, have been developed to
that degree of clearness in which he possesses them by the
assiduous exercise of the senses and the mind from the
earliest stage of infancy, and that these Ideas are capable
of being still further unfolded into long trains of
speculative truth, he is unable to conceive the manner in
which animals possess such Ideas as their instinctive
actions disclose:--Ideas which neither require to be
unfolded nor admit of unfolding; which are adequate for
practical purposes without any previous exercise, and
inadequate for speculative purposes with whatever labour
cultivated.

I have ventured to make these few remarks on Instinct since
it may, perhaps, justly be considered as the last province
of Biology, where we reach the boundary line of Psychology.
I have now, before quitting this subject, only one other
principle to speak of.

{{239}}
CHAPTER VI.

OF THE IDEA OF FINAL CAUSES.

1. BY an examination of those notions which enter into all
our reasonings and judgments on living things, it appeared
that we conceive animal life as a vortex or cycle of moving
matter in which the form of the vortex determines the
motions, and these motions again support the form of the
vortex: the stationary parts circulate the fluids, and the
fluids nourish the permanent parts. Each portion ministers
to the others, each depends upon the other. The parts make
up the whole, but the existence of the whole is essential to
the preservation of the parts. But parts existing under such
conditions are _organs_, and the whole is _organized_. This
is the fundamental conception of organization. 'Organized
beings,' says the physiologist[99\9], 'are composed of a
number of essential and mutually dependent parts.' 'An
organized product of nature,' says the great
metaphysician[100\9], 'is that in which all the parts are
mutually ends and means.'

[Note 99\9: Müller, _Elem._ p. 18.]

[Note 100\9: Kant, _Urtheilskraft_, p. 296.]

2. It will be observed that we do not content ourselves with
saying that in such a whole, all the parts are _mutually
dependent_. This might be true even of a mechanical
structure; it would be easy to imagine a framework in which
each part should be necessary to the support of each of the
others; for example, an arch of several stones. But in such
a structure, the parts have no properties which they derive
from the whole. They are beams or stones when separate; they
are no more when joined. But the same is not the case in an
organized whole. The limb of an animal separated {240} from
the body, loses the properties of a limb, and soon ceases to
retain even its form.

3. Nor do we content ourselves with saying that the parts
are _mutually causes and effects_. This is the case in
machinery. In a clock, the pendulum by means of the
escapement causes the descent of the weight, the weight by
the same escapement keeps up the motion of the pendulum. But
things of this kind may happen by accident. Stones slide
from a rock down the side of a hill and cause it to be
smooth; the smoothness of the slope causes stones still to
slide. Yet no one would call such a slide an organized
system. The system is organized, when the effects which take
place among the parts are _essential to our conception of
the whole_; when the whole would not _be_ a whole, nor the
parts, parts, except these effects were produced; when the
effects not only happen in fact, but are included in the
idea of the object; when they are not only seen, but
foreseen; not only expected, but intended: in short when,
instead of being causes and effects, they are _ends_ and
_means_, as they are termed in the above definition.

Thus we necessarily include, in our Idea of Organization,
the notion of an End, a Purpose, a Design; or, to use
another phrase which has been peculiarly appropriated in
this case, a _Final Cause_. This idea of a Final Cause is an
essential condition in order to the pursuing our researches
respecting organized bodies.

4. This Idea of Final Cause is not _deduced_ from the
phenomena by reasoning, but is _assumed_ as the only
condition under which we can reason on such subjects at all.
We do not deduce the Idea of Space, or Time, or efficient
Cause from the phenomena about us, but necessarily look at
phenomena as subordinate to these Ideas from the beginning
of our reasoning. It is true, our ideas of relations of
Space, and Time, and Force, may become much more clear by
our familiarizing ourselves with particular phenomena: but
still, the Fundamental Ideas are not generated, but
unfolded; not extracted from the external world, but evolved
from the world within. In like manner, in the contemplation
of organic structures, we consider {241} each part as
subservient to some use, and we cannot study the structure
as organic without such a conception. This notion of
adaptation,--this Idea of an End,--may become much more
clear and impressive by seeing it exemplified in particular
cases. But still, though suggested and evoked by special
cases, it is not furnished by them. If it be not supplied by
the mind itself, it can never be logically deduced from the
phenomena. It is not a portion of the facts which we study,
but it is a principle which connects, includes, and renders
them intelligible; as our other Fundamental Ideas do the
classes of facts to which they respectively apply.

5. This has already been confirmed by reference to fact; in
the History of Physiology, I have shown that those who
studied the structure of animals were irresistibly led to
the conviction that the parts of this structure have each
its end or purpose;--that each member and organ not merely
produces a certain effect or answers a certain use, but is
so framed as to impress us with the persuasion that it was
constructed _for_ that use:--that it was _intended_ to
produce the effect. It was there seen that this persuasion
was repeatedly expressed in the most emphatic manner by
Galen;--that it directed the researches and led to the
discoveries of Harvey;--that it has always been dwelt upon
as a favourite contemplation, and followed as a certain
guide, by the best anatomists;--and that it is inculcated by
the physiologists of the profoundest views and most
extensive knowledge of our own time. All these persons have
deemed it a most certain and important principle of
physiology, that in every organized structure, plant or
animal, each intelligible part has its allotted
office:--each organ is designed for its appropriate
function:--that nature, in these cases, produces nothing in
vain: that, in short, each portion of the whole arrangement
has its _final cause_; an End to which it is adapted, and in
this End, the reason that it is where and what it is.

6. This Notion of Design in organized bodies must, I say, be
supplied by the student of organization out of his own mind:
a truth which will become clearer if {242} we attend to the
most conspicuous and acknowledged instances of _design_. The
structure of the Eye, in which the parts are curiously
adjusted so as to produce a distinct image on the retina, as
in an optical instrument;--the Trochlear Muscle of the eye,
in which the tendon passes round a support and turns back,
like a rope round a pulley;--the prospective contrivances
for the preservation of animals, provided long before they
are wanted, as the Milk of the mother, the Teeth of the
child, the Eyes and Lungs of the fœtus:--these arrangements,
and innumerable others, call up in us a persuasion that
Design has entered into the plan of animal form and
progress. And if we bring in our minds this conception of
Design, nothing can more fully square with and fit it, than
such instances as these. But if we did not already possess
the Idea of Design;--if we had not had our notion of
mechanical contrivance awakened by inspection of optical
instruments, or pulleys, or in some other way:--if we had
never been conscious ourselves of providing for the
future;--if this were the case, we could not recognize
contrivance and prospectiveness in such instances as we have
referred to. The facts are, indeed, admirably in accordance
with these conceptions, when the two are brought together:
but the facts and the conceptions come together from
different quarters--from without and from within.

7. We may further illustrate this point by referring to the
relations of travellers who tell us that when consummate
examples of human mechanical contrivance have been set
before savages, they have appeared incapable of apprehending
them as proofs of design. This shows that in such cases the
Idea of Design had not been developed in the minds of the
people who were thus unintelligent: but it no more proves
that such an idea does not naturally and necessarily arise,
in the progress of men's minds, than the confused manner in
which the same savages apprehend the relations of space, or
number, or cause, proves that these ideas do not naturally
belong to their intellects. All men have these ideas; and it
is because they {243} cannot help referring their sensations
to such ideas, that they apprehend the world as existing in
time and space, and as a series of causes and effects. It
would be very erroneous to say that the belief of such
truths is obtained by logical reasoning from facts. And in
like manner we cannot logically deduce design from the
contemplation of organic structures; although it is
impossible for us, when the facts are clearly before us, not
to find a reference to design operating in our minds.

8. Again; the evidence of the doctrine of Final Causes as a
fundamental principle of Biology may be obscured and
weakened in some minds by the constant habit of viewing this
doctrine with suspicion as unphilosophical and at variance
with Morphology. By cherishing such views, it is probable
that many persons, physiologists and others, have gradually
brought themselves to suppose that many or most of the
arrangements which are familiarly adduced as instances of
design may be accounted for, or explained away;--that there
is a certain degree of prejudice and narrowness of
comprehension in that lively admiration of the adaptation of
means to ends which common minds derive from the spectacle
of organic arrangements. And yet, even in persons accustomed
to these views, the strong and natural influence of the Idea
of a Final Cause, the spontaneous recognition of the
relation of Means to an End as the assumption which makes
organic arrangements intelligible, breaks forth when we
bring before them a new case, with regard to which their
genuine convictions have not yet been modified by their
intellectual habits. I will offer, as an example which may
serve to illustrate this, the discoveries recently made with
regard to the process of Suckling in the Kangaroo. In the
case of this, as of other pouched animals, the young animal
is removed, while very small and imperfectly formed, from
the womb to the pouch, in which the teats are, and is there
placed with its lips against one of the nipples. But the
young animal taken altogether is not so large as the nipple,
and is therefore incapable of sucking after the manner of
common mammals. Here is a difficulty: {244} how is it
overcome?--By an appropriate _contrivance_: the nipple,
which in common mammals is not furnished with any muscle, is
in the kangaroo provided with a powerful extrusory muscle by
which the mother can inject the milk into the mouth of her
offspring. And again; in order to give attachment to this
muscle there is a bone which is not found in animals of
other kinds. But this mode of solving the problem of
suckling so small a creature introduces another difficulty.
If the milk is injected into the mouth of the young one,
without any action of its own muscles, what is to prevent
the fluid entering the windpipe and producing suffocation?
How is this danger avoided?--By another appropriate
_contrivance_: there is a funnel in the back of the throat
by which the air passage is completely separated from the
passage for nutriment, and the injected milk passes in a
divided stream on each side of the larynx to the
œsophagus[101\9]. And as if to show that this apparatus is
really formed with a view to the wants of the young one, the
structure alters in the course of the animal's growth; and
the funnel, no longer needed, is modified and disappears.

[Note 101\9: Mr. Owen, in _Phil. Trans._ 1834, p. 348.]

With regard to this and similar examples, the remark which I
would urge is this:--that no one, however prejudiced or
unphilosophical he may in general deem the reference to
Final Causes, can, at the first impression, help regarding
this curious system of arrangement as the Means to an End.
So contemplated, it becomes significant, intelligible,
admirable: without such a principle, it is an unmeaning
complexity, a collection of contradictions, producing an
almost impossible result by a portentous conflict of
chances. The parts of this apparatus cannot have produced
one another: one part is in the mother; another part in the
young one: without their harmony they could not be
effective; but nothing except design can operate to make
them harmonious. They are _intended_ to work together; and
we cannot resist the conviction of this intention when the
facts first come before us. Perhaps {245} there may
hereafter be physiologists who, tracing the gradual
development of the parts of which we have spoken, and the
analogies which connect them with the structures of other
animals, may think that this development, these analogies,
account for the conformation we have described; and may
hence think lightly of the explanation derived from the
reference to Final Causes. Yet surely it is clear, on a calm
consideration of the subject, that the latter explanation is
not disturbed by the former; and that the observer's first
impression, that this is 'an irrefragable evidence of
creative foresight[102\9],' can never be obliterated;
however much it may be obscured in the minds of those who
confuse this view by mixing it with others which are utterly
heterogeneous to it, and therefore cannot be contradictory.

[Note 102\9: Mr. Owen, in _Phil. Trans._ 1834, p. 349.]

9. I have elsewhere[103\9] remarked how physiologists, who
thus look with suspicion and dislike upon the introduction
of Final Causes into physiology, have still been unable to
exclude from their speculations causes of this kind. Thus
Cabanis says[104\9], 'I regard with the great Bacon, the
philosophy of Final Causes as sterile; but I have elsewhere
acknowledged that it was very difficult for the most
cautious man never to have recourse to them in his
explanations.' Accordingly, he says, 'The partisans of Final
Causes nowhere find arguments so strong in favour of their
way of looking at nature as in the laws which preside and
the circumstances of all kinds which concur in the
reproduction of living races. In no case do the means
employed appear so clearly relative to the end.' And it
would be easy to find similar acknowledgments, express or
virtual, in other writers of the same kind. Thus Bichat,
after noting the difference between the organic sensibility
by which the organs are made to perform their offices, and
the animal sensibility of which the {246} nervous center is
the seat, says[105\9], 'No doubt it will be asked,
_why_'--that is, as we shall see, for what _end_--'the
organs of internal life have received from nature an
inferior degree of sensibility only, and why they do not
transmit to the brain the impressions which they receive,
while all the acts of the animal life imply this
transmission? The reason is simply this, that all the
phenomena which establish our connexions with surrounding
objects _ought to be_, and are in fact, under the influence
of the Will; while all those which serve for the purpose of
assimilation only, escape, and _ought_ indeed to escape,
such influence.' The _reason_ here assigned is the Final
Cause; which, as Bichat justly says, we cannot help asking
for.

[Note 103\9: _Bridgewater Treatise_, p. 352.]

[Note 104\9: _Rapports du Physique et du Moral_, i. 299.]

[Note 105\9: _Life and Death_, (trans.) p. 32.]

10. Again; I may quote from the writer last mentioned
another remark, which shows that in the organical sciences,
and in them alone, the Idea of forces as Means acting to an
End, is inevitably assumed and acknowledged as of supreme
authority. In Biology alone, observes Bichat[106\9], have we
to contemplate the state of _Disease_. 'Physiology is to the
movements of living bodies, what astronomy, dynamics,
hydraulics, &e., are to those of inert matter: but these
latter sciences have no branches which correspond to them as
Pathology corresponds to Physiology. For the same reason all
notion of a Medicament is repugnant to the physical
sciences. A Medicament has for its object to bring the
properties of the system back to their Natural Type; but the
physical properties never depart from this Type, and have no
need to be brought back to it: and thus there is nothing in
the physical sciences which holds the place of Therapeutick
in Physiology.' Or, as we might express it otherwise, of
inert forces we have no conception of what they _ought to
do_, except what they _do_. The forces of gravity,
elasticity, affinity, never act in a _diseased_ manner; we
never conceive them as failing in their purpose; for we do
not conceive them as having any purpose which is answered by
one mode of their action rather than {247} another. But with
_organical_ forces the case is different; they are
necessarily conceived as acting for the preservation and
development of the system in which they reside. If they do
not do this, they fail, they are deranged, diseased. They
have for their object to conform the living being to a
certain type; and if they cause or allow it to deviate from
this type, their action is distorted, morbid, contrary to
the ends of nature. And thus this conception of organized
beings as susceptible of disease, implies the recognition of
a state of health, and of the organs and the vital forces as
means for preserving this normal condition. The state of
health, and of perpetual development, is necessarily
contemplated as the Final Cause of the processes and powers
with which the different parts of plants and animals are
endowed.

[Note 106\9: _Anatomie Générale_, i. liii.]

11. This Idea of a Final Cause is applicable as a
fundamental and regulative idea to our speculations
concerning organized creatures only. That there is a purpose
in many other parts of the creation, we find abundant reason
to believe, from the arrangements and laws which prevail
around us. But this persuasion is not to be allowed to
regulate and direct our reasonings with regard to inorganic
matter, of which conception the relation of means and end
forms no essential part. In mere Physics, Final Causes, as
Bacon has observed, are not to be admitted as a principle of
reasoning. But in the organical sciences, the assumption of
design and purpose in every part of every whole, that is,
the pervading idea of Final Cause, is the basis of sound
reasoning and the source of true doctrine.

12. The Idea of Final Cause, of end, purpose, design,
intention, is altogether different from the Idea of Cause,
as Efficient Cause, which we formerly had to consider; and
on this account the use of the word Cause in this phrase has
been objected to. If the idea be clearly entertained and
steadily applied, the word is a question of subordinate
importance. The term Final Cause has been long familiarly
used, and appears not likely to lead to confusion. {248}

13. The consideration of Final Causes, both in physiology
and in other subjects, has at all times attracted much
attention, in consequence of its bearing upon the belief of
an Intelligent Author of the Universe. I do not intend, in
this place, to pursue the subject far in this view: but
there is one antithesis of opinion, already noticed in the
History of Physiology, on which I will again make a few
remarks[107\9].

[Note 107\9: _Hist. Ind. Sc._ b. xvii. c. viii. On the
Doctrine of Final Causes in Physiology.]

It has appeared to some persons that the mere aspect of
order and symmetry in the works of nature--the contemplation
of comprehensive and consistent law--is sufficient to lead
us to the conception of a design and intelligence producing
the order and carrying into effect the law. Without here
attempting to decide whether this is true, we may discern,
after what has been said, that the conception of Design,
arrived at in this manner, is altogether different from that
Idea of Design which is suggested to us by organized bodies,
and which we describe as the doctrine of Final Causes. The
regular form of a crystal, whatever beautiful symmetry it
may exhibit, whatever general laws it may exemplify, does
not prove design in the same manner in which design is
proved by the provisions for the preservation and growth of
the seeds of plants, and of the young of animals. The law of
universal gravitation, however wide and simple, does not
impress us with the belief of a purpose, as does that
propensity by which the two sexes of each animal are brought
together. If it could be shown that the symmetrical
structure of a flower results from laws of the same kind as
those which determine the regular forms of crystals, or the
motions of the planets, the discovery might be very striking
and important, but it would not at all come under our idea
of Final Cause.

14. Accordingly, there have been, in modern times, two
different schools of physiologists, the one proceeding upon
the idea of Final Causes, the other school {249} seeking in
the realm of organized bodies wide laws and analogies from
which that idea is excluded. All the great biologists of
preceding times, and some of the greatest of modern times,
have belonged to the former school; and especially Cuvier,
who may be considered as the head of it. It was solely by
the assiduous application of this principle of Final Cause,
as he himself constantly declared, that he was enabled to
make the discoveries which have rendered his name so
illustrious, and which contain a far larger portion of
important anatomical and biological truth than it ever
before fell to the lot of one man to contribute to the science.

The opinions which have been put in opposition to the
principle of Final Causes have, for the most part, been
stated vaguely and ambiguously. Among the most definite of
such principles, is that which, in the History of the
subject, I have termed the Principle of Metamorphosed and
Developed Symmetry, upon which has been founded the science
of Morphology.

The reality and importance of this principle are not to be
denied by us: we have shown how they are proved by its
application in various sciences, and especially in botany.
But those advocates of this principle who have placed it in
antithesis to the doctrine of Final Causes, have, by this
means, done far more injustice to their own favourite
doctrine than damage to the one which they opposed. The
adaptation of the bones of the skeleton to the muscles, the
provision of fulcrums, projecting processes, channels, so
that the motions and forces shall be such as the needs of
life require, cannot possibly become less striking and
convincing, from any discovery of general analogies of one
animal frame with another, or of laws connecting the
development of different parts. Whenever such laws are
discovered, we can only consider them as the means of
producing that adaptation which we so much admire. Our
conviction that the Artist works intelligently, is not
destroyed, though it may be modified and transferred, when
we obtain a sight of his tools. Our discovery of laws cannot
contradict our persuasion of ends; our Morphology cannot
prejudice our Teleology. {250}

15. The irresistible and constant apprehension of a purpose
in the forms and functions of animals has introduced into
the writings of speculators on these subjects various forms
of expression, more or less precise, more or less
figurative; as, that 'animals are framed with a view to the
part which they have to play;'--that 'nature does nothing in
vain;' that 'she employs the best means for her ends;' and
the like. However metaphorical or inexact any of these
phrases may be in particular, yet taken altogether, they
convey, clearly and definitely enough to preclude any
serious errour, a principle of the most profound reality and
of the highest importance in the organical sciences. But
some adherents of the morphological school of which 1 have
spoken reject, and even ridicule, all such modes of
expression. 'I know nothing,' says M. Geoffroy Saint
Hilaire, 'of animals which have to play a part in nature. I
cannot make of nature an intelligent being who does nothing
in vain; who acts by the shortest mode; who does all for the
best.' The philosophers of this school, therefore, do not,
it would seem, feel any of the admiration which is
irresistibly excited in all the rest of mankind at the
contemplation of the various and wonderful adaptations for
the preservation, the enjoyment, the continuation of the
creatures which people the globe;--at the survey of the
mechanical contrivances, the chemical agencies, the
prospective arrangements, the compensations, the minute
adaptations, the comprehensive interdependencies, which
zoology and physiology have brought into view, more and
more, the further their researches have been carried. Yet
the clear and deep-seated conviction of the reality of these
provisions, which the study of anatomy produces in its most
profound and accurate cultivators, cannot be shaken by any
objections to the metaphors or terms in which this
conviction is clothed. In regard to the Idea of a Purpose in
organization, as in regard to any other idea, we cannot
fully express our meaning by phrases borrowed from any
extraneous source; but that impossibility arises precisely
from the circumstance of its being a Fundamental Idea which
is inevitably assumed in our {251} representation of each
special fact. The same objection has been made to the idea
of mechanical _force_, on account of its being often
expressed in metaphorical language; for writers have spoken
of an _energy_, _effort_, or _solicitation_ to motion; and
bodies have been said to be _animated_ by a force. Such
language, it has been urged, implies volition, and the act
of animated beings. But the idea of Force as distinct from
mere motion,--as the Cause of motion, or of tendency to
motion,--is not on that account less real. We endeavour in
vain to conduct our mechanical reasonings without the aid of
this idea, and must express it as we can. Just as little can
we reason concerning organized beings without assuming that
each part has its function, each function its purpose; and
so far as our phrases imply this, they will not mislead us,
however inexact, or however figurative they be.

16. The doctrine of a purpose in Organization has been
sometimes called the doctrine of _the Conditions of
Existence_; and has been stated as teaching that each animal
must be so framed as to contain in its structure the
Conditions which its existence requires. When expressed in
this manner, it has given rise to the objection, that it
merely offers an identical proposition; since no animal can
exist without such conditions. But in reality, such
expressions as those just quoted give an inadequate
statement of the Principle of a Final Cause. For we discover
in innumerable cases, arrangements in an animal, of which we
see, indeed, that they are subservient to its well being;
but the nature of which we never should have been able at
all to conjecture, from considering what was necessary to
its existence, and which strike us, no less by their
unexpectedness than by their adaptation: so far are they
from being presented by any perceptible necessity. Who would
venture to say that the trochlear muscle, or the power of
articulate speech, must occur in man, because they are the
necessary conditions of his existence? When, indeed, the
general scheme and mode of being of an animal are known, the
expert and profound anatomist can reason concerning the
proportions and {252} form of its various parts and organs,
and prove in some measure what their relations must be. We
can assert, with Cuvier, that certain forms of the viscera
require certain forms of the teeth, certain forms of the
limbs, certain powers of the senses. But in all this, the
functions of self-nutrition and digestion are supposed
already existing as ends: and it being taken for granted, as
the only conceivable basis of reasoning, that the organs are
means to these ends, we may discover what modifications of
these organs are necessarily related to and connected with
each other. Instead of terming this rule of speculation
merely 'the Principle of the Conditions of Existence,' we
might term it 'the Principle of the conditions of organs as
_Means_ adapted to animal existence as their _End_.' And how
far this principle is from being a mere barren truism, the
extraordinary discoveries made by the great assertor of the
principle, and universally assented to by naturalists,
abundantly prove. The vast extinct creation which is
recalled to life in Cuvier's great work, the _Ossemens
Fossiles_, cannot be the consequence of a mere identical
proposition.

17. It has been objected, also, that the doctrine of Final
Causes supposes us to be acquainted with the intentions of
the Creator; which, it is insinuated, is a most presumptuous
and irrational basis for our reasonings. But there can be
nothing presumptuous or irrational in reasoning on that
basis, which if we reject, we cannot reason at all. If men
really can discern, and cannot help discerning, a design in
certain portions of the works of creation, this perception
is the soundest and most satisfactory ground for the
convictions to which it leads. The Ideas which we
necessarily employ in the contemplation of the world around
us, afford us the only natural means of forming any
conception of the Creator and Governor of the Universe; and
if we are by such means enabled to elevate our thoughts,
however inadequately, towards Him, where is the presumption
of doing so? or rather, where is the wisdom of refusing to
open our minds to contemplations so animating and elevating,
and yet {253} so entirely convincing? We possess the ideas
of Time and Space, under which all the objects of the
universe present themselves to us; and in virtue of these
ideas thus possessed, we believe the Creator to be eternal
and omnipotent. When we find that we, in like manner,
possess the idea of a Design in Creation, and that with
regard to ourselves, and creatures more or less resembling
ourselves, we cannot but contemplate their constitution
under this idea, we cannot abstain from ascribing to the
Creator the infinite profundity and extent of design to
which all these special instances belong as parts of a whole.

18. I have here considered Design as manifest in
organization only: for in that field of speculation it is
forced upon us as contained in all the phenomena, and as the
only mode of our understanding them. The existence of Final
Causes has often been pointed out in other portions of the
creation;--for instance, in the apparent adaptations of the
various parts of the earth and of the solar system to each
other and to organized beings. In these provinces of
speculation, however, the principle of Final Causes is no
longer the basis and guide, but the sequel and result of our
physical reasonings. If in looking at the universe, we
follow the widest analogies of which we obtain a view, we
see, however dimly, reason to believe that all its laws are
adapted to each other, and intended to work together for the
benefit of its organic population, and for the general
welfare of its rational tenants. On this subject, however,
not immediately included in the principle of Final Causes as
here stated, I shall not dwell. I will only make this
remark; that the assertion appears to be quite unfounded,
that as science advances from point to point, Final Causes
recede before it, and disappear one after the other. The
principle of design changes its mode of application indeed,
but it loses none of its force. We no longer consider
particular facts as produced by special interpositions, but
we consider design as exhibited in the establishment and
adjustment of the laws by which particular facts are
produced. We do not look upon each particular {254} cloud as
brought near us that it may drop fatness on our fields; but
the general adaptation of the laws of heat, and air, and
moisture, to the promotion of vegetation, does not become
doubtful. We do not consider the sun as less intended to
warm and vivify the tribes of plants and animals, because we
find that, instead of revolving round the earth as an
attendant, the earth along with other planets revolves round
him. We are rather, by the discovery of the general laws of
nature, led into a scene of wider design, of deeper
contrivance, of more comprehensive adjustments. Final
causes, if they appear driven further from us by such an
extension of our views, embrace us only with a vaster and
more majestic circuit: instead of a few threads' connecting
some detached objects, they become a stupendous net-work,
which is wound round and round the universal frame of things.

19. I now quit the subject of Biology, and with it the
circle of sciences depending upon separate original Ideas
and permanent relations. If from the general relations which
permanently prevail and constantly recur among the objects
around us, we turn to the inquiry of what has actually
happened,--if from Science we turn to History,--we find
ourselves in a new field. In this region of speculation we
can rarely obtain a complete and scientific view of the
connexion between objects and events. The past History of
Man, of the Arts, of Languages, of the Earth, of the Solar
System, offers a vast series of problems, of which perhaps
not one has been rigorously solved. Still, man, as his
speculative powers unfold themselves, cannot but feel
prompted and invited to employ his thoughts even on these
problems. He cannot but wish and endeavour to understand the
connexion between the successive links of such chains of
events. He attempts to form a Science which shall be
applicable to each of these Histories; and thus he begins to
construct the class of sciences to which I now, in the last
place, proceed.

{{255}}
BOOK X.

THE
PHILOSOPHY
OF
PALÆTIOLOGY.

τὴν μὲν οὖν τοιαύτην _Αἰτιολογίαν_ ἧττον ἄν τις ἀποδέξαιτο·
μᾶλλον _δ᾽ ἀπὸ τῶν φανερωτέρων_ καὶ τῶν καθ᾽ ἡμέραν τρόπον
τινὰ ὁρωμένων ἀναπτέον τὸν λόγον. Καὶ γὰρ κατακλυσμοὶ, καὶ
σεισμοὶ, καὶ ἀναφυσήματα, καὶ ἀνοιδήσεις τῆς ὑφάλου γῆς,
μετεωρίζουσι καὶ τὴν θάλατταν· αἱ δὲ συνιζήσεις ταπεινοῦσιν
αὐτήν.

STRABO, _Geogr._ 1. p. 54.

IT is therefore, not so much what these forms of the earth
actually are, as what they are continually becoming, that we
have to observe; nor is it possible thus to observe them
without an instinctive reference to the first state out of
which they have been brought.... Yet to such questions
continually suggesting themselves, it is never possible to
give a complete answer. For a certain distance, the past
work of existing forces can be traced; but then gradually
the mist gathers, and the footsteps of more gigantic
agencies are traceable in the darkness; and still as we
endeavour to penetrate further and further into departed
time, the thunder of the Almighty power sounds louder and
louder, and the clouds gather broader and more fearfully,
until at last the Sinai of the world is seen altogether upon
a smoke, and the fence of its foot is reached, where none
can break through.

RUSKIN, _Modern Painters_, Vol. IV. p. 143.

{{257}}
BOOK X.

THE PHILOSOPHY OF PALÆTIOLOGY.

CHAPTER I.

OF PALÆTIOLOGICAL SCIENCES IN GENERAL.

1. I HAVE already stated in the _History of the
Sciences_[1\10], that the class of Sciences which I
designate as _Palætiological_ are those in which the object
is to ascend from the present state of things to a more
ancient condition, from which the present is derived by
intelligible causes. As conspicuous examples of this class
we may take Geology, Glossology or Comparative Philology,
and Comparative Archæology. These provinces of knowledge
might perhaps be intelligibly described as _Histories_; the
History of the Earth,--the History of Languages,--the
History of Arts. But these phrases would not fully describe
the sciences we have in view; for the object to which we now
suppose their investigations to be directed is, not merely
to ascertain what the series of events has been, as in the
common forms of History, but also how it has been brought
about. These sciences are to treat of causes as well as of
effects. Such researches might be termed _Philosophical
History_; or, in order to mark more distinctly that the
_causes_ of events are the leading object of attention,
_Ætiological History_. But since {258} it will be more
convenient to describe this class of sciences by a single
appellation, I have taken the liberty of proposing to call
them[2\10] the _Palætiological_ Sciences.

[Note 1\10: B. xviii. Introd.]

[Note 2\10: A philological writer, in a very interesting
work (Mr. Donaldson, in his _New Cratylus_, p. 12),
expresses his dislike of this word, and suggests that I must
mean _palæ-ætiological_. I think the word is more likely to
obtain currency in the more compact and euphonious form in
which I have used it. It has been adopted by Mr. Winning, in
his _Manual of Comparative Philology_, and more recently, by
other writers.]

While Palæontology describes the beings which have lived in
former ages without investigating their causes, and
_Ætiology_ treats of causes without distinguishing
historical from mechanical causation; _Palætiology_ is a
combination of the two sciences; exploring, by means of the
second, the phenomena presented by the first. The portions
of knowledge which I include in this term are
palæontological ætiological sciences.

2. All these sciences are connected by this bond;--that they
all endeavour to ascend to a past state, by considering what
is the present state of things, and what are the causes of
change. Geology examines the existing appearance of the
materials which form the earth, infers from them previous
conditions, and speculates concerning the forces by which
one condition has been made to succeed another. Another
science, cultivated with great zeal and success in modern
times, compares the languages of different countries and
nations, and by an examination of their materials and
structure, endeavours to determine their descent from one
another: this science has been termed _Comparative
Philology_, or _Ethnography_; and by the French,
_Linguistique_, a word which we might imitate in order to
have a single name for the science, but the Greek derivative
_Glossology_ appears to be more convenient in its form. The
progress of the Arts (Architecture and the like);--how one
stage of the culture produced another; and how far we can
trace their maturest and most complete condition to their
earliest form in various nations;--are problems of great
interest belonging to another subject, which we may for the
present term {259} _Comparative Archæology_. I have already
noticed, in the History[3\10] how the researches into the
origin of natural objects, and those relating to works of
art, pass by slight gradations into each other; how the
examination of the changes which have affected an ancient
temple or fortress, harbour or river, may concern alike the
geologist and the antiquary. Cuvier's assertion that the
geologist is an antiquary of a new order, is perfectly
correct, for both are palætiologists.

[Note 3\10: B. xviii. Introd.]

3. We are very far from having exhausted, by this
enumeration, the class of sciences which are thus connected.
We may easily point out many other subjects of speculation
of the same kind. As we may look back towards the first
condition of our planet, we may in like manner turn our
thoughts towards the first condition of the solar system,
and try whether we can discern any traces of an order of
things antecedent to that which is now established; and if
we find, as some great mathematicians have conceived,
indications of an earlier state in which the planets were
not yet gathered into their present forms, we have, in the
pursuit of this train of research, a palætiological portion
of Astronomy. Again, as we may inquire how languages, and
how man, have been diffused over the earth's surface from
place to place, we may make the like inquiry with regard to
the races of plants and animals, founding our inferences
upon the existing geographical distribution of the animal
and vegetable kingdoms: and thus the Geography of Plants and
of Animals also becomes a portion of Palætiology. Again, as
we can in some measure trace the progress of Arts from
nation to nation and from age to age, we can also pursue a
similar investigation with respect to the progress of
Mythology, of Poetry, of Government, of Law. Thus the
philosophical history of the human race, viewed with
reference to these subjects, if it can give rise to
knowledge so exact as to be properly called Science, will
supply Sciences belonging to the class I am now to consider. {260}

4. It is not an arbitrary and useless proceeding to
construct such a Class of Sciences. For wide and various as
their subjects are, it will be found that they have all
certain principles, maxims, and rules of procedure in
common; and thus may reflect light upon each other by being
treated of together. Indeed it will, I trust, appear, that
we may by such a juxtaposition of different speculations,
obtain most salutary lessons. And questions, which, when
viewed as they first present themselves under the aspect of
a special science, disturb and alarm men's minds, may
perhaps be contemplated more calmly, as well as more
clearly, when they are considered as general problems of
palætiology.

5. It will at once occur to the reader that, if we include
in the circuit of our classification such subjects as have
been mentioned,--politics and law, mythology and poetry,--we
are travelling very far beyond the material sciences within
whose limits we at the outset proposed to confine our
discussion of principles. But we shall remain faithful to
our original plan; and for that purpose shall confine
ourselves, in this work, to those palætiological sciences
which deal with material things. It is true, that the
general principles and maxims which regulate these sciences
apply also to investigations of a parallel kind respecting
the products which result from man's imaginative and social
endowments. But although there may be a similarity in the
general form of such portions of knowledge, their materials
are so different from those with which we have been hitherto
dealing, that we cannot hope to take them into our present
account with any profit. Language, Government, Law, Poetry,
Art, embrace a number of peculiar Fundamental Ideas,
hitherto not touched upon in the disquisitions in which we
have been engaged; and most of them involved in far greater
perplexity and ambiguity, the subject of controversies far
more vehement, than the Ideas we have hitherto been
examining. We must therefore avoid resting any part of our
philosophy upon sciences, or supposed sciences, which treat
of such subjects. To attend to this caution, {261} is the
only way in which we can secure the advantage we proposed to
ourselves at the outset, of taking, as the basis of our
speculations, none but systems of undisputed truths, clearly
understood and expressed[4\10]. We have already said that we
must, knowingly and voluntarily, resign that livelier and
warmer interest which doctrines on subjects of Polity or Art
possess, and content ourselves with the cold truths of the
material sciences, in order that we may avoid having the
very foundations of our philosophy involved in controversy,
doubt, and obscurity.

[Note 4\10: See Introd. p. 9.]

6. We may remark, however, that the necessity of rejecting
from our survey a large portion of the researches which the
general notion of Palætiology includes, suggests one
consideration which adds to the interest of our task. We
began our inquiry with the trust that any sound views which
we should be able to obtain respecting the nature of Truth
in the physical sciences, and the mode of discovering it,
must also tend to throw light upon the nature and prospects
of knowledge of all other kinds;--must be useful to us in
moral, political, and philological researches. We stated
this as a confident anticipation; and the evidence of the
justice of our belief already begins to appear. We have
seen, in the last Book, that biology leads us to psychology,
if we choose to follow the path; and thus the passage from
the material to the immaterial has already unfolded itself
at one point; and we now perceive that there are several
large provinces of speculation which concern subjects
belonging to man's immaterial nature, and which are governed
by the same laws as sciences altogether physical. It is not
our business here to dwell on the prospects which our
philosophy thus opens to our contemplation; but we may allow
ourselves, in this last stage of our pilgrimage among the
foundations of the physical sciences, to be cheered and
animated by the ray {262} that thus beams upon us, however
dimly, from a higher and brighter region.

But in our reasonings and examples we shall mainly confine
ourselves to the physical sciences; and for the most part to
Geology, which in the _History_ I have put forwards as the
best representative of the Palætiological Sciences.

{{263}}
CHAPTER II.

OF THE THREE MEMBERS OF A PALÆTIOLOGICAL SCIENCE.

1. _Divisions of such Sciences._--IN each of the Sciences of
this class we consider some particular order of phenomena
now existing:--from our knowledge of the causes of change
among such phenomena, we endeavour to infer the causes which
have made this order of things what it is:--we ascend in
this manner to some previous stage of such phenomena;--and
from that, by a similar course of inference, to a still
earlier stage, and to its causes. Hence it will be seen that
each such science will consist of two parts,--the knowledge
of the Phenomena, and the knowledge of their Causes. And
such a division is, in fact, generally recognized in such
sciences: thus we have History, and the Philosophy of
History; we have Comparison of Languages, and the Theories
of the Origin and Progress of Language; we have Descriptive
Geology, and Theoretical or Physical Geology. In all these
cases, the relation between the two parts in these several
provinces of knowledge is nearly the same; and it may, on
some occasions at least, be useful to express the
distinction in a uniform or general manner. The
investigation of Causes has been termed _Ætiology_ by
philosophical writers, and this term we may use, in
contradistinction to the mere _Phenomenology_ of each such
department of knowledge. And thus we should have _Phenomenal
Geology_ and _Ætiological Geology_, for the two divisions of
the science which we have above termed _Descriptive_ and
_Theoretical Geology_.

2. _The Study of Causes._--But our knowledge respecting the
causes which actually _have_ produced any {264} order of
phenomena must be arrived at by ascertaining what the causes
of change in such matters _can_ do. In order to learn, for
example, what share earthquakes, and volcanoes, and the
beating of the ocean against its shores, ought to have in
our Theory of Geology, we must make out what effects these
agents of change are able to produce. And this must be done,
not hastily, or unsystematically, but in a careful and
connected manner; in short, this study of the causes of
change in each order of phenomena must become a distinct
body of Science, which must include a large amount of
knowledge, both comprehensive and precise, before it can be
applied to the construction of a theory. We must have an
Ætiology corresponding to each order of phenomena.

3. _Ætiology._--In the History of Geology, I have spoken of
the necessity for such an Ætiology with regard to geological
phenomena: this necessity I have compared with that which,
at the time of Kepler, required the formation of a separate
science of Dynamics (the doctrine of the Causes of Motion),
before Physical Astronomy could grow out of Phenomenal
Astronomy. In pursuance of this analogy, I have there given
the name of _Geological Dynamics_ to the science which
treats of the causes of geological change in general. But,
as I have there intimated, in a large portion of the subject
the changes are so utterly different in their nature from
any modification of motion, that the term _Dynamics_, so
applied, sounds harsh and strange. For in this science we
have to treat, not only of the subterraneous forces by which
parts of the earth's crust are shaken, elevated, or
ruptured, but also of the causes which may change the
climate of a portion of the earth's surface, making a
country hotter or colder than in former ages; again, we have
to treat of the causes which modify the forms and habits of
animals and vegetables, and of the extent to which the
effects of such causes can proceed; whether, for instance,
they can extinguish old species and produce new. These and
other similar investigations would not be naturally included
in the notion of _Dynamics_; and therefore it {265} might
perhaps be better to use the term _Ætiology_ when we wish to
group together all those researches which have it for their
object to determine the laws of such changes. In the same
manner the Comparison and History of Languages, if it is to
lead to any stable and exact knowledge, must have appended
to it an Ætiology, which aims at determining the nature and
the amount of the causes which really do produce changes in
language; as colonization, conquest, the mixture of races,
civilization, literature, and the like. And the same rule
applies to all sciences of this class. We shall now make a
few remarks on the characteristics of such branches of
science as those to which we are led by the above
considerations.

4. _Phenomenology requires Classification. Phenomenal
Geology._--The Phenomenal portions of each science imply
Classification, for no description of a large and varied
mass of phenomena can be useful or intelligible without
classification. A representation of phenomena, in order to
answer the purposes of science, must be systematic.
Accordingly, in giving the History of Descriptive or
Phenomenal Geology, I have called it _Systematic Geology_,
just as Classificatory Botany is termed _Systematic Botany_.
Moreover, as we have already seen, Classification can never
be an arbitrary process, but always implies some natural
connexion among the objects of the same Class; for if this
connexion did not exist, the Classes could not be made the
subjects of any true assertion. Yet though the classes of
phenomena which our system acknowledges must be such as
already exist in nature, the discovery of these classes is,
for the most part, very far from obvious or easy. To detect
the true principles of Natural Classes, and to select marks
by which these may be recognized, are steps which require
genius and good fortune, and which fall to the lot only of
the most eminent persons in each science. In the History, I
have pointed out Werner, William Smith, and Cuvier, as the
three great authors of Systematic Geology of Europe. The
mode of classifying the materials of the earth's surface
which was found, by these philosophers, fitted to {266}
enunciate such general facts as came under their notice, was
to consider the rocks and other materials as divided into
successive layers or strata, superimposed one on another,
and variously inclined and broken. The German geologist
distinguished his strata for the most part by their
mineralogical character; the other two, by the remains of
animals and plants which the rocks contained. After a
beginning had thus been made in giving a genuine scientific
form to phenomenal geology, other steps followed in rapid
succession, as has already been related in the
History[5\10]. The Classification of the Strata was fixed by
a suitable Nomenclature. Attempts were made to apply to
other countries the order of strata which had been found to
prevail in that first studied: and in this manner it was
ascertained what rocks in distant regions are the synonyms,
or _Equivalents_[6\10],--of each other. The knowledge thus
collected and systematized was exhibited in the form of
Geological Maps.

[Note 5\10: _Hist. Ind. Sc._ b. xviii. c. iii.]

[Note 6\10: _Ib._ sect. 4.]

Moreover, among the phenomena of geology we have Laws of
Nature as well as Classes. The general form of
mountain-chains; the relations of the direction and
inclination of different chains to each other; the general
features of mineral veins, faults, and fissures; the
prevalent characters of slaty cleavage;--were the subjects
of laws established, or supposed to be established, by
extensive observation of facts. In like manner the organic
fossils discovered in the strata were found to follow
certain laws with reference to the climate which they
appeared to have lived in; and the evidence which they gave
of a regular zoological development. And thus, by the
assiduous labours of many accomplished and active
philosophers, Descriptive or Phenomenal Geology was carried
towards a state of completeness.

5. _Phenomenal Uranography._--In like manner in other
palætiological researches, as soon as they approach to an
exact and scientific form, we find the necessity of
constructing in the first place a science of {267}
classification and exact description, by means of which the
phenomena may be correctly represented and compared; and of
obtaining by this step a solid basis for an inquiry into the
causes which have produced them. Thus the Palætiology of the
Solar System has, in recent times, drawn the attention of
speculators; and a hypothesis has been started, that our sun
and his attendant planets have been produced by the
condensation of a mass of diffused matter, such as that
which constitutes the nebulous patches which we observe in
the starry heavens. But the sagest and most enlightened
astronomers have not failed to acknowledge, that to verify
or to disprove this conjecture, must be the work of many
ages of observation and thought. They have perceived also
that the first step of the labour requisite for the
advancement of this portion of science must be to obtain and
to record the most exact knowledge at present within our
reach, respecting the phenomena of these nebulæ, with which
we thus compare our own system; and, as a necessary element
of such knowledge, they have seen the importance of a
classification of these objects, and of others, such as
Double Stars, of the same kind. Sir William Herschel, who
first perceived the bearing of the phenomena of nebulæ upon
the history of the solar system, made the observation of
such objects his business, with truly admirable zeal and
skill; and in the account of the results of his labours,
gave a classification of Nebulæ; separating them into,
first, _Clusters of Stars_; second, _Resolvable Nebulæ_;
third, _Proper Nebulæ_; fourth, _Planetary Nebulæ_; fifth,
_Stellar Nebulæ_; sixth, _Nebulous Stars_[7\10]. And since,
in order to obtain from these remote appearances, any
probable knowledge respecting our own system, we must
discover whether they undergo any changes in the course of
ages, he devoted himself to the task of forming a record of
their number and appearance in his own time, that thus the
astronomers of succeeding generations might have a {268}
definite and exact standard with which to compare their
observations. Still, this task would have been executed only
for that part of the heavens which is visible in this
country, if this Hipparchus of the Nebulæ and Double Stars
had not left behind him a son who inherited all his father's
zeal and more than his father's knowledge. Sir John Herschel
in 1833 went to the Cape of Good Hope to complete what Sir
William Herschel left wanting; and in the course of five
years observed with care all the nebulæ and double stars of
the Southern hemisphere. This great _Herschelian Survey of
the Heavens_, the completion of which is the noblest
monument ever erected by a son to a father, must necessarily
be, to all ages, the basis of all speculations concerning
the history and origin of the solar system; and has
completed, so far as at present it can be completed, the
phenomenal portion of Astronomical Palætiology.

[Note 7\10: _Phil. Trans._ 1786 and 1789, and Sir J.
Herschel's _Astronomy_, Art. 616.]

6. _Phenomenal Geography of Plants and Animals._--Again,
there is another Palætiological Science, closely connected
with the speculations forced upon the geologist by the
organic fossils which he discovers imbedded in the strata of
the earth;--namely, the Science which has for its object the
Causes of the Diffusion and Distribution of the various
kinds of Plants and Animals. And the science also has for
its first portion and indispensable foundation a description
and classification of the existing phenomena. Such portions
of science have recently been cultivated with great zeal and
success, under the titles of the _Geography of Plants_, and
the _Geography of Animals_. And the results of the inquiries
thus undertaken have assumed a definite and scientific form
by leading to a division of the earth's surface into a
certain number of botanical and zoological _Provinces_, each
province occupied by its own peculiar vegetable and animal
population. We find, too, in the course of these
investigations, various general laws of the phenomena
offered to our notice; such, for instance, as this:--that
the difference of the animals originally occupying each
province, which is clear and entire for the higher orders of
{269} animals and plants, becomes more doubtful and
indistinct when we descend to the lower kinds of
organizations; as Infusoria and Zoophytes[8\10] in the
animal kingdom, Grasses and Mosses among vegetables. Again,
other laws discovered by those who have studied the
geography of plants are these:--that countries separated
from each other by wide tracts of sea, as the opposite
shores of the Mediterranean, the islands of the Indian and
Pacific Oceans, have usually much that is common in their
vegetation:--and again, that in parallel climates, analogous
tribes replace each other. It would be easy to adduce other
laws, but those already stated may serve to show the great
extent of the portions of knowledge which have just been
mentioned, even considered as merely Sciences of Phenomena.

[Note 8\10: Prichard, _Researches into the Physical History
of Mankind_, i. 55, 28.]

7. _Phenomenal Glossology._--It is not my purpose in the
present work to borrow my leading illustrations from any
portions of knowledge but those which are concerned with the
study of material nature; and I shall, therefore, not dwell
upon a branch of research, singularly interesting, and
closely connected with the one just mentioned, but dealing
with relations of thought rather than of things;--I mean the
Palætiology of Language;--the theory, so far as the facts
enable us to form a theory, of the causes which have led to
the resemblances and differences of human speech in various
regions and various ages. This, indeed, would be only a
portion of the study of the history and origin of the
diffusion of animals, if we were to include man among the
animals whose dispersion we thus investigate; for language
is one of the most clear and imperishable records of the
early events in the career of the human race. But the
peculiar nature of the faculty of speech, and the ideas
which the use of it involves, make it proper to treat
_Glossology_ as a distinct science. And of this science, the
first part must necessarily be, as in the other sciences of
this order, a {270} classification and comparison of
languages governed in many respects by the same rules, and
presenting the same **difficulties, as other sciences of
classification. Such, accordingly, has been the procedure of
the most philosophical glossologists. They have been led to
throw the languages of the earth into certain large classes
or _Families_, according to various kinds of resemblance; as
the _Semitic_ Family, to which belong Hebrew, Arabic,
Chaldean, Syrian, Phoenician, Ethiopian, and the like; the
_Indo-European_, which includes Sanskrit, Persian, Greek,
Latin, and German; the _Monosyllabic_ languages, Chinese,
Tibetan, Birman, Siamese; the _Polysynthetic_ languages, a
class including most of the North-American Indian dialects;
and others. And this work of classification has been the
result of the labour and study of many very profound
linguists, and has advanced gradually from step to step.
Thus the Indo-European Family was first formed on an
observation of the coincidences between Sanskrit, Greek, and
Latin; but it was soon found to include the Teutonic
languages, and more recently Dr. Prichard[9\10] has shown
beyond doubt that the Celtic must be included in the same
Family. Other general resemblances and differences of
languages have been marked by appropriate terms: thus August
von Schlegel has denominated them _synthetical_ and
_analytical_, according as they form their conjugations and
declensions by auxiliary verbs and prepositions, or by
changes in the word itself: and the _polysynthetic_
languages are so named by M. Duponceau, in consequence of
their still more complex mode of inflexion. Nor are there
wanting, in this science also, general laws of phenomena;
such, for instance, is the curious rule of the interchange
of consonants in the cognate words of Greek, Gothic, and
German, which has been discovered by James Grimm. All these
remarkable portions of knowledge, and the great works which
have appeared on Glossology, such, for example, as the
_Mithridates_ of Adelung and Vater, contain, for their
largest, and {271} hitherto probably their most valuable
part, the phenomenal portion of the science, the comparison
of languages as they now are. And beyond all doubt, until we
have brought this Comparative Philology to a considerable
degree of completeness, all our speculations respecting the
causes which have operated to produce the languages of the
earth must be idle and unsubstantial dreams.

[Note 9\10: Dr Prichard, _On the Eastern Origin of the
Celtic Nations_. 1831.]

Thus in all Palætiological Sciences, in all attempts to
trace back the history and discover the origin of the
present state of things, the portion of the science which
must first be formed is that which classifies the phenomena,
and discovers general laws prevailing among them. When this
work is performed, and not till then, we may begin to
speculate successfully concerning causes, and to make some
progress in our attempts to go back to an origin. We must
have a _Phenomenal_ science preparatory to each
_Ætiological_ one.

8. _The Study of Phenomena leads to Theory._--As we have
just said, we cannot, in any subject, speculate successfully
concerning the causes of the present state of things, till
we have obtained a tolerably complete and systematic view of
the phenomena. Yet in reality men have not in any instance
waited for this completeness and system in their knowledge
of facts before they have begun to form theories. Nor was it
natural, considering the speculative propensities of the
human mind, and how incessantly it is endeavouring to apply
the Idea of Cause, that it should thus restrain itself. I
have already noticed this in the History of Geology. 'While
we have been giving an account,' it is there said, 'of the
objects with which Descriptive Geology is occupied, it must
have been felt how difficult it is, in contemplating such
facts, to confine ourselves to description and
classification. Conjectures and reasonings respecting the
causes of the phenomena force themselves upon us at every
step; and even influence our classification and
nomenclature. Our Descriptive Geology impels us to construct
a Physical Geology.' And the same is the case with regard to
the other subjects which I have mentioned. The mere {272}
consideration of the different degrees of condensation of
different Nebulæ led Herschel and Laplace to contemplate the
hypothesis that our solar system is a condensed Nebula.
Immediately upon the division of the earth's surface into
botanical and zoological provinces, and even at an earlier
period, the opposite hypotheses of the Origin of all the
animals of each kind from a single pair, and of their
original diffusion all over the earth, were under
discussion. And the consideration of the families of
languages irresistibly led to speculations concerning the
Families of the earliest human inhabitants of the earth. In
all cases the contemplation of a very few phenomena, the
discovery of a very few steps in the history, made men wish
for and attempt to form a theory of the history from the
very beginning of things.

9. _No sound Theory without Ætiology._--But though man is
thus impelled by the natural propensities of his intellect
to trace each order of things to its causes, he does not at
first discern the only sure way of obtaining such knowledge:
he does not suspect how much labour and how much method are
requisite for success in this undertaking: he is not aware
that for each order of phenomena he must construct, by the
accumulated results of multiplied observation and distinct
thought, a separate Æiology. Thus, as I have elsewhere
remarked[10\10], when men had for the first time become
acquainted with some of the leading phenomena of Geology,
and had proceeded to speculate concerning the past changes
and revolutions by which such results had been produced,
they forthwith supposed themselves able to judge what would
be the effects of any of the obvious agents of change, as
Water or Volcanic Fire. It did not at first occur to them to
suspect that their common and extemporaneous judgment on
such points was by no means sufficient for sound knowledge.
They did not foresee that, before they could determine what
share these or any other causes had had in producing the
present condition of the earth, they must create {273} a
special science whose object should be to estimate the
general laws and effects of such assumed causes;--that
before they could obtain any sound Geological Theory, they
must carefully cultivate Geological Ætiology.

[Note 10\10: _Hist. Ind. Sc._ b. xviii. c. v. sect. 1.]

The same disposition to proceed immediately from the facts
to the theory, without constructing, as an intermediate
step, a Science of Causes, might be pointed out in the other
sciences of this order. But in all of them this errour has
been corrected by the failures to which it led. It soon
appeared, for instance, that a more careful inquiry into the
effects which climate, food, habit and circumstances can
produce in animals, was requisite in order to determine how
the diversities of animals in different countries have
originated. The Ætiology of Animal Life (if we may be
allowed to give this name to that study of such causes of
change which is at present so zealously cultivated, and
which yet has no distinctive designation, except so far as
it coincides with the _Organic Geological Dynamics_ of our
History) is now perceived to be a necessary portion of all
attempts to construct a history of the earth and its
inhabitants.

10. _Cause, in Palætiology._--We are thus led to contemplate
a class of Sciences which are commenced with the study of
Causes. We have already considered sciences which depended
mainly upon the Idea of Cause, namely, the Mechanical
Sciences. But it is obvious that the Idea of Cause in the
researches now under our consideration must be employed in a
very different way from that in which we applied it
formerly. Force is the _Cause_ of motion, because force at
all times and under all circumstances, if not counteracted,
produces motion; but the Cause of the present condition and
elevation of the Alps, whatever it was, was manifested in a
series of events of which each happened but once, and
occupied its proper place in the series of time. The former
is _mechanical_, the latter _historical_, _cause_. In our
present investigations, we consider the events which we
contemplate, of whatever order they be, as forming a chain
which is extended {274} from the beginning of things down to
the present time; and the causes of which we now speak are
those which connect the successive links of this chain.
Every occurrence which has taken place in the history of the
solar system, or the earth, or its vegetable and animal
creation, or man, has been at the same time effect and
cause;--the effect of what preceded, the cause of what
succeeded. By being effect and cause, it has occupied some
certain portion of time; and the times which have thus been
occupied by effects and causes, summed up and taken
altogether, make up the total of Past Time. The Past has
been a series of events connected by this historical
causation, and the Present is the last term of this series.
The problem in the Palætiological Sciences, with which we
are here concerned, is, to determine the manner in which
each term is derived from the preceding, and thus, if
possible, to calculate backwards to the origin of the series.

11. _Various kinds of Cause._--Those modes by which one term
in the natural series of events is derived from
another,--the forms of historical causation,--the kinds of
connexion between the links of the infinite chain of
time,--are very various; nor need we attempt to enumerate
them. But these kinds of causation being distinguished from
each other, and separately studied, each becomes the subject
of a separate Ætiology. Thus the causes of change in the
earth's surface, residing in the elements, fire and water,
form the main subject of Geological Ætiology. The Ætiology
of the vegetable and animal kingdoms investigates the causes
by which the forms and distribution of species of plants and
animals are affected. The study of causes in Glossology
leads to an Ætiology of Language, which shall distinguish,
analyse, and estimate the causes by which certain changes
are produced in the languages of nations; in like manner we
may expect to have an Ætiology of Art, which shall
scrutinise the influences by which the various forms of art
have each given birth to its successor: by which, for
example, there have been brought into being those various
forms of architecture which we term Egyptian, {275} Doric,
Ionic, Roman, Byzantine, Romanesque, Gothic, Italian,
Elizabethan. It is easily seen by this slight survey how
manifold and diverse are the kinds of cause which the
Palætiological Sciences bring under our consideration. But
in each of those sciences we shall obtain solid and complete
systems of knowledge, only so far as we study, with steady
thought and careful observation, that peculiar kind of cause
which is appropriate to the phenomena under our
consideration.

12. _Hypothetical Order of Palætiological Causes._--The
various kinds of historical cause are not only connected
with each other by their common bearing upon the historical
sciences, but they form a kind of progression which we may
represent to ourselves as having acted in succession in the
hypothetical history of the earth and its inhabitants. Thus
assuming, merely as a momentary hypothesis, the origin of
the Solar System by the condensation of a Nebula, we have to
contemplate, first, the causes by which the luminous
incandescent diffused mass of which a nebula is supposed to
be constituted, is gradually condensed, cooled, collected
into definite masses, solidified, and each portion made to
revolve about its axis, and the whole to travel about
another body. We have no difficulty in ascribing the
globular form of each mass to the mutual attraction of its
particles: but when this form was once assumed, and covered
with a solid crust, are there, we may ask, in the
constitution of such a body, any causes at work by which the
crust might be again broken up and portions of it displaced,
and covered with other matter? Again, if we can thus explain
the origin of the Earth, can we with like success account
for the presence of the Atmosphere and the Waters of earth
and ocean? Supposing this done, we have then to consider by
what causes such a body could become stocked with vegetable
and animal Life; for there have not been wanting persons,
extravagant speculators, no doubt, who have conceived that
even this event in the history of the world might be the
work of natural causes. Supposing an origin given to life
{276} upon our earth, we have then, brought before us by
geological observations, a series of different forms of
vegetable and animal existence; occurring in different
strata, and, as the phenomena appear irresistibly to prove,
existing at successive periods: and we are compelled to
inquire what can have been the causes by which the forms of
each period have passed into those of the next. We find,
too, that strata, which must have been at first horizontal
and continuous, have undergone enormous dislocations and
ruptures, and we have to consider the possible effect of
aqueous and volcanic causes to produce such changes in the
earth's crust. We are thus led to the causes which have
produced the present state of things on the earth; and these
are causes to which we may hypothetically ascribe, not only
the form and position of the inert materials of the earth,
but also the nature and distribution of its animal and
vegetable population. Man too, no less than other animals,
is affected by the operation of such causes as we have
referred to, and must, therefore, be included in such
speculations. But man's history only begins, where that of
other animals ends, with his mere existence. They are
stationary, he is progressive. Other species of animals,
once brought into being, continue the same through all ages;
man is changing, from age to age, his language, his
thoughts, his works. Yet even these changes are bound
together by laws of causation; and these causes too may
become objects of scientific study. And such causes, though
not to be dwelt upon now, since we permit ourselves to found
our philosophy upon the material sciences only, must still,
when treated scientifically, fall within the principles of
our philosophy, and must be governed by the same general
rules to which all science is subject. And thus we are led
by a close and natural connexion, through a series of
causes, extending from those which regulate the
imperceptible changes of the remotest nebulæ in the heavens,
to those which determine the diversities of language, the
mutations of art, and even the progress of civilization,
polity, and literature. {277}

While I have been speaking of this supposed series of
events, including in its course the formation of the earth,
the introduction of animal and vegetable life, and the
revolutions by which one collection of species has succeeded
another, it must not be forgotten, that though I have thus
hypothetically spoken of these events as occurring by force
of natural causes, this has been done only that the true
efficacy of such causes might be brought under our
consideration and made the subject of scientific
examination. It may be found, that such occurrences as these
are quite inexplicable by the aid of any natural causes with
which we are acquainted; and thus, the result of our
investigations, conducted with strict regard to scientific
principles, may be, that we must either contemplate
supernatural influences as part of the past series of
events, or declare ourselves altogether unable to form this
series into a connected chain.

13. _Mode of Cultivating Ætiology:--In Geology._--In what
manner, it may be asked, is Ætiology, with regard to each
subject such as we have enumerated, to be cultivated? In
order to answer this question, we must, according to our
method of proceeding, take the most successful and complete
examples which we possess of such portions of science. But
in truth, we can as yet refer to few examples of this kind.
In Geology, it is only very recently, and principally
through the example and influence of Sir Charles Lyell, that
the Ætiology has been detached from the descriptive portion
of the science; and cultivated with direct attention: in
other sciences the separation has hardly yet been made. But
if we examine what has already been done in Geological
Ætiology, or as in the History it is termed, _Geological
Dynamics_, we shall find a number of different kinds of
investigation which, by the aid of our general principles
respecting the formation of sciences, may suffice to supply
very useful suggestions for Ætiology in general.

In Geological Ætiology, causes have been studied, in many
instances, by attending to their action in the phenomena of
the present state of things, and by inferring {278} from
this the nature and extent of the action which they may have
exercised in former times. This has been done, for example,
by Von Hoff, Sir Charles Lyell, and others, with regard to
the operations of rivers, seas, springs, glaciers, and other
aqueous causes of change, Again, the same course has been
followed by the same philosophers with respect to volcanoes,
earthquakes, and other violent agents. Sir Charles Lyell has
attempted to show, too, that there take place, in our own
time, not only violent agitations, but slow motions of parts
of the earth's crust, of the same kind and order with those
which have assisted in producing all anterior changes.

But while we thus seek instruction in the phenomena of the
present state of things, we are led to the question, What
are the limits of this 'present' period? For instance, among
the currents of lava which we trace as part of the shores of
Italy and Sicily, _which_ shall we select as belonging to
the existing order of things? In going backwards in time,
where shall we draw the line? and why at such particular
point? These questions are important, for our estimate of
the efficacy of known causes will vary with the extent of
the effects which we ascribe to them. Hence the mode in
which we group together rocks is not only a step in
geological classification, but is also important to
Ætiology. Thus, when the vast masses of trap rocks in the
Western Isles of Scotland and in other countries, which had
been maintained by the Wernerians to be of aqueous origin,
were, principally by the sagacity and industry of
Macculloch, identified as to their nature with the products
of recent volcanoes, the amount of effect which might
justifiably be ascribed to volcanic agency was materially
extended.

In other cases, instead of observing the current effects of
our geological causes, we have to estimate the results from
what we know of the causes themselves; as when, with
Herschel, we calculate the alterations in the temperature of
the earth which astronomical changes may possibly produce;
or when, with Fourier, we try to calculate the rate of
cooling of the earth's {279} surface, on the hypothesis of
an incandescent central mass. In other cases, again, we are
not able to calculate the effects of our causes rigorously,
but estimate them as well as we can; partly by physical
reasonings, and partly by comparison with such analogous
cases as we can find in the present state of things. Thus
Sir Charles Lyell infers the change of climate which would
result if land were transferred from the neighbourhood of
the poles to that of the equator, by reasonings on the power
of land and water to contain and communicate heat, supported
by a reference to the different actual climates of places,
lying under the same latitude, but under different
conditions as to the distribution of land and water.

Thus our Ætiology is constructed partly from calculation and
reasoning, partly from phenomena. But we may observe that
when we reason from phenomena to causes, we usually do so by
various steps; often ascending from phenomena to mere laws
of phenomena, before we can venture to connect the
phenomenon confidently with its cause. Thus the law of
subterranean heat, that it increases in descending below the
surface, is now well established, although the doctrine
which ascribes this effect to a central heat is not
universally assented to.

14. _In the Geography of Plants and Animals._--We may find
in other subjects also, considerable contributions towards
Ætiology, though not as yet a complete System of Science.
The Ætiology of Vegetables and Animals, indeed, has been
studied with great zeal in modern times, as an essential
preparative to geological theory; for how can we decide
whether any assumed causes have produced the succession of
species which we find in the earth's strata, except we know
what effect of this kind given causes can produce?
Accordingly, we find in Sir Charles Lyell's _Treatise on
Geology_ the most complete discussion of such questions as
belong to these subjects:--for example, the question whether
species can be transmuted into other species by the
long-continued influence of external causes, as climate,
food, domestication, combined with internal {280} causes, as
habits, appetencies, progressive tendencies. We may observe,
too, that as we have brought before us, the inquiry what
change difference of climate can produce in any species, we
have also the inverse problem, how far a different
development of the species, or a different collection of
species, proves a difference of climate. In the same way,
the geologist of the present day considers the question,
whether, in virtue of causes now in action, species are from
time to time extinguished; and in like manner, the
geologists of an earlier period discussed the question, now
long completely decided, whether fossil species in general
are really extinct species.

15. _In Languages._--Even with reference to the Ætiology of
Language, although this branch of science has hardly been
considered separately from the glossological investigations
in which it is employed or assumed to be employed, it might
perhaps be possible to point out causes or conditions of
change which, being general in their nature, must operate
upon all languages alike. Changes made for the sake of
euphony when words are modified and combined, occur in all
dialects. Who can doubt that such changes of consonants as
those by which the Greek roots become Gothic, and the
Gothic, German, have for their cause some general principle
in the pronunciation of each language? Again, we might
attempt to decide other questions of no small interest. Have
the terminations of verbs arisen from the accretion of
pronouns; or, on the other hand, does the modification of a
verb imply a simpler mental process than the insulation of a
pronoun, as Adam Smith has maintained? Again, when the
language of a nation is changed by the invasion and
permanent mixture of an enemy of different speech, is it
generally true that it is changed from a synthetic to an
analytical structure? I will mention only one more of these
wide and general glossological inquiries. Is it true, as Dr.
Prichard has suggested[11\10], that languages have become
more permanent as we come down {281} towards later times?
May we justifiably suppose, with him, that in the very
earliest times, nations, when they had separated from one
stock, might lose all traces of this common origin out of
their languages, though retaining strong evidences of it in
their mythology, social forms, and arts, as appears to be
the case with the ancient Egyptians and the Indians[12\10].

[Note 11\10: _Researches_, ii. 221.]

[Note 12\10: _Researches_, ii. 192.]

Large questions of this nature cannot be treated profitably
in any other way than by an assiduous study of the most
varied forms of living and dead languages. But on the other
hand, the study of languages should be prosecuted not only
by a direct comparison of one with another, but also with a
view to the formation of a science of causes and general
principles, embracing such discussions as I have pointed
out. It is only when such a science has been formed, that we
can hope to obtain any solid and certain results in the
Palætiology of Language;--to determine, with any degree of
substantial proof, what is the real evidence which the
wonderful faculty of speech, under its present developments
and forms, bears to the events which have taken place in its
own history, and in the history of man since his first origin.

16. _Construction of Theories._--When we have thus obtained,
with reference to any such subject as those we have here
spoken of, these two portions of science, a Systematic
Description of the Facts, and a rigorous Analysis of the
Causes,--the _Phenomenology_ and the _Ætiology_ of the
subject,--we are prepared for the third member which
completes the science, the _Theory_ of the actual facts. We
can then take a view of the events which really have
happened, discerning their connexion, interpreting their
evidence, supplying from the context the parts which are
unapparent. We can account for known facts by intelligible
causes; we can infer latent facts from manifest effects, so
as to obtain a distinct insight into the whole history of
events up to the present time, and to see the last result of
the whole in the present condition of things. {282} The term
_Theory_, when rigorously employed in such sciences as those
which we here consider, bears nearly the sense which I have
adopted: it implies a consistent and systematic view of the
actual facts, combined with a true apprehension of their
connexion and causes. Thus if we speak of 'a Theory of Mount
Etna,' or 'a Theory of the Paris Basin,' we mean a connected
and intelligible view of the events by which the rocks in
these localities have come into their present condition.
Undoubtedly the term _Theory_ has often been used in a
looser sense; and men have put forth '_Theories of the
Earth_,' which, instead of including the whole mass of
actual geological facts and their causes, only assigned, in
a vague manner, some causes by which some few phenomena
might, it was conceived, be accounted for. Perhaps the
portion of our Palætiological Sciences which we now wish to
designate, would be more generally understood if we were to
describe it as _Theoretical_ or _Philosophical History_; as
when we talk of 'the Theoretical History of Architecture,'
or 'the Philosophical History of Language.' And in the same
manner we might speak of the Theoretical History of the
Animal and Vegetable Kingdoms; meaning, a distinct account
of the events which have produced the present distribution
of species and families. But by whatever phrase we describe
this portion of science, it is plain that such a Theory,
such a Theoretical History, must result from the application
of causes well understood to facts well ascertained. And if
the term _Theory_ be here employed, we must recollect that
it is to be understood, not in its narrower sense as opposed
to facts, but in its wider signification, as including all
known facts and differing from them only in introducing
among them principles of intelligible connexion. The
Theories of which we now speak are true _Theories_,
precisely because they are identical with the total system
of the _Facts_.

17. _No sound Palætiological Theory yet extant._--It is not
to disparage unjustly the present state of science, to say
that as yet no such theory exists on any subject. 'Theories
of the Earth' have been {283} repeatedly published; but when
we consider that even the facts of geology have been
observed only on a small portion of the earth's surface, and
even within those narrow bounds very imperfectly studied, we
shall be able to judge how impossible it is that geologists
should have yet obtained a well-established Theoretical
History of the changes which have taken place in the crust
of the terrestrial globe from its first origin. Accordingly,
I have ventured in my History to designate the most
prominent of the Theories which have hitherto prevailed as
_premature_ geological theories[13\10]: and we shall soon
see that geological theory has not advanced beyond a few
conjectures, and that its cultivators are at present mainly
occupied with a controversy in which the two extreme
hypotheses which first offer themselves to men's minds are
opposed to each other. And if we have no theoretical History
of the Earth which merits any confidence, still less have we
any theoretical History of Language, or of the Arts, which
we can consider as satisfactory. The Theoretical History of
the Vegetable and Animal Kingdoms is closely connected with
that of the Earth on which they subsist, and must follow the
fortunes of Geology. And thus we may venture to say that no
Palætiological Science, as yet, possesses all its three
members. Indeed most of them are very far from having
completed and systematized their Phenomenology: in all, the
cultivation of Ætiology is but just begun, or is not begun;
in all, the Theory must reward the exertions of future,
probably of distant, generations.

[Note 13\10: _Hist. Ind. Sc._ b. xviii. c. vii. sect. 3.]

But in the mean time we may derive some instruction from the
comparison of the two antagonist hypotheses of which I have spoken.

{{284}}
CHAPTER III.

OF THE DOCTRINE OF CATASTROPHES AND THE DOCTRINE OF
UNIFORMITY.

1. _Doctrine of Catastrophes._--I HAVE already shown, in the
History of Geology, that the attempts to frame a theory of
the earth have brought into view two completely opposite
opinions:--one, which represents the course of nature as
_uniform_ through all ages, the causes which produce change
having had the same intensity in former times which they
have at the present day;--the other opinion, which sees, in
the present condition of things, evidences of
_catastrophes_;--changes of a more sweeping kind, and
produced by more powerful agencies than those which occur in
recent times. Geologists who held the latter opinion,
maintained that the forces which have elevated the Alps or
the Andes to their present height could not have been any
forces which are now in action: they pointed to vast masses
of strata hundreds of miles long, thousands of feet thick,
thrown into highly-inclined positions, fractured,
dislocated, crushed: they remarked that upon the shattered
edges of such strata they found enormous accumulations of
fragments and rubbish, rounded by the action of water, so as
to denote ages of violent aqueous action: they conceived
that they saw instances in which whole mountains of rock in
a state of igneous fusion, must have burst the earth's crust
from below: they found that in the course of the revolutions
by which one stratum of rock was placed upon another, the
whole collection of animal species which tenanted the earth
and the seas had been removed, and a new set of living
things introduced in its place: finally, they found, above
all the strata, {285} vast masses of sand and gravel
containing bones of animals, and apparently the work of a
mighty deluge. With all these proofs before their eyes, they
thought it impossible not to judge that the agents of change
by which the world was urged from one condition to another
till it reached its present state must have been more
violent, more powerful, than any which we see at work around
us. They conceived that the evidence of 'catastrophes' was
irresistible.

2. _Doctrine of Uniformity._--I need not here repeat the
narrative (given in the History[14\10]) of the process by
which this formidable array of proofs was, in the minds of
some eminent geologists, weakened, and at last overcome.
This was done by showing that the sudden breaks in the
succession of strata were apparent only, the discontinuity
of the series which occurred in one country being removed by
terms interposed in another locality:--by urging that the
total effect produced by existing causes, taking into
account the accumulated result of long periods, is far
greater than a casual speculator would think possible:--by
making it appear that there are in many parts of the world
evidences of a slow and imperceptible rising of the land
since it was the habitation of now existing species:--by
proving that it is not universally true that the strata
separated in time by supposed catastrophes contain distinct
species of animals:--by pointing out the limited fields of
the supposed diluvial action:--and finally, by remarking
that though the _creation_ of species is a mystery, the
_extinction_ of species is going on in our own day.
Hypotheses were suggested, too, by which it was conceived
that the change of climate might be explained, which, as the
consideration of the fossil remains seemed to show, must
have taken place between the ancient and the modern times.
In this manner the whole evidence of catastrophes was
explained away: the notion of a series of paroxysms of
violence in the causes of change was represented as a
delusion arising from our {286} contemplating short periods
only, in the action of present causes: length of time was
called in to take the place of intensity of force: and it
was declared that Geology need not despair of accounting for
the revolutions of the earth, as Astronomy accounts for the
revolutions of the heavens, by the universal action of
causes which are close at hand to us, operating through time
and space without variation or decay.

[Note 14\10: _Hist. Ind. Sc._ b. xviii. c. viii. sect. 2.]

An antagonism of opinions, somewhat of the same kind as
this, will be found to manifest itself in the other
Palætiological Sciences as well as in Geology; and it will
be instructive to endeavour to balance these opposite
doctrines. I will mention some of the considerations which
bear upon the subject in its general form.

3. _Is Uniformity probable à priori?_--The doctrine of
Uniformity in the course of nature has sometimes been
represented by its adherents as possessing a great degree of
_à priori_ probability. It is highly unphilosophical, it has
been urged, to assume that the causes of the geological
events of former times were of a different kind from causes
now in action, if causes of this latter kind can in any way
be made to explain the facts. The analogy of all other
sciences compels us, it was said, to explain phenomena by
known, not by unknown, causes. And on these grounds the
geological teacher recommended[15\10] 'an earnest and
patient endeavour to reconcile the indications of former
change with the evidence of gradual mutations now in
progress.'

[Note 15\10: Lyell, 4th ed. b. iv. c. i. p. 328.]

But on this we may remark, that if by _known_ causes we mean
causes acting with the same intensity which they have had
during historical times, the restriction is altogether
arbitrary and groundless. Let it be granted, for instance,
that many parts of the earth's surface are now undergoing an
imperceptible rise. It is not pretended that the rate of
this elevation is rigorously uniform; what, then, are the
limits of its velocity? Why may it not increase so as to
assume that character of violence which we may term a {287}
_catastrophe_ with reference to all changes hitherto
recorded? Why may not the rate of elevation be such that we
may conceive the strata to assume _suddenly_ a position
nearly vertical? And is it, in fact, easy to conceive a
position of strata nearly vertical, a position which occurs
so frequently, to be _gradually_ assumed? In cases where the
strata are nearly vertical, as in the Isle of Wight, and
hundreds of other places, or where they are actually
inverted, as sometimes occurs, are not the causes which have
produced the effect as truly known causes, as those which
have raised the coasts where we trace the former beach in an
elevated terrace? If the latter case proves _slow_
elevation, does not the former case prove _rapid_ elevation?
In neither case have we any measure of the time employed in
the change; but does not the very nature of the results
enable us to discern, that if one was gradual, the other was
comparatively sudden?

The causes which are now elevating a portion of Scandinavia
can be called known _causes_, only because we know the
_effect_. Are not the causes which have elevated the Alps
and the Andes known causes in the same sense? We know
nothing in either case which confines the intensity of the
force within any limit, or prescribes to it any law of
uniformity. Why, then, should we make a merit of cramping
our speculations by such assumptions? Whether the causes of
change do act uniformly;--whether they oscillate only within
narrow limits;--whether their intensity in former times was
nearly the same as it now is;--these are precisely the
questions which we wish Science to answer to us impartially
and truly: where is then the wisdom of 'an earnest and
patient endeavour' to secure an _affirmative_ reply?

Thus I conceive that the assertion of an _à priori_ claim to
probability and philosophical spirit in favour of the
doctrine of uniformity, is quite untenable. We must learn
from an examination of all the facts, and not from any
assumption of our own, whether the course of nature be
uniform. The limit of intensity being really unknown,
catastrophes are just as probable {288} as uniformity. If a
volcano may repose for a thousand years, and then break out
and destroy a city; why may not another volcano repose for
ten thousand years, and then destroy a continent; or if a
continent, why not the whole habitable surface of the earth?

4. _Cycle of Uniformity indefinite._--But this argument may
be put in another form. When it is said that the course of
nature is uniform, the assertion is not intended to exclude
certain smaller variations of violence and rest, such as we
have just spoken of;--alternations of activity and repose in
volcanoes; or earthquakes, deluges, and storms, interposed
in a more tranquil state of things. With regard to such
occurrences, terrible as they appear at the time, they may
not much affect the average rate of change; there may be a
_cycle_, though an irregular one, of rapid and slow change;
and if such cycles go on succeeding each other, we may still
call the order of nature uniform, notwithstanding the
periods of violence which it involves. The maximum and
minimum intensities of the forces of mutation alternate with
one another; and we may estimate the average course of
nature as that which corresponds to something between the
two extremes.

But if we thus attempt to maintain the uniformity of nature
by representing it as a series of _cycles_, we find that we
cannot discover, in this conception, any solid ground for
excluding catastrophes. What is the length of that cycle,
the repetition of which constitutes uniformity? What
interval from the maximum to the minimum does it admit of?
We may take for our cycle a hundred or a thousand years, but
evidently such a proceeding is altogether arbitrary. We may
mark our cycles by the greatest known paroxysms of volcanic
and terremotive agency, but this procedure is no less
indefinite and inconclusive than the other.

But further; since the cycle in which violence and repose
alternate is thus indefinite in its length and in its range
of activity, what ground have we for assuming more than one
such cycle, extending from the origin of things to the
present time? Why may we not suppose the maximum force of
the causes of change {289} to have taken place at the
earliest period, and the tendency towards the minimum to
have gone on ever since? Or instead of only one cycle, there
may have been several, but of such length that our
historical period forms a portion only of the last;--the
feeblest portion of the latest cycle. And thus violence and
repose may alternate upon a scale of time and intensity so
large, that man's experience supplies no evidence enabling
him to estimate the amount. The course of things is
_uniform_, to an Intelligence which can embrace the
succession of several cycles, but it is _catastrophic_ to
the contemplation of man, whose survey can grasp a part only
of one cycle. And thus the hypothesis of uniformity, since
it cannot exclude degrees of change, nor limit the range of
these degrees, nor define the interval of their recurrence,
cannot possess any essential simplicity which, previous to
inquiry, gives it a claim upon our assent superior to that
of the opposite catastrophic hypothesis.

5. _Uniformitarian Arguments are Negative only._--There is
an opposite tendency in the mode of maintaining the
catastrophist and the uniformitarian opinions, which depends
upon their fundamental principles, and shows itself in all
the controversies between them. The Catastrophist is
affirmative, the Uniformitarian is negative in his
assertions: the former is constantly attempting to construct
a theory; the latter delights in demolishing all theories.
The one is constantly bringing fresh evidence of some great
past event, or series of events, of a striking and definite
kind; his antagonist is at every step explaining away the
evidence, and showing that it proves nothing. One geologist
adduces his proofs of a vast universal deluge; but another
endeavours to show that the proofs do not establish either
the universality or the vastness of such an event. The
inclined broken edges of a certain formation, covered with
their own fragments, beneath superjacent horizontal
deposits, are at one time supposed to prove a catastrophic
breaking up of the earlier strata; but this opinion is
controverted by showing that the same formations, when
pursued into other countries, {290} exhibit a uniform
gradation from the lower to the upper, with no trace of
violence. Extensive and lofty elevations of the coast,
continents of igneous rock, at first appear to indicate
operations far more gigantic than those which now occur; but
attempts are soon made to show that time only is wanting to
enable the present age to rival the past in the production
of such changes. Each new fact adduced by the catastrophist
is at first striking and apparently convincing; but as it
becomes familiar, it strikes the imagination less
powerfully; and the uniformitarian, constantly labouring to
produce some imitation of it by the machinery which he has
so well studied, at last in every case seems to himself to
succeed, so far as to destroy the effect of his opponent's
evidence.

This is so with regard to more remote, as well as with
regard to immediate evidences of change. When it is
ascertained that in every part of the earth's crust the
temperature increases as we descend below the surface, at
first this fact seems to indicate a central heat: and a
central heat naturally suggests an earlier state of the
mass, in which it was incandescent, and from which it is now
cooling. But this original incandescence of the globe of the
earth is manifestly an entire violation of the present
course of things; it belongs to the catastrophist view, and
the advocates of uniformity have to explain it away.
Accordingly, one of them holds that this increase of heat in
descending below the surface may very possibly not go on all
the way to the center. The heat which increases at first as
we descend, may, he conceives, afterwards decrease; and he
suggests causes which may have produced such a succession of
hotter and colder shells within the mass of the earth. I
have mentioned this suggestion in the History of Geology;
and have given my reasons for believing it altogether
untenable[16\10]. Other persons also, desirous of
reconciling this subterraneous heat with the tenet of
uniformity, have {291} offered another suggestion:--that the
warmth or incandescence of the interior parts of the earth
does not arise out of an originally hot condition from which
it is gradually cooling, but results from chemical action
constantly going on among the materials of the earth's
substance. And thus new attempts are perpetually making, to
escape from the cogency of the reasonings which send us
towards an original state of things different from the
present. Those who theorize concerning an origin go on
building up the fabric of their speculations, while those
who think such theories unphilosophical, ever and anon dig
away the foundation of this structure. As we have already
said, the uniformitarian's doctrines are a collection of
negatives.

[Note 16\10: _Hist. Ind. Sc._ b. xviii. c. v. sect. 5, and note.]

This is so entirely the case, that the uniformitarian would
for the most part shrink from maintaining as positive tenets
the explanations which he so willingly uses as instruments
of controversy. He puts forward his suggestions as
difficulties, but he will not stand by them as doctrines.
And this is in accordance with his general tendency; for any
of his hypotheses, if insisted upon as positive theories,
would be found inconsistent with the assertion of
uniformity. For example, the nebular hypothesis appears to
give to the history of the heavens an aspect which
obliterates all special acts of creation, for, according to
that hypothesis, new planetary systems are constantly
forming; but when asserted as the origin of our own solar
system, it brings with it an original incandescence, and an
origin of the organic world. And if, instead of using the
chemical theory of subterraneous heat to neutralize the
evidence of original incandescence, we assert it as a
positive tenet, we can no longer maintain the infinite past
duration of the earth; for chemical forces, as well as
mechanical, tend to equilibrium; and that condition once
attained, their efficacy ceases. Chemical affinities tend to
form new compounds; and though, when many and various
elements are mingled together, the play of synthesis and
analysis may go on for a long time, it must at last end. If,
for instance, a large portion of the earth's mass were
originally pure potassium, we {292} can imagine violent
igneous action to go on so long as any part remained
unoxidized; but when the oxidation of the whole has once
taken place, this action must be at an end; for there is in
the hypothesis no agency which can reproduce the deoxidized
metal. Thus a perpetual motion is impossible in chemistry,
as it is in mechanics; and a theory of constant change
continued through infinite time, is untenable when asserted
upon chemical, no less than upon mechanical principles. And
thus the Skepticism of the uniformitarian is of force only
so long as it is employed against the Dogmatism of the
catastrophist. When the Doubts are erected into Dogmas, they
are no longer consistent with the tenet of Uniformity. When
the Negations become Affirmations, the Negation of an Origin
vanishes also.

6. _Uniformity in the Organic World._--In speaking of the
violent and sudden changes which constitute catastrophes,
our thoughts naturally turn at first to great _mechanical_
and _physical_ effects;--ruptures and displacements of
strata; extensive submersions and emersions of land; rapid
changes of temperature. But the catastrophes which we have
to consider in geology affect the _organic_ as well as the
inorganic world. The sudden extinction of one collection of
species, and the introduction of another in their place, is
a Catastrophe, even if unaccompanied by mechanical violence.
Accordingly, the antagonism of the catastrophist and
uniformitarian schools has shown itself in this department
of the subject, as well as in the other. When geologists had
first discovered that the successive strata are each
distinguished by appropriate organic fossils, they assumed
at once that each of these collections of living things
belonged to a separate creation. But this conclusion, as I
have already said, Sir C. Lyell has attempted to invalidate,
by proving that in the existing order of things, some
species become extinct; and by suggesting it as possible,
that in the same order, it may be true that new species are
from time to time produced, even in the present course of
nature. And in this, as in the other part of the subject, he
calls in {293} the aid of vast periods of time, in order
that the violence of the changes may be softened down: and
he appears disposed to believe that the actual extinction
and creation of species may be so slow as to excite no more
notice than it has hitherto obtained; and yet may be rapid
enough, considering the immensity of geological periods, to
produce such a succession of different collections of
species as we find in the strata of the earth's surface.

7. _Origin of the present Organic World._--The last great
event in the history of the vegetable and animal kingdoms
was that by which their various tribes were placed in their
present seats. And we may form various hypotheses with
regard to the sudden or gradual manner in which we may
suppose this distribution to have taken place. We may assume
that at the beginning of the present order of things, a
stock of each species was placed in the vegetable or animal
_province_ to which it belongs, by some cause out of the
common order of nature; or we may take a uniformitarian view
of the subject, and suppose that the provinces of the
organic world derived their population from some anterior
state of things by the operation of natural causes.

Nothing has been pointed out in the existing order of things
which has any analogy or resemblance, of any valid kind, to
that creative energy which must be exerted in the production
of a new species. And to assume the introduction of new
species as 'a part of the order of nature,' without pointing
out any natural fact with which such an event can be
classed, would be to reject creation by an arbitrary act.
Hence, even on natural grounds, the most intelligible view
of the history of the animal and vegetable kingdoms seems to
be, that each period which is marked by a distinct
collection of species forms a cycle; and that at the
beginning of each such cycle a creative power was exerted,
of a kind to which there was nothing at all analogous in the
succeeding part of the same cycle. If it be urged that in
some cases the same species, or the same genus, runs through
two geological formations, {294} which must, on other
grounds, be referred to different cycles of creative energy,
we may reply that the creation of many new species does not
imply the extinction of all the old ones.

Thus we are led by our reasonings to this view, that the
present order of things was commenced by an act of creative
power entirely different to any agency which has been
exerted since. None of the influences which have modified
the present races of animals and plants since they were
placed in their habitations on the earth's surface can have
had any efficacy in producing them at first. We are
necessarily driven to assume, as the beginning of the
present cycle of organic nature, an event not included in
the course of nature. And we may remark that this necessity
is the more cogent, precisely because other cycles have
preceded the present.

8. _Nebular Origin of the Solar System._--If we attempt to
apply the same antithesis of opinion (the doctrines of
Catastrophe and Uniformity) to the other subjects of
palætiological sciences, we shall be led to similar
conclusions. Thus, if we turn our attention to Astronomical
Palætiology, we perceive that the Nebular Hypothesis has a
uniformitarian tendency. According to this hypothesis the
formation of this our system of sun, planets, and
satellites, was a process of the same kind as those which
are still going on in the heavens. One after another, nebulæ
condense into separate masses, which begin to revolve about
each other by mechanical necessity, and form systems of
which our solar system is a finished example. But we may
remark, that the uniformitarian doctrine on this subject
rests on most unstable foundations. We have as yet only very
vague and imperfect reasonings to show that by such
condensation a _material_ system such as ours could result;
and the introduction of _organized_ beings into such a
material system is utterly out of the reach of our
philosophy. Here again, therefore, we are led to regard the
present order of the world as pointing towards an origin
altogether of a different kind from anything which our
material science can grasp. {295}

9. _Origin of Languages._--We may venture to say that we
should be led to the same conclusion once more, if we were
to take into our consideration those palætiological sciences
which are beyond the domain of matter; for instance, the
History of Languages. We may explain many of the differences
and changes which we become acquainted with, by referring to
the action of causes of change which still operate. But what
glossologist will venture to declare that the efficacy of
such causes has been uniform;--that the influences which
mould a language, or make one language differ from others of
the same stock, operated formerly with no more efficacy than
they exercise now. 'Where,' as has elsewhere been asked, 'do
we now find a language in the process of formation,
unfolding itself in inflexions, terminations, changes of
vowels by grammatical relations, such as characterise the
oldest known languages?' Again, as another proof how little
the history of languages suggests to the philosophical
glossologist the persuasion of a uniform action of the
causes of change, I may refer to the conjecture of Dr.
Prichard, that the varieties of language produced by the
separation of one stock into several, have been greater and
greater as we go backwards in history:--that[17\10] the
formation of sister dialects from a common language (as the
Scandinavian, German, and Saxon dialects from the Teutonic,
or the Gaelic, Erse and Welsh from the Celtic) belongs to
the first millennium before the Christian era; while the
formation of cognate languages of the same family, as the
Sanskrit, Latin, Greek and Gothic, must be placed at least
two thousand years before that era; and at a still earlier
period took place the separation of the great families
themselves, the Indo-European, Semitic, and others, in which
it is now difficult to trace the features of a common
origin. No hypothesis except one of this kind will explain
the existence of the families, groups, and dialects of
languages, which we find in existence. Yet this is an
entirely different view from that which {296} the hypothesis
of the uniform progress of change would give. And thus, in
the earliest stages of man's career, the revolutions of
language must have been, even by the evidence of the
theoretical history of language itself, of an order
altogether different from any which have taken place within
the recent history of man. And we may add, that as the early
stages of the progress of language must have been widely
different from those later ones of which we can in some
measure trace the natural causes, we cannot place the origin
of language in any point of view in which it comes under the
jurisdiction of natural causation at all.

[Note 17\10: _Researches_, ii. 224.]

10. _No Natural Origin discoverable._--We are thus led by a
survey of several of the palætiological sciences to a
confirmation of the principle formerly asserted[18\10], That
in no palætiological science has man been able to arrive at
a beginning which is homogeneous with the known course of
events. We can in such sciences often go very far
back;--determine many of the remote circumstances of the
past series of events;--ascend to a point which seems to be
near the origin;--and limit the hypotheses respecting the
origin itself: but philosophers never have demonstrated,
and, so far as we can judge, probably never will be able to
demonstrate, what was that primitive state of things from
which the progressive course of the world took its first
departure. In all these paths of research, when we travel
far backwards, the aspect of the earlier portions becomes
very different from that of the advanced part on which we
now stand; but in all cases the path is lost in obscurity as
it is traced backwards towards its starting-point: it
becomes not only invisible, but unimaginable; it is not only
an interruption, but an abyss, which interposes itself
between us and any intelligible beginning of things.

[Note 18\10: _Hist. Ind. Sc._ b. xviii. c. vi. sect 5.]

{{297}}
CHAPTER IV.

OF THE RELATION OF TRADITION TO PALÆTIOLOGY.

1. _Importance of Tradition._--SINCE the Palætiological
Sciences have it for their business to study the train of
past events produced by natural causes down to the present
time, the knowledge concerning such events which is supplied
by the remembrance and records of man, in whatever form,
must have an important bearing upon these sciences. All
changes in the condition and extent of land and sea, which
have taken place within man's observation, all effects of
deluges, sea-waves, rivers, springs, volcanoes, earthquakes,
and the like, which come within the reach of human history,
have a strong interest for the palætiologist. Nor is he less
concerned in all recorded instances of the modification of
the forms and habits of plants and animals, by the
operations of man, or by transfer from one land to another.
And when we come to the Palætiology of Language, of Art, of
Civilization, we find our subject still more closely
connected with history; for in truth these are historical,
no less than palætiological investigations. But, confining
ourselves at present to the material sciences, we may
observe that though the importance of the information which
tradition gives us, in the sciences now under our
consideration, as, for instance, geology, has long been
tacitly recognised; yet it is only recently that geologists
have employed themselves in collecting their historical
facts upon such a scale and with such comprehensive views as
are required by the interest and use of collections of this
kind. The Essay of Von {298} Hoff[19\10], _On the Natural
Alterations in the Surface of the Earth which are proved by
Tradition_, was the work which first opened the eyes of
geologists to the extent and importance of this kind of
investigation. Since that time the same path of research has
been pursued with great perseverance by others, especially
by Sir C. Lyell; and is now justly considered as an
essential portion of Geology.

[Note 19\10: Vol. i. 1822; vol. ii. 1824.]

2. _Connexion of Tradition and Science._--Events which we
might naturally expect to have some bearing on geology, are
narrated in the historical writings which, even on mere
human grounds, have the strongest claim to our respect as
records of the early history of the world, and are confirmed
by the traditions of various nations all over the globe;
namely, the formation of the earth and of its population,
and a subsequent deluge. It has been made a matter of
controversy how the narrative of these events is to be
understood, so as to make it agree with the facts which an
examination of the earth's surface and of its vegetable and
animal population discloses to us. Such controversies, when
they are considered as merely archæological, may occur in
any of the palætiological sciences. We may have to compare
and to reconcile the evidence of existing phenomena with
that of historical tradition. But under some circumstances
this process of conciliation may assume an interest of
another kind, on which we will make a few remarks.

3. _Natural and Providential History of the World._--We may
contemplate the existence of man upon the earth, his origin
and his progress, in the same manner as we contemplate the
existence of any other race of animals; namely, in a purely
palætiological view. We may consider how far our knowledge
of laws of causation enables us to explain his diffusion and
migration, his differences and resemblances, his actions and
works. And this is the view of man as a member of the
_Natural_ Course of Things. {299}

But man, at the same time the contemplator and the subject
of his own contemplation, endowed with faculties and powers
which make him a being of a different nature from other
animals, cannot help regarding his own actions and
enjoyments, his recollections and his hopes, under an aspect
quite different from any that we have yet had presented to
us. We have been endeavouring to place in a clear light the
Fundamental Ideas, such as that of Cause, on which depends
our knowledge of the natural course of things. But there are
other Ideas to which man necessarily refers his actions; he
is led by his nature, not only to consider his own actions,
and those of his fellow-men, as springing out of this or
that cause, leading to this or that material result; but
also as _good_ or _bad_, as what they _ought_ or _ought not_
to be. He has Ideas of moral relations as well as those
Ideas of material relations with which we have hitherto been
occupied. He is a moral as well as a natural agent.

Contemplating himself and the world around him by the light
of his Moral Ideas, man is led to the conviction that his
moral faculties were bestowed upon him by design and for a
purpose; that he is the subject of a Moral Government; that
the course of the world is directed by the Power which
governs it, to the unfolding and perfecting of man's moral
nature; that this guidance may be traced in the career of
individuals and of the world; that there is a _Providential_
as well as a Natural Course of Things.

Yet this view is beset by no small difficulties. The full
development of man's moral faculties;--the perfection of his
nature up to the measure of his own ideas;--the adaptation
of his moral being to an ultimate destination, by its
transit through a world full of moral evil, in which evil
each person has his share;--are effects for which the
economy of the world appears to contain no adequate
provision. Man, though aware of his moral nature, and ready
to believe in an ultimate destination of purity and
blessedness, is too feeble to resist the temptation of evil,
and too helpless to restore his purity when once lost. He
cannot but look for {300} some confirmation of that
providential order which he has begun to believe; some
provision for those deficiencies in his moral condition
which he has begun to feel.

He looks at the history of the world, and he finds that at a
certain period it offers to him the promise of what he
seeks. When the natural powers of man had been developed to
their full extent, and were beginning to exhibit symptoms of
decay;--when the intellectual progress of the world appeared
to have reached its limit, without supplying man's moral
needs;--we find the great Epoch in the Providential History
of the world. We find the announcement of a Dispensation by
which man's deficiencies shall be supplied and his
aspirations fulfilled: we find a provision for the
purification, the support, and the ultimate beatification of
those who use the provided means. And thus the providential
course of the world becomes consistent and intelligible.

4. _The Sacred Narrative._--But with the new Dispensation,
we receive, not only an account of its own scheme and
history, but also a written narrative of the providential
course of the world from the earliest times, and even from
its first creation. This narrative is recognized and
authorized by the new dispensation, and accredited by some
of the same evidences as the dispensation itself. That the
existence of such a sacred narrative should be a part of the
providential order of things, cannot but appear natural;
but, naturally also, the study of it leads to some
difficulties.

The Sacred Narrative in some of its earliest portions speaks
of natural objects and occurrences respecting them. In the
very beginning of the course of the world, we may readily
believe (indeed, as we have seen in the last chapter, our
scientific researches lead us to believe) that such
occurrences were very different from anything which now
takes place;--different to an extent and in a manner which
we cannot estimate. Now the narrative must speak of objects
and occurrences in the words and phrases which have derived
their meaning from their application to the existing natural
state of things. When applied to an initial {301}
supernatural state therefore, these words and phrases cannot
help being to us obscure and mysterious, perhaps ambiguous
and seemingly contradictory.

5. _Difficulties in interpreting the Sacred Narrative._--The
moral and providential relations of man's condition are so
much more important to him than mere natural relations, that
at first we may well suppose he will accept the Sacred
Narrative, as not only unquestionable in its true import,
but also as a guide in his views even of mere natural
things. He will try to modify the conceptions which he
entertains of objects and their properties, so that the
Sacred Narrative of the supernatural condition shall retain
the first meaning which he had put upon it in virtue of his
own habits in the usage of language.

But man is so constituted that he cannot persist in this
procedure. The powers and tendencies of his intellect are
such that he cannot help trying to attain true conceptions
of objects and their properties by the study of things
themselves. For instance, when he at first read of a
firmament dividing the waters above from the waters below,
he perhaps conceived a transparent floor in the skies, on
which the superior waters rested, which descend in rain; but
as his observations and his reasonings satisfied him that
such a floor could not exist, he became willing to allow (as
St. Augustine allowed) that the waters above the firmament
are in a state of vapour. And in like manner in other
subjects, men, as their views of nature became more distinct
and precise, modified, so far as it was necessary for
consistency's sake, their first rude interpretations of the
Sacred Narrative; so that, without in any degree losing its
import as a view of the providential course of the world, it
should be so conceived as not to contradict what they knew
of the natural order of things.

But this accommodation was not always made without painful
struggles and angry controversies. When men had conceived
the occurrences of the Sacred Narrative in a particular
manner, they could not readily and willingly adopt a new
mode of conception; and all attempts to recommend to them
such novelties, they {302} resisted as attacks upon the
sacredness of the Narrative. They had clothed their belief
of the workings of Providence in certain images; and they
clung to those images with the persuasion that, without
them, their belief could not subsist. Thus they imagined to
themselves that the earth was a flat floor, solidly and
broadly laid for the convenience of man; and they felt as if
the kindness of Providence was disparaged, when it was
maintained that the earth was a globe held together only by
the mutual attraction of its parts.

The most memorable instance of a struggle of this kind is to
be found in the circumstances which attended the
introduction of the Heliocentric Theory of Copernicus to
general acceptance. On this controversy I have already made
some remarks in the _History of Science_[20\10], and have
attempted to draw from it some lessons which may be useful
to us when any similar conflict of opinions may occur. I
will here add a few reflections with a similar view.

[Note 20\10: B. v. c. iii. sect. 4.]

6. _Such difficulties inevitable._--In the first place, I
remark that such modifications of the current interpretation
of the words of Scripture appear to be an inevitable
consequence of the progressive character of Natural Science.
Science is constantly teaching us to describe known facts in
new language; but the language of Scripture is always the
same. And not only so, but the language of Scripture is
necessarily adapted to the common state of man's
intellectual development, in which he is supposed not to be
possessed of science. Hence the phrases used by Scripture
are precisely those which science soon teaches man to
consider as inaccurate. Yet they are not, on that account,
the less fitted for their proper purpose: for if any terms
had been used, adapted to a more advanced state of
knowledge, they must have been unintelligible among those to
whom the Scripture was first addressed. If the Jews had been
told that water existed in the clouds in small drops, they
would have marvelled that it did {303} not constantly
descend; and to have explained the reason of this, would
have been to teach Atmology in the sacred writings. If they
had read in their Scripture that the earth was a sphere,
when it appeared to be a plain, they would only have been
disturbed in their thoughts or driven to some wild and
baseless imaginations, by a declaration to them so strange.
If the Divine Speaker, instead of saying that he would set
his bow in the clouds, had been made to declare that he
would give to water the property of refracting different
colours at different angles, how utterly unmeaning to the
hearers would the words have been! And in these cases, the
expressions, being unintelligible, startling, and
bewildering, would have been such as tended to unfit the
Sacred Narrative for its place in the providential
dispensation of the world.

Accordingly, in the great controversy which took place in
Galileo's time between the defenders of the then customary
interpretations of Scripture, and the assertors of the
Copernican system of the universe, when the innovators were
upbraided with maintaining opinions contrary to Scripture,
they replied that Scripture was not intended to teach men
astronomy, and that it expressed the acts of divine power in
images which were suited to the ideas of unscientific men.
To speak of the rising and setting and travelling of the
sun, of the fixity and of the foundations of the earth, was
to use the only language which would have made the Sacred
Narrative intelligible. To extract from these and the like
expressions doctrines of science, was, they declared, in the
highest degree unjustifiable; and such a course could lead,
they held, to no result but a weakening of the authority of
Scripture in proportion as its credit was identified with
that of these modes of applying it. And this judgment has
since been generally assented to by those who most reverence
and value the study of the designs of Providence as well as
that of the works of nature.

7. _Science tells us nothing concerning Creation._--Other
apparent difficulties arise from the accounts given in the
Scripture of the first origin of the world {304} in which we
live: for example, Light is represented as created before
the Sun. With regard to difficulties of this kind, it
appears that we may derive some instruction from the result
to which we were led in the last chapter;--namely, that in
the sciences which trace the progress of natural
occurrences, we can in no case go back to an origin, but in
every instance appear to find ourselves separated from it by
a state of things, and an order of events, of a kind
altogether different from those which come under our
experience. The thread of induction respecting the natural
course of the world snaps in our fingers, when we try to
ascertain where its beginning is. Since, then, science can
teach us nothing positive respecting the beginning of
things, she can neither contradict nor confirm what is
taught by Scripture on that subject; and thus, as it is
unworthy timidity in the lover of Scripture to fear
contradiction, so is it ungrounded presumption to look for
confirmation, in such cases. The providential history of the
world has its own beginning, and its own evidence; and we
can only render the system insecure, by making it lean on
our material sciences. If any one were to suggest that the
nebular hypothesis countenances the Scripture history of the
formation of this system, by showing how the luminous matter
of the sun might exist previous to the sun itself, we should
act wisely in rejecting such an attempt to weave together
these two heterogeneous threads;--the one a part of a
providential scheme, the other a fragment of a physical
speculation.

We shall best learn those lessons of the true philosophy of
science which it is our object to collect, by attending to
portions of science which have gone through such crises as
we are now considering; nor is it requisite, for this
purpose, to bring forwards any subjects which are still
under discussion. It may, however, be mentioned that such
maxims as we are now endeavouring to establish, and the one
before us in particular, bear with a peculiar force upon
those Palætiological Sciences of which we have been treating
in the present Book. {305}

8. _Scientific views, when familiar, do not disturb the
authority of Scripture._--There is another reflection which
may serve to console and encourage us in the painful
struggles which thus take place, between those who maintain
interpretations of Scripture already prevalent and those who
contend for such new ones as the new discoveries of science
require. It is this;--that though the new opinion is
resisted by one party as something destructive of the credit
of Scripture and the reverence which is its due, yet, in
fact, when the new interpretation has been generally
established and incorporated with men's current thoughts, it
ceases to disturb their views of the authority of the
Scripture or of the truth of its teaching. When the language
of Scripture, invested with its new meaning, has become
familiar to men, it is found that the ideas which it calls
up are quite as reconcileable as the former ones were, with
the most entire acceptance of the providential dispensation.
And when this has been found to be the case, all cultivated
persons look back with surprise at the mistake of those who
thought that the essence of the revelation was involved in
their own arbitrary version of some collateral circumstance
in the revealed narrative. At the present day, we can hardly
conceive how reasonable men could ever have imagined that
religious reflections on the stability of the earth, and the
beauty and use of the luminaries which revolve round it,
would be interfered with by an acknowledgment that this rest
and motion are apparent only[21\10]. And thus the authority
of revelation is not shaken by any changes introduced by the
progress of science in the mode of interpreting expressions
which describe physical objects and occurrences; provided
the new interpretation is admitted at a proper season, and
in a proper spirit; so as to soften, as much as possible,
both the public controversies and the private scruples which
almost inevitably accompany such an alteration.

[Note 21\10: I have here borrowed a sentence or two from my
own _History_.]

9. _When should old Interpretations be given up?_--But the
question then occurs, What is the proper {306} season for a
religious and enlightened commentator to make such a change
in the current interpretation of sacred Scripture? At what
period ought the established exposition of a passage to be
given up, and a new mode of understanding the passage, such
as is, or seems to be, required by new discoveries
respecting the laws of nature, accepted in its place? It is
plain, that to introduce such an alteration lightly and
hastily would be a procedure fraught with inconvenience; for
if the change were made in such a manner, it might be
afterwards discovered that it had been adopted without
sufficient reason, and that it was necessary to reinstate
the old exposition. And the minds of the readers of
Scripture, always to a certain extent and for a time
disturbed by the subversion of their long-established
notions, would be distressed without any need, and might be
seriously unsettled. While, on the other hand, a too
protracted and obstinate resistance to the innovation, on
the part of the scriptural expositors, would tend to
identify, at least in the minds of many, the authority of
the Scripture with the truth of the exposition; and
therefore would bring discredit upon the revealed word, when
the established interpretation was finally proved to be
untenable.

A rule on this subject, propounded by some of the most
enlightened dignitaries of the Roman Catholic church, on the
occasion of the great Copernican controversy begun by
Galileo, seems well worthy of our attention. The following
was the opinion given by Cardinal Bellarmine at the
time:--'When a _demonstration_ shall be found to establish the
earth's motion, it will be proper to interpret the sacred
Scriptures otherwise than they have hitherto been
interpreted in those passages where mention is made of the
stability of the earth and movement of the heavens.' This
appears to be a judicious and reasonable maxim for such
cases in general. So long as the supposed scientific
discovery is doubtful, the exposition of the meaning of
Scripture given by commentators of established credit is not
wantonly to be disturbed: but when a scientific theory,
irreconcileable with this ancient {307} interpretation, is
clearly proved, we must give up the interpretation, and seek
some new mode of understanding the passage in question, by
means of which it may be consistent with what we know; for
if it be not, our conception of the things so described is
no longer consistent with itself.

It may be said that this rule is indefinite, for who shall
decide when a new theory is completely demonstrated, and the
old interpretation become untenable? But to this we may
reply, that if the rule be assented to, its application will
not be very difficult. For when men have admitted as a
general rule, that the current interpretations of scriptural
expressions respecting natural objects and events may
possibly require, and in some cases certainly will require,
to be abandoned, and new ones admitted, they will hardly
allow themselves to contend for such interpretations as if
they were essential parts of revelation; and will look upon
the change of exposition, whether it come sooner or later,
without alarm or anger. And when men lend themselves to the
progress of truth in this spirit, it is not of any material
importance at what period a new and satisfactory
interpretation of the scriptural difficulty is found; since
a scientific exactness in our apprehension of the meaning of
such passages as are now referred to is very far from being
essential to our full acceptance of revelation.

10. _In what Spirit should the Change be accepted?_--Still
these revolutions in scriptural interpretation must always
have in them something which distresses and disturbs
religious communities. And such uneasy feelings will take a
different shape, according as the community acknowledges or
rejects a paramount interpretative authority in its
religious leaders. In the case in which the interpretation
of the Church is binding upon all its members, the more
placid minds rest in peace upon the ancient exposition, till
the spiritual authorities announce that the time for the
adoption of a new view has arrived; but in these
circumstances, the more stirring and inquisitive minds,
which cannot refrain from the pursuit of new truths {308}
and exact conceptions, are led to opinions which, being
contrary to those of the Church, are held to be sinful. On
the other hand, if the religious constitution of the
community allow and encourage each man to study and
interpret for himself the Sacred Writings, we are met by
evils of another kind. In this case, although, by the
unforced influence of admired commentators, there may
prevail a general agreement in the usual interpretation of
difficult passages, yet as each reader of the Scripture
looks upon the sense which he has adopted as being his own
interpretation, he maintains it, not with the tranquil
acquiescence of one who has deposited his judgment in the
hands of his Church, but with the keenness and strenuousness
of self-love. In such a state of things, though no judicial
severities can be employed against the innovators, there may
arise more angry controversies than in the other case.

It is impossible to overlook the lesson which here offers
itself, that it is in the highest degree unwise in the
friends of religion, whether individuals or communities,
unnecessarily to embark their credit in expositions of
Scripture on matters which appertain to natural Science. By
delivering physical doctrines as the teaching of revelation,
religion may lose much, but cannot gain anything. This maxim
of practical wisdom has often been urged by Christian
writers. Thus St. Augustine says[22\10]: 'In obscure matters
and things far removed from our senses, if we read anything,
even in the divine Scripture, which may produce diverse
opinions without damaging the faith which we cherish, let us
not rush headlong by positive assertion to either the one
opinion or the other; lest, when a more thorough discussion
has shown the opinion which we had adopted to be false, our
faith may fall with it: and we should be found contending,
not for the doctrine of the sacred Scriptures, but for our
own; endeavouring to make our doctrine to be that of the
Scriptures, instead of taking the doctrine of the Scriptures
to be ours.' And in nearly the same spirit, at the {309}
time of the Copernican controversy, it was thought proper to
append to the work of Copernicus a postil, to say that the
work was written to account for the phenomena, and that
people must not run on blindly and condemn either of the
opposite opinions. Even when the Inquisition, in 1616,
thought itself compelled to pronounce a decision upon this
subject, the verdict was delivered in very moderate
language;--that 'the doctrine of the earth's motion appeared
to be contrary to Scripture:' and yet, moderate as this
expression is, it has been blamed by judicious members of
the Roman church as deciding a point such as religious
authorities ought not to pretend to decide; and has brought
upon that church no ordinary weight of general condemnation.
Kepler pointed out, in his lively manner, the imprudence of
employing the force of religious authorities on such
subjects: _Acies dolabræ in ferrum illisa, postea nec in
lignum valet amplius. Capiat hoc cujus interest_. 'If you
_will_ try to chop iron, the axe becomes unable to cut even
wood. I warn those whom it concerns.'

[Note 22\10: Lib. i. _de Genesi_, cap. xviii.]

11. _In what Spirit should the Change be urged?_--But while
we thus endeavour to show in what manner the interpreters of
Scripture may most safely and most properly accept the
discoveries of science, we must not forget that there may be
errours committed on the other side also; and that men of
science, in bringing forward views which may for a time
disturb the minds of lovers of Scripture, should consider
themselves as bound by strict rules of candour, moderation,
and prudence. Intentionally to make their supposed
discoveries a means of discrediting, contradicting, or
slighting the sacred Scriptures, or the authority of
religion, is in them unpardonable. As men who make the
science of Truth the business of their lives, and are
persuaded of her genuine superiority, and certain of her
ultimate triumph, they are peculiarly bound to urge her
claims in a calm and temperate spirit; not forgetting that
there are other kinds of truth besides that which they
peculiarly study. They may properly reject authority in
matters of science; but they are to leave {310} it its
proper office in matters of religion. I may here again quote
Kepler's expressions: 'In Theology we balance authorities,
in Philosophy we weigh reasons. A holy man was Lactantius
who denied that the earth was round; a holy man was
Augustine, who granted the rotundity, but denied the
antipodes; a holy thing to me is the Inquisition, which
allows the smallness of the earth, but denies its motion;
but more holy to me is Truth; and hence I prove, from
philosophy, that the earth is round, and inhabited on every
side, of small size, and in motion among the stars,--and
this I do with no disrespect to the Doctors.' I the more
willingly quote such a passage from Kepler, because the
entire ingenuousness and sincere piety of his character does
not allow us to suspect him in anything of hypocrisy or
latent irony. That similar professions of respect may be
made ironically, we have a noted example in the celebrated
Introduction to _Galileo's Dialogue on the Copernican
System_; probably the part which was most offensive to the
authorities. 'Some years ago,' he begins, 'a wholesome edict
was promulgated at Rome, which, in order to check the
perilous scandals of the present age, imposed silence upon
the Pythagorean opinion of the mobility of the earth. There
were not wanting,' he proceeds, 'persons who rashly asserted
that this decree was the result, not of a judicious inquiry,
but of passion ill-informed; and complaints were heard that
councillors, utterly unacquainted with astronomical
observation, ought not to be allowed, with their sudden
prohibitions, to clip the wings of speculative intellects.
_At the hearing of rash lamentations like these, my zeal
could not keep silence._' And he then goes on to say, that
he wishes, in his _Dialogue_, to show that the subject had
been fully examined at Rome. Here the irony is quite
transparent, and the sarcasm glaringly obvious. I think we
may venture to say that this is not the temper in which
scientific questions should be treated; although by some,
perhaps, the prohibition of public discussion may be
considered as justifying any evasion which is likely to pass
unpunished. {311}

12. _Duty of Mutual Forbearance._--We may add, as a further
reason for mutual forbearance in such cases, that the true
interests of both parties are the same. The man of science
is concerned, no less than any other person, in the truth
and import of the divine dispensation; the religious man, no
less than the man of science, is, by the nature of his
intellect, incapable of believing two contradictory
declarations. Hence they have both alike a need for
understanding the Scripture in some way in which it shall be
consistent with their understanding of nature. It is for
their common advantage to conciliate, as Kepler says, the
finger and the tongue of God, his works and his word. And
they may find abundant reason to bear with each other, even
if they should adopt for this purpose different
interpretations, each finding one satisfactory to himself;
or if any one should decline employing his thoughts on such
subjects at all. I have elsewhere[23\10] quoted a passage
from Kepler[24\10] which appears to me written in a most
suitable spirit: 'I beseech my reader that, not unmindful of
the divine goodness bestowed upon man, he do with me praise
and celebrate the wisdom of the Creator, which I open to him
from a more inward explication of the form of the world,
from a searching of causes, from a detection of the errours
of vision; and that thus not only in the firmness and
stability of the earth may we perceive with gratitude the
preservation of all living things in nature as the gift of
God: but also that in its motion, so recondite, so
admirable, we may acknowledge the wisdom of the Creator. But
whoever is too dull to receive this science, or too weak to
believe the Copernican system without harm to his piety,
him, I say, I advise that, leaving the school of astronomy,
and condemning, if so he please, any doctrines of the
philosophers, he follow his own path, and desist from this
wandering through the universe; and that, lifting up his
natural eyes, with which alone he can see, {312} he pour
himself out from his own heart in worship of God the
Creator, being certain that he gives no less worship to God
than the astronomer, to whom God has given to see more
clearly with his inward eyes, and who, from what he has
himself discovered, both can and will glorify God.'

[Note 23\10: _Bridgewater Tr._ p. 314.]

[Note 24\10: _Com. Stell. Mart._ Introd.]

13. _Case of Galileo._--I may perhaps venture here to make a
remark or two upon this subject with reference to a charge
brought against a certain portion of the _History of the
Inductive Sciences_. Complaint has been made[25\10] that the
character of the Roman church, as shown in its behaviour
towards Galileo, is misrepresented in the account given of
it in the History of Astronomy. It is asserted that Galileo
provoked the condemnation he incurred; first, by
pertinaciously demanding the assent of the ecclesiastical
authorities to his opinion of the consistency of the
Copernican doctrine with Scripture; and afterwards by
contumaciously, and, as we have seen, contumeliously
violating the silence which the Church had enjoined upon
him. It is further declared that the statement which
represents it as the habit of the Roman church to dogmatize
on points of natural science is unfounded; as well as the
opinion that in consequence of this habit, new scientific
truths were promulgated less boldly in Italy than in other
countries. I shall reply very briefly on these subjects; for
the decision of them is by no means requisite in order to
establish the doctrines to which I have been led in the
present chapter, nor, I hope, to satisfy my reader that my
views have been collected from an impartial consideration of
scientific history.

[Note 25\10: _Dublin Review_, No. ix. July, 1838, p. 72.]

With regard to Galileo, I do not think it can be denied that
he obtruded his opinions upon the ecclesiastical authorities
in an unnecessary and imprudent manner. He was of an ardent
character, strongly convinced himself, and urged on still
more by the conviction which he produced among his
disciples, and {313} thus he became impatient for the
triumph of truth. This judgment of him has recently been
delivered by various independent authorities, and has
undoubtedly considerable foundation[26\10]. As to the
question whether authority in matters of natural science
were habitually claimed by the authorities of the Church of
Rome, I have to allow that I cannot produce instances which
establish such a habit. We, who have been accustomed to have
daily before our eyes the Monition which the Romish editors
of Newton thought it necessary to prefix--_Cæterum latis a
summo Pontifice contra telluris motum Decretis, nos obsequi
profitemur_--were not likely to conjecture that this was a
solitary instance of the interposition of the Papal
authority on such subjects. But although it would be easy to
find declarations of heresy delivered by Romish
Universities, and writers of great authority, against tenets
belonging to the natural sciences, I am not aware that any
other case can be adduced in which the Church or the Pope
can be shown to have pronounced such a sentence. I am well
contented to acknowledge this; for I should be far more
gratified by finding myself compelled to hold up the
seventeenth century as a model for the nineteenth in this
respect, than by having to sow enmity between the admirers
of the past and the present through any disparaging
contrast[27\10].

[Note 26\10: Besides the _Dublin Review_, I may quote the
_Edinburgh Review_, which I suppose will not be thought
likely to have a bias in favour of the exercise of
ecclesiastical authority in matters of science; though
certainly there is a puerility in the critic's phraseology
which does not add to the weight of his judgment. 'Galileo
contrived to surround the truth with every variety of
obstruction. The tide of knowledge, which had hitherto
advanced in peace, he crested with angry breakers, and he
involved in its surf both his friends and his foes.'--_Ed.
Rev._ No. cxxiii. p. 126.]

[Note 27\10: I may add that the most candid of the adherents
of the Church of Rome condemn the assumption of authority in
matters of science, made, in this one instance at least, by
the ecclesiastical tribunals. The author of the _Ages of
Faith_ (book viii. p. 248), says, 'A Congregation, it is to
be lamented, declared the new system to be opposed to
Scripture, and therefore heretical.']

{314} With respect to the attempt made in my History to
characterize the intellectual habits of Italy as produced by
her religious condition,--certainly it would ill become any
student of the history of science to speak slightingly of
that country, always the mother of sciences, always ready to
catch the dawn and hail the rising of any new light of
knowledge. But I think our admiration of this activity and
acuteness of mind is by no means inconsistent with the
opinion, that new truths were promulgated more boldly beyond
the Alps, and that the subtilty of the Italian intellect
loved to insinuate what the rough German bluntly asserted.
Of the decent duplicity with which forbidden opinions were
handled, the reviewer himself gives us instances, when he
boasts of the liberality with which Copernican professors
were placed in important stations by the ecclesiastical
authorities, soon after the doctrine of the motion of the
earth had been declared by the same authorities to be
contrary to Scripture. And in the same spirit is the process
of demanding from Galileo a public and official recantation
of opinions which he had repeatedly been told by his
ecclesiastical superiors he might hold as much as he
pleased. I think it is easy to believe that among persons so
little careful to reconcile public profession with private
conviction, official decorum was all that was demanded. When
Galileo had made his renunciation of the earth's motion on
his knees, he rose and said, as we are told, _E pur si
muove_--'and yet it _does_ move.' This is sometimes
represented as the heroic soliloquy of a mind cherishing its
conviction of the truth, in spite of persecution; I think we
may more naturally conceive it uttered as a playful epigram
in the ear of a cardinal's secretary, with a full knowledge
that it would be immediately repeated to his master[28\10].

[Note 28\10: I have somewhat further discussed the case of
Galileo in the later editions of the _History_, book v.
chap. iii. sect. 4.]

Besides the Ideas involved in the material sciences, {315}
of which we have already examined the principal ones, there
is one Idea or Conception which our Sciences do not indeed
include, but to which they not obscurely point; and the
importance of this Idea will make it proper to speak of it,
though this must be done very briefly.

{{316}}
CHAPTER V.

OF THE CONCEPTION OF A FIRST CAUSE.

1. AT the end of the last chapter but one, we were led to
this result,--that we cannot, in any of the Palætiological
Sciences, ascend to a beginning which is of the same nature
as the existing cause of events, and which depends upon
causes that are still in operation. Philosophers never have
demonstrated, and probably never will be able to
demonstrate, what was the original condition of the solar
system, of the earth, of the vegetable and animal worlds, of
languages, of arts. On all these subjects the course of
investigation, followed backwards as far as our materials
allow us to pursue it, ends at last in an impenetrable
gloom. We strain our eyes in vain when we try, by our
natural faculties, to discern an origin.

2. Yet speculative men have been constantly employed in
attempts to arrive at that which thus seems to be placed out
of their reach. The Origin of Languages, the Origin of the
present Distribution of Plants and Animals, the Origin of
the Earth, have been common subjects of diligent and
persevering inquiry. Indeed inquiries respecting such
subjects have been, at least till lately, the usual form
which Palætiological researches have assumed. _Cosmogony_,
the Origin of the World, of which, in such speculations, the
earth was considered as a principal part, has been a
favourite study both of ancient and of modern times: and
most of the attempts at Geology previous to the present
period have been _Cosmogonies_ or _Geogonies_, rather than
that more genuine science which we have endeavoured to
delineate. Again: Glossology, though now an extensive body
of solid knowledge, was {317} mainly brought into being by
inquiries concerning the Original Language spoken by men;
and the nature of the first separation and diffusion of
languages, the first peopling of the earth by man and by
animals, were long sought after with ardent curiosity,
although of course with reference to the authority of the
Scriptures, as well as the evidence of natural phenomena.
Indeed the interest of such inquiries even yet is far from
being extinguished. The disposition to explore the past in
the hope of finding, by the light of natural reasoning as
well as by the aid of revelation, the origin of the present
course of things, appears to be unconquerable. 'What was the
beginning?' is a question which the human race cannot desist
from perpetually asking. And no failure in obtaining a
satisfactory answer can prevent inquisitive spirits from
again and again repeating the inquiry, although the blank
abyss into which it is uttered does not even return an echo.

3. What, then, is the reason of an attempt so pertinacious
yet so fruitless? By what motive are we impelled thus
constantly to seek what we can never find? Why are the
errour of our conjectures, the futility of our reasonings,
the precariousness of our interpretations, over and over
again proved to us in vain? Why is it impossible for us to
acquiesce in our ignorance and to relinquish the inquiry?
Why cannot we content ourselves with examining those links
of the chain of causes which are nearest to us,--those in
which the connexion is intelligible and clear; instead of
fixing our attention upon those remote portions where we can
no longer estimate its coherence? In short, why did not men
from the first take for the subject of their speculations
the Course of Nature rather than the Origin of Things?

To this we reply, that in doing what they have thus done, in
seeking what they have sought, men are impelled by an
intellectual necessity. They cannot conceive a Series of
connected occurrences without a Commencement; they cannot
help supposing a cause for the Whole, as well as a cause for
each part; they cannot be satisfied with a succession of
causes without {318} assuming a First Cause. Such an
assumption is necessarily impressed upon our minds by our
contemplation of a series of causes and effects; that _there
must be a First Cause_, is accepted by all intelligent
reasoners as an Axiom: and like other Axioms, its truth is
necessarily implied in the Idea which it involves.

4. The evidence of this axiom may be illustrated in several
ways. In the first place, the axiom is assumed in the
argument usually offered to prove the existence of the
Deity. Since, it is said, the world now exists, and since
nothing cannot produce something, something must have
existed from eternity. This Something is the First Cause: it
is God.

Now what I have to remark here is this:--the conclusiveness
of this argument, as a proof of the existence of one
independent, immutable Deity, depends entirely upon the
assumption of the axiom above stated. The World, a **series
of causes and effects, exists: therefore there must be, not
only this series of causes and effects, but also a First
Cause. It will be easily seen, that without the axiom, that
in every series of causes and effects there must be a First
Cause, the reasoning is altogether inconclusive.

5. Or to put the matter otherwise: The argument for the
existence of the Deity was stated thus: Something exists,
therefore something must have existed from eternity.
'Granted,' the opponent might say; 'but this something which
has existed from eternity, why may it not be this very
series of causes and effects which is now going on, and
which appears to contain in itself no indication of
beginning or end?' And thus, without the assumption of the
necessity of a First Cause, the force of the argument may be
resisted.

6. But, it may be asked, how do those who have written to
prove the existence of the Deity reply to such an objection
as the one just stated? It is natural to suppose that, on a
subject so interesting and so long discussed, all the
obvious arguments with their replies, have been fully
brought into view. What is the result in this case? {319}

The principal modes of replying to the above objection, that
the series of causes and effects which now exists, may have
existed from eternity, appear to be these.

In the first place, our minds cannot be satisfied with a
series of successive, dependent, causes and effects, without
something first and independent. We pass from effect to
cause, and from that to a higher cause, in search of
something on which the mind can rest; but if we can do
nothing but repeat this process, there is no use in it. We
move our limbs, but make no advance. Our question is not
answered, but evaded. The mind cannot acquiesce in the
destiny thus presented to it, of being referred from event
to event, from object to object, along an interminable vista
of causation and time. Now this mode of stating the
reply,--to say that the mind _cannot thus be satisfied_,
appears to be equivalent to saying that the mind is
conscious of a Principle, in virtue of which such a view as
this must be rejected;--the mind takes refuge in the
assumption of a First Cause, from an employment inconsistent
with its own nature.

7. Or again, we may avoid the objection, by putting the
argument for the existence of a Deity in this form: The
series of causes and effects which we call the _world_, or
the _course of nature_, may be considered as a _whole_, and
this whole must have a cause of its existence. The whole
collection of objects and events may be comprehended as a
single effect, and of this effect there must be a cause.
This Cause of the Universe must be superior to, and
independent of the special events, which, happening in time,
make up the universe of which He is the cause. He must exist
and exercise causation, before these events can begin: He
must be the First Cause.

Although the argument is here somewhat modified in form, the
substance is the same as before. For the assumption that we
may consider the whole series of causes and effects as a
_single effect_, is equivalent to the assumption that
besides partial causes we must have a First Cause. And thus
the Idea of a First Cause, and {320} the axiom which asserts
its necessity, are recognized in the usual argumentation on
this subject.

8. This Idea of a First Cause, and the principle involved in
the Idea, have been the subject of discussion in another
manner. As we have already said, we assume as an axiom that
a First Cause must exist; and we assert that God, the First
Cause, exists eternal and immutable, by the necessity which
the axiom implies. Hence God is said to exist
necessarily;--to be a necessarily existing being. And when
this _necessary existence_ of God had been spoken of, it
soon began to be contemplated as a sufficient reason, and as
an absolute demonstration of His existence; without any need
of referring to the world as an effect, in order to arrive
at God as the cause. And thus men conceived that they had
obtained a proof of the existence of the Deity, _à priori_,
from Ideas, as well as _à posteriori_, from Effects.

9. Thus, Thomas Aquinas employs this reasoning to prove the
_eternity_ of God[29\10]: 'Oportet ponere aliquod primum
necessarium quod est per se ipsum necessarium; et hoc est
Deus, cum sit prima causa ut dictum est: igitur Deus æternus
est, cum omne necessarium per se sit æternum.' It is true
that the schoolmen never professed to be able to prove the
_existence_ of the Deity _à priori_: but they made use of
this conception of necessary existence in a manner which
approached very near to such an attempt. Thus Suarez[30\10]
discusses the question, 'Utrum aliquo modo possit _à priori_
demonstrari Deum esse.' And resolves the question in this
manner: 'Ad hunc ergo modum dicendum est: Demonstrato _à
posteriori_ Deum esse ens necessarium et a se, ex hoc
attributo posse _à priori_ demonstrari præter illud non
posse esse aliud ens necessarium et a se, et consequenter
demonstrari Deum esse.'

[Note 29\10: Aquin. _Cont. Gentil._ lib. i. c. xiv. p. 21.]

[Note 30\10: _Metaphys._ tom. ii. disp. xxix. sect. 3, p. 28.]

But in modern times attempts were made by Descartes and
Samuel Clarke, to prove the Divine {321} existence at once
_à priori_, from the conception of necessary existence;
which, it was argued, could not subsist without actual
existence. This argumentation was acutely and severely
criticised by Dr. Waterland.

10. Without dwelling upon a subject, the discussion of which
does not enter into the design of the present work, I may
remark that the question whether an _à priori_ proof of the
existence of a First Cause be possible, is a question
concerning the nature of our Ideas, and the evidence of the
axioms which they involve, of the same kind as many
questions which we have already had to discuss. Is our
Conception or Idea of a First Cause gathered from the
effects we see around us? It is plain that we must answer,
here as in other cases, that the Idea is not extracted from
the phenomena, but assumed in order that the phenomena may
become intelligible to the mind;--that the Idea is a
necessary one, inasmuch as it does not depend upon
observation for its evidence; but that it depends upon
observation for its development, since without some
observation, we cannot conceive the mind to be cognizant of
the relation of causation at all. In this respect, however,
the Idea of a First Cause is no less necessary than the
ideas of Space, or Time, or Cause in general. And whether we
call the reasoning derived from such a necessity an argument
_à priori_ or _à posteriori_, in either case it possesses
the genuine character of demonstration, being founded upon
axioms which command universal assent.

11. I have, however, spoken of our _Conception_ rather than
of our _Idea_ of a First Cause; for the notion of a First
Cause appears to be rather a modification of the Fundamental
Idea of Cause, which was formerly discussed, than a separate
and peculiar Idea. And the Axiom, _that there must be a
First Cause_, is recognised by most persons as an
application of the general Axiom of Causation, _that every
effect must have a Cause_; this latter Axiom being applied
to the World, considered in its totality, as a single
Effect. This distinction, however, between an Idea and a
Conception, is of no material consequence to our argument;
provided we {322} allow the maxim, that there must be a
First Cause, to be necessarily and evidently true; whether
it be thought better to speak of it as an independent Axiom,
or to consider it as derived from the general Axiom of Causation.

12. Thus we necessarily infer a First Cause, although the
Palætiological Sciences only point _towards_ it, and do not
lead us _to_ it. But I must observe further; that in each of
the series of events which form the subject of
Palætiological research, the First Cause is the _same_.
Without here resting upon reasoning founded upon our
Conception of a First Cause, I may remark that this identity
is proved by the close connexion of all the branches of
natural science, and the way in which the causes and the
events of each are interwoven with those which belong to the
others. We must needs believe that the First Cause which
produced the earth and its atmosphere is also the Cause of
the plants which clothe its surface; that the First Cause of
the vegetable and of the animal world are the same; that the
First Cause which produced light produced also eyes; that
the First Cause which produced air and organs of
articulation produced also language and the faculties by
which language is rendered possible: and if _those_
faculties, then also all man's other faculties;--the powers
by which, as we have said, he discerns right and wrong, and
recognises a providential as well as a natural course of
things. Nor can we think otherwise than that the Being who
gave these faculties, bestowed them for some
purpose;--bestowed them for that purpose which alone is
compatible with their nature:--the purpose, namely, of
guiding and elevating man in his present career, and of
preparing him for another state of being to which they
irresistibly direct his hopes. And thus, although, as we
have said, no one of the Palætiological Sciences can be
traced continuously to an Origin, yet they not only each
point to an Origin, but all to the same Origin. Their lines
are broken indeed, as they run backwards into the early
periods of the world, but yet they all appear to converge to
the same invisible point. And {323} this point, thus
indicated by the natural course of things, can be no other
than that which is disclosed to us as the starting-point of
the providential course of the world; for we are persuaded
by such reasons as have just been hinted, that the Creator
of the natural world can be no other than the Author and
Governor and Judge of the moral and spiritual world.

13. Thus we are led, by our material Sciences, and
especially by the Palætiological class of them, to the
borders of a higher region, and to a point of view from
which we have a prospect of other provinces of
knowledge;--to contemplations in which other faculties of
man are concerned besides his intellectual, other interests
involved besides those of speculation. On these it does not
belong to our present plan to dwell: but even such a brief
glance as we have taken of the connexion of material with
moral speculations may not be useless, since it may serve to
show that the principles of truth which we are now
laboriously collecting among the results of the physical
sciences, may possibly find some application in those parts
of knowledge towards which men most naturally look with
deeper interest and more serious reverence.

We have been employed hitherto in examining the materials of
knowledge, Facts and Ideas;--Facts in our former History,
and Ideas in the present History. We have dwelt at length on
this latter element; inasmuch as the consideration of it is,
on various accounts, and especially at the present time, by
far the most important, having hitherto been least
distinctly attended to as a special element of scientific
knowledge.

There still remains an important task, with a view to which
we have undertaken this survey of the past course of human
thought and discovery:--namely, the task of determining the
processes by which these materials may actually be made to
constitute knowledge. {324} We have surveyed the stones
which lie before us, partly built and partly ready for
building: we have found them exactly squared, and often
curiously covered with significant imagery and important
inscriptions. We have now to discover how they may best be
fitted into their places, and cemented together, so that
rising stage above stage, they may grow at last into that
fair and lofty temple of Truth, for which we cannot doubt
that they were intended by the Great Architect.

This task, the description of the processes by which
Scientific Truth is discovered and established, we shall, as
has already been said, entitle, in reference to previous
attempts of the same kind, _Novum Organum Renovatum_.

END OF VOL. II.

_Cambridge: Printed at the University Press._

Transcriber's Note

Whewell published the first edition of the _Philosophy of the
Inductive Sciences_ in 1840, as a companion to the 1837
_History of the Inductive Sciences_. Revised second editions
of both works appeared in 1847. The third editions saw a
major reshaping of the _Philosophy_: a two volume _History
of Scientific Ideas_ (1858 - the present text, relying upon
resources kindly provided by the Internet Archive), _Novum
Organon Renovatum_ (1858), and _ On the Philosophy of
Discovery: chapters historical and critical_ (1860 - already
in LibraryBlog's collection: #5155).

The present text has combined the two volumes into one continuous
text. Footnotes are numbered by Book and marked [m\n] where m =
the number of the note within the Book, and n = the number of the
Book. In the original, notes were numbered by chapter. Page numbers
appear in { }, or {{ }} where there is no printed number; where a
word was hyphenated across pages the number has been placed before
the word.

Superscripts are marked with ^.

There is one significant problem to report. For Book IX chapter VI,
the Table of Contents lists 20 articles, but the actual text has
only 19 numbered paragraphs. The text version leaves this
inconsistency untouched; in the htm version, a correction has been
made by numbering the paragraph beginning on p. 244 as #9, and
renumbering those that follow, thereby matching the descriptions in
the Table of Contents.

Other corrections to the text are marked with ** and are listed
below.

Location Text of printed edition Emendation
Vol. 1
p. 71 conlcusion conclusion
p. 87 vi. vii.
p. 157 sciences science
note 1\3 Book 1. chap. xii. Book 3. chap. ii.
p. 231 Marriotte Mariotte
p. 377 Winter's Winterl's
Vol. 2
p. 22 ingedient ingredient
p. 124 wich which
p. 159 attemps attempts
p. 172 knowlege knowledge
note 60\9 Their. Theor.
p. 270 dfficulties difficulties
p. 318 serious series

*** End of this LibraryBlog Digital Book "History of scientific ideas" ***

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