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Title: Preliminary Discourse on the Study of Natural Philosophy
Author: Herschel, John F. W.
Language: English
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  _PRELIMINARY DISCOURSE_
  on the Study of
  NATURAL PHILOSOPHY

  BY
  SIR JOHN F. W. HERSCHEL, BART. K.H.
  _M.A.--D.C.L.--F.R.S.L&E.--M.R.I.A.--F.R.A.S.
  F.G.S.--M.C.U.P.S.--&c. &c._


  NEW EDITION.
  1851.

[Illustration:

  _H. Corbould del._      _E. Finden. sculp._

NATURÆ MINISTER ET INTERPRES.]


  NEW EDITION.

  London:
  PRINTED FOR LONGMAN, BROWN, GREEN & LONGMANS, PATERNOSTER ROW



CONTENTS.


                                                                    Page
                                PART I.

        OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF THE
                           PHYSICAL SCIENCES.


  CHAP. I.

  Of Man regarded as a Creature of Instinct, of Reason, and
    Speculation.--General Influence of Scientific Pursuits on
    the Mind.                                                          1


  CHAP. II.

  Of abstract Science as a Preparation for the Study of Physics.--
    A profound Acquaintance with it not indispensable for a
    clear Understanding of Physical Laws.--How a Conviction
    of their Truth may be obtained without it.--Instances.--
    Further Division of the Subject.                                  18


  CHAP. III.

  Of the Nature and Objects, immediate and collateral, of
    Physical Science, as regarded in itself, and in its
    Application to the practical Purposes of Life, and its
    Influence on the Well-being and Progress of Society.              35


                                PART II.

  OF THE PRINCIPLES ON WHICH PHYSICAL SCIENCE RELIES FOR ITS
    SUCCESSFUL PROSECUTION, AND THE RULES BY WHICH A SYSTEMATIC
    EXAMINATION OF NATURE SHOULD BE CONDUCTED, WITH ILLUSTRATIONS
    OF THEIR INFLUENCE AS EXEMPLIFIED IN THE HISTORY OF ITS
    PROGRESS.


  CHAP. I.

  Of Experience as the Source of our Knowledge.--Of the
    Dismissal of Prejudices.--Of the Evidence of our Senses.          75


  CHAP. II.

  Of the Analysis of Phenomena.                                       85


  CHAP. III.

  Of the State of Physical Science in General, previous to the
    Age of Galileo and Bacon.                                        104


  CHAP. IV.

  Of the Observation of Facts and the Collection of Instances.       118


  CHAP. V.

  Of the Classification of Natural Objects and Phenomena, and of
    Nomenclature.                                                    135


  CHAP. VI.

  Of the First Stage of Induction.--The Discovery of Proximate
    Causes, and Laws of the lowest Degree of Generality, and
    their Verification.                                              144


  CHAP. VII.

  Of the higher Degrees of Inductive Generalization, and of the
    Formation and Verification of Theories.                          190


                               PART III.

    OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES, AND THEIR
                           MUTUAL RELATIONS.


  CHAP. I.

  Of the Phenomena of Force, and of the Constitution of Natural
    Bodies.                                                          221


  CHAP. II.

  Of the Communication of Motion through Bodies.--Of Sound and
    Light.                                                           246


  CHAP. III.

  Of Cosmical Phenomena.                                             265


  CHAP. IV.

  Of the Examination of the material Constituents of the World.
                                                                     290


  CHAP. V.

  Of the Imponderable Forms of Matter.                               310


  CHAP. VI.

  Of the Causes of the actual rapid Advance of the Physical
    Sciences compared with their Progress at an earlier Period.      347



    “In primis, hominis est propria VERI inquisitio atque
    investigatio. Itaque cum sumus negotiis necessariis, curisque
    vacui, tum avemus aliquid videre, audire, ac dicere,
    cognitionemque rerum, aut occultarum aut admirabilium, ad benè
    beatéque vivendum necessariam ducimus;--ex quo intelligitur,
    quod VERUM, simplex, sincerumque sit, id esse naturæe hominis
    aptissimum. Huic veri videndi cupiditati adjuncta est appetitio
    quædam principatûs, ut nemini parere animus benè a naturâ
    informatus velit, nisi præcipienti, aut docenti, aut utilitatis
    causa justè et legitimè imperanti: ex quo animi magnitudo
    existit, et humanararum rerum contemtio.”

                                  CICERO, DE OFFICIIS, Lib. 1. § 13.


    Before all other things, man is distinguished by his pursuit
    and investigation of TRUTH. And hence, when free from needful
    business and cares, we delight to see, to hear, and to
    communicate, and consider a knowledge of many admirable and
    abstruse things necessary to the good conduct and happiness of
    our lives: whence it is clear that whatsoever is TRUE, simple,
    and direct, the same is most congenial to our nature as men.
    Closely allied with this earnest longing to see and know the
    truth, is a kind of dignified and princely sentiment which
    forbids a mind, naturally well constituted, to submit its
    faculties to any but those who announce it in precept or in
    doctrine, or to yield obedience to any orders but such as are
    at once just, lawful, and founded on utility. From this source
    spring greatness of mind and contempt of worldly advantages and
    troubles.



                         PRELIMINARY DISCOURSE
                                   ON
                               THE STUDY
                                   OF
                          NATURAL PHILOSOPHY.



                                PART I.

          OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF
                         THE PHYSICAL SCIENCES



CHAPTER I.

  OF MAN REGARDED AS A CREATURE OF INSTINCT, OF REASON, AND
    SPECULATION.--GENERAL INFLUENCE OF SCIENTIFIC PURSUITS ON THE
    MIND.


(1.) The situation of man on the globe he inhabits, and over which he
has obtained the control, is in many respects exceedingly remarkable.
Compared with its other denizens, he seems, if we regard only his
physical constitution, in almost every respect their inferior, and
equally unprovided for the supply of his natural wants and his defence
against the innumerable enemies which surround him. No other animal
passes so large a portion of its existence in a state of absolute
helplessness, or falls in old age into such protracted and lamentable
imbecility. To no other warm-blooded animal has nature denied that
indispensable covering without which the vicissitudes of a temperate
and the rigours of a cold climate are equally insupportable; and to
scarcely any has she been so sparing in external weapons, whether for
attack or defence. Destitute alike of speed to avoid and of arms to
repel the aggressions of his voracious foes; tenderly susceptible of
atmospheric influences; and unfitted for the coarse aliments which the
earth affords spontaneously during at least two thirds of the year,
even in temperate climates,--man, if abandoned to mere instinct, would
be of all creatures the most destitute and miserable. Distracted by
terror and goaded by famine; driven to the most abject expedients
for concealment from his enemies, and to the most cowardly devices
for the seizure and destruction of his nobler prey, his existence
would be one continued subterfuge or stratagem;--his dwelling would
be in dens of the earth, in clefts of rocks, or in the hollows of
trees; his food worms, and the lower reptiles, or such few and crude
productions of the soil as his organs could be brought to assimilate,
varied with occasional relics, mangled by more powerful beasts of prey,
or contemned by their more pampered choice. Remarkable only for the
absence of those powers and qualities which obtain for other animals a
degree of security and respect, he would be disregarded by some, and
hunted down by others, till after a few generations his species would
become altogether extinct, or, at best, would be restricted to a few
islands in tropical regions, where the warmth of the climate, the
paucity of enemies, and the abundance of vegetable food, might permit
it to linger.

(2.) Yet man is the undisputed lord of the creation. The strongest
and fiercest of his fellow-creatures,--the whale, the elephant, the
eagle, and the tiger,--are slaughtered by him to supply his most
capricious wants, or tamed to do him service, or imprisoned to make
him sport. The spoils of all nature are in daily requisition for his
most common uses, yielded with more or less readiness, or wrested with
reluctance, from the mine, the forest, the ocean, and the air. Such
are the first fruits of reason. Were they the only or the principal
ones, were the mere acquisition of power over the materials, and the
less gifted animals which surround us, and the consequent increase
of our external comforts, and our means of preservation and sensual
enjoyment, the sum of the privileges which the possession of this
faculty conferred, we should after all have little to plume ourselves
upon. But this is so far from being the case, that every one who passes
his life in tolerable ease and comfort, or rather whose whole time
is not anxiously consumed in providing the absolute necessaries of
existence, is conscious of wants and cravings in which the senses have
no part, of a series of pains and pleasures totally distinct in kind
from any which the infliction of bodily misery or the gratification
of bodily appetites has ever afforded him; and if he has experienced
these pleasures and these pains in any degree of intensity, he will
readily admit them to hold a much higher rank, and to deserve much
more attention, than the former class. Independent of the pleasures
of fancy and imagination, and social converse, man is constituted a
speculative being; he contemplates the world, and the objects around
him, not with a passive, indifferent gaze, as a set of phenomena in
which he has no further interest than as they affect his immediate
situation, and can be rendered subservient to his comfort, but as
a system disposed with order and design. He approves and feels the
highest admiration for the harmony of its parts, the skill and
efficiency of its contrivances. Some of these which he can best trace
and understand he attempts to imitate, and finds that to a certain
extent, though rudely and imperfectly, he can succeed,--in others, that
although he can comprehend the nature of the contrivance, he is totally
destitute of all means of imitation;--while in others, again, and those
evidently the most important, though he sees the effect produced,
yet the means by which it is done are alike beyond his knowledge
and his control. Thus he is led to the conception of a Power and an
Intelligence superior to his own, and adequate to the production and
maintenance of all that he sees in nature,--a Power and Intelligence to
which he may well apply the term infinite, since he not only sees no
actual limit to the instances in which they are manifested, but finds,
on the contrary, that the farther he enquires, and the wider his sphere
of observation extends, they continually open upon him in increasing
abundance; and that as the study of one prepares him to understand and
appreciate another, refinement follows on refinement, wonder on wonder,
till his faculties become bewildered in admiration, and his intellect
falls back on itself in utter hopelessness of arriving at an end.

(3.) When from external objects he turns his view upon himself, on his
own vital and intellectual faculties, he finds that he possesses a
power of examining and analysing his own nature to a certain extent,
but no farther. In his corporeal frame he is sensible of a power to
communicate a certain moderate amount of motion to himself and other
objects; that this power depends on his will, and that its exertion
can be suspended or increased at pleasure within certain limits; but
_how_ his will acts on his limbs he has no consciousness: and whence he
derives the power he thus exercises, there is nothing to assure him,
however he may long to know. His senses, too, inform him of a multitude
of particulars respecting the external world, and he perceives an
apparatus by which impressions from without may be transmitted, as a
sort of signals to the interior of his person, and ultimately to his
brain, wherein he is obscurely sensible that the thinking, feeling,
reasoning being he calls _himself_, more especially resides; but by
what means he becomes conscious of these impressions, and what is the
nature of the immediate communication between that inward sentient
being, and that machinery, his outward man, he has not the slightest
conception.

(4.) Again, when he contemplates still more attentively the thoughts,
acts, and passions of this his sentient intelligent self, he finds,
indeed, that he can remember, and by the aid of memory can compare
and discriminate, can judge and resolve, and, above all, that he is
irresistibly impelled, from the perception of any phenomenon without
or within him, to infer the existence of something prior which stands
to it in the relation of a _cause_, without which it would not be, and
that this knowledge of causes and their consequences is what, in almost
every instance, determines his choice and will, in cases where he is
nevertheless conscious of perfect freedom to act or not to act. He
finds, too, that it is in his power to acquire more or less knowledge
of causes and effects according to the degree of attention he bestows
upon them, which attention is again in great measure a voluntary act;
and often when his choice has been decided on imperfect knowledge or
insufficient attention, he finds reason to correct his judgment, though
perhaps too late to influence his decision by after consideration. A
world within him is thus opened to his intellectual view, abounding
with phenomena and relations, and of the highest immediate interest.
But while he cannot help perceiving that the insight he is enabled to
obtain into this internal sphere of thought and feeling is in reality
the source of all his power, the very fountain of his predominance over
external nature, he yet feels himself capable of entering only very
imperfectly into these recesses of his own bosom, and analysing the
operations of his mind,--in this as in all other things, in short, “_a
being darkly wise_;” seeing that all the longest life and most vigorous
intellect can give him power to discover by his own research, or time
to know by availing himself of that of others, serves only to place
him on the very frontier of knowledge, and afford a distant glimpse
of boundless realms beyond, where no human thought has penetrated,
but which yet he is sure must be no less familiarly known to that
Intelligence which he traces throughout creation than the most obvious
truths which he himself daily applies to his most trifling purposes.
Is it wonderful that a being so constituted should first encourage a
hope, and by degrees acknowledge an assurance, that his intellectual
existence will not terminate with the dissolution of his corporeal
frame, but rather that in a future state of being, disencumbered of
a thousand obstructions which his present situation throws in his
way, endowed with acuter senses, and higher faculties, he shall drink
deep at that fountain of beneficent wisdom for which the slight taste
obtained on earth has given him so keen a relish?

(5.) Nothing, then, can be more unfounded than the objection which has
been taken, _in limine_, by persons, well meaning perhaps, certainly
narrow-minded, against the study of natural philosophy, and indeed
against all science,--that it fosters in its cultivators an undue and
overweening self-conceit, leads them to doubt the immortality of the
soul, and to scoff at revealed religion. Its natural effect, we may
confidently assert, on every well constituted mind is and must be
the direct contrary. No doubt, the testimony of natural reason, on
whatever exercised, must of necessity stop short of those truths which
it is the object of revelation to make known; but, while it places
the existence and principal attributes of a Deity on such grounds as
to render doubt impossible, it unquestionably opposes no natural or
necessary obstacle to further progress: on the contrary, by cherishing
as a vital principle an unbounded spirit of enquiry, and ardency of
expectation, it unfetters the mind from prejudices of every kind, and
leaves it open and free to every impression of a higher nature which
it is susceptible of receiving, guarding only against enthusiasm and
self-deception by a habit of strict investigation, but encouraging,
rather than suppressing, every thing that can offer a prospect or a
hope beyond the present obscure and unsatisfactory state. The character
of the true philosopher is to hope all things not impossible, and to
believe all things not unreasonable. He who has seen obscurities which
appeared impenetrable in physical and mathematical science suddenly
dispelled, and the most barren and unpromising fields of enquiry
converted, as if by inspiration, into rich and inexhaustible springs
of knowledge and power on a simple change of our point of view, or
by merely bringing to bear on them some principle which it never
occurred before to try, will surely be the very last to acquiesce in
any dispiriting prospects of either the present or future destinies of
mankind; while, on the other hand, the boundless views of intellectual
and moral as well as material relations which open on him on all hands
in the course of these pursuits, the knowledge of the trivial place he
occupies in the scale of creation, and the sense continually pressed
upon him of his own weakness and incapacity to suspend or modify the
slightest movement of the machinery he sees in action around him, must
effectually convince him that humility of pretension, no less than
confidence of hope, is what best becomes his character.

(6.) But while we thus vindicate the study of natural philosophy from a
charge at one time formidable, owing to the pertinacity and acrimony
with which it was urged, and still occasionally brought forward to
the distress and disgust of every well constituted mind, we must
take care that the testimony afforded by science to religion, be its
extent or value what it may, shall be at least independent, unbiassed,
and spontaneous. We do not here allude to such reasoners as would
make all nature bend to their narrow interpretations of obscure and
difficult passages in the sacred writings: such a course might well
become the persecutors of Galileo and the other bigots of the fifteenth
and sixteenth centuries, but can only be adopted by dreamers in the
present age. But, without going these lengths, it is no uncommon thing
to find persons, earnestly attached to science and anxious for its
promotion, who yet manifest a morbid sensibility on points of this
kind,--who exult and applaud when any fact starts up explanatory (as
they suppose) of some scriptural allusion and who feel pained and
disappointed when the general course of discovery in any department
of science runs wide of the notions with which particular passages in
the Bible may have impressed themselves. To persons of such a frame of
mind it ought to suffice to remark, on the one hand, that truth can
never be opposed to truth, and, on the other, that error is only to be
effectually confounded by searching deep and tracing it to its source.
Nevertheless, it were much to be wished that such persons, estimable
and excellent as many of them are, before they throw the weight of
their applause or discredit into the scale of scientific opinion on
such grounds, would reflect, first, that the credit and respectability
of _any_ evidence may be destroyed by tampering with its _honesty_;
and, secondly, that this very disposition of mind implies a lurking
mistrust in its own principles, since the grand and indeed only
character of truth is its capability of enduring the test of universal
experience, and coming unchanged out of every possible form of _fair_
discussion.

(7.) But if science may be vilified by representing it as opposed to
religion, or trammelled by mistaken notions of the danger of free
enquiry, there is yet another mode by which it may be degraded from
its native dignity, and that is by placing it in the light of a mere
appendage to and caterer for our pampered appetites. The question
“_cui bono_” to what practical end and advantage do your researches
tend? is one which the speculative philosopher who loves knowledge
for its own sake, and enjoys, as a rational being should enjoy, the
mere contemplation of harmonious and mutually dependent truths, can
seldom hear without a sense of humiliation. He feels that there is a
lofty and disinterested pleasure in his speculations which ought to
exempt them from such questioning; communicating as they do to his own
mind the purest happiness (after the exercise of the benevolent and
moral feelings) of which human nature is susceptible, and tending to
the injury of no one, he might surely allege _this_ as a sufficient
and direct reply to those who, having themselves little capacity, and
less relish for intellectual pursuits, are constantly repeating upon
him this enquiry. But if he can bring himself to descend from this
high but fair ground, and justify himself, his pursuits, and his
pleasures in the eyes of those around him, he has only to point to the
history of all science, where speculations, apparently unprofitable,
have, in innumerable instances, been those from which great practical
applications have emanated. What, for instance, could be more so than
the dry speculations of the ancient geometers on the properties of the
conic sections, or than the dreams of Kepler (as they would naturally
appear to his contemporaries) about the numerical harmonies of the
universe? Yet these are the steps by which we have risen to a knowledge
of the elliptic motions of the planets and the law of gravitation,
with all its splendid theoretical consequences, and its inestimable
practical results. The ridicule attached to “_Swing-swangs_” in
Hooke’s time[1] did not prevent him from reviving the proposal of the
_pendulum_ as a standard of measure, since so effectually wrought into
practice by the genius and perseverance of Captain Kater;--nor did
that which Boyle encountered in his researches on the elasticity and
pressure of the air act as any obstacle to the train of discovery which
terminated in the steam-engine. The dreams of the alchemists led them
on in the path of experiment, and drew attention to the wonders of
chemistry, while they brought their advocates (it must be admitted) to
merited contempt and ruin. But in this case it was moral dereliction
which gave to ridicule a weight and power not necessarily or naturally
belonging to it: but among the alchemists were men of superior minds,
who reasoned while they worked, and who, not content to grope always in
the dark, and blunder on their object, sought carefully in the observed
nature of their agents for guides in their pursuit. To these we owe the
creation of experimental philosophy.

(8.) Not that it is meant, by any thing above said, to assert
that there is no such thing as a great or a little in speculative
philosophy, or to place the solution of an enigma on a level with
the developement of a law of nature, still less to adopt the homely
definition of Smith[2], that a philosopher is a person whose trade it
is to do nothing, and speculate on every thing. The speculations of
the natural philosopher, however remote they may for a time lead him
from beaten tracks and every-day uses, being grounded in the realities
of nature, have all, of necessity, a practical application,--nay
more, such applications form the very criterions of their truth,
they afford the readiest and completest verifications of his
theories;--verifications which he will no more neglect to test them by
than an arithmetician would omit to _prove_ his sums, or a cautious
geometer to try his general theorems by particular cases.[3]

(9.) After all, however, it must be confessed, that to minds
unacquainted with science, and unused to consider the mutual
dependencies of its various branches, there is something neither
unnatural nor altogether blamable in the ready occurrence of this
question of direct advantage. It requires some habit of abstraction,
some penetration of the mind with a tincture of scientific enquiry,
some conviction of the value of those estimable and treasured
principles which lie concealed in the most common and homely
facts,--some experience, in fine, of success in developing and placing
them in evidence, announcing them in precise terms, and applying them
to the explanation of other facts of a less familiar character, or to
the accomplishment of some obviously useful purpose:--to cure the mind
of this tendency to rush at once upon its object, to undervalue the
means in over-estimation of the end, and while gazing too intently at
the goal which alone it has been accustomed to desire, to lose sight
of the richness and variety of the prospects that offer themselves on
either hand on the road.

(10.) We must never forget that it is principles, not phenomena,--the
interpretation, not the mere knowledge of facts,--which are the
objects of enquiry to the natural philosopher. As truth is single,
and consistent with itself, a principle may be as completely and as
plainly elucidated by the most familiar and simple fact, as by the
most imposing and uncommon phenomenon. The colours which glitter on
a soap-bubble are the immediate consequence of a principle the most
important from the variety of phenomena it explains, and the most
beautiful, from its simplicity and compendious neatness, in the whole
science of optics. If the nature of periodical colours can be made
intelligible by the contemplation of such a trivial object, from that
moment it becomes a noble instrument in the eye of correct judgment;
and to blow a large, regular, and durable soap-bubble may become the
serious and praiseworthy endeavour of a sage, while children stand
round and scoff, or children of a larger growth hold up their hands
in astonishment at such waste of time and trouble. To the natural
philosopher there is no natural object unimportant or trifling. From
the least of nature’s works he may learn the greatest lessons. The fall
of an apple to the ground may raise his thoughts to the laws which
govern the revolutions of the planets in their orbits; or the situation
of a pebble may afford him evidence of the state of the globe he
inhabits, myriads of ages ago, before his species became its denizens.

(11.) And this is, in fact, one of the great sources of delight
which the study of natural science imparts to its votaries. A mind
which has once imbibed a taste for scientific enquiry, and has
learnt the habit of applying its principles readily to the cases
which occur, has within itself an inexhaustible source of pure and
exciting contemplations:--one would think that Shakspeare had such
a mind in view when he describes a contemplative man as finding all
nature eloquent--the very trees, the brooks, and the stones reading
to him lessons of deep and serious import. Accustomed to trace the
operation of general causes, and the exemplification of general laws,
in circumstances where the uninformed and unenquiring eye perceives
neither novelty nor beauty, he walks in the midst of wonders: every
object which falls in his way elucidates some principle, affords some
instruction, and impresses him with a sense of harmony and order. Nor
is it a mere passive pleasure which is thus communicated. A thousand
questions are continually arising in his mind, a thousand subjects of
enquiry presenting themselves, which keep his faculties in constant
exercise, and his thoughts perpetually on the wing, so that lassitude
is excluded from his life, and that craving after artificial excitement
and dissipation of mind, which leads so many into frivolous, unworthy,
and destructive pursuits, is altogether eradicated from his bosom.

(12.) It is not one of the least advantages of these pursuits, which,
however, they possess in common with every class of intellectual
pleasures, that they are altogether independent of external
circumstances, and are to be enjoyed in every situation in which a man
can be placed in life. The highest degrees of worldly prosperity are so
far from being incompatible with them, that they supply inestimable
advantages for their pursuit, and that sort of fresh and renewed relish
which arises partly from the sense of contrast, partly from experience
of the peculiar pre-eminence they possess over the pleasures of sense
in their capability of unlimited increase and continual repetition
without satiety or distaste. They may be enjoyed, too, in the intervals
of the most active business; and the calm and dispassionate interest
with which they fill the mind renders them a most delightful retreat
from the agitations and dissensions of the world, and from the conflict
of passions, prejudices, and interests in which the man of business
finds himself involved. There is something in the contemplation of
general laws which powerfully induces and persuades us to merge
individual feeling, and to commit ourselves unreservedly to their
disposal; while the observation of the calm, energetic regularity of
nature, the immense scale of her operations, and the certainty with
which her ends are attained, tends, irresistibly, to tranquillize and
re-assure the mind, and render it less accessible to repining, selfish,
and turbulent emotions. And this it does, not by debasing our nature
into weak compliances and abject submission to circumstances, but by
filling us, as from an inward spring, with a sense of nobleness and
power which enables us to rise superior to them; by showing us our
strength and innate dignity, and by calling upon us for the exercise
of those powers and faculties by which we are susceptible of the
comprehension of so much greatness, and which form, as it were, a link
between ourselves and the best and noblest benefactors of our species,
with whom we hold communion in thoughts and participate in discoveries
which have raised them above their fellow-mortals, and brought them
nearer to their Creator.



CHAP. II.

  OF ABSTRACT SCIENCE AS A PREPARATION FOR THE STUDY OF PHYSICS.--A
    PROFOUND ACQUAINTANCE WITH IT NOT INDISPENSABLE FOR A CLEAR
    UNDERSTANDING OF PHYSICAL LAWS.--HOW A CONVICTION OF THEIR TRUTH
    MAY BE OBTAINED WITHOUT IT.--INSTANCES.--FURTHER DIVISION OF THE
    SUBJECT.


(13.) Science is the knowledge of many, orderly and methodically
digested and arranged, so as to become attainable by one. The knowledge
of reasons and their conclusions constitutes _abstract_, that of causes
and their effects, and of the laws of nature, _natural science_.

(14.) Abstract science is independent of a system of nature,--of a
creation,--of every thing, in short, except memory, thought, and
reason. Its objects are, first, those primary existences and relations
which we cannot even conceive not to _be_, such as space, time,
number, order, &c.; and, secondly, those artificial forms, or symbols,
which thought has the power of creating for itself at pleasure, and
substituting as representatives, by the aid of memory, for combinations
of those primary objects and of its own conceptions,--either to
facilitate the act of reasoning respecting them, or as convenient
deposits of its own conclusions, or for their communication to others.
Such are, first, _language_, oral or written; its conventional forms,
which constitute grammar, and the rules for its use in argument,
in which consists the logic of the schools; secondly, _notation_,
which, applied to _number_, is _arithmetic_,--and, to the more general
relations of abstract quantity or order, is _algebra_; and, thirdly,
that higher kind of logic, which teaches us to use our reason in the
most advantageous manner for the discovery of truth; which points
out the criterions by which we may be sure we have attained it; and
which, by detecting the sources of error, and exposing the haunts where
fallacies are apt to lurk, at once warns us of their danger, and shows
us how to avoid them. This greater logic may be termed _rational_[4];
while, to that inferior department which is conversant with words
alone, the epithet _verbal_[5] may, for distinction, be applied.

(15.) A certain moderate degree of acquaintance with abstract science
is highly desirable to every one who would make any considerable
progress in physics. As the universe exists in time and place; and as
motion, velocity, quantity, number, and order, are main elements of
our knowledge of external things and their changes, an acquaintance
with these, abstractedly considered, (that is to say, independent of
any consideration of the particular things moved, measured, counted,
or arranged,) must evidently be a useful preparation for the more
complex study of nature. But there is yet another recommendation of
such sciences as a preparation for the study of natural philosophy.
Their objects are so definite, and our notions of them so distinct,
that we can reason about them with an assurance, that the words and
signs used in our reasonings are full and true representatives of the
things signified; and, consequently, that when we use language or signs
in argument, we neither, by their use, introduce extraneous notions,
nor exclude any part of the case before us from consideration. For
example: the words space, square, circle, a hundred, &c., convey to
the mind notions so complete in themselves, and so distinct from every
thing else, that we are sure when we use them we know and have in
view the whole of our own meaning. It is widely different with words
expressing natural objects and mixed relations. Take, for instance,
iron. Different persons attach very different ideas to this word. One
who has never heard of magnetism has a widely different notion of
_iron_ from one in the contrary predicament. The vulgar, who regard
this metal as incombustible, and the chemist, who sees it burn with the
utmost fury, and who has other reasons for regarding it as one of the
most combustible bodies in nature;--the poet, who uses it as an emblem
of rigidity; and the smith and engineer, in whose hands it is plastic,
and moulded like wax into every form;--the jailer, who prizes it as
an obstruction, and the electrician, who sees in it only a channel of
open communication by which that most impassable of obstacles, the
air, may be traversed by his imprisoned fluid, have all different, and
all imperfect, notions of the same word. The meaning of such a term
is like a rainbow--every body sees a different one, and all maintain
it to be the same. So it is with nearly all our terms of sense. Some
are indefinite, as hard or soft, light or heavy (terms which were at
one time the sources of innumerable mistakes and controversies); some
excessively complex, as man, life, instinct. But, what is worst of
all, some, nay most, have two or three meanings; sufficiently distinct
from each other to make a proposition true in one sense and false in
another, or even false altogether; yet not distinct enough to keep us
from confounding them in the process by which we arrived at it, or
to enable us immediately to recognise the fallacy when led to it by
a train of reasoning, each step of which we _think_ we have examined
and approved. Surely those who thus attach two senses to one word, or
superadd a new meaning to an old one, act as absurdly as colonists who
distribute themselves over the world, naming every place they come
to by the names of those they have left, till all distinctions of
geographical nomenclature are confounded, and till we are unable to
decide whether an occurrence stated to have happened at Windsor took
place in Europe, America, or Australia.[6]

(16.) It is, in fact, in this double or incomplete sense of words that
we must look for the origin of a very large portion of the errors
into which we fall. Now, the study of the abstract sciences, such as
arithmetic, geometry, algebra, &c., while they afford scope for the
exercise of reasoning about objects that are, or, at least, may be
conceived to be, external to us; yet, being free from these sources
of error and mistake, accustom us to the strict use of language as
an instrument of reason, and by familiarizing us, in our progress
towards truth, to walk uprightly and straight-forward on firm ground,
give us that proper and dignified carriage of mind which could never
be acquired by having always to pick our steps among obstructions
and loose fragments, or to steady them in the reeling tempest of
conflicting meanings.

(17.) But there is yet another point of view under which some
acquaintance with abstract science may be regarded as highly desirable
in general education, if not indispensably necessary, to impress on us
the distinction between strict and vague reasoning, to show us what
demonstration really _is_, and to give us thereby a full and intimate
sense of the nature and strength of the evidence on which our knowledge
of the actual system of nature, and the laws of natural phenomena,
rests. For this purpose, however, a very moderate acquaintance with the
more elementary branches of mathematics may suffice. The chain is laid
before us, and every link is submitted to our unreserved examination,
if we have patience and inclination to enter on such detail. Hundreds
have gone through it, and will continue to do so; but, for the
generality of mankind, it is enough to satisfy themselves of the
solidity and adamantine texture of its materials, and the unreserved
exposure of its weakest, as well as its strongest, parts. If, however,
we content ourselves with this general view of the matter, we must be
content also to take on trust, that is, on the authority of those who
have examined deeper, every conclusion which cannot be made apparent
to our senses. Now, among these there are many so very surprising,
indeed apparently so extravagant, that it is quite impossible for any
enquiring mind to rest contented with a mere hearsay statement of
them,--we feel irresistibly impelled to enquire further into their
truth. What mere assertion will make any man believe, that in one
second of time, in one beat of the pendulum of a clock, a ray of light
travels over 192,000 miles, and would therefore perform the tour of the
world in about the same time that it requires to wink with our eyelids,
and in much less than a swift runner occupies in taking a single
stride? What mortal can be made to believe, without demonstration, that
the sun is almost a million times larger than the earth? and that,
although so remote from us, that a cannon ball shot directly towards
it, and maintaining its full speed, would be twenty years in reaching
it, it yet affects the earth by its attraction in an inappreciable
instant of time?--a closeness of union of which we can form but a
feeble, and totally inadequate, idea, by comparing it to any material
connection; since the communication of an impulse to such a distance,
by any solid intermedium we are acquainted with, would require, not
moments, but whole years. And when, with pain and difficulty we have
strained our imagination to conceive a distance so vast, a force so
intense and penetrating, if we are told that the one dwindles to an
insensible point, and the other is unfelt at the nearest of the fixed
stars, from the mere effect of their remoteness, while among those
very stars are some whose actual splendour exceeds by many hundred
times that of the sun itself, although we may not deny the truth of the
assertion, we cannot but feel the keenest curiosity to know _how_ such
things were ever made out.

(18.) The foregoing are among those results of scientific research
which, by their magnitude, seem to transcend our powers of conception.
There are others, again, which, from their minuteness, would appear
to elude the grasp of thought, much more of distinct and accurate
measurement. Who would not ask for demonstration, when told that a
gnat’s wing, in its ordinary flight, beats many hundred times in a
second? or that there exist animated and regularly organized beings,
many thousands of whose bodies laid close together would not extend an
inch? But what are these to the astonishing truths which modern optical
enquiries have disclosed, which teach us that every point of a medium
through which a ray of light passes is affected with a succession of
periodical movements, regularly recurring at equal intervals, no less
than five hundred millions of millions of times in a single second!
that it is by such movements, communicated to the nerves of our eyes,
that we see:--nay more, that it is the _difference_ in the frequency of
their recurrence which affects us with the sense of the diversity of
colour; that, for instance, in acquiring the sensation of redness our
eyes are affected four hundred and eighty-two millions of millions of
times; of yellowness, five hundred and forty-two millions of millions
of times; and of violet, seven hundred and seven millions of millions
of times per second.[7] Do not such things sound more like the ravings
of madmen, than the sober conclusions of people in their waking senses?

(19.) They are, nevertheless, conclusions to which any one may most
certainly arrive, who will only be at the trouble of examining the
chain of reasoning by which they have been deduced; but, in order
to do this, something beyond the mere elements of abstract science
is required. Waving, however, such instances as these, which, after
all, are rather calculated to surprise and astound than for any other
purpose, it must be observed that it is not possible to satisfy
ourselves completely that we _have_ arrived at a true statement of any
law of nature, until, setting out from such statement, and making it
a foundation of reasoning, we can show, by strict argument, that the
facts observed must follow from it as necessary logical consequences,
and _this_, not vaguely and generally, but with all possible precision
in time, place, weight, and measure.

(20.) To do this, however, as we shall presently see, requires in many
cases a degree of knowledge of mathematics and geometry altogether
unattainable by the generality of mankind, who have not the leisure,
even if they all had the capacity, to enter into such enquiries,
some of which are indeed of that degree of difficulty that they can
be only successfully prosecuted by persons who devote to them their
whole attention, and make them the serious business of their lives.
But there is scarcely any person of good ordinary understanding,
however little exercised in abstract enquiries, who may not be readily
made to comprehend at least the general train of reasoning by which
any of the great truths of physics are deduced, and the essential
bearings and connections of the several parts of natural philosophy.
There are whole branches too and very extensive and important ones, to
which mathematical reasoning has never been at all applied; such as
chemistry, geology, and natural history in general, and many others,
in which it plays a very subordinate part, and of which the essential
principles, and the grounds of application to useful purposes, may
be perfectly well understood by a student who possesses no more
mathematical knowledge than the rules of arithmetic; so that no one
need be deterred from the acquisition of knowledge, or even from
active original research in such subjects, by a want of mathematical
information. Even in those branches which, like astronomy, optics, and
dynamics, are almost exclusively under the dominion of mathematics, and
in which no effectual progress can be made without _some_ acquaintance
with geometry, the principal _results_ may be perfectly understood
without it. To one incapable of following out the intricacies of
mathematical demonstration, the conviction afforded by verified
predictions must stand in the place of that purer and more satisfactory
reliance which a verification of every step in the process of reasoning
can alone afford, since every one will acknowledge the validity of
pretensions which he is in the daily habit of seeing brought to the
test of practice.

(21.) Among the verifications of this practical kind which abound
in every department of physics, there are none more imposing than
the precise prediction of the greater phenomena of astronomy; none,
certainly, which carry a broader conviction home to every mind from
their notoriety and unequivocal character. The prediction of eclipses
has accordingly from the earliest ages excited the admiration of
mankind, and been one grand instrument by which their allegiance (so
to speak) to natural science, and their respect for its professors,
has been maintained; and though strangely abused in unenlightened ages
by the supernatural pretensions of astrologers, the credence given
even to their absurdities shows the force of this kind of evidence on
men’s minds. The predictions of astronomers are, however, now far too
familiar to endanger the just equipoise of our judgment, since even the
return of comets, true to their paths and exact to the hour of their
appointment, has ceased to amaze, though it must ever delight all who
have souls capable of being penetrated by such beautiful instances of
accordance between theory and facts. But the age of mere wonder in
such things is past, and men prefer being guided and enlightened, to
being astonished and dazzled. Eclipses, comets, and the like, afford
but rare and transient displays of the powers of calculation, and of
the certainty of the principles on which it is grounded. A page of
“lunar distances” from the Nautical Almanack is worth all the eclipses
that have ever happened for inspiring this necessary confidence in the
conclusions of science. That a man, by merely measuring the moon’s
apparent distance from a star with a little portable instrument held
in his hand, and applied to his eye, even with so unstable a footing
as the deck of a ship, shall say positively, within five miles, where
he is, on a boundless ocean, cannot but appear to persons ignorant of
physical astronomy an approach to the miraculous. Yet, the alternatives
of life and death, wealth and ruin, are daily and hourly staked with
perfect confidence on these marvellous computations, which might
almost seem to have been devised on purpose to show how closely the
extremes of speculative refinement and practical utility can be brought
to approximate. We have before us an anecdote communicated to us by
a naval officer[8], distinguished for the extent and variety of his
attainments, which shows how impressive such results may become in
practice. He sailed from San Blas on the west coast of Mexico, and
after a voyage of 8000 miles, occupying 89 days, arrived off Rio de
Janeiro, having, in this interval, passed through the Pacific Ocean,
rounded Cape Horn, and crossed the South Atlantic, without making any
land, or even seeing a single sail, with the exception of an American
whaler off Cape Horn. Arrived within a week’s sail of Rio, he set
seriously about determining, by lunar observations, the precise line
of the ship’s course and its situation in it at a determinate moment,
and having ascertained this within from five to ten miles, ran the
rest of the way by those more ready and compendious methods, known to
navigators, which can be safely employed for short trips between one
known point and another, but which cannot be trusted in long voyages,
where the moon is the only sure guide. The rest of the tale we are
enabled by his kindness to state in his own words:--“We steered towards
Rio de Janeiro for some days after taking the lunars above described,
and having arrived within fifteen or twenty miles of the coast, I hove
to at four in the morning till the day should break, and then bore
up; for although it was very hazy, we could see before us a couple of
miles or so. About eight o’clock it became so foggy that I did not
like to stand in farther, and was just bringing the ship to the wind
again before sending the people to breakfast, when it suddenly cleared
off, and I had the satisfaction of seeing the great Sugar Loaf Rock,
which stands on one side of the harbour’s mouth, so nearly right ahead
that we had not to alter our course above a point in order to hit the
entrance of Rio. This was the first land we had seen for three months,
after crossing so many seas and being set backwards and forwards by
innumerable currents and foul winds.” The effect on all on board might
well be conceived to have been electric; and it is needless to remark
how essentially the authority of a commanding officer over his crew may
be strengthened by the occurrence of such incidents, indicative of a
degree of knowledge and consequent power beyond their reach.

(22.) But even such results as these, striking as they are, yet fall
short of the force with which conviction is urged upon us when,
through the medium of reasoning too abstract for common apprehension,
we arrive at conclusions which outrun experience, and describe
beforehand what will happen under new combinations, or even correct
imperfect experiments, and lead us to a knowledge of facts contrary
to received analogies drawn from an experience wrongly interpreted
or overhastily generalised. To give an example:--every body knows
that objects viewed through a transparent medium, such as water or
glass, appear distorted or displaced. Thus, a stick in water appears
bent, and an object seen through a prism or wedge of glass seems to
be thrown aside from its true place. This effect is owing to what is
called the _refraction_ of light; and a simple rule discovered by
Willebrod Snell enables any one to say exactly _how much_ the stick
will be bent, and _how far_, and in what _direction_, the apparent
situation of an object seen through the glass will deviate from the
real one. If a shilling be laid at the bottom of a basin of water
and viewed obliquely, it will appear to be raised by the water; if
instead of water spirits of wine be used it will appear more raised;
if oil, still more:--but in none of these cases will it appear to be
thrown _aside_ to the _right_ or _left_ of its true place, however
the eye be situated. The _plane_, in which are contained the eye,
the object, and the point in the surface of the liquid at which the
object is seen, is an upright or _vertical_ plane; and this is one of
the principal characters in the _ordinary refraction_ of light, viz.
that the ray by which we see an object through a refracting surface,
although it undergoes a bending, and is, as it were, broken at the
surface, yet, in pursuing its course to the eye, does not _quit a plane
perpendicular to the refracting surface_. But there are again other
substances, such as rock-crystal, and especially Iceland spar, which
possess the singular property of _doubling_ the image or appearance
of an object seen through them in certain directions; so that instead
of seeing one object we see two, side by side, when such a crystal or
spar is interposed between the object and the eye; and if a ray or
small sunbeam be thrown upon a surface of either of these substances,
it will be split into two, making an angle with each other, and each
pursuing its own separate course,--this is called _double refraction_.
Now, of these images or doubly refracted rays, one always follows
the same rule as if the substance were glass or water: its deviation
can be correctly calculated by Snell’s law above mentioned, and it
does not quit the plane perpendicular to the refracting surface. The
other ray, on the contrary, (which is therefore said to have undergone
_extraordinary refraction_) _does_ quit that plane, and the amount of
its deviation from its former course requires for its determination a
much more complicated rule, which cannot be understood or even stated
without a pretty intimate knowledge of geometry. Now, rock-crystal
and Iceland spar differ from glass in a very remarkable circumstance.
They affect naturally certain regular figures, not being found in
shapeless lumps, but in determinate geometrical forms; and they are
susceptible of being cleft or split much easier in certain directions
than in others--they have a _grain_ which glass has not. When other
substances having this peculiarity (and which are called _crystallized_
substances) were examined, they were all, or by far the greater part,
found to possess this singular property of _double refraction_; and
it was very natural to conclude, therefore, that the same thing took
place in all of them, viz. that of the two rays, into which any beam of
light falling on the surface of such a substance was split, or of the
two images of an object seen through it, _one_ only was turned aside
out of its _plane_ and _extraordinarily_ refracted, while the other
followed the _ordinary_ rule. Accordingly this was supposed to be the
case; and not only so, but from some trials and measurements purposely
made by a philosopher of great eminence, it was considered to be a fact
sufficiently established by experiment.

(23.) Perhaps we might have remained long under this impression, for
the measurements are delicate, and the subject very difficult. But
it has lately been demonstrated by an eminent French philosopher and
mathematician, M. Fresnel, that, granting certain _principles_ or
postulates, all the phenomena of double refraction, including perhaps
the greatest variety of facts that have ever yet been arranged under
one general head, may be satisfactorily explained and deduced from them
by strict mathematical calculation; and _that_, when applied to the
cases first mentioned, these principles give a satisfactory account
of the _want_ of the extraordinary image; _that_ when applied to such
cases as those of rock-crystal or Iceland spar, they also give a
correct account of both the images, and agree in their conclusions with
the rules before ascertained for them: but so far from coinciding with
that part of the previous statement, which would make these conclusions
extend to all crystallised substances, M. Fresnel’s principles lead
to a conclusion quite opposite, and point to a _fact_ which had never
been observed, viz. that in by far the greater number of crystallized
substances which possess the property of double refraction, _neither_
of the images follows the ordinary law, but both undergo a deviation
from their original plane. Now this had never been observed to be
the case in any previous trial, and all opinion was against it. But
when put to the test of experiment in a great variety of new and
ingenious methods, it was found to be fully verified; and to complete
the evidence, the substances on whose imperfect examination the
first erroneous conclusion was founded, having been lately subjected
to a fresh and more scrupulous examination, the result has shown
the insufficiency of the former measurements, and proved in perfect
accordance with the newly discovered laws. Now it will be observed
in this case, first, that, so far from the principles assumed by M.
Fresnel being at all obvious, they are extremely remote from ordinary
observation; and, secondly, that the chain of reasoning by which they
are brought to the test is one of such length and complexity, and the
purely mathematical difficulty of their application so great, that
no _mere_ good common sense, no general tact or ordinary practical
reasoning, would afford the slightest chance of threading their
mazes. Cases like this are the triumph of theories. They show at once
how large a part pure reason has to perform in our examination of
nature, and how implicit our reliance ought to be on that powerful and
methodical system of rules and processes which constitute the modern
mathematical analysis, in all the more difficult applications of exact
calculation to her phenomena.

(24.) To take an instance more within ordinary apprehension. An
eminent living geometer had proved by calculations, founded on strict
optical principles, that in the _centre of the shadow_ of a small
circular plate of metal, exposed in a dark room to a beam of light
emanating from a _very small brilliant point_, there ought to be no
darkness,--in fact, _no shadow_ at that place; but, on the contrary, a
degree of illumination precisely as bright as if the metal plate were
away. Strange and even impossible as this conclusion may seem, it has
been put to the trial, and found perfectly correct.[9]

(25.) We shall now proceed to consider more particularly, and in
detail,--

    I. The nature and objects immediate and collateral of physical
         science, as regarded in itself, and in its application to
         the practical purposes of life, and its influence on the
         well-being and progress of society.

   II. The principles on which it relies for its successful
         prosecution, and the rules by which a systematic examination
         of nature should be conducted, with examples illustrative of
         their influence.

  III. The subdivision of physical science into distinct branches,
         and their mutual relations.



CHAP. III.

  OF THE NATURE AND OBJECTS, IMMEDIATE AND COLLATERAL, OF PHYSICAL
    SCIENCE, AS REGARDED IN ITSELF, AND IN ITS APPLICATION TO THE
    PRACTICAL PURPOSES OF LIFE, AND ITS INFLUENCE ON THE WELL-BEING
    AND PROGRESS OF SOCIETY.


(26.) The first thing impressed on us from our earliest infancy is,
that events do not succeed one another at random, but with a certain
degree of order, regularity, and connection;--some constantly, and, as
we are apt to think, immutably,--as the alternation of day and night,
summer and winter,--others contingently, as the motion of a body from
its place, if pushed, or the burning of a stick if thrust into the
fire. The knowledge that the former class of events _has_ gone on,
uninterruptedly, for ages beyond all memory, impresses us with a strong
expectation that it will continue to do so in the same manner; and
thus our notion of an _order of nature_ is originated and confirmed.
If every thing were equally regular and periodical, and the succession
of events liable to no change depending on our own will, it may be
doubted whether we should ever think of looking for causes. No one
regards the night as the cause of the day, or the day of night. They
are alternate effects of a common cause, which their regular succession
alone gives us no sufficient clue for determining. It is chiefly,
perhaps entirely, from the other or contingent class of events that
we gain our notions of cause and effect. From them alone we gather
that there are such things as laws of nature. The very idea of a law
includes that of contingency. “_Si quis mala carmina condidisset, fuste
ferito_;” if such a case arise, such a course shall be followed,--if
the match be applied to the gunpowder, it will explode. Every law is a
provision for cases which _may_ occur, and has relation to an infinite
number of cases that never have occurred, and never will. Now, it is
this provision, _à priori_, for contingencies, this contemplation
of possible occurrences, and predisposal of what shall happen, that
impresses us with the notion of a _law_ and a _cause_. Among all the
possible combinations of the fifty or sixty elements which chemistry
shows to exist on the earth, it is likely, nay almost certain, that
_some_ have never been formed; that some elements, in some proportions,
and under some circumstances, have never yet been placed in relation
with one another. Yet no chemist can doubt that it is _already fixed_
what they will do when the case does occur. They will obey certain
laws, of which we know nothing at present, but which must _be_ already
fixed, or they could not be laws. It is not by habit, or by trial
and failure, that they will learn what to do. When the contingency
occurs, there will be no hesitation, no consultation;--their course
will at once be decided, and will always be the same if it occur ever
so often in succession, or in ever so many places at one and the same
instant. This is the perfection of a law, that it includes all possible
contingencies, and ensures implicit obedience,--and of this kind are
the laws of nature.

(27.) This use of the word _law_, however, our readers will of course
perceive has relation to us as understanding, rather than to the
materials of which the universe consists as obeying, certain rules.
To obey a law, to act in _compliance_ with a rule, supposes an
understanding and a will, a power of complying or not, in the being who
obeys and complies, which we do not admit as belonging to mere matter.
The Divine Author of the universe cannot be supposed to have laid down
particular laws, enumerating all individual contingencies, which his
materials have understood and obey,--this would be to attribute to
him the imperfections of human legislation;--but rather, by creating
them, endued with certain fixed qualities and powers, he has impressed
them in their origin with the _spirit_, not the _letter_, of his law,
and made all their subsequent combinations and relations inevitable
consequences of this first impression, by which, however, we would no
way be understood to deny the constant exercise of his direct power in
maintaining the system of nature, or the ultimate emanation of every
energy which material agents exert from his immediate will, acting in
conformity with his own laws.

(28.) The discoveries of modern chemistry have gone far to establish
the truth of an opinion entertained by some of the ancients, that
the universe consists of distinct, separate, indivisible _atoms_,
or individual beings so minute as to escape our senses, except when
united by millions, and by this aggregation making up bodies of even
the smallest visible bulk; and we have the strongest evidence that,
although there exist great and essential differences in individuals
among these atoms, they may yet all be arranged in a very limited
number of groups or classes, all the individuals of each of which
are, to all intents and purposes, _exactly alike_ in all their
properties. Now, when we see a great number of things precisely alike,
we do not believe this similarity to have originated except from a
common principle independent of them; and that we recognise this
likeness, chiefly by the identity of their deportment under similar
circumstances, strengthens rather than weakens the conclusion. A line
of spinning-jennies[10], or a regiment of soldiers dressed exactly
alike, and going through precisely the same evolutions, gives us no
idea of independent existence: we must see them act out of concert
before we can believe them to have independent wills and properties,
not impressed on them from without. And this conclusion, which would
be strong even were there only two individuals precisely alike in
_all_ respects and _for ever_, acquires irresistible force when their
number is multiplied beyond the power of imagination to conceive. If
we mistake not, then, the discoveries alluded to effectually destroy
the idea of an _eternal self-existent matter_, by giving to each of its
atoms the essential characters, at once, of a _manufactured article_,
and a _subordinate agent_.

(29.) But to ascend to the origin of things, and speculate on the
creation, is not the business of the natural philosopher. An humbler
field is sufficient for him in the endeavour to discover, as far
as our faculties will permit, what _are_ these primary qualities
originally and unalterably impressed on matter, and to discover the
_spirit_ of the laws of nature, which includes groups and classes of
relations and facts from the _letter_ which, as before observed, is
presented to us by single phenomena: or if, after all, this should
prove impossible; if such a step be beyond our faculties; and the
essential qualities of material agents be really _occult_, or incapable
of being expressed in any form intelligible to our understandings, at
least to approach as near to their comprehension as the nature of the
case will allow; and devise such forms of words as shall include and
_represent_ the greatest possible multitude and variety of phenomena.

(30.) Now, in this research there would seem one great question to
be disposed of before our enquiries can even be commenced with any
thing like a prospect of success, which is, whether the laws of
nature themselves _have_ that degree of permanence and fixity which
can render them subjects of systematic discussion; or whether, on the
other hand, the qualities of natural agents are subject to mutation
from the lapse of time. To the ancients, who lived in the infancy of
the world, or rather, in the infancy of man’s experience, this was a
very rational subject of question, and hence their distinctions between
corruptible and incorruptible matter. Thus, according to some among
them, the matter only of the celestial spaces is pure, immutable, and
incorruptible, while all sublunary things are in a constant state of
lapse and change; the world becoming paralysed and effete with age,
and man himself deteriorating in character, and diminishing at once in
intellectual and bodily stature. But to us, who have the experience
of some additional thousands of years, the question of permanence is
already, in a great measure, decided in the affirmative. The refined
speculations of modern astronomy, grounding their conclusions on
observations made at very remote periods, have proved to demonstration,
that one at least of the great powers of nature, the force of
gravitation, the main bond and support of the material universe, has
undergone no change in intensity from a high antiquity. The stature of
mankind is just what it was three thousand years ago, as the specimens
of mummies which have been examined at various times sufficiently
show. The intellect of Newton, Laplace, or Lagrange, may stand in
fair competition with that of Archimedes, Aristotle, or Plato; and the
virtues and patriotism of Washington with the brightest examples of
ancient history.

(31.) Again, the researches of chemists have shown that what the
vulgar call corruption, destruction, &c., is nothing but a change of
arrangement of the same ingredient elements, the disposition of the
same materials into other forms, without the loss or actual destruction
of a single atom; and thus any doubts of the permanence of natural
laws are discountenanced, and the whole weight of _appearances_ thrown
into the opposite scale. One of the most obvious cases of apparent
destruction is, when any thing is ground to dust and scattered to the
winds. But it is one thing to grind a fabric to powder, and another to
annihilate its materials: scattered as they may be, they must fall
somewhere, and continue, if only as ingredients of the soil, to perform
their humble but useful part in the economy of nature. The destruction
produced by fire is more striking: in many cases, as in the burning
of a piece of charcoal or a taper, there is no smoke, nothing visibly
dissipated and carried away; the burning body wastes and disappears,
while nothing _seems_ to be produced but warmth and light, which we
are not in the habit of considering as substances; and when all has
disappeared, except perhaps some trifling ashes, we naturally enough
suppose it is gone, lost, destroyed. But when the question is examined
more exactly, we detect, in the invisible stream of heated air which
ascends from the glowing coal or flaming wax, the _whole_ ponderable
matter, only united in a new combination with the air, and dissolved in
it. Yet, so far from being thereby destroyed, it is only become again
what it was before it existed in the form of charcoal or wax, an active
agent in the business of the world, and a main support of vegetable
and animal life, and is still susceptible of running again and again
the same round, as circumstances may determine; so that, for aught we
can see to the contrary, the same identical atom may lie concealed for
thousands of centuries in a limestone rock; may at length be quarried,
set free in the limekiln, mix with the air, be absorbed from it by
plants, and, in succession, become a part of the frames of myriads of
living beings, till some concurrence of events consigns it once more to
a long repose, which, however, no way unfits it from again resuming its
former activity.

(32.) Now, this absolute indestructibility of the ultimate materials
of the world, in periods commensurate to our experience, and their
obstinate retention of the same properties, under whatever variety of
circumstances we choose to place them, however violent and seemingly
contradictory to their natures, is, of itself, enough to render it
highly improbable that time alone should have any influence over
them. All that age or decay can do seems to be included in a wasting
of parts which are only dissipated, not destroyed, or in a change of
sensible properties, which chemistry demonstrates to arise only from
new combinations of the same ingredients. But, after all, the question
is one entirely of experience: we cannot be sure, _à priori_, that
the laws of nature are _immutable_; but we can ascertain, by enquiry,
_whether they change or not_; and to this enquiry all experience
answers in the negative. It is not, of course, intended here to
deny that great operations, productive of extensive changes in the
visible state of nature,--such as, for instance, those contemplated
by the geologists, and embracing for their completion vast periods
of time,--are constantly going on; but these are consequences and
fulfilments of the laws of nature, not contradictions or exceptions
to them. No theorist regards such changes as alterations in the
fundamental principles of nature; he only endeavours to reconcile them,
and show how they result from laws already known, and judges of the
correctness of his theory by their ultimate agreement.

(33.) But the laws of nature are not only permanent, but consistent,
intelligible, and discoverable with such a moderate degree of
research, as is calculated rather to stimulate than to weary curiosity.
If we were set down, as creatures of another world, in any existing
society of mankind, and began to speculate on their actions, we should
find it difficult at first to ascertain whether they were subject to
any laws at all: but when, by degrees, we had found out that they did
consider themselves to be so; and would then proceed to ascertain, from
their conduct and its consequences, what these laws were, and in what
spirit conceived; though we might not perhaps have much difficulty
in discovering single rules applicable to particular cases, yet, the
moment we came to generalize, and endeavour from these to ascend, step
by step, and discover any steady pervading principle, the mass of
incongruities, absurdities, and contradictions, we should encounter,
would either dishearten us from further enquiry or satisfy us that what
we were in search of did not exist. It is quite the contrary in nature;
there we find no contradictions, no incongruities, but all is harmony.
What once is learnt we never have to unlearn. As rules advance in
generality, apparent exceptions become regular; and equivoque, in her
sublime legislation, is as unheard of as maladministration.

(34.) Living, then, in a world where such laws obtain, and under their
immediate dominion, it is manifestly of the utmost importance to know
them, were it for no other reason than to be sure, in all we undertake,
to have, at least, the law on our side, so as not to struggle in vain
against some insuperable difficulty opposed to us by natural causes.
What pains and expense would not the alchemists, for instance, have
been spared by a knowledge of those simple laws of composition and
decomposition, which now preclude all idea of the attainment of their
declared object! what an amount of ingenuity, thrown away on the
pursuit of the perpetual motion, might have been turned to better
use, if the simplest laws of mechanics had been known and attended to
by the inventors of innumerable contrivances destined to that end!
What tortures, inflicted on patients by imaginary cures of incurable
diseases, might have been dispensed with, had a few simple principles
of physiology been earlier recognised!

(35.) But if the laws of nature, on the one hand, are invincible
opponents, on the other, they are irresistible auxiliaries; and it
will not be amiss if we regard them in each of those characters, and
consider the great importance of a knowledge of them to mankind,--

    I. _In showing us how to avoid attempting impossibilities._

   II. _In securing us from important mistakes in attempting what
        is, in itself, possible, by means either inadequate, or
        actually opposed, to the end in view._

  III. _In enabling us to accomplish our ends in the easiest,
        shortest, most economical, and most effectual manner._

   IV. _In inducing us to attempt, and enabling us to accomplish,
        objects which, but for such knowledge, we should never have
        thought of undertaking._

We shall therefore proceed to illustrate by examples the effect of
physical knowledge under each of these heads:--

(36.) Ex. 1. (35.) I. It is not many years since an attempt was made
to establish a colliery at Bexhill, in Sussex. The appearance of
thin seams and sheets of fossil-wood and wood-coal, with some other
indications similar to what occur in the neighbourhood of the great
coal-beds in the north of England, having led to the sinking of a
shaft, and the erection of machinery on a scale of vast expense, not
less than eighty thousand pounds are said to have been laid out on
this project, which, it is almost needless to add, proved completely
abortive, as every geologist would have at once declared it must, the
whole assemblage of geological facts being adverse to the existence
of a regular coal-bed _in_ the Hastings’ _sand_; while this, on which
Bexhill is situated, is separated from the _coal-strata_ by a series
of interposed beds of such enormous thickness as to render all idea of
penetrating _through_ them absurd. The history of mining operations
is full of similar cases, where a very moderate acquaintance with the
_usual order of nature_, to say nothing of theoretical views, would
have saved many a sanguine adventurer from utter ruin.

(37.) Ex. 2. (35.) II. The smelting of iron requires the application
of the most violent heat that can be raised, and is commonly performed
in tall furnaces, urged by great iron bellows driven by steam-engines.
Instead of employing this power to force _air_ into the furnace through
the intervention of bellows, it was, on one occasion, attempted to
employ the steam itself in, apparently, a much less circuitous manner;
viz. by directing the current of steam in a violent blast, from the
boiler at once into the fire. From one of the known ingredients of
steam being a highly inflammable body, and the other that essential
part of the air which supports combustion, it was imagined that this
would have the effect of increasing the fire to tenfold fury, whereas
it simply _blew it out_; a result which a slight consideration of the
laws of chemical combination, and the state in which the ingredient
elements exist in steam, would have enabled any one to predict without
a trial.

(38.) Ex. 3. (35.) II. After the invention of the diving-bell, and its
success in subaqueous processes, it was considered highly desirable
to devise some means of remaining for any length of time under water,
and rising at pleasure without assistance, so as either to examine,
at leisure, the bottom, or perform, at ease, any work that might be
required. Some years ago, an ingenious individual proposed a project
by which this end was to be accomplished. It consisted in sinking
the hull of a ship made quite water-tight, with the decks and sides
strongly supported by shores, and the only entry secured by a stout
trap-door, in such a manner, that by disengaging, from within, the
weights employed to sink it, it might rise of itself to the surface. To
render the trial more satisfactory, and the result more striking, the
projector himself made the first essay. It was agreed that he should
sink in twenty fathoms water, and rise again without assistance at
the expiration of twenty-four hours. Accordingly, making all secure,
fastening down his trap-door, and provided with all necessaries, as
well as with the means of making signals to indicate his situation,
this unhappy victim of his own ingenuity entered and was sunk. No
signal was made, and the time appointed elapsed. An immense concourse
of people had assembled to witness his rising, but in vain; for the
vessel was never seen more. The pressure of the water at so great a
depth had, no doubt, been completely under-estimated, and the sides of
the vessel being at once crushed in, the unfortunate projector perished
before he could even make the signal concerted to indicate his distress.

(39.) Ex. 4. (35.) III. In the granite quarries near Seringapatam the
most enormous blocks are separated from the solid rock by the following
neat and simple process. The workman having found a portion of the rock
sufficiently extensive, and situated near the edge of the part already
quarried, lays bare the upper surface, and marks on it a line in the
direction of the intended separation, along which a groove is cut with
a chisel about a couple of inches in depth. Above this groove a narrow
line of fire is then kindled, and maintained till the rock below is
thoroughly heated, immediately on which a line of men and women, each
provided with a pot full of cold water, suddenly sweep off the ashes,
and pour the water into the heated groove, when the rock at once
splits with a clean fracture. Square blocks of six feet in the side,
and upwards of eighty feet in length, are sometimes detached by this
method, or by another equally simple and efficacious, but not easily
explained without entering into particulars of mineralogical detail.[11]

(40.) Ex. 5. (35.) III. Hardly less simple and efficacious is the
process used in some parts of France, where mill-stones are made. When
a mass of stone sufficiently large is found, it is cut into a cylinder
several feet high, and the question then arises how to subdivide
this into horizontal pieces so as to make as many mill-stones. For
this purpose horizontal indentations or grooves are chiselled out
quite round the cylinder, at distances corresponding to the thickness
intended to be given to the mill-stones, into which wedges of dried
wood are driven. These are then wetted, or exposed to the night dew,
and next morning the different pieces are found separated from each
other by the expansion of the wood, consequent on its absorption of
moisture; an irresistible natural power thus accomplishing, almost
without any trouble, and at no expense, an operation which, from
the peculiar hardness and texture of the stone, would otherwise
be impracticable but by the most powerful machinery or the most
persevering labour.

(41.) Ex. 6. (35.) III. To accomplish our ends quickly is often of, at
least, as much importance as to accomplish them with little labour and
expense. There are innumerable processes which, if left to themselves,
_i. e._ to the ordinary operation of natural causes, are done, and well
done, but with extreme slowness, and in such cases it is often of
the highest practical importance to accelerate them. The bleaching of
linen, for instance, performed in the natural way by exposure to sun,
rain, and wind, requires many weeks or even months for its completion;
whereas, by the simple immersion of the cloth in a liquid, chemically
prepared, the same effect is produced in a few hours. The whole circle
of the arts, indeed, is nothing but one continued comment upon this
head of our subject. The instances above given are selected, not on
account of their superior importance, but for the simplicity and
_directness_ of application of the principles on which they depend, to
the objects intended to be attained.

(42.) But so constituted is the mind of man, that his views enlarge,
and his desires and wants increase, in the full proportion of the
facilities afforded to their gratification, and, indeed, with augmented
rapidity, so that no sooner has the successful exercise of his powers
accomplished any considerable simplification or improvement of
processes subservient to his use or comfort, than his faculties are
again on the stretch to extend the limits of his newly acquired power;
and having once experienced the advantages which are to be gathered
by availing himself of some of the powers of nature to accomplish
his ends, he is led thenceforward to regard them all as a treasure
placed at his disposal, if he have only the art, the industry, or the
good fortune, to penetrate those recesses which conceal them from
immediate view. Having once learned to look on knowledge as power, and
to avail himself of it as such, he is no longer content to limit his
enterprises to the beaten track of former usage, but is constantly
led onwards to contemplate objects which, in a previous stage of his
progress, he would have regarded as unattainable and visionary, had he
even thought of them at all. It is here that the investigation of the
hidden powers of nature becomes a mine, every vein of which is pregnant
with inexhaustible wealth, and whose ramifications appear to extend in
all directions wherever human wants or curiosity may lead us to explore.

(43.) Between the physical sciences and the arts of life there subsists
a constant mutual interchange of good offices, and no considerable
progress can be made in the one without of necessity giving rise to
corresponding steps in the other. On the one hand, every art is in
some measure, and many entirely, dependent on those very powers and
qualities of the material world which it is the object of physical
enquiry to investigate and explain; and, accordingly, abundant examples
might be cited of cases where the remarks of experienced artists, or
even ordinary workmen, have led to the discovery of natural qualities,
elements, or combinations which have proved of the highest importance
in physics. Thus (to give an instance), a soap-manufacturer remarks
that the residuum of his ley, when exhausted of the alkali for which
he employs it, produces a corrosion of his copper boiler for which he
cannot account. He puts it into the hands of a scientific chemist for
analysis, and the result is the discovery of one of the most singular
and important chemical elements, iodine. The properties of this,
being studied, are found to occur most appositely in illustration
and support of a variety of new, curious, and instructive views then
gaining ground in chemistry, and thus exercise a marked influence
over the whole body of that science. Curiosity is excited: the origin
of the new substance is traced to the sea-plants from whose ashes
the principal ingredient of soap is obtained, and ultimately to the
sea-water itself. It is thence hunted through nature, discovered in
salt mines and springs, and pursued into all bodies which have a marine
origin; among the rest, into sponge. A medical practitioner[12] then
calls to mind a reputed remedy for the cure of one of the most grievous
and unsightly disorders to which the human species is subject--the
_goître_--which infests the inhabitants of mountainous districts to
an extent that in this favoured land we have happily no experience
of, and which was said to have been originally cured by the ashes of
burnt sponge. Led by this indication he tries the effect of iodine on
that complaint, and the result establishes the extraordinary fact that
this singular substance, taken as a medicine, acts with the utmost
promptitude and energy on _goître_, dissipating the largest and most
inveterate in a short time, and acting (of course, like all medicines,
even the most approved, with occasional failures,) as a specific, or
natural antagonist, against that odious deformity. It is thus that
any accession to our knowledge of nature is sure, sooner or later, to
make itself felt in some practical application, and that a benefit
conferred on science by the casual observation or shrewd remark of even
an unscientific or illiterate person infallibly repays itself with
interest, though often in a way that could never have been at first
contemplated.

(44.) It is to such observation, reflected upon, however, and matured
into a rational and scientific form by a mind deeply imbued with the
best principles of sound philosophy, that we owe the practice of
vaccination; a practice which has effectually subdued, in every country
where it has been introduced, one of the most frightful scourges of
the human race, and in some extirpated it altogether. Happily for us
we know only by tradition the ravages of the small-pox, as it existed
among us hardly more than a century ago, and as it would in a few
years infallibly exist again, were the barriers which this practice,
and that of inoculation, oppose to its progress abandoned. Hardly
inferior to this terrible scourge on land was, within the last seventy
or eighty years, the scurvy at sea. The sufferings and destruction
produced by this horrid disorder on board our ships when, as a matter
of course, it broke out after a few months’ voyage, seem now almost
incredible. Deaths to the amount of eight or ten a day in a moderate
ship’s company; bodies sewn up in hammocks and washing about the decks
for want of strength and spirits on the part of the miserable survivors
to cast them overboard; and every form of loathsome and excruciating
misery of which the human frame is susceptible:--such are the pictures
which the narratives of nautical adventure in those days continually
offer.[13] At present the scurvy is almost completely eradicated in
the navy, partly, no doubt, from increased and increasing attention to
general cleanliness, comfort, and diet; but mainly from the constant
use of a simple and palatable preventive, the acid of the lemon,
served out in daily rations. If the gratitude of mankind be allowed on
all hands to be the just meed of the philosophic physician, to whose
discernment in seizing, and perseverance in forcing it on public notice
we owe the great safeguard of infant life, it ought not to be denied to
those[14] whose skill and discrimination have thus strengthened the
sinews of our most powerful arm, and obliterated one of the darkest
features in the most glorious of all professions.

(45.) These last, however, are instances of simple observation,
limited to the point immediately in view, and assuming only so far the
character of science as a systematic adoption of good and rejection of
evil, when grounded on experience carefully weighed, justly entitle
it to do. They are not on that account less appositely cited as
instances of the importance of a knowledge of nature and its laws to
our well-being; though, like the great inventions of the mariner’s
compass and of gunpowder, they may have stood, in their origin,
unconnected with more general views. They are rather to be looked upon
as the spontaneous produce of a territory essentially fertile, than as
forming part of the succession of harvests which the same bountiful
soil, diligently cultivated, is capable of yielding. The history of
iodine above related affords, however, a perfect specimen of the
manner in which a knowledge of natural properties and laws, collected
from facts having no reference to the object to which they have
been subsequently applied, enables us to set in array the resources
of nature against herself; and deliberately, of afore-thought, to
devise remedies against the dangers and inconveniences which beset
us. In this view we might instance, too, the _conductor_, which, in
countries where thunder-storms are more frequent and violent than in
our own, and at sea (where they are attended with peculiar danger,
both from the greater probability of accident, and its more terrible
consequences when it does occur,) forms a most real and efficient
preservative against the effects of lightning[15]:--the _safety-lamp_,
which enables us to walk with light and security while surrounded with
an atmosphere more explosive than gunpowder:--the _life-boat_, which
cannot be sunk, and which offers relief in circumstances of all others
the most distressing to humanity, and of which a recent invention
promises to extend the principle to ships of the largest class:--the
_lighthouse_, with the capital improvements which the lenses of
Brewster and Fresnel, and the elegant lamp of lieutenant Drummond, have
conferred, and promise yet to confer by their wonderful powers, the one
of producing the most intense light yet known, the others of conveying
it undispersed to great distances:--the discovery of the disinfectant
powers of chlorine, and its application to the destruction of miasma
and contagion:--that of _quinine_, the essential principle in which
reside the febrifuge qualities of the Peruvian bark, a discovery by
which posterity is yet to benefit in its full extent, but which has
already begun to diffuse _comparative_ comfort and health through
regions almost desolated by pestiferous exhalations[16];--and, if we
desist, it is not because the list is exhausted, but because a sample,
not a catalogue, is intended.

(46.) One instance more, however, we will add, to illustrate the
manner in which a most familiar effect, which seemed destined only
to amuse children, or, at best, to furnish a philosophic toy, may
become a safeguard of human life, and a remedy for a most serious
and distressing evil. In needle manufactories the workmen who point
the needles are constantly exposed to excessively minute particles of
steel which fly from the grindstones, and mix, though imperceptible
to the eye, as the finest dust in the air, and are inhaled with their
breath. The effect, though imperceptible on a short exposure, yet,
being constantly repeated from day to day, produces a constitutional
irritation dependent on the tonic properties of the steel, which is
sure to terminate in pulmonary consumption; insomuch, that persons
employed in this kind of work used scarcely ever to attain the age of
forty years.[17] In vain was it attempted to purify the air before its
entry into the lungs by gauzes or linen guards; the dust was too fine
and penetrating to be obstructed by such coarse expedients, till some
ingenious person bethought him of that wonderful power which every
child who searches for its mother’s needle with a magnet, or admires
the motions and arrangement of a few steel filings on a sheet of paper
held above it, sees in exercise. Masks of magnetized steel wire are now
constructed and adapted to the faces of the workmen. By these the air
is not merely _strained_ but _searched_ in its passage through them,
and each obnoxious atom arrested and removed.

(47.) Perhaps there is no result which places in a stronger light the
advantages which are to be derived from a mere knowledge of the _usual
order of nature_, without any attempt on our part to modify it, and
apart from all consideration of its causes, than the institution of
life-assurances. Nothing is more uncertain than the life of a single
individual; and it is the sense of this insecurity which has given
rise to such institutions. They are, in their nature and objects,
the precise reverse of gambling speculations, their object being to
equalize vicissitude, and to place the pecuniary relations of numerous
masses of mankind, in so far as they extend, on a footing independent
of individual casualty. To do this with the greatest possible
advantage, or indeed with any advantage at all, it is necessary to know
the _laws of mortality_, or the average numbers of individuals, out
of a great multitude, who die at every period of life from infancy to
extreme old age. At first sight this would seem a hopeless enquiry; to
some, perhaps, a presumptuous one. But it has been made; and the result
is, that, abating extraordinary causes, such as wars, pestilence, and
the like, a remarkable regularity _does_ obtain, quite sufficient
to afford grounds not only for general estimations, but for nice
calculations of risk and adventure, such as infallibly to insure the
success of any such institution founded on good computations; and thus
to confer such stability on the fortunes of families dependent on the
exertions of one individual as to constitute an important feature in
modern civilization. The only thing to be feared in such institutions
is their too great multiplication and consequent competition, by which
a spirit of gambling and underbidding is liable to be generated among
their conductors, and the very mischief may be produced, on a scale of
frightful extent, which they are especially intended to prevent.

(48.) We have hitherto considered only cases in which a knowledge of
natural laws enables us to improve our condition, by counteracting
evils of which, but for its possession, we must have remained forever
the helpless victims. Let us now take a similar view of those in which
we are enabled to call in nature as an auxiliary to augment our actual
power, and capacitate us for undertakings, which without such aid might
seem to be hopeless. Now, to this end, it is necessary that we should
form a just conception of what those hidden powers of nature _are_,
which we can at pleasure call into action;--how far they transcend
the measure of human force, and set at naught the efforts not only of
individuals but of whole nations of men.

(49.) It is well known to modern engineers, that _there is virtue_ in a
bushel of coals properly consumed, to raise seventy millions of pounds
weight a foot high. This is actually the _average_ effect of an engine
at this moment working in Cornwall.[18] Let us pause a moment, and
consider what this is equivalent to in matters of practice.

(50.) The ascent of Mont Blanc from the valley of Chamouni is
considered, and with justice, as the most toilsome feat that a strong
man can execute in two days. The combustion of two pounds of coal would
place him on the summit.[19]

(51.) The Menai Bridge, one of the most stupendous works of art that
has been raised by man in modern ages, consists of a mass of iron, not
less than four millions of pounds in weight, suspended at a medium
height of about 120 feet above the sea. The consumption of seven
bushels of coal would suffice to raise it to the place where it hangs.

(52.) The great pyramid of Egypt is composed of granite. It is 700 feet
in the side of its base, and 500 in perpendicular height, and stands on
eleven acres of ground. Its weight is, therefore, 12,760 millions of
pounds, at a medium height of 125 feet; consequently it would be raised
by the effort of about 630 chaldrons of coal, a quantity consumed in
some founderies in a week.

(53.) The annual consumption of coal in London is estimated at
1,500,000 chaldrons. The effort of this quantity would suffice to raise
a cubical block of marble, 2200 feet in the side, through a space equal
to its own height, or to pile one such mountain upon another. The Monte
Nuovo, near Pozzuoli, (which was erupted in a single night by volcanic
fire,) might have been raised by such an effort, from a depth of 40,000
feet, or about eight miles.

(54.) It will be observed, that, in the above statement, the inherent
power of fuel is, of necessity, greatly under-rated. It is not
pretended by engineers that the economy of fuel is yet pushed to its
utmost limit, or that the whole effective power is obtained in any
application of fire yet devised; so that were we to say 100 millions
instead of 70, we should probably be nearer the truth.

(55.) The powers of wind and water, which we are constantly impressing
into our service, can scarcely be called latent or hidden, yet it
is not fully considered, in general, what they _do_ effect for us.
Those who would judge of what advantage may be taken of the wind, for
example, even on land (not to speak of navigation), may turn their
eyes on Holland. A great portion of the most valuable and populous
tract of this country lies much below the level of the sea, and is only
preserved from inundation by the maintenance of embankments. Though
these suffice to keep out the abrupt influx of the ocean, they cannot
oppose that law of nature, by which fluids, in seeking their level,
insinuate themselves through the pores and subterraneous channels
of a loose sandy soil, and keep the country in a constant state of
infiltration from below upwards. To counteract this tendency, as well
as to get rid of the rain water, which has no natural outlet, pumps
worked by windmills are established in great numbers, on the dams
and embankments, which pour out the water, as from a leaky ship, and
in effect preserve the country from submersion, by taking advantage
of every wind that blows. To drain the Haarlem lake[20] would seem a
hopeless project to any speculators but those who had the steam-engine
at their command, or had learnt in Holland what might be accomplished
by the constant agency of the desultory but unwearied powers of wind.
But the Dutch engineer measures his surface, calculates the number of
his pumps, and, trusting to time and his experience of the operation of
the winds for the success of his undertaking, boldly forms his plans to
lay dry the bed of an inland sea, of which those who stand on one shore
cannot see the other.[21]

(56.) To gunpowder, as a source of mechanical power, it seems hardly
necessary to call attention; yet it is only when we endeavour to
_confine_ it, that we get a full conception of the immense energy of
that astonishing agent. In count Rumford’s experiments, twenty-eight
grains of powder confined in a cylindrical space, _which it just
filled_, tore asunder a piece of iron which would have resisted
a strain of 400,000 lbs.[22], applied at no greater mechanical
disadvantage.

(57.) But chemistry furnishes us with means of calling into sudden
action forces of a character infinitely more tremendous than that
of gunpowder. The terrific violence of the different fulminating
compositions is such, that they can only be compared to those
untameable animals, whose ferocious strength has hitherto defied all
useful management, or rather to spirits evoked by the spells of a
magician, manifesting a destructive and unapproachable power, which
makes him but too happy to close his book, and break his wand, as the
price of escaping: unhurt from the storm he has raised. Such powers are
not yet subdued to our purposes, whatever they may hereafter be; but,
in the expansive force of gases, liberated slowly and manageably from
chemical mixtures, we have a host of inferior, yet still most powerful,
energies, capable of being employed in a variety of useful ways,
according to emergencies.[23]

(58.) Such are the forces which nature lends us for the accomplishment
of our purposes, and which it is the province of practical Mechanics to
teach us to combine and apply in the most advantageous manner; without
which the mere command of power would amount to nothing. Practical
Mechanics is, in the most pre-eminent sense, a _scientific art_; and
it may be truly asserted, that almost all the great combinations of
modern mechanism, and many of its refinements and nicer improvements,
are creations of pure intellect, grounding its exertion upon a moderate
number of very elementary propositions in theoretical mechanics and
geometry. On this head we might dwell long, and find ample matter,
both for reflection and wonder; but it would require not volumes
merely, but libraries, to enumerate and describe the prodigies of
ingenuity which have been lavished on every thing connected with
machinery and engineering. By these it is that we are enabled to
diffuse over the whole earth the productions of any part of it; to fill
every corner of it with miracles of art and labour, in exchange for its
peculiar commodities; and to concentrate around us, in our dwellings,
apparel and utensils, the skill and workmanship not of a few expert
individuals, but of all who, in the present and past generations, have
contributed their improvements to the processes of our manufactures.

(59.) The transformations of chemistry, by which we are enabled to
convert the most apparently useless materials into important objects
in the arts, are opening up to us every day sources of wealth and
convenience of which former ages had no idea, and which have been
pure gifts of science to man. Every department of art has felt their
influence, and new instances are continually starting forth of the
unlimited resources which this wonderful science developes in the
most sterile parts of nature. Not to mention the impulse which its
progress has given to a host of other sciences, which will come more
particularly under consideration in another part of this discourse,
what strange and unexpected results has it not brought to light in its
application to some of the most common objects! Who, for instance,
would have conceived that linen rags were capable of producing _more
than their own weight_ of sugar, by the simple agency of one of the
cheapest and most abundant acids?[24]--that dry bones could be a
magazine of nutriment, capable of preservation for years, and ready to
yield up their sustenance in the form best adapted to the support of
life, on the application of that powerful agent, steam, which enters
so largely into all our processes, or of an acid at once cheap and
durable?[25]--that sawdust itself is susceptible of conversion into
a substance bearing no remote analogy to bread; and though certainly
less palatable than that of flour, yet no way disagreeable, and
both wholesome and digestible as well as highly nutritive?[26] What
economy, in all processes where chemical agents are employed, is
introduced by the exact knowledge of the proportions in which natural
elements unite, and their mutual powers of displacing each other! What
perfection in all the arts where fire is employed, either in its more
violent applications, (as, for instance, in the smelting of metals by
the introduction of well adapted fluxes, whereby we obtain the whole
produce of the ore in its purest state,) or in its milder forms, as
in sugar-refining (the whole modern practice of which depends on a
curious and delicate remark of a late eminent scientific chemist on the
nice adjustment of temperature at which the crystallization of syrup
takes place); and a thousand other arts which it would be tedious to
enumerate!

(60.) Armed with such powers and resources, it is no wonder if the
enterprise of man should lead him to form and execute projects
which, to one uninformed of their grounds, would seem altogether
disproportionate. Were they to have been proposed at once, we should,
no doubt, have rejected them as such: but developed, as they have been,
in the slow succession of ages, they have only taught us that things
regarded impossible in one generation may become easy in the next; and
that the power of man over nature is limited only by the one condition,
that it must be exercised in conformity with the laws of nature. He
must study those laws as he would the disposition of a horse he would
ride, or the character of a nation he would govern; and the moment he
presumes either to thwart her fundamental rules, or ventures to measure
his strength with hers, he is at once rendered severely sensible of
his imbecility, and meets the deserved punishment of his rashness and
folly. But if, on the other hand, he will consent to use, without
abusing, the resources thus abundantly placed at his disposal, and obey
that he may command, there seems scarcely any conceivable limit to the
degree in which the _average_ physical condition of great masses of
mankind may be improved, their wants supplied, and their conveniences
and comforts increased. Without adopting such an exaggerated view,
as to assert that the meanest inhabitant of a civilized society is
superior in physical condition to the lordly savage, whose energy and
uncultivated ability gives him a natural predominance over his fellow
denizens of the forest,--at least, if we compare like with like, and
consider the multitude of human beings who are enabled, in an advanced
state of society, to subsist in a degree of comfort and abundance,
which at best only a few of the most fortunate in a less civilized
state could command, we shall not be at a loss to perceive the
principle on which we ought to rest our estimate of the advantages of
civilization; and which applies with hardly less force to every degree
of it, when contrasted with that next inferior, than to the broad
distinction between civilized and barbarous life in general.

(61.) The difference of the degrees in which the individuals of a great
community enjoy the good things of life has been a theme of declamation
and discontent in all ages; and it is doubtless our paramount duty, in
every state of society, to alleviate the pressure of the purely evil
part of this distribution as much as possible, and, by all the means
we can devise, secure the lower links in the chain of society from
dragging in dishonour and wretchedness: but there is a point of view
in which the picture is at least materially altered in its expression.
In comparing society on its present immense scale, with its infant
or less developed state, we must at least take care to enlarge every
feature in the same proportion. If, on comparing the _very_ lowest
states in civilized and savage life, we admit a difficulty in deciding
to which the preference is due, at least in every superior grade we
cannot hesitate a moment; and if we institute a similar comparison in
every different stage of its progress, we cannot fail to be struck with
the rapid _rate of dilatation_ which every degree upward of the scale,
so to speak, exhibits, and which, in an estimate of averages, gives
an immense preponderance to the present over every former condition
of mankind, and, for aught we can see to the contrary, will place
succeeding generations in the same degree of superior relation to the
present that this holds to those passed away. Or we may put the same
proposition in other words, and, admitting the existence of every
inferior grade of advantage in a higher state of civilization which
subsisted in the preceding, we shall find, first, that, taking state
for state, the proportional numbers of those who enjoy the higher
degrees of advantage increases with a constantly accelerated rapidity
as society advances; and, secondly, that the superior extremity of
the scale is constantly enlarging by the addition of new degrees. The
condition of a European prince is now as far superior, in the command
of real comforts and conveniences, to that of one in the middle ages,
as that to the condition of one of his own dependants.

(62.) The advantages conferred by the augmentation of our physical
resources through the medium of increased knowledge and improved art
have this peculiar and remarkable property,--that they are in their
nature diffusive, and cannot be enjoyed in any exclusive manner by a
few. An eastern despot may extort the riches and monopolize the art
of his subjects for his own personal use; he may spread around him an
unnatural splendour and luxury, and stand in strange and preposterous
contrast with the general penury and discomfort of his people; he may
glitter in jewels of gold and raiment of needlework; but the wonders
of well contrived and executed manufacture which we use daily, and
the comforts which have been invented, tried, and improved upon by
thousands, in every form of domestic convenience, and for every
ordinary purpose of life, can never be enjoyed by him. To produce a
state of things in which the physical advantages of civilized life
can exist in a high degree, the stimulus of increasing comforts and
constantly elevated desires, must have been felt by millions; since it
is not in the power of a few individuals to create that wide demand
for useful and ingenious applications, which alone can lead to great
and rapid improvements, unless backed by that arising from the speedy
diffusion of the same advantages among the mass of mankind.

(63.) If this be true of physical advantages, it applies with still
greater force to intellectual. Knowledge can neither be adequately
cultivated nor adequately enjoyed by a few; and although the conditions
of our existence on earth may be such as to preclude an abundant
supply of the physical necessities of all who may be born, there
is no such law of nature in force against that of our intellectual
and moral wants. Knowledge is not, like food, destroyed by use, but
rather augmented and perfected. It acquires not, perhaps, a greater
certainty, but at least a confirmed authority and a probable duration,
by universal assent; and there is no body of knowledge so complete,
but that it may acquire accession, or so free from error but that it
may receive correction in passing through the minds of millions. Those
who admire and love knowledge for its own sake ought to wish to see
its elements made accessible to all, were it only that they may be
the more thoroughly examined into, and more effectually developed in
their consequences, and receive that ductility and plastic quality
which the pressure of minds of all descriptions, constantly moulding
them to their purposes, can alone bestow. But to this end it is
necessary that it should be divested, as far as possible, of artificial
difficulties, and stripped of all such technicalities as tend to place
it in the light of a craft and a mystery, inaccessible without a kind
of apprenticeship. Science, of course, like every thing else, has its
own peculiar terms, and, so to speak, its idioms of language; and these
it would be unwise, were it even possible, to relinquish: but every
thing that tends to clothe it in a strange and repulsive garb, and
especially every thing that, to keep up an appearance of superiority
in its professors over the rest of mankind, assumes an unnecessary
guise of profundity and obscurity, should be sacrificed without mercy.
Not to do this, is to deliberately reject the light which the natural
unencumbered good sense of mankind is capable of throwing on every
subject, even in the elucidation of principles: but where principles
are to be applied to practical uses it becomes absolutely necessary;
as all mankind have then an interest in their being so familiarly
understood, that no mistakes shall arise in their application.

(64.) The same remark applies to arts. They cannot be perfected till
their whole processes are laid open, and their language simplified and
rendered universally intelligible. Art is the application of knowledge
to a practical end. If the knowledge be merely accumulated experience,
the art is _empirical_; but if it be experience reasoned upon and
brought under general principles, it assumes a higher character, and
becomes a _scientific art_. In the progress of mankind from barbarism
to civilised life, the arts necessarily precede science. The wants and
cravings of our animal constitution must be satisfied; the comforts,
and some of the luxuries, of life must exist. Something must be given
to the vanity of show, and more to the pride of power: the round of
baser pleasures must have been tried and found insufficient, before
intellectual ones can gain a footing; and when they have obtained it,
the delights of poetry and its sister arts still take precedence of
contemplative enjoyments, and the severer pursuits of thought; and
when these in time begin to charm from their novelty, and sciences
begin to arise, they will at first be those of pure speculation. The
mind delights to escape from the trammels which had bound it to earth,
and luxuriates in its newly found powers. Hence, the abstractions of
geometry--the properties of numbers--the movements of the celestial
spheres--whatever is abstruse, remote, and extramundane--become the
first objects of infant science. Applications come late: the arts
continue slowly progressive, but their realm remains separated from
that of science by a wide gulf which can only be passed by a powerful
spring. They form their own language and their own conventions, which
none but artists can understand. The whole tendency of empirical
art, is to bury itself in technicalities, and to place its pride in
particular short cuts and mysteries known only to adepts; to surprise
and astonish by results, but conceal processes. The character of
science is the direct contrary. It delights to lay itself open to
enquiry, and is not satisfied with its conclusions, till it can make
the road to them broad and beaten: and in its applications it preserves
the same character; its whole aim being to strip away all technical
mystery, to illuminate every dark recess, and to gain free access to
all processes, with a view to improve them on rational principles.
It would seem that a union of two qualities almost opposite to each
other--a going forth of the thoughts in two directions, and a sudden
transfer of ideas from a remote station in one to an equally distant
one in the other--is required to start the first idea of _applying
science_. Among the Greeks, this point was attained by Archimedes, but
attained too late, on the eve of that great eclipse of science which
was destined to continue for nearly eighteen centuries, till Galileo in
Italy, and Bacon in England, at once dispelled the darkness: the one,
by his inventions and discoveries; the other, by the irresistible force
of his arguments and eloquence.

(65.) Finally, the improvement effected in the condition of mankind
by advances in physical science as applied to the useful purposes of
life, is very far from being limited to their direct consequences in
the more abundant supply of our physical wants, and the increase of our
comforts. Great as these benefits are, they are yet but steps to others
of a still higher kind. The successful results of our experiments and
reasonings in natural philosophy, and the incalculable advantages which
experience, systematically consulted and dispassionately reasoned on,
has conferred in matters purely physical, tend of necessity to impress
something of the well weighed and progressive character of science on
the more complicated conduct of our social and moral relations. It
is thus that legislation and politics become gradually regarded as
experimental sciences; and history, not, as formerly, the mere record
of tyrannies and slaughters, which, by immortalizing the execrable
actions of one age, perpetuates the ambition of committing them in
every succeeding one, but as the archive of experiments, successful
and unsuccessful, gradually accumulating towards the solution of the
grand problem--how the advantages of government are to be secured
with the least possible inconvenience to the governed. The celebrated
apophthegm, that nations never profit by experience, becomes yearly
more and more untrue. Political economy, at least, is found to have
sound principles, founded in the moral and physical nature of man,
which, however lost sight of in particular measures--however even
temporarily controverted and borne down by clamour--have yet a stronger
and stronger testimony borne to them in each succeeding generation, by
which they must, sooner or later, prevail. The idea once conceived and
verified, that great and noble ends are to be achieved, by which the
condition of the whole human species shall be permanently bettered,
by bringing into exercise a sufficient quantity of sober thought, and
by a proper adaptation of means, is of itself sufficient to set us
earnestly on reflecting what ends _are_ truly great and noble, either
in themselves, or as conducive to others of a still loftier character;
because we are not now, as heretofore, hopeless of attaining them. It
is not now equally harmless and insignificant, whether we are right
or wrong; since we are no longer supinely and helplessly carried down
the stream of events, but feel ourselves capable of buffetting at
least with its waves, and perhaps of riding triumphantly over them:
for why should we despair that the reason which has enabled us to
subdue all nature to our purposes, should (if permitted and assisted
by the providence of God) achieve a far more difficult conquest; and
ultimately find some means of enabling the collective wisdom of mankind
to bear down those obstacles which individual short-sightedness,
selfishness, and passion, oppose to all improvements, and by which
the highest hopes are continually blighted, and the fairest prospects
marred.



                                PART II.

  OF THE PRINCIPLES ON WHICH PHYSICAL SCIENCE RELIES FOR ITS
    SUCCESSFUL PROSECUTION, AND THE RULES BY WHICH A SYSTEMATIC
    EXAMINATION OF NATURE SHOULD BE CONDUCTED, WITH ILLUSTRATIONS OF
    THEIR INFLUENCE AS EXEMPLIFIED IN THE HISTORY OF ITS PROGRESS.



CHAPTER I.

  OF EXPERIENCE AS THE SOURCE OF OUR KNOWLEDGE.--OF THE DISMISSAL OF
    PREJUDICES.--OF THE EVIDENCE OF OUR SENSES.


(66.) Into abstract science, as we have before observed, the notion of
cause does not enter. The truths it is conversant with are _necessary_
ones, and exist independent of cause. There may be no such real _thing_
as a right-lined triangle marked out in space; but the moment we
conceive one in our minds, we cannot refuse to admit the sum of its
three angles to be equal to two right angles; and if in addition we
conceive one of its angles to be a right angle, we cannot thenceforth
refuse to admit that the sum of the squares on the two sides, including
the right angle, is equal to the square on the side subtending it. To
maintain the contrary, would be, in effect, to deny its being right
angled. No one _causes_ or _makes_ all the diameters of an ellipse
to be bisected in its centre. To assert the contrary, would not be
to rebel against a power, but to deny our own words. But in natural
science _cause_ and _effect_ are the ultimate relations we contemplate;
and _laws_, whether imposed or maintained, which, for aught we can
perceive, might have been other than they are. This distinction is
very important. A clever man, shut up alone and allowed unlimited
time, might reason out for himself all the truths of mathematics, by
proceeding from those simple notions of space and number of which he
cannot divest himself without ceasing to think. But he could never
tell, by any effort of reasoning, what would become of a lump of sugar
if immersed in water, or what impression would be produced on his eye
by mixing the colours yellow and blue.

(67.) We have thus pointed out to us, as the great, and indeed only
ultimate source of our knowledge of nature and its laws, EXPERIENCE;
by which we mean, not the experience of one man only, or of one
generation, but the accumulated experience of all mankind in all ages,
registered in books or recorded by tradition. But experience may be
acquired in two ways: either, first, by noticing facts as they occur,
without any attempt to influence the frequency of their occurrence, or
to vary the circumstances under which they occur; this is OBSERVATION:
or, secondly, by putting in action causes and agents over which we
have control, and purposely varying their combinations, and noticing
what effects take place; this is EXPERIMENT. To these two sources we
must look as the fountains of all natural science. It is not intended,
however, by thus distinguishing observation from experiment, to
place them in any kind of contrast. Essentially they are much alike,
and differ rather in degree than in kind; so that, perhaps, the
terms _passive_ and _active observation_ might better express their
distinction; but it is, nevertheless, highly important to mark the
different states of mind in inquiries carried on by their respective
aids, as well as their different effects in promoting the progress of
science. In the former, we sit still and listen to a tale, told us,
perhaps obscurely, piecemeal, and at long intervals of time, with our
attention more or less awake. It is only by after-rumination that we
gather its full import; and often, when the opportunity is gone by, we
have to regret that our attention was not more particularly directed to
some point which, at the time, appeared of little moment, but of which
we at length appretiate the importance. In the latter, on the other
hand, we cross-examine our witness, and by comparing one part of his
evidence with the other, while he is yet before us, and reasoning upon
it in his presence, are enabled to put pointed and searching questions,
the answer to which may at once enable us to make up our minds.
Accordingly it has been found invariably, that in those departments
of physics where the phenomena are beyond our control, or into which
experimental enquiry, from other causes, has not been carried, the
progress of knowledge has been slow, uncertain, and irregular; while in
such as admit of experiment, and in which mankind have agreed to its
adoption, it has been rapid, sure, and steady. For example, in our
knowledge of the nature and causes of volcanoes, earthquakes, the fall
of stones from the sky, the appearance of new stars and disappearance
of old ones, and other of those great phenomena of nature which are
altogether beyond our command, and at the same time are of too rare
occurrence to permit any one to repeat and rectify his impressions
respecting them, we know little more now than in the earliest times.
Here our tale is told us slowly, and in broken sentences. In astronomy,
again, we have at least an uninterrupted narrative; the opportunity
of observation is constantly present, and makes up in some measure
for the impossibility of varying our point of view, and calling for
information at the precise moment it is wanted. Accordingly, astronomy,
regarded as a science of mere observation, arrived, though by very
slow degrees, to a state of considerable maturity. But the moment that
it became a branch of mechanics, a science essentially experimental,
(that is to say, one in which any principle laid down can be subjected
to immediate and decisive _trial_, and where experience does not
require to be waited for,) its progress suddenly acquired a tenfold
acceleration; nay, to such a degree, that it has been asserted, and
we believe with truth, that were the records of all observations from
the earliest ages annihilated, leaving only those made in a single
observatory[27], during a single lifetime[28], the whole of this most
perfect of sciences might, from those data, and as to the objects
included in them, be at once reconstructed, and appear precisely as
it stood at their conclusion. To take another instance: mineralogy,
till modern times, could hardly be said to exist. The description
of even the precious stones in Theophrastus and Pliny are, in most
cases, hardly sufficient to identify them, and in many fall short
even of that humble object; more recent observers, by attending more
carefully to the obvious characters of minerals, had formed a pretty
extensive catalogue of them, and made various attempts to arrange and
methodize the knowledge thus acquired, and even to deduce some general
conclusions respecting the forms they habitually assume: but from the
moment that chemical analysis was applied to resolve them into their
constituent elements, and that, led by a happy accident, the genius
of Bergmann discovered the general fact, that they could be _cloven_
or split in such directions as to lay bare their peculiar primitive
or fundamental forms, (which lay concealed within them, as the statue
might be conceived encrusted in its marble envelope,)--from that
moment, mineralogy ceased to be an unmeaning list of names, a mere
laborious cataloguing of stones and rubbish, and became, what it now
is, a regular, methodical, and most important science, in which every
year is bringing to light new relations, new laws, and new practical
applications.

(68.) Experience once recognized as the fountain of all our knowledge
of nature, it follows that, in the study of nature and its laws, we
ought at once to make up our minds to dismiss as idle prejudices, or
at least suspend as premature, any preconceived notion of what might
or what ought to be the order of nature in any proposed case, and
content ourselves with observing, as a plain matter of fact, what _is_.
To experience we refer, as the only ground of all physical enquiry.
But before experience itself can be used with advantage, there is one
preliminary step to make, which depends wholly on ourselves: it is
the absolute dismissal and clearing the mind of all prejudice, from
whatever source arising, and the determination to stand and fall by
the result of a direct appeal to facts in the first instance, and of
strict logical deduction from them afterwards. Now, it is necessary
to distinguish between two kinds of prejudices, which exercise very
different dominion over the mind, and, moreover, differ extremely
in the difficulty of dispossessing them, and the process to be gone
through for that purpose. These are,--

  1. Prejudices of opinion.
  2. Prejudices of sense.

(69.) By prejudices of opinion, we mean opinions hastily taken up,
either from the assertion of others, from our own superficial views,
or from vulgar observation, and which, from being constantly admitted
without dispute, have obtained the strong hold of habit on our minds.
Such were the opinions once maintained that the earth is the greatest
body in the universe, and placed immovable in its centre, and all the
rest of the universe created for its sole use; that it is the nature
of fire and of sounds to ascend; that the moonlight is cold; that dews
_fall_ from the air, &c.

(70.) To combat and destroy such prejudices we may proceed in two ways,
either by demonstrating the falsehood of the facts alleged in their
support, or by showing how the appearances, which seem to countenance
them, are more satisfactorily accounted for without their admission.
But it is unfortunately the nature of prejudices of opinion to adhere,
in a certain degree, to every mind, and to some with pertinacious
obstinacy, _pigris radicibus_, after all ground for their reasonable
entertainment is destroyed. Against such a disposition the student of
natural science must contend with all his power. Not that we are so
unreasonable as to demand of him an instant and peremptory dismission
of all his former opinions and judgments; all we require is, that
he will hold them without bigotry, retain till he shall see reason
to question them, and be ready to resign them when fairly proved
untenable, and to doubt them when the weight of probability is shown to
lie against them. If he refuse this, he is incapable of science.

(71.) Our resistance against the destruction of the other class of
prejudices, those of sense, is commonly more violent at first, but less
persistent, than in the case of those of opinion. Not to trust the
evidence of our senses, seems, indeed, a hard condition, and one which,
if proposed, none would comply with. But it is not the direct evidence
of our senses that we are in any case called upon to reject, but only
the erroneous judgments we unconsciously form from them, and this only
when they can be shown to be so _by counter evidence of the same sort_;
when one sense is brought to testify against another, for instance; or
the same sense against itself, and the obvious conclusions in the two
cases disagree, so as to compel us to acknowledge that one or other
must be wrong. For example, nothing at first can seem a more rational,
obvious, and incontrovertible conclusion, than that the _colour_ of
an object is an inherent quality, like its weight, hardness, &c. and
that to _see_ the object, and see it _of its own colour_, when nothing
intervenes between our eyes and it, are one and the same thing. Yet
this is only a prejudice; and that it is so, is shown by bringing
forward the same sense of vision which led to its adoption, as evidence
on the other side; for, when the differently coloured prismatic rays
are thrown, in a dark room, in succession upon any object, whatever be
the colour we are in the habit of calling its own, it will appear of
the particular hue of the light which falls upon it: a yellow paper,
for instance, will appear scarlet when illuminated by red rays, yellow
when by yellow, green by green, and blue by blue rays; its own (so
called) proper colour _not in the least degree mixing with that it so
exhibits_.

(72.) To give one or two more examples of the kind of illusion which
the senses practise on us, or rather which we practise on ourselves,
by a misinterpretation of their evidence: the moon at its rising
and setting appears much larger than when high up in the sky. This
is, however, a mere erroneous judgment; for when we come to measure
its diameter, so far from finding our conclusion borne out by fact,
we actually find it to measure materially less. Here is eyesight
opposed to eyesight, with the advantage of deliberate measurement.
In ventriloquism we have the hearing at variance with all the other
senses, and especially with the sight, which is sometimes contradicted
by it in a very extraordinary and surprising manner, as when the voice
is made to seem to issue from an inanimate and motionless object. If
we plunge our hands, one into ice-cold water, and the other into water
as hot as can be borne, and, after letting them stay awhile, suddenly
transfer them both to a vessel full of water at a blood heat, the one
will feel a sensation of heat, the other of cold. And if we cross the
two first fingers of one hand, and place a pea in the fork between
them, moving and rolling it about on a table, we shall (especially if
we close our eyes) be fully persuaded we have two peas. If the nose
be held while we are eating cinnamon, we shall perceive no difference
between its flavour and that of a deal shaving.

(73.) These, and innumerable instances we might cite, will convince
us, that though we are never deceived in the _sensible impression_
made by external objects on us, yet in forming our judgments of them
we are greatly at the mercy of circumstances, which either modify the
impressions actually received, or combine them with adjuncts which have
become habitually associated with different judgments; and, therefore,
that, in estimating the degree of confidence we are to place in our
conclusions, we must, of necessity, take into account these modifying
or accompanying circumstances, whatever they may be. We do not, of
course, here speak of deranged organization; such as, for instance,
a distortion of the eye, producing double vision, and still less of
mental delusion, which absolutely perverts the meaning of sensible
impressions.

(74.) As the mind exists not in the place of sensible objects, and
is not brought into immediate relation with them, we can only regard
sensible impressions as signals conveyed from them by a wonderful, and,
to us, inexplicable mechanism, to our minds, which receives and reviews
them, and, by habit and association, connects them with corresponding
qualities or affections in the objects; just as a person writing down
and comparing the signals of a telegraph might interpret their meaning.
As, for instance, if he had constantly observed that the exhibition of
a certain signal was sure to be followed next day by the announcement
of the arrival of a ship at Portsmouth, he would connect the two facts
by a link of the very same nature with that which connects the notion
of a large wooden building, filled with sailors, with the impression of
her outline on the retina of a spectator on the beach.

(75.) In captain Head’s amusing and vivid description of his journey
across the Pampas of South America occurs an anecdote quite in point.
His guide one day suddenly stopped him, and, pointing high into the
air, cried out, “A lion!” Surprised at such an exclamation, accompanied
with such an act, he turned up his eyes, and with difficulty perceived,
at an immeasurable height, a flight of condors soaring in circles in
a particular spot. Beneath that spot, far out of sight of himself or
guide, lay the carcass of a horse, and over that carcass stood (as the
guide well knew) the lion, whom the condors were eyeing with envy from
their airy height. The signal of the birds was to him what the sight of
the lion alone could have been to the traveller, a full assurance of
its existence.



CHAP. II.

OF THE ANALYSIS OF PHENOMENA


(76.) _Phenomena_, then, or appearances, as the word is literally
rendered, are the sensible results of processes and operations carried
on among external objects, or their constituent principles, of which
they are only signals, conveyed to our minds as aforesaid. Now, these
processes themselves may be in many instances rendered _sensible_;
that is to say, analysed, and shown to consist in the motions or other
affections of sensible objects themselves. For instance, the phenomenon
of the sound produced by a musical string, or a bell, when struck,
may be shown to be the result of a process consisting in the rapid
vibratory motion of its parts communicated to the air, and thence to
our ears; though the immediate effect on our organs of hearing does
not excite the least idea of such a motion. On the other hand, there
are innumerable instances of sensible impressions which (at least
at present) we are incapable of tracing beyond the mere sensation;
for example, in the sensations of bitterness, sweetness, &c. These,
accordingly, if we were inclined to form hasty decisions, might be
regarded as ultimate qualities; but the instance of sounds, just
adduced, alone would teach us caution in such decisions, and incline
us to believe them mere results of some secret process going on in
our organs of taste, which is too subtle for us to trace. A simple
experiment will serve to set this in a clearer light. A solution of
the salt called by chemists _nitrate of silver_, and another of the
_hyposulphite of soda_, have each of them separately, when taken into
the mouth, a disgustingly bitter taste; but if they be mixed, or if
one be tasted before the mouth is thoroughly cleared of the other,
the sensible impression is that of intense sweetness. Again, the salt
called _tungstate of soda_ when first tasted is sweet, but speedily
changes to an intense and pure bitter, like quassia.[29]

(77.) How far we may ever be enabled to attain a knowledge of the
ultimate and inward processes of nature in the production of phenomena,
we have no means of knowing; but, to judge from the degree of obscurity
which hangs about the only case in which we feel within ourselves
a _direct_ power to produce any one, there seems no great hope of
penetrating so far. The case alluded to is the production of motion by
the exertion of force. We are conscious of a power to move our limbs,
and by their intervention other bodies; and that this effect is the
result of a certain inexplicable process which we are aware of, but
can no way describe in words, by which we exert _force_. And even when
such exertion produces no visible effect, (as when we press our two
hands violently together, so as just to oppose each other’s effort,) we
still perceive, by the fatigue and exhaustion, and by the impossibility
of maintaining the effort long, that something is going on within us,
of which the mind is the agent, and the will the determining cause.
This impression which we receive of the nature of force, from our own
effort and our sense of fatigue, is quite different from that which
we obtain of it from seeing the effect of force exerted by others in
producing _motion_. Were there no such thing as motion, had we been
from infancy shut up in a dark dungeon, and every limb encrusted with
plaster, this internal consciousness would give us a complete idea
of _force_; but when set at liberty, habit alone would enable us to
recognize its exertion by its _signal_, motion, and _that_ only by
finding that the same action of the mind which in our confined state
enables us to fatigue and exhaust ourselves by the tension of our
muscles, puts it in our power, when at liberty, to move ourselves and
other bodies. But how obscure is our knowledge of the process going on
within us in the exercise of this important privilege, in virtue of
which alone we act as direct _causes_, we may judge from this, that
when we put any limb in motion, the seat of the exertion seems to us to
be _in_ the limb, whereas it is demonstrably no such thing, but either
in the brain or in the spinal marrow; the proof of which is, that if a
little fibre, called a nerve, which forms a communication between the
limb and the brain, or spine, be divided in any part of its course,
however we may make the effort, the limb will not move.

(78.) This one instance of the obscurity which hangs about the only act
of direct _causation_ of which we have an immediate consciousness, will
suffice to show how little prospect there is that, in our investigation
of nature, we shall ever be able to arrive at a knowledge of ultimate
causes, and will teach us to limit our views to that of _laws_, and
to the analysis of complex phenomena by which they are resolved into
simpler ones, which, appearing to us incapable of further analysis, we
must consent to regard as causes. Nor let any one complain of this as a
limitation of his faculties. We have here “ample room and verge enough”
for the full exercise of all the powers we possess; and, besides, it
does so happen, that we are actually able to trace up a very large
portion of the phenomena of the universe to this one _cause_, viz. the
exertion of mechanical _force_; indeed, so large a portion, that it has
been made a matter of speculation whether this is not the only one that
is capable of acting on material beings.

(79.) What we mean by the analysis of complex phenomena into simpler
ones, will best be understood by an instance. Let us, therefore,
take the phenomenon of sound, and, by considering the various cases
in which sounds of all kinds are produced, we shall find that they
all agree in these points:--1st, The excitement of a motion in the
sounding body. 2dly, The communication of this motion to the air or
other intermedium which is interposed between the sounding body and our
ears. 3dly, The propagation of such motion from particle to particle
of such intermedium in due succession. 4thly, Its communication, from
the particles of the intermedium adjacent to the ear, to the ear
itself. 5thly, Its conveyance in the ear, by a certain mechanism, to
the auditory nerves. 6thly, The excitement of sensation. Now, in this
analysis, we perceive that two principal matters must be understood,
before we can have a true and complete knowledge of sound:--1st,
The excitement and propagation of motion. 2dly, The production of
sensation. These, then, are two other phenomena, of a simpler, or, it
would be more correct to say, of a more general or elementary order,
into which the complex phenomenon of sound resolves itself. But again,
if we consider the communication of motion from body to body, or from
one part to another of the same, we shall perceive that it is again
resolvable into several other phenomena. 1st, The original setting in
motion of a material body, or any part of one. 2dly, The behaviour of
a particle set in motion, when it meets another lying in its way, or
is otherwise impeded or influenced by its connection with surrounding
particles. 3dly, The behaviour of the particles so impeding or
influencing it under such circumstances; besides which, the last two
point out another phenomenon, which it is necessary also to consider,
viz. the phenomenon of the connection of the parts of material bodies
in masses, by which they form aggregates, and are enabled to influence
each other’s motions.

(80.) Thus, then, we see that an analysis of the phenomenon of sound
leads to the enquiry, 1st, of two _causes_, viz. the cause of motion,
and the cause of sensation, these being phenomena which (at least as
human knowledge stands at present) we are unable to analyse further;
and, therefore, we set them down as simple, elementary, and referable,
for any thing we can see to the contrary, to the immediate action of
their causes. 2dly, Of several questions relating to the connection
between the motion of material bodies and its cause, such as, _What
will happen_ when a moving body is surrounded on all sides by others
not in motion? _What will happen_ when a body not in motion is advanced
upon by a moving one? It is evident that the answers to such questions
as these can be no other than _laws of motion_, in the sense we have
above attributed to laws of nature, viz. a statement in words of what
will happen in such and such proposed general contingencies. Lastly,
we are led, by pursuing the analysis, and considering the phenomenon
of the aggregation of the parts of material bodies, and the way in
which they influence each other, to two other general phenomena, viz.,
the cohesion and elasticity of matter; and these we have no means
of analysing further, and must, therefore, regard them (till we see
reasons to the contrary) as _ultimate phenomena_, and referable to the
direct action of causes, viz. an attractive and a repulsive _force_.

(81.) Of force, as counterbalanced by opposing force, we have, as
already said, an internal consciousness; and though it may seem strange
to us that matter should be capable of exerting on matter the same kind
of effort, which, judging alone from this consciousness, we might be
led to regard as a mental one; yet we cannot refuse the direct evidence
of our senses, which shows us that when we keep a spring stretched with
one hand, we feel our effort opposed exactly in the same way as if we
had ourselves opposed it with the other hand, or as it would be by
that of another person. The enquiry, therefore, into the aggregation
of matter resolves itself into the general question, What will be the
behaviour of material particles under the mutual action of opposing
forces capable of counterbalancing each other? and the answer to
this question can be no other than the announcement of the _law_ of
equilibrium, whatever law that may be.

(82.) With regard to the cause of sensation, it must be regarded as
much more obscure than that of motion, inasmuch as we have no conscious
knowledge of it, _i. e._ we have no power, by any act of our minds
and will, to call up a sensation. It is true, we are not destitute
of an approach to it, since, by an effort of memory and imagination,
we can produce in our minds an impression, or idea, of a sensation
which, in peculiar cases, may even approach in vividness to actual
reality. In dreams, too, and, in some cases of disordered nerves, we
have sensations without objects. But if force, as a cause of motion,
is obscure to us, even while we are in the act of exercising it, how
much more so is this other cause, whose exercise we can only imitate
imperfectly by any voluntary act, and of whose purely internal action
we are only fully conscious when in a state that incapacitates us from
reasoning, and almost from observation!

(83.) Dismissing, then, as beyond our reach, the enquiry into causes,
we must be content at present to concentrate our attention on the laws
which prevail among phenomena, and which seem to be their immediate
results. From the instance we have just given, we may perceive that
every enquiry into the intimate nature of a complex phenomenon
branches out into as many different and distinct enquiries as there
are simple or elementary phenomena into which it may be analysed; and
that, therefore, it would greatly assist us in our study of nature, if
we could, by any means, ascertain what _are_ the ultimate phenomena
into which all the composite ones presented by it may be resolved.
There is, however, clearly no way by which this can be ascertained _à
priori_. We must go to nature itself, and be guided by the same kind
of rule as the chemist in his analysis, who accounts every ingredient
an _element_ till it can be decompounded and resolved into others. So,
in natural philosophy, we must account every phenomenon an elementary
or simple one till we can analyse it, and show that it is the result
of others, which in their turn become elementary. Thus, in a modified
and relative sense, we may still continue to speak of causes, not
intending thereby those ultimate principles of action on whose exertion
the whole frame of nature depends, but of those proximate links which
connect phenomena with others of a simpler, higher, and more general or
elementary kind. For example: we may regard the vibration of a musical
string as the proximate cause of the sound it yields, receiving it,
so far, as an ultimate fact, and waving or deferring enquiry into the
cause of vibrations, which is of a higher and more general nature.

(84.) Moreover, as in chemistry we are sometimes compelled to
acknowledge the existence of elements different from those already
identified and known, though we cannot insulate them, and to perceive
that substances have the characters of compounds, and must therefore
be susceptible of analysis, though we do not see how it is to be set
about; so, in physics, we may perceive the complexity of a phenomenon,
without being able to perform its analysis. For example: in magnetism,
the agency of electricity is clearly made out, and they are shown to
stand to one another in the relation of effect and cause. But the
analysis of magnetism, in its relation to particular metals, is not
yet quite satisfactorily performed; and we are compelled to admit
the existence of some cause, whether proximate or ultimate, whose
presence in different metals, or in different states of the same metal,
determines that peculiar electric condition which constitutes permanent
magnetism. Cases like these, of all which science presents, offer the
highest interest. They excite enquiry, like the near approach to the
solution of an enigma; they show us that there is light, could only a
certain veil be drawn aside.

(85.) In pursuing the analysis of any phenomenon, the moment we find
ourselves stopped by one of which we perceive no analysis, and which,
therefore, we are forced to refer (at least provisionally) to the
class of ultimate facts, and to regard as elementary, the study of
that phenomenon and of its laws becomes a separate branch of science.
If we encounter the same elementary phenomenon in the analysis of
several composite ones, it becomes still more interesting, and assumes
additional importance; while at the same time we acquire information
respecting the phenomenon itself, by observing those with which it
is habitually associated, that may help us at length to its analysis.
It is thus that sciences increase, and acquire a mutual relation and
dependency. It is thus, too, that we are at length enabled to trace
parallels and analogies between great branches of science themselves,
which at length terminate in a perception of their dependence on some
common phenomenon of a more general and elementary nature than that
which form the subject of either separately. It was thus, for example,
that, previous to Oërsted’s great discovery of electro-magnetism,
a general resemblance between the two sciences of electricity and
magnetism was recognised, and many of the chief phenomena in each were
ascertained to have their parallels, _mutatis mutandis_, in the other.
It was thus, too, that an analogy subsisting between sound and light
has been gradually traced into a closeness of agreement, which can
hardly leave any reasonable doubt of their ultimate coincidence in one
common phenomenon, the vibratory motion of an elastic medium. If it be
allowed to pursue our illustration from chemistry, and to ground its
application not on what has been, but on what may one day be, done,
it is thus that the general family resemblance between certain groups
of bodies, now regarded as elementary, (as nickel and cobalt, for
instance, chlorine, iode, and brome,) will, perhaps, lead us hereafter
to perceive relations between them of a more intimate kind than we can
at present trace.

(86.) On those phenomena which are most frequently encountered in
an analysis of nature and which most decidedly resist further
decomposition, it is evident that the greatest pains and attention
ought to be bestowed, not only because they furnish a key to the
greatest number of enquiries, and serve to group and classify together
the greatest range of phenomena, but by reason of their higher nature,
and because it is in these that we must look for the direct action of
causes, and the most extensive and general enunciation of the laws of
nature. These, once discovered, place in our power the explanation of
all particular facts, and become grounds of reasoning, independent of
particular trial: thus playing the same part in natural philosophy
that axioms do in geometry; containing, in a refined and condensed
state, and as it were in a quintessence, all that our reason has
occasion to draw from experience to enable it to follow out the truths
of physics by the mere application of logical argument. Indeed, the
axioms of geometry themselves may be regarded as in some sort an appeal
to experience, not corporeal, but mental. When we say, the whole is
greater than its part, we announce a general fact, which rests, it
is true, on our ideas of whole and part; but, in abstracting these
notions, we begin by considering them as subsisting in space, and time,
and body, and again, in linear, and superficial, and solid space.
Again, when we say, the equals of equals are equal, we mentally make
comparisons, in equal spaces, equal times, &c.; so that these axioms,
however self-evident, are still general propositions so far of the
inductive kind, that, independently of experience, they would not
present themselves to the mind.

The only difference between these and axioms obtained from extensive
induction is this, that, in raising the axioms of geometry, the
instances offer themselves spontaneously, and without the trouble of
search, and are few and simple; in raising those of nature, they are
infinitely numerous, complicated, and remote; so that the most diligent
research and the utmost acuteness are required to unravel their web,
and place their meaning in evidence.

(87.) By far the most general phenomenon with which we are acquainted,
and that which occurs most constantly, in every enquiry into which we
enter, is motion, and its communication. Dynamics, then, or the science
of force and motion, is thus placed at the head of all the sciences;
and, happily for human knowledge, it is one in which the highest
certainty is attainable, a certainty no way inferior to mathematical
demonstration. As its axioms are few, simple, and in the highest degree
distinct and definite, so they have at the same time an immediate
relation to geometrical quantity, space, time, and direction, and
thus accommodate themselves with remarkable facility to geometrical
reasoning. Accordingly, their consequences may be pursued, by arguments
purely mathematical, to any extent, insomuch that the limit of our
knowledge of dynamics is determined only by that of pure mathematics,
which is the case in no other branch of physical science.

(88.) But, it will now be asked, how we are to proceed to analyse a
composite phenomenon into simpler ones, and whether any general rules
can be given for this important process? We answer, None; any more
than (to pursue the illustration we have already had recourse to)
general rules can be laid down by the chemist for the analysis of
substances of which all the ingredients are unknown. Such rules, could
they be discovered, would include the whole of natural science; but
we are very far, indeed, from being able to propound them. However,
we are to recollect that the analysis of phenomena, philosophically
speaking, is principally useful, as it enables us to recognize, and
mark for special investigation, those which appear to us simple; to
set methodically about determining their laws, and thus to facilitate
the work of raising up general axioms, or forms of words, which shall
include the whole of them; which shall, as it were, transplant them
out of the external into the intellectual world, render them creatures
of pure thought, and enable us to reason them out _à priori_. And what
renders the power of doing this so eminently desirable is, that, in
thus reasoning back from generals to particulars, the propositions
at which we arrive apply to an immense multitude of combinations and
cases, which were never individually contemplated in the mental process
by which our axioms were first discovered; and that, consequently, when
our reasonings are pushed to the utmost limit of particularity, their
results appear in the form of _individual facts_, of which we might
have had no knowledge from immediate experience; and thus we are not
only furnished with the explanation of all known facts, but with the
actual discovery of such as were before unknown. A remarkable example
of this has already been mentioned in Fresnel’s _à priori_ discovery
of the extraordinary refraction of both rays in a doubly refracting
medium. To give another example:--The law of gravitation is a physical
axiom of a very high and universal kind, and has been raised by a
succession of inductions and abstractions drawn from the observation
of numerous facts and subordinate laws in the planetary system. When
this law is taken for granted, and laid down as a basis of reasoning,
and applied to the actual condition of our own planet, one of the
consequences to which it leads is, that the earth, instead of being an
exact sphere, must be compressed or flattened in the direction of its
polar diameter, the one diameter being about thirty miles shorter than
the other; and this conclusion, deduced at first by mere reasoning, has
been since found to be true in fact. All astronomical predictions are
examples of the same thing.

(89.) In the important business of raising these axioms of nature, we
are not, as in the analysis of phenomena, left wholly without a guide.
The nature of abstract or general reasoning points out in a great
measure the course we must pursue. A law of nature, being the statement
of what will happen in certain general contingencies, may be regarded
as the announcement, in the same words, of a whole group or class of
phenomena. Whenever, therefore, we perceive that two or more phenomena
agree in so many or so remarkable points, as to lead us to regard
them as forming a class or group, if we lay out of consideration, or
_abstract_, all the circumstances in which they disagree, and retain in
our minds those only in which they agree, and then, under this kind of
mental convention, frame a definition or statement of one of them, in
such words that it shall apply equally to them all, such statement will
appear in the form of a general proposition, having so far at least the
character of a law of nature.

(90.) For example: a great number of transparent substances, when
exposed, in a certain particular manner, to a beam of light which has
been prepared by undergoing certain reflexions or refractions, (and has
thereby acquired peculiar properties, and is said to be “_polarized_,”)
exhibit very vivid and beautiful colours, disposed in streaks, bands,
&c. of great regularity, which seem to arise within the substance, and
which, from a certain regular succession observed in their appearance,
are called “periodical colours.” Among the substances which exhibit
these periodical colours occur a great variety of transparent solids,
but no fluids and no opake solids. Here, then, there seems to be
sufficient community of nature to enable us to use a general term, and
to state the proposition as a law, viz. _transparent solids_ exhibit
periodical colours by exposure to polarized light. However, this,
though true of many, does not apply to _all_ transparent solids, and
therefore we cannot state it as a general truth or law of nature in
this form; although the reverse proposition, that all solids which
exhibit such colours in such circumstances are _transparent_, would
be correct and general. It becomes necessary, then, to make a list of
those to which it does apply; and thus a great number of substances of
all kinds become grouped together, in a class linked by this common
property. If we examine the individuals of this group, we find among
them the utmost variety of colour, texture, weight, hardness, form and
composition; so that, in these respects, we seem to have fallen upon
an assemblage of contraries. But when we come to examine them closely,
in all their properties, we find they have all one point of agreement,
in the property of double refraction, (see page 30.) and therefore we
may describe them all truly as _doubly refracting substances_. We may,
therefore, state the fact in the form, “Doubly refracting substances
exhibit periodical colours by exposure to polarized light;” and in
this form it is found, on further examination, to be true, not only
for those particular instances which we had in view when we first
propounded it, but in all cases which have since occurred on further
enquiry, without a single exception; so that the proposition is
general, and entitled to be regarded as a law of nature.

(91.) We may therefore regard a law of nature either, 1st, as a general
proposition, announcing, in abstract terms, a whole group of particular
facts relating to the behaviour of natural agents in proposed
circumstances; or, 2dly, as a proposition announcing that a whole
class of individuals agreeing in one character agree also in another.
For example: in the case before us, the law arrived at includes, in
its general announcement, among others, the particular facts, that
rock crystal and saltpetre exhibit periodical colours; for these are
both of them doubly refracting substances. Or, it may be regarded as
announcing a relation between the two phenomena of double refraction,
and the exhibition of periodical colours; which in the actual case is
one of the most important, viz. the relation of _constant association_,
inasmuch as it asserts that in whatever individual the one character is
found, the other will invariably be found also.

(92.) These two lights, in which the announcement of a general law may
be regarded, though at bottom they come to the same thing, yet differ
widely in their influence on our minds. The former exhibits a law as
little more than a kind of artificial memory; but in the latter it
becomes a step in philosophical investigation, leading directly to
the consideration of a proximate, if not an ultimate, cause; inasmuch
as, whenever two phenomena are observed to be invariably connected
together, we conclude them to be related to each other, either as cause
and effect, or as common effects of a single cause.

(93.) There is still another light in which we may regard a law of
the kind in question, viz. as a proposition asserting the mutual
connection, or in some cases the entire identity, of two classes of
individuals (whether individual objects or individual facts); and this
is, perhaps, the simplest and most instructive way in which it can be
conceived, and that which furnishes the readiest handle to further
generalization in the raising of yet higher axioms. For example: in
the case above mentioned, if observation had enabled us to establish
the existence of a class of bodies possessing the property of double
refraction, and observations of another kind had, independently of the
former, led as to recognize a class possessing that of the exhibition
of periodical colours in polarized light, a mere comparison of lists
would at once demonstrate the identity of the two classes, or enable us
to ascertain whether one was or was not included in the other.

(94.) It is thus we perceive the high importance in physical science of
just and accurate classifications of particular facts, or individual
objects, under general well considered heads or points of agreement
(for which there are none better adapted than the simple phenomena
themselves into which they can be analysed in the first instance); for
by so doing each of such phenomena, or heads of classification, becomes
not a particular but a general fact; and when we have amassed a great
store of such _general facts_, they become the objects of another and
higher species of classification, and are themselves included in laws
which, as they dispose of groups, not individuals, have a far superior
degree of generality, till at length, by continuing the process, we
arrive at _axioms_ of the highest degree of generality of which science
is capable.

(95.) This process is what we mean by induction; and, from what
has been said, it appears that induction may be carried on in two
different ways,--either by the simple juxta-position and comparison of
ascertained classes, and marking their agreements and disagreements;
or by considering the individuals of a class, and casting about, as
it were to find in what particular they all agree, besides that which
serves as their principle of classification. Either of these methods
may be put in practice as one or the other may afford facilities in
any case; but it will naturally happen that, where facts are numerous,
well observed, and methodically arranged, the former will be more
applicable than in the contrary case: the one is better adapted to the
maturity, the other to the infancy, of science: the one employs, as an
engine, the division of labour; the other mainly relies on individual
penetration, and requires a union of many branches of knowledge in one
person.



CHAP. III.

OF THE STATE OF PHYSICAL SCIENCE IN GENERAL, PREVIOUS TO THE AGE OF
GALILEO AND BACON.


(96.) It is to our immortal countryman Bacon that we owe the broad
announcement of this grand and fertile principle; and the developement
of the idea, that the whole of natural philosophy consists entirely
of a series of inductive generalizations, commencing with the most
circumstantially stated particulars, and carried up to universal laws,
or axioms, which comprehend in their statements every subordinate
degree of generality, and of a corresponding series of inverted
reasoning from generals to particulars, by which these axioms are
traced back into their remotest consequences, and all particular
propositions deduced from them; as well those by whose immediate
consideration we rose to their discovery, as those of which we had
no previous knowledge. In the course of this descent to particulars,
we must of necessity encounter all those facts on which the arts and
works that tend to the accommodation of human life depend, and acquire
thereby the command of an unlimited practice, and a disposal of the
powers of nature co-extensive with those powers themselves. A noble
promise, indeed, and one which ought, surely, to animate us to the
highest exertion of our faculties; especially since we have already
such convincing proof that it is neither vain nor rash, but, on the
contrary, has been, and continues to be, fulfilled, with a promptness
and liberality which even its illustrious author in his most sanguine
mood would have hardly ventured to anticipate.

(97.) Previous to the publication of the Novum Organum of Bacon,
natural philosophy, in any legitimate and extensive sense of the word,
could hardly be said to exist. Among the Greek philosophers, of whose
attainments in science alone, in the earlier ages of the world, we
have any positive knowledge, and that but a very limited one, we are
struck with the remarkable contrast between their powers of acute and
subtle disputation, their extraordinary success in abstract reasoning,
and their intimate familiarity with subjects purely intellectual,
on the one hand; and, on the other, with their loose and careless
consideration of external nature, their grossly illogical deductions of
principles of sweeping generality from few and ill-observed facts, in
some cases; and their reckless assumption of abstract principles having
no foundation but in their own imaginations, in others; mere forms of
words, with nothing corresponding to them in nature, from which, as
from mathematical definitions, postulates, and axioms, they imagined
that all phenomena could be derived, all the laws of nature deduced.
Thus, for instance, having settled it in their own minds, that a
circle is the most perfect of figures, they concluded, of course, that
the movements of the heavenly bodies must all be performed in exact
circles, and with uniform motions; and when the plainest observation
demonstrated the contrary, instead of doubting the principle, they saw
no better way of getting out of the difficulty than by having recourse
to endless combinations of circular motions to preserve their ideal
perfection.

(98.) Undoubtedly among the Greek philosophers were many men of
transcendent talents and virtues, the ornaments of their species,
and justly entitled to the veneration of all posterity; but regarded
as a body they can hardly be considered otherwise than as a knot of
disputatious candidates for popular favour, too busy in maintaining
their ascendency over their followers and admirers, by an ostentatious
display of superior knowledge, to have the leisure (had they always the
inclination) to base their pretensions on a deep and sure foundation,
and yet too sensible of the disgrace and inconvenience of failure,
not to defend their dogmas, however shallow, when once promulgated,
against their keen and sagacious opponents, by every art of sophism
or appeal to passion. Hence the crudities and chimerical views with
which their systems of philosophy, both natural and moral, were
overloaded; their endless disputes about verbal subtleties, and, last
and worst, the proud assumption with which they sheltered ignorance
and indolence under the screen of unintelligible jargon or dogmatical
assertion. Perhaps, however, this character applies rather to the
later than to the earlier of the Greek philosophers. The spirit of
rational enquiry into nature seems, if we can judge from the uncertain
and often contradictory notices handed down to us of their tenets, to
have been far more alive, and less warped by this vain and arrogant
turn, then than at a later period. We know not now what was the
precise meaning attached by Thales to his opinion, that water was
the origin of all things; but modern geologists will not be at a loss
to conceive how an observant traveller might become impressed with
this notion, without having recourse to the mystic records of Egypt
or Chaldea. His ideas of eclipses and of the nature of the moon were
sound; and his prediction of an eclipse of the sun, in particular,
was attended with circumstances so remarkable as to have made it a
matter of important investigation to modern astronomers. Anaxagoras,
among a number of crude and imperfectly explained notions, speculated
rationally enough on the cause of the winds and of the rainbow, and
less absurdly on earthquakes than many modern geologists have done, and
appears generally to have had his attention alive to nature, and his
mind open to just reasoning on its phenomena; while Pythagoras, whether
he reasoned it out for himself, or borrowed the notion from Egypt or
India, had attained a just conception of the general disposition of
the parts of the solar system, and the place held by the earth in it;
nay, according to some accounts, had even raised his views so far as to
speculate on the attraction of the sun as the bond of its union.

(99.) But the successors of these _bonâ fide_ enquirers into nature
debased the standard of truth; and, taking advantage of the credit
justly attached to their discoveries, renounced the modest character
of learners, and erected themselves into teachers, and, to maintain
their pretensions to this character, adopted the tone of men who had
nothing further to learn. Unfortunately for true science, the national
character gave every encouragement to pretensions of this kind. That
restless craving after novelty, which distinguished the Greeks in their
civil and political relations, pursued them into their philosophy.
Whatever speculations were only ingenious and new had irresistible
charms; and the teacher who could embody a clever thought in elegant
language, or at once save his followers and himself the trouble of
thinking or reasoning, by bold assertion, was too often induced to
acquire cheaply the reputation of superior knowledge, snatch a few
superficial notions from the most ordinary and obvious facts, envelope
them in a parade of abstruse words, declare them the primary and
ultimate principles of all things, and denounce as absurd and impious
all opinions opposed to his own.

(100.) In this war of words the study of nature was neglected, and
an humble and patient enquiry after facts altogether despised, as
unworthy of the high _priori_ ground a true philosopher ought to take.
It was the radical error of the Greek philosophy to imagine that the
same method which proved so eminently successful in mathematical,
would be equally so in physical, enquiries, and that, by setting out
from a few simple and almost self-evident notions, or _axioms_, every
thing could be reasoned out. Accordingly, we find them constantly
straining their invention to discover these principles, which were to
prove so pregnant. One makes _fire_ the essential matter and origin
of the universe; another, _air_; a third, discovers the key to every
difficulty, and the explanation of all phenomena, in the “το απειρον”
or infinitude of things; a fourth, in the το ὁν and the το μη ὁν, that
is to say, in entity and nonentity;--till at length an authority,
which was destined to command opinions for nearly two thousand years,
settled this important point, by deciding, that _matter_, _form_, and
_privation_, were to be considered the principles of all things.

(101.) It were to do injustice to Aristotle, however, to judge of him
by _such_ a sample of his philosophy. He, at least, saw the necessity
of having recourse to nature for something like principles of physical
science; and, as an observer, a collector and recorder of facts and
phenomena, stood without an equal in his age. It was the fault of that
age, and of the perverse and flimsy style of verbal disputation which
had infected all learning, rather than his own, that he allowed himself
to be contented with vague and loose notions drawn from general and
vulgar observation, in place of seeking carefully, in well arranged
and thoroughly considered instances, for the true laws of nature. His
voluminous works, on every department of human knowledge existing in
his time, have nearly all perished. From his work on animals, which
has descended to us, we are, however, enabled to appreciate his powers
of observation; and a parallel drawn by an eminent Oxford professor
between his classifications and those of the most illustrious of
living naturalists, shows him to have attained a view of animated
nature in a remarkable degree comprehensive, and which contrasts
strikingly with the confusion, vagueness, and assumption of his
physical opinions and dogmas. In these it is easy to recognize a mind
not at home, and an impression of the necessity of saying something
learned and systematic, without knowing what to say. Thus he divides
motions into natural and unnatural; the natural motion of fire and
light bodies being upwards, those of heavy downwards, each seeking its
kindred nature in the heavens and the earth. Thus, too, the immediate
impressions made on us by external objects, such as hardness, colour,
heat, &c. are referred at once, in the Aristotelian philosophy, to
occult qualities, in virtue of which they are as they are, and beyond
which it is useless to enquire.[30] Of course there will occur a limit
beyond which it _is_ useless for merely human faculties to enquire; but
where that limit is placed, experience alone can teach us; and at least
to assert that we _have_ attained it, is now universally recognized as
the sure criterion of dogmatism.

(102.) In the early ages of the church the writings of Aristotle were
condemned, as allowing too much to reason and sense; and even so late
as the twelfth century they were sought out and burned, and their
readers excommunicated. By degrees, however, the extreme injustice
of this impeachment of their character was acknowledged: they became
the favourite study of the schoolmen, and furnished the keenest
weapons of their controversy, being appealed to in all disputes as of
sovereign authority; so that the slightest dissent from any opinion
of the “great master,” however absurd or unintelligible, was at once
drowned by clamour, or silenced by the still more effectual argument of
bitter persecution. If the logic of that gloomy period could be justly
described as “the art of talking unintelligibly on matters of which we
are ignorant,” its physics might, with equal truth, be summed up in a
deliberate preference of ignorance to knowledge, in matters of every
day’s experience and use.

(103.) In “this opake of nature and of soul,” the perverse activity of
the alchemists from time to time struck out a doubtful spark[31]; and
our illustrious countryman, Roger Bacon, shone out at the obscurest
moment, like an early star predicting dawn. It was not, however, till
the sixteenth century that the light of nature began to break forth
with a regular and progressive increase. The vaunts of Paracelsus
of the power of his chemical remedies and elixirs, and his open
condemnation of the ancient pharmacy, backed as they were by many
surprising cures, convinced all rational physicians that chemistry
could furnish many excellent remedies, unknown till that time[32], and
a number of valuable experiments began to be made by physicians and
chemists, desirous of discovering and describing new chemical remedies.
The chemical and metallurgic arts, exercised by persons empirically
acquainted with their secrets, began to be seriously studied with a
view to the acquisition of rational and useful knowledge, and regular
treatises on branches of natural science at length to appear. George
Agricola, in particular, devoted himself with ardour to the study
of mineralogy and metallurgy in the mining districts of Bohemia and
Schemnitz, and published copious and methodical accounts of all
the facts within his knowledge: and our countryman, Dr. Gilbert of
Colchester, in 1590, published a treatise on magnetism, full of
valuable facts and experiments, ingeniously reasoned on; and he
likewise extended his enquiries to a variety of other subjects, in
particular to electricity.

(104.) But, as the decisive mark of a great commencing change in the
direction of the human faculties, astronomy, the only science in which
the ancients had made any real progress, and ascended to any thing like
large and general conceptions, began once more to be studied in the
best spirit of a candid philosophy; and the Copernican or Pythagorean
system arose or revived, and rapidly gained advocates. Galileo at
length appeared, and openly attacked and refuted the Aristotelian
dogmas respecting motion, by direct appeal to the evidence of sense,
and by experiments of the most convincing kind. The persecutions
which such a step drew upon him, the record of his perseverance and
sufferings, and the ultimate triumph of his opinions and reasonings,
have been too lately and too well related[33] to require repetition
here.

(105.) By the discoveries of Copernicus, Kepler, and Galileo, the
errors of the Aristotelian philosophy were effectually overturned on a
plain appeal to the facts of nature; but it remained to show on broad
and general principles, how and why Aristotle was in the wrong; to set
in evidence the peculiar weakness of his method of philosophizing,
and to substitute in its place a stronger and better. This important
task was executed by Francis Bacon, Lord Verulam, who will, therefore,
justly be looked upon in all future ages as the great reformer of
philosophy, though his own actual contributions to the stock of
physical truths were small, and his ideas of particular points strongly
tinctured with mistakes and errors, which were the fault rather of the
general want of physical information of the age than of any narrowness
of view on his own part; and of this he was fully aware. It has been
attempted by some to lessen the merit of this great achievement, by
showing that the inductive method had been practised in many instances,
both ancient and modern, by the mere instinct of mankind; but it is not
the introduction of inductive reasoning, as a new and hitherto untried
process, which characterizes the Baconian philosophy, but his keen
perception, and his broad and spirit-stirring, almost enthusiastic,
announcement of its paramount importance, as the alpha and omega of
science, as the grand and only chain for the linking together of
physical truths, and the eventual key to every discovery and every
application. Those who would deny him his just glory on such grounds
would refuse to Jenner or to Howard their civic crowns, because a few
farmers in a remote province had, time out of mind, been acquainted
with vaccination, or philanthropists, in all ages, had occasionally
visited the prisoner in his dungeon.

(106.) An immense impulse was now given to science, and it seemed as
if the genius of mankind, long pent up, had at length rushed eagerly
upon Nature, and commenced, with one accord, the great work of
turning up her hitherto unbroken soil, and exposing the treasures
so long concealed. A general sense now prevailed of the poverty and
insufficiency of existing knowledge in _matters of fact_; and, as
information flowed fast in, an era of excitement and wonder commenced,
to which the annals of mankind had furnished nothing similar. It
seemed, too, as if Nature herself seconded the impulse; and, while
she supplied new and extraordinary aids to those senses which were
henceforth to be exercised in her investigation,--while the telescope
and the microscope laid open _the infinite_ in both directions,--as
if to call attention to her wonders, and signalize the epoch, she
displayed the rarest, the most splendid and mysterious, of all
astronomical phenomena, the appearance and subsequent total extinction
of a new and brilliant fixed star twice within the lifetime of Galileo
himself.[34]

(107.) The immediate followers of Bacon and Galileo ransacked all
nature for new and surprising facts, with something of that craving
for the marvellous, which might be regarded as a remnant of the age of
alchemy and natural magic, but which, under proper regulation, is a
most powerful and useful stimulus to experimental enquiry. Boyle, in
particular, seemed animated by an enthusiasm of ardour, which hurried
him from subject to subject, and from experiment to experiment,
without a moment’s intermission, and with a sort of undistinguishing
appetite; while Hooke (the great contemporary, and almost the worthy
rival, of Newton) carried a keener eye of scrutinizing reason into a
range of research even yet more extensive. As facts multiplied, leading
phenomena became prominent, laws began to emerge, and generalizations
to commence; and so rapid was the career of discovery, so signal the
triumph of the inductive philosophy, that a single generation and the
efforts of a single mind sufficed for the establishment of the system
of the universe, on a basis never after to be shaken.

(108.) We shall now endeavour to enumerate and explain in detail the
principal steps by which legitimate and extensive inductions are
arrived at, and the processes by which the mind, in the investigation
of natural laws, purges itself by successive degrees of the
superfluities and incumbrances which hang about particulars, and
obscure the perception of their points of resemblance and connection.
We shall state the helps which may be afforded us, in a work of so
much thought and labour, by a methodical course of proceeding, and
by a careful notice of those means which have at any time been found
successful, with a view to their better understanding and adaptation
to other cases: a species of mental induction of no mean utility and
extent in itself; inasmuch as by pursuing it alone we can attain a more
intimate knowledge than we actually possess of the laws which regulate
our discovery of truth, and of the rules, so far as they extend, to
which invention is reducible. In doing this, we shall commence at the
beginning, with experience itself, considered as the accumulation of
the knowledge of individual objects and facts.



CHAP. IV.

OF THE OBSERVATION OF FACTS AND THE COLLECTION OF INSTANCES.


(109.) Nature offers us two sorts of subjects of contemplation in the
external world,--objects, and their mutual actions. But, after what
has been said on the subject of sensation, the reader will be at no
loss to perceive that we know nothing of the objects themselves which
compose the universe, except through the medium of the impressions they
excite in us, which impressions are the results of certain actions and
processes in which sensible objects and the material parts of ourselves
are directly concerned. Thus, our observation of external nature is
limited to the mutual action of material objects on one another; and
to facts, that is, the associations of phenomena or appearances. We
gain no information by perceiving merely that an object is black; but
if we also perceive it to be fluid, we at least acquire the knowledge
that blackness is not incompatible with fluidity, and have thus made
a step, however trifling, to a knowledge of the more intimate nature
of these two qualities. Whenever, therefore, we would either analyse
a phenomenon into simpler ones, or ascertain what is the course or
law of nature under any proposed general contingency, the first step
is to accumulate a sufficient quantity of well ascertained facts or
recorded instances, bearing on the point in question. Common sense
dictates this, as affording us the means of examining the same subject
in several points of view; and it would also dictate, that the more
different these collected facts are in all other circumstances but that
which forms the subject of enquiry, the better; because they are then
in some sort brought into contrast with one another in their points of
disagreement, and thus tend to render those in which they agree more
prominent and striking.

(110.) The only facts which can ever become useful as grounds of
physical enquiry are those which happen uniformly and invariably
under the same circumstances. This is evident: for if they have
not this character they cannot be included in laws; they want that
universality which fits them to enter as elementary particles into the
constitution of those universal axioms which we aim at discovering.
If one and the same result does not constantly happen under a given
combination of circumstances, apparently the same, one of two things
must be supposed,--caprice (_i. e._ the arbitrary intervention of
mental agency), or differences in the circumstances themselves,
really existing, but unobserved by us. In either case, though we may
record such facts as curiosities, or as awaiting explanation when
the difference of circumstances shall be understood, we can make
no use of them in scientific enquiry. Hence, whenever we notice a
remarkable effect of any kind, our first question ought to be, Can it
be reproduced? What are the circumstances under which it has happened?
And will it _always_ happen again if those circumstances, so far as we
have been able to collect them, co-exist?

(111.) The circumstances, then, which accompany any observed fact, are
main features in its observation, at least until it is ascertained
by sufficient experience what circumstances have nothing to do with
it, and might therefore have been left unobserved without sacrificing
_the fact_. In observing and recording a fact, therefore, altogether
new, we ought not to omit any circumstance capable of being noted,
lest some one of the omitted circumstances should be essentially
connected with the fact, and its omission should, therefore, reduce
the implied statement of a _law of nature_ to the mere record of an
_historical event_. For instance, in the fall of meteoric stones,
flashes of fire are seen proceeding from a cloud, and a loud rattling
noise like thunder is heard. These circumstances, and the sudden stroke
and destruction ensuing, long caused them to be confounded with an
effect of lightning, and called thunderbolts. But one circumstance is
enough to mark the difference: the flash and sound have been perceived
occasionally to emanate from a _very small cloud_ insulated in _a clear
sky_; a combination of circumstances which never happens in a thunder
storm, but which is undoubtedly intimately connected with their real
origin.

(112.) Recorded observation consists of two distinct parts: 1st, an
exact notice of the thing observed, and of all the particulars which
may be supposed to have any natural connection with it; and, 2dly, a
true and faithful record of them. As our senses are the only inlets
by which we receive impressions of facts, we must take care, in
observing, to have them all in activity, and to let nothing escape
notice which affects any one of them. Thus, if lightning were to
strike the house we inhabit, we ought to notice what kind of light we
saw--whether a sheet of flame, a darting spark, or a broken zig-zag;
in what direction moving, to what objects adhering, its colour, its
duration, &c.; what sounds were heard--explosive, crashing, rattling,
momentary, or gradually increasing and fading, &c.; whether any smell
of fire was perceptible, and if sulphureous, metallic, or such as
would arise merely from substances scorched by the flash, &c.; whether
we felt any shock, stroke, or peculiar sensation, or experienced any
strange taste in our mouths. Then, besides detailing the effects of the
stroke, all the circumstances which might in any degree seem likely to
attract, produce, or modify it, such as the presence of conductors,
neighbouring objects, the state of the atmosphere, the barometer,
thermometer, &c., and the disposition of the clouds, should be noted;
and after all this particularity, the question _how_ the house _came
to be struck?_ might ultimately depend on the fact that a flash of
lightning twenty miles off passed at that particular moment _from
the ground to the clouds_, by an effect of what has been termed the
returning stroke.

(113.) A writer in the Edinburgh Philosophical Journal[35] states
himself to have been led into a series of investigations on the
chemical nature of a peculiar acid, by noticing, accidentally, a bitter
taste in a liquid about to be thrown away. Chemistry is full of such
incidents.

(114.) In transient phenomena, if the number of particulars be
great, and the time to observe them short, we must consult our
memory before they have had time to fade, or refresh it by placing
ourselves as nearly as possible in the same circumstances again; go
back to the spot, for instance, and try the words of our statement
by appeal to all remaining indications, &c. This is most especially
necessary where we have not observed ourselves, but only collect and
record the observations of others, particularly of illiterate or
prejudiced persons, on any rare phenomenon, such as the passing of
a great meteor,--the fall of a stone from the sky,--the shock of an
earthquake,--an extraordinary hailstorm, &c.

(115.) In all cases which admit of numeration or measurement, it is of
the utmost consequence to obtain precise numerical statements, whether
in the measure of time, space, or quantity of any kind. To omit this,
is, in the first place, to expose ourselves to illusions of sense which
may lead to the grossest errors. Thus, in alpine countries, we are
constantly deceived in heights and distances; and when we have overcome
the first impression which leads us to under-estimate them, we are then
hardly less apt to run into the opposite extreme. But it is not merely
in preserving us from exaggerated impressions that numerical precision
is desirable. It is the very soul of science; and its attainment
affords the only criterion, or at least the best, of the truth of
theories, and the correctness of experiments. Thus, it was entirely
to the omission of exact numerical determinations of quantity that the
mistakes and confusion of the Stahlian chemistry were attributable,--a
confusion which dissipated like a morning mist as soon as precision,
in this respect, came to be regarded as essential. Chemistry is in the
most pre-eminent degree a science of quantity; and to enumerate the
discoveries which have arisen in it, from the mere determination of
weights and measures, would be nearly to give a synopsis of this branch
of knowledge. We need only mention the law of definite proportions,
which fixes the composition of every body in nature in determinate
proportional weights of its ingredients.

(116.) Indeed, it is a character of all the higher laws of nature to
assume the form of precise _quantitative_ statement. Thus, the law of
gravitation, the most universal truth at which human reason has yet
arrived, expresses not merely the general fact of the mutual attraction
of all matter; not merely the vague statement that its influence
decreases as the distance increases, but the exact numerical rate at
which that decrease takes place; so that when its amount is known at
any one distance it may be calculated exactly for any other. Thus, too,
the laws of crystallography, which limit the forms assumed by natural
substances, when left to their own inherent powers of aggregation, to
precise geometrical figures, with fixed angles and proportions, have
the same essential character of strict mathematical expression, without
which no exact particular conclusions could ever be drawn from them.

(117.) But, to arrive at laws of this description, it is evident that
every step of our enquiry must be perfectly free from the slightest
degree of looseness and indecision, and carry with it the full force of
strict numerical announcement; and that, therefore, the observations
themselves on which all laws ultimately rest ought to have the same
property. None of our senses, however, gives us direct information
for the exact comparison of quantity. Number, indeed, that is to
say, integer number, is an object of sense, because we can count;
but we can neither weigh, measure, nor form any precise estimate of
fractional parts by the unassisted senses. Scarcely any man could tell
the difference between twenty pounds and the same weight increased or
diminished by a few ounces; still less could he judge of the proportion
between an ounce of gold and a hundred grains of cotton by balancing
them in his hands. To take another instance: the eye is no judge of the
proportion of different degrees of illumination, even when seen side
by side; and if an interval elapses, and circumstances change, nothing
can be more vague than its judgments. When we gaze with admiration
at the gorgeous spectacle of the golden clouds at sunset, which seem
drenched in light and glowing like flames of real fire, it is hardly
by any effort we can persuade ourselves to regard them as the very
same objects which at noonday pass unnoticed as mere white clouds
basking in the sun, only participating, from their great horizontal
distance, in the ruddy tint which luminaries acquire by shining through
a great extent of the vapours of the atmosphere, and thereby even
losing something of their light. So it is with our estimates of time,
velocity, and all other matters of quantity; they are absolutely vague,
and inadequate to form a foundation for any exact conclusion.

(118.) In this emergency we are obliged to have recourse to
instrumental aids, that is, to contrivances which shall substitute for
the vague impressions of sense the precise one of number, and reduce
all measurement to counting. As a first preliminary towards effecting
this, we fix on convenient _standards_ of weight, dimension, time,
&c., and invent contrivances for readily and correctly repeating them
as often as we please, and counting how often such a standard unit is
contained in the thing, be it weight, space, time, or angle, we wish to
measure; and if there be a fractional part over, we measure this as a
new quantity by aliquot parts of the former standard.

(119.) If every scientific enquirer observed only for his own
satisfaction, and reasoned only on his own observations, it would be
of little importance what standards he used, or what contrivances (if
only just ones) he employed for this purpose; but if it be intended
(as it is most important they should) that observations once made
should remain as records to all mankind, and to all posterity, it is
evidently of the highest consequence that all enquirers should agree on
the use of a common standard, and that this should be one not liable
to change by lapse of time. The selection and verification of such
standards, however, will easily be understood to be a matter of extreme
difficulty, if only from the mere circumstance that, to verify the
permanence of one standard, we must compare it with others, which it
is possible may be themselves inaccurate, or, at least, stand in need
of verification.

(120.) Here we can only call to our assistance the presumed permanence
of the great laws of Nature, with all experience in its favour, and the
strong impression we have of the general composure and steadiness of
every thing relating to the gigantic mass we inhabit--“the great globe
itself.” In its uniform rotation on its axis, accordingly, we find a
standard of time, which nothing has ever given us reason to regard
as subject to change, and which, compared with other periods which
the revolutions of the planets about the sun afford, has demonstrably
undergone none since the earliest history. In the dimensions of the
earth we find a natural unit of the measure of space, which possesses
in perfection every quality that can be desired; and in its attraction
combined with its rotation the researches of dynamical science have
enabled us, through the medium of the pendulum, to obtain another
invariable standard, more refined and less obvious, it is true, in
its origin, but possessing a great advantage in its capability of
ready verification, and therefore easily made to serve as a check on
the other. The former, viz. direct measurement of the dimensions of
the earth, is the origin of the _mètre_, the French unit of linear
measure; the latter, of the British yard. Theoretically speaking,
they are equally eligible; but when we consider that the _quantity
directly measured_, in the case of the mètre, is a length a great many
thousand times the final unit, and in the pendulum or yard very nearly
the unit itself, there can be no hesitation in giving the preference
as an original measure to the former, because any error committed in
the process by which that is determined becomes subdivided in the
final result; while, on the other hand, any minute error committed
in determining the length of the pendulum becomes multiplied by the
repetition of the unit in all measurements of considerable lengths
performed in yards.

(121.) The same admirable invention of the pendulum affords a means of
subdividing time to an almost unlimited nicety. A clock is nothing more
than a piece of mechanism for counting the oscillations of a pendulum;
and by that peculiar property of the pendulum, that one vibration
commences exactly where the last terminates, no part of time is lost
or gained in the juxta-position of the units so counted, so that the
precise fractional part of a day can be ascertained which each such
unit measures.

(122.) It is owing to this peculiar property by which the
_juxta-position_ of units of time and weight can be performed _without
error_, that the whole of the accuracy with which time and weight can
be multiplied and subdivided is owing.[36] The same thing cannot be
accomplished in _space_, by any method we are yet acquainted with, so
that our means of subdividing space are much inferior in precision.
The beautiful principle of repetition, invented by Borda, offers the
nearest approach to it, but cannot be said to be absolutely free from
the source of error in question. The method of “double weighing,” which
we owe to the same distinguished observer, affords an instance of the
direct comparison of two equal weights independent of almost every
source of error which can affect the comparison of one object with
another. It has been remarked by Biot, that previous to the invention
of this elegant method, instruments afforded no perfect means of
ascertaining the weight of a body.

(123.) But it is not enough to possess a standard of this abstract
kind: a real material measure must be constructed, and exact copies of
it taken. This, however, is not very difficult; the great difficulty
is to preserve it unaltered from age to age; for unless we transmit to
posterity the units of our measurements, _such as we have ourselves
used them_, we, in fact, only half bequeath to them our observations.
This is a point too much lost sight of, and it were much to be wished
that some direct provision for so important an object were made.[37]

(124.) But, it may be asked, if our measurement of quantity is thus
unavoidably liable to error, how is it possible that our observations
can possess that quality of numerical veracity which is requisite to
render them the foundation of laws, whose distinguishing perfection
consists in their strict mathematical expression? To this the reply is
twofold. 1st, that though we admit the necessary existence of numerical
error in every observation, we can always assign a limit which such
error cannot possibly exceed; and the extent of this _latitude of
error of observation_ is less in proportion to the perfection of
the instrumental means we possess, and the care bestowed on their
employment. In the greater part of modern measurements it is, in point
of fact, extremely minute, and may be still further diminished, almost
to any required extent, by repeating the measurements a great number of
times, and under a great variety of circumstances, and taking a mean of
the results, when errors of opposite kinds will, at length, compensate
each other. But, 2dly, there exists a much more fundamental reply to
this objection. In reasoning upon our observations, the existence and
possible amount of quantitative error is always to be allowed for; and
the extent to which theories may be affected by it is never to be lost
sight of. In reasoning upwards, from observations confessedly imperfect
to general laws, we must take care always to regard our conclusions
as conditional, so far as they may be affected by such unavoidable
imperfections; and when at length we shall have arrived at our highest
point, and attained to axioms which admit of general and deductive
reasoning, the question, whether they _are_ vitiated by the errors of
observation or not, will still remain to be decided, and must become
the object of subsequent verification. This point will be made the
subject of more distinct consideration hereafter, when we come to speak
of the verification of theories and the laws of probability.

(125.) With respect to our record of observations, it should be not
only circumstantial but _faithful_; by which we mean, that it should
contain all we did _observe_, and nothing else. Without any intention
of falsifying our record, we may do so unperceived by ourselves, owing
to a mixture of the views and language of an erroneous theory with
that of simple fact. Thus, for example, if, in describing the effect
of lightning, we should say, “The thunderbolt struck with violence
against the side of the house, and beat in the wall,” a fact would be
stated which we did not see, and would lead our hearers to believe that
a solid or ponderable projectile was concerned. The “strong smell of
sulphur,” which is sometimes said to accompany lightning, is a remnant
of the theory which made thunder and lightning the explosion of a kind
of aërial gunpowder, composed of sulphureous and nitrous exhalations.
There are some subjects particularly infested with this mixture of
theory in the statement of observed fact. The older chemistry was
so overborne by this mischief, as quite to confound and nullify the
descriptions of innumerable curious and laborious experiments. And in
geology, till a very recent period, it was often extremely difficult,
from this circumstance, to know what _were_ the facts observed. Thus,
Faujas de St. Fond, in his work on the volcanoes of central France,
describes with every appearance of minute precision craters existing
no where but in his own imagination. There is no greater fault (direct
falsification of fact excepted) which can be committed by an observer.

(126.) When particular branches of science have acquired that degree
of consistency and generality, which admits of an abstract statement
of laws, and legitimate deductive reasoning, the principle of the
division of labour tends to separate the province of the observer from
that of the theorist. There is no accounting for the difference of
minds or inclinations, which leads one man to observe with interest
the developements of phenomena, another to speculate on their causes;
but were it not for this happy disagreement, it may be doubted whether
the higher sciences could ever have attained even their present degree
of perfection. As laws acquire generality, the influence of individual
observations becomes less, and a higher and higher degree of
refinement in their performance, as well as a great multiplication in
their number, becomes necessary to give them importance. In astronomy,
for instance, the superior departments of theory are completely
disjoined from the routine of practical observation.

(127.) To make a perfect observer, however, either in astronomy
or in any other department of science, an extensive acquaintance
is requisite, not only with the particular science to which his
observations relate, but with every branch of knowledge which may
enable him to appretiate and neutralize the effect of extraneous
disturbing causes. Thus furnished, he will be prepared to seize on any
of those minute indications, which (such is the subtlety of nature)
often connect phenomena which seem quite remote from each other. He
will have his eyes as it were opened, that they may be struck at once
with any occurrence which, according to received theories, ought
not to happen; for these are the facts which serve as clews to new
discoveries. The deviation of the magnetic needle, by the influence
of an electrified wire, must have happened a thousand times to a
perceptible amount, under the eyes of persons engaged in galvanic
experiments, with philosophical apparatus of all kinds standing around
them; but it required the eye of a philosopher such as Oërsted to
seize the indication, refer it to its origin, and thereby connect
two great branches of science. The grand discovery of Malus of the
polarization of light by reflection originated in his casual remark of
the disappearance of one of the images of a window in the Luxembourg
palace, one evening, when strongly illuminated by the setting sun,
viewed through a doubly refracting prism.

(128.) To avail ourselves as far as possible of the advantages which
a division of labour may afford for the collection of facts, by the
industry and activity which the general diffusion of information,
in the present age, brings into exercise, is an object of great
importance. There is scarcely any well-informed person, who, if he
has but the will, has not also the power to add something essential
to the general stock of knowledge, if he will only observe regularly
and methodically some particular class of facts which may most excite
his attention, or which his situation may best enable him to study
with effect. To instance one or two subjects, which can only be
effectually improved by the united observations of great numbers widely
dispersed:--Meteorology, one of the most complicated but important
branches of science, is at the same time one in which any person
who will attend to plain rules, and bestow the necessary degree of
attention, may do effectual service. What benefits has not Geology
reaped from the activity of industrious individuals, who, setting
aside all theoretical views, have been content to exercise the useful
and highly entertaining occupation of collecting specimens from the
countries which they visit? In short, there is no branch of science
whatever in which, at least, if useful and sensible queries were
distinctly proposed, an immense mass of valuable information might not
be collected from those who, in their various lines of life, at home
or abroad, stationary or in travel, would gladly avail themselves of
opportunities of being useful. Nothing would tend better to attain
this end than the circulation of printed skeleton forms, on various
subjects, which should be so formed as, 1st, to ask distinct and
pertinent questions, admitting of short and definite answers; 2dly, To
call for exact numerical statement on all principal points; 3dly, To
point out the attendant circumstances most likely to prove influential,
and which ought to be observed; 4thly, To call for their transmission
to a common centre.



CHAP. V.

OF THE CLASSIFICATION OF NATURAL OBJECTS AND PHENOMENA, AND OF
NOMENCLATURE.


(129.) The number and variety of objects and relations which the
observation of nature brings before us are so great as to distract
the attention, unless assisted and methodized by such judicious
distribution of them in classes as shall limit our view to a few at
a time, or to groups so bound together by general resemblances that,
for the immediate purpose for which we consider them, they may be
regarded as individuals. Before we can enter into any thing which
deserves to be called a general and systematic view of nature, it is
necessary that we should possess an enumeration, if not complete, at
least of considerable extent, of her materials and combinations; and
that those which appear in any degree important should be distinguished
by names which may not only tend to fix them in our recollection,
but may constitute, as it were, nuclei or centres, about which
information may collect into masses. The imposition of a name on any
subject of contemplation, be it a material object, a phenomenon of
nature, or a group of facts and relations, looked upon in a peculiar
point of view, is an epoch in its history of great importance. It not
only enables us readily to refer to it in conversation or writing,
without circumlocution, but, what is of more consequence, it gives
it a recognized existence in our own minds, as a matter for separate
and peculiar consideration; places it on a list for examination;
and renders it a head or title, under which information of various
descriptions may be arranged; and, in consequence, fits it to perform
the office of a connecting link between all the subjects to which such
information may refer.

(130.) For these purposes, however, a temporary or provisional name,
or one adapted for common parlance, may suffice. But when a very great
multitude of objects come to be referred to one class, especially of
such as do not offer very obvious and remarkable distinctions, a more
systematic and regular nomenclature becomes necessary, in which the
names shall recall the differences as well as the resemblances between
the individuals of a class, and in which the direct relation between
the name and the object shall materially assist the solution of the
problem, “_given the one, to determine the other_.” How necessary
this may become, will be at once seen, when we consider the immense
number of individual objects, or rather species, presented by almost
every branch of science of any extent; which absolutely require to be
distinguished by names. Thus, the botanist is conversant with from
80,000 to 100,000 species of plants; the entomologist with, perhaps,
as many, of insects: the chemist has to register the properties of
combinations, by twos, threes, fours, and upwards, in various doses
of upwards of fifty different elements, all distinguished from each
other by essential differences; and of which though a great many
thousands are known, by far the greater part have never yet been
formed, although hundreds of new ones are coming to light, in perpetual
succession, as the science advances; all of which are to be named as
they arise. The objects of astronomy are, literally, as numerous as the
stars of heaven; and although not more than one or two thousand require
to be expressed by distinct names, yet the number, respecting which
particular information is required, is not less than a hundred times
that amount; and all these must be registered in lists, (so as to be
at once referred to, and so that none shall escape,) if not by actual
names, at least by some equivalent means.

(131.) Nomenclature, then, is, in itself, undoubtedly an important
part of science, as it prevents our being lost in a wilderness of
particulars, and involved in inextricable confusion. Happily, in those
great branches of science where the objects of classification are most
numerous, and the necessity for a clear and convenient nomenclature
most pressing, no very great difficulty in its establishment is felt.
The very multitude of the objects themselves affords the power of
grouping them in subordinate classes, sufficiently well defined to
admit of names, and these again into others, whose names may become
attached to, or compounded with, the former, till at length the
particular species is identified. The facility with which the botanist,
the entomologist, or the chemist, refers by name to any individual
object in his science shows what may be accomplished in this way
when characters are themselves distinct. In other branches, however,
considerable difficulty is experienced. This arises mostly where the
species to be distinguished are separated from each other chiefly by
difference in degree, of certain qualities common to all, and where the
degrees shade into each other insensibly. Perhaps such subjects can
hardly be considered ripe for systematic nomenclature; and that the
attempt to apply it ought only to be partial, embracing such groups
and parcels of individuals as agree in characters evidently natural
and generic, and leaving the remainder under trivial or provisional
denominations, till they shall be better known, and capable of being
scientifically grouped.

(132.) Indeed, nomenclature, in a systematic point of view, is as
much, perhaps more, a consequence than a cause of extended knowledge.
Any one may give an arbitrary name to a thing, merely to be able to
talk of it; but, to give a name which shall at once refer it to a
place in a system, we must know its properties; and we must _have_ a
system, large enough, and regular enough, to receive it in a place
which belongs to it, and to no other. It appears, therefore, doubtful
whether it is desirable, for the essential purposes of science, that
extreme refinement in systematic nomenclature should be insisted on.
Were science perfect, indeed, systems of classification might be
agreed on, which should assign to every object in nature a place in
some class, to which it more remarkably and pre-eminently belonged
than to any other, and under which it might acquire a name, never
afterwards subject to change. But, so long as this is not the case,
and new relations are daily discovered, we must be very cautious how
we insist strongly on the establishment and extension of classes
which have in them any thing artificial, as a basis of a rigid
nomenclature; and especially how we mistake the means for the end, and
sacrifice convenience and distinctness to a rage for arrangement. Every
nomenclature dependent on artificial classifications is necessarily
subject to fluctuations; and hardly any thing can counterbalance the
evil of disturbing well-established names, which have once acquired a
general circulation. In nature, one and the same object makes a part of
an infinite number of different systems,--an individual in an infinite
number of groups, some of greater, some of less importance, according
to the different points of view in which they may be considered. Hence,
as many different systems of nomenclature may be imagined as there can
be discovered different heads of classification, while yet it is highly
desirable that each object should be universally spoken of under one
name, _if possible_. Consequently, in all subjects where comprehensive
heads of classification do not prominently offer themselves, all
nomenclature must be a balance of difficulties, and a good, short,
_unmeaning_ name, which has once obtained a footing in usage, is
preferable to almost any other.

(133.) There is no science in which the evils resulting from a rage for
nomenclature have been felt to such an extent as in mineralogy. The
number of simple minerals actually recognised by mineralogists does not
exceed a few hundreds, yet there is scarcely one which has not four or
five names in different books. The consequence is most unhappy. No name
is suffered to endure long enough to take root; and every new writer
on this interesting science begins, as a matter of course, by making a
_tabula rasa_ of all former nomenclature, and proposing a new one in
its place. The climax has at length been put to this most inconvenient
and bewildering state of things by the appearance of a system supported
by extraordinary merit in other respects, and therefore carrying
the highest authority, in which names which had acquired universal
circulation, and had hitherto maintained their ground in the midst of
the general confusion, and even worked their way into common language,
as denotive of _species_ too definite to admit of mistake, are actually
rendered _generic_, and extended to whole groups, comprising objects
agreeing in nothing but the arbitrary heads of a classification
from which the most important natural relations are professedly and
purposely rejected.[38]

(134.) The classifications by which science is advanced, however, are
widely different from those which serve as bases for artificial systems
of nomenclature. They cross and intersect one another, as it were, in
every possible way, and have for their very aim to interweave all the
objects of nature in a close and compact web of mutual relations and
dependence. As soon, then, as any resemblance or analogy, any point of
agreement whatever, is perceived between any two or more things,--be
they what they will, whether objects, or phenomena, or laws,--they
immediately and _ipso facto_ constitute themselves into a group or
class, which may become enlarged to any extent by the accession of
such new objects, phenomena, or laws, agreeing in the same point, as
may come to be subsequently ascertained. It is thus that the materials
of the world become grouped in natural families, such as chemistry
furnishes examples of, in its various groups of acids, alkalies,
sulphurets, &c.; or botany, in its euphorbiaceæ, umbelliferæ, &c. It is
thus, too, that phenomena assume their places under general points of
resemblance; as, in optics, those which refer themselves to the class
of periodic colours, double refraction, &c.; and that resemblances
themselves become traced, which it is the business of induction to
generalize and include in abstract propositions.

(135.) But every class formed on a positive resemblance of characters,
or on a distinct analogy, draws with it the consideration of a negative
class, in which that resemblance either does not subsist at all, or the
contrary takes place; and again, there are classes in which a given
quality is possessed by the different individuals in a descending scale
of intensity. Now, it is of consequence to distinguish between cases
in which there is a real opposition of quality, or a mere diminution
of intensity, in some quality susceptible of degrees, till it becomes
imperceptible. For example, between transparency and opacity there
would at first sight appear a direct opposition; but, on nearer
consideration, when we consider the gradations by which transparency
diminishes in natural substances, we shall see reason to admit that
the latter quality, instead of being the _opposite_ of the former,
is only its _extreme lowest degree_. Again, in the arrangement of
natural objects under the head of weight or specific gravity, the scale
extends through all nature, and we know of no natural body in which the
opposite of gravity, or positive _levity_, subsists. On the other hand,
the opposite electricities; the north and south magnetic polarities;
the alkaline and acid qualities of chemical agents; the positive and
negative rotations impressed by plates of rock crystal on the planes
of polarization of the rays of light, and many other cases, exemplify
not merely a negation, but an active opposition of quality. Both these
modes of classification have their peculiar importance in the inductive
process: the one, as affording an opportunity of tracing a relation
between phenomena by the observation of a correspondence in their
scales of intensity; the other, by that of contrast, as we shall show
more at large in the next section.

(136.) There is a very wide distinction, too, to be taken between such
classes as turn upon a single head of resemblance among individuals
otherwise very different, and such as bind together in natural groups,
by a great variety of analogies, objects which yet differ in many
remarkable particulars. For example: if we make colourless transparency
a head of classification, the list of the class will comprise objects
differing most widely in their nature, such as water, air, diamond,
spirit of wine, glass, &c. On the other hand, the chemical families of
alkalies, metals, &c. are instances of groups of the other kind; which,
with properties in many respects different, still agree in a general
resemblance of several others, which at once decides us in considering
them as having a natural relation. In the former cases, our ingenuity
is exercised to determine what can be the cause of their resemblance,
in the latter, of their difference; the former belong to the province
of inductive generalization, and afford the most instructive cases for
the investigation of causes; the latter appertain to the more secret
recesses of nature; the very existence of such families being in itself
one of the great and complicated phenomena of the universe, which we
cannot hope to unriddle without an intimate and extensive acquaintance
with the highest laws.[39]



CHAP. VI.

  OF THE FIRST STAGE OF INDUCTION.--THE DISCOVERY OF PROXIMATE
    CAUSES, AND LAWS OF THE LOWEST DEGREE OF GENERALITY, AND THEIR
    VERIFICATION.


(137.) The first thing that a philosophic mind considers, when any
new phenomenon presents itself, is its _explanation_, or reference
to an immediate producing cause. If that cannot be ascertained, the
next is to _generalize_ the phenomenon, and include it, with others
analogous to it, in the expression of some law, in the hope that its
consideration, in a more advanced state of knowledge, may lead to the
discovery of an adequate proximate cause.

(138.) Experience having shown us the manner in which one phenomenon
depends on another in a great variety of cases, we find ourselves
provided, as science extends, with a continually increasing stock
of such antecedent phenomena, or causes (meaning at present merely
proximate causes), competent, under different modifications, to the
production of a great multitude of effects, besides those which
originally led to a knowledge of them. To such causes Newton has
applied the term _veræ causæ_; that is, causes recognized as having a
real existence in nature, and not being mere hypotheses or figments
of the mind. To exemplify the distinction:--The phenomenon of shells
found in rocks, at a great height above the sea, has been attributed
to several causes. By some it has been ascribed to a plastic virtue in
the soil; by some, to fermentation; by some, to the influence of the
celestial bodies; by some, to the casual passage of pilgrims with their
scallops; by some, to birds feeding on shell-fish; and by all modern
geologists, with one consent, to the life and death of real mollusca
at the bottom of the sea, and a subsequent alteration of the relative
level of the land and sea. Of these, the plastic virtue and celestial
influence belong to the class of figments of fancy. Casual transport
by pilgrims is a real cause, and might account for a few shells here
and there dropped on frequented passes, but is not extensive enough for
the purpose of explanation. Fermentation, generally, is a real cause,
so far as that there _is such a thing_; but it is not a real cause
of the production of a shell in a rock, since no such thing was ever
witnessed as one of its effects, and rocks and stones do not ferment.
On the other hand, for a shell-fish dying at the bottom of the sea to
leave his shell in the mud, where it becomes silted over and imbedded,
happens daily; and the elevation of the bottom of the sea to become dry
land has really been witnessed so often, and on such a scale, as to
qualify it for a _vera causa_ available in sound philosophy.

(139.) To take another instance, likewise drawn from the same
deservedly popular science:--The fact of a great change in the general
climate of large tracts of the globe, if not of the whole earth,
and of a diminution of general temperature, having been recognised
by geologists, from their examination of the remains of animals and
vegetables of former ages enclosed in the strata, various causes for
such diminution of temperature have been assigned. Some consider
the whole globe as having gradually cooled from absolute fusion;
some regard the immensely superior activity of former volcanoes, and
consequent more copious communication of internal heat to the surface,
in former ages, as the cause. Neither of these can be regarded as
real causes in the sense here intended; for we do not _know_ that the
globe has so cooled from fusion, nor are we sure that such supposed
greater activity of former than of present volcanoes really did exist.
A cause, possessing the essential requisites of a _vera causa_, has,
however, been brought forward[40] in the varying influence of the
distribution of land and sea over the surface of the globe: a change
of such distribution, in the lapse of ages, by the degradation of the
old continents, and the elevation of new, being a demonstrated fact;
and the influence of such a change on the climates of particular
regions, if not of the whole globe, being a perfectly fair conclusion,
from what we know of continental, insular, and oceanic climates by
actual observation. Here, then, we have, at least, a cause on which a
philosopher may consent to reason; though, whether the changes actually
going on are such as to warrant the whole extent of the conclusion,
or are even taking place in the right direction, may be considered as
undecided till the matter has been more thoroughly examined.

(140.) To this we may add another, which has likewise the essential
characters of a _vera causa_, in the astronomical _fact_ of the actual
slow diminution of the eccentricity of the earth’s orbit round the
sun; and which, as a general one, affecting the _mean temperature of
the whole globe_, and as one of which the effect is both inevitable,
and susceptible, to a certain degree, of exact estimation, deserves
consideration. It is evident that the _mean_ temperature of the
whole surface of the globe, in so far as it is maintained by the
action of the sun at a higher degree than it would have were the sun
extinguished, must depend on the mean quantity of the sun’s rays which
it receives, or, which comes to the same thing, on the _total_ quantity
received in a given invariable time: and the length of the year
being unchangeable in all the fluctuations of the planetary system,
it follows, that the total _annual_ amount of solar radiation will
determine, _cæteris paribus_, the general climate of the earth. Now,
it is not difficult to show that this amount is inversely proportional
to the minor axis of the ellipse described by the earth about the
sun, regarded as slowly variable; and that, therefore, the major axis
remaining, as we know it to be, constant, and the orbit being actually
in a state of approach to a circle, and, consequently, the minor axis
being on the _increase_, the mean annual amount of solar radiation
received by the whole earth must be actually on the _decrease_. We have
here, therefore, an evident real cause, of sufficient universality, and
acting _in the right direction_, to account for the phenomenon. Its
adequacy is another consideration.[41]

(141.) Whenever, therefore, any phenomenon presents itself for
explanation, we naturally seek, in the first instance, to refer it to
some one or other of those real causes which experience has shown to
exist, and to be efficacious in producing similar phenomena. In this
attempt our probability of success will, of course, mainly depend,
1st, On the number and variety of causes experience has placed at our
disposal; 2dly, On our habit of applying them to the explanation of
natural phenomena; and, 3dly, On the number of analogous phenomena
we can collect, which have either been explained, or which admit of
explanation by some one or other of those causes, and the closeness of
their analogy with that in question.

(142.) Here, then, we see the great importance of possessing a stock
of analogous instances or phenomena which class themselves with that
under consideration, the explanation of one among which may naturally
be expected to lead to that of all the rest. If the analogy of two
phenomena be very close and striking, while, at the same time, the
cause of one is very obvious, it becomes scarcely possible to refuse
to admit the action of an analogous cause in the other, though not so
obvious in itself. For instance, when we see a stone whirled round in a
sling, describing a circular orbit round the hand, keeping the string
stretched, and flying away the moment it breaks, we never hesitate
to regard it as retained in its orbit by the tension of the string,
that is, by _a force_ directed to the centre; for we feel that we do
really exert such a force. We have here _the direct perception_ of the
cause. When, therefore, we see a great body like the moon circulating
round the earth and not flying off, we cannot help believing it to
be prevented from so doing, not indeed by a material tie, but by
that which operates in the other case through the intermedium of the
string,--a _force_ directed constantly to the centre. It is thus that
we are continually acquiring a knowledge of the existence of causes
acting under circumstances of such concealment as effectually to
prevent their direct discovery.

(143.) In general we must observe that motion, wherever produced or
changed, invariably points out the existence of _force_ as its cause;
and thus the forces of nature become known and measured by the
motions they produce. Thus, the _force_ of magnetism becomes known by
the deviation produced by iron in a compass needle, or by a needle
leaping up to a magnet held over it, as certainly as by that adhesion
to it, when in contact and at rest, which requires force to break the
connection; and thus the currents produced in the surface of a quantity
of quicksilver, electrified under a conducting fluid, have pointed out
the existence and direction of forces of enormous intensity developed
by the electric circuit, of which we should not otherwise have had the
least suspicion.[42]

(144.) But when the cause of a phenomenon neither presents itself
obviously on the consideration of the phenomenon itself, nor is as it
were forced on our attention by a case of strong analogy, such as above
described, we have then no resource but in a deliberate assemblage of
all the parallel instances we can muster; that is, to the formation
of a class of facts, having the phenomenon in question for a head of
classification; and to a search among the individuals of this class
for some other common points of agreement, among which the cause will
of necessity be found. But if more than one cause should appear, we
must then endeavour to find, or, if we cannot find, to _produce, new
facts_, in which each of these in succession shall be wanting, while
yet they agree in the general point in question. Here we find the use
of what Bacon terms “_crucial instances_,” which are phenomena brought
forward to decide between two causes, each having the same analogies in
its favour. And here, too, we perceive the utility of _experiment_ as
distinguished from mere passive observation. We make an experiment of
the crucial kind when we form combinations, and put in action causes
from which some particular one shall be deliberately excluded, and
some other purposely admitted; and by the agreement or disagreement of
the resulting phenomena with those of the class under examination, we
decide our judgment.

(145.) When we would lay down general rules for guiding and
facilitating our search, among a great mass of assembled facts, for
their common cause, we must have regard to the characters of that
relation which we intend by cause and effect. Now, these are,--

  1st, Invariable connection, and, in particular, invariable
    antecedence of the cause and consequence of the effect, unless
    prevented by some counteracting cause. But it must be observed,
    that, in a great number of natural phenomena, the effect is
    produced gradually, while the cause often goes on increasing in
    intensity; so that the antecedence of the one and consequence
    of the other becomes difficult to trace, though it really
    exists. On the other hand, the effect often follows the cause
    so instantaneously, that the interval cannot be perceived. In
    consequence of this, it is sometimes difficult to decide, of two
    phenomena constantly accompanying one another, which is cause or
    which effect.

  2d, Invariable negation of the effect with absence of the cause,
    unless some other cause be capable of producing the same effect.

  3d, Increase or diminution of the effect, with the increased
    or diminished intensity of the cause, in cases which admit of
    increase and diminution.

  4th, Proportionality of the effect to its cause in all cases of
    _direct unimpeded_ action.

  5th, Reversal of the effect with that of the cause.

(146.) From these characters we are led to the following observations,
which may be considered as so many propositions readily applicable to
particular cases, or rules of philosophizing: we conclude, 1st, That if
in our group of facts there be one in which any assigned peculiarity,
or attendant circumstance, is wanting or opposite, such peculiarity
cannot be the cause we seek.

(147.) 2d, That any circumstance in which all the facts without
exception agree, _may_ be the cause in question, or, if not, at least
a collateral effect of the same cause: if there be but one such point
of agreement, this possibility becomes a certainty; and, on the other
hand, if there be more than one, they may be concurrent causes.

(148.) 3d, That we are not to deny the existence of a cause in favour
of which we have a unanimous agreement of strong analogies, though
it may not be apparent how such a cause can produce the effect, or
even though it may be difficult to conceive its existence under the
circumstances of the case; in such cases we should rather appeal to
experience when possible, than decide _à priori_ against the cause, and
try whether it cannot be made apparent.

(149.) For instance: seeing the sun vividly luminous, every analogy
leads us to conclude it intensely hot. How heat can produce light,
we know not; and how such a heat can be maintained, we can form no
conception. Yet we are not, therefore, entitled to deny the inference.

(150.) 4th, That contrary or opposing facts are equally instructive for
the discovery of causes with favourable ones.

(151.) For instance: when air is confined with moistened iron filings
in a close vessel over water, its bulk is diminished, by a certain
portion of it being abstracted and combining with the iron, producing
_rust_. And, if the remainder be examined, it is found that it will
_not_ support flame or animal life. This contrary fact shows that the
cause of the support of flame and animal life is to be looked for in
that part of the air which the iron abstracts, and which rusts it.

(152.) 5th, That causes will very frequently become obvious, by a
mere arrangement of our facts in the order of intensity in which
some peculiar quality subsists; though not of necessity, because
counteracting or modifying causes may be at the same time in action.

(153.) For example: sound consists in impulses communicated to our ears
by the air. If a series of impulses of equal force be communicated
to it at equal intervals of time, at first in slow succession, and
by degrees more and more rapidly, we hear at first a rattling noise,
then a low murmur, and then a hum, which by degrees acquires the
character of a musical note, rising higher and higher in acuteness,
till its pitch becomes too high for the ear to follow. And from
this correspondence between the pitch of the note and the rapidity
of succession of the impulse, we conclude that our sensation of
the different pitches of musical notes originates in the different
rapidities with which their impulses are communicated to our ears.

(154.) 6th, That such counteracting or modifying causes may subsist
unperceived, and annul the effects of the cause we seek, in instances
which, but for their action, would have come into our class of
favourable facts; and that, therefore, exceptions may often be made
to disappear by removing or allowing for such counteracting causes.
This remark becomes of the greatest importance, when (as is often the
case) a single striking exception stands out, as it were, against an
otherwise unanimous array of facts in favour of a certain cause.

(155.) Thus, in chemistry, the _alkaline_ quality of the alkaline
and earthy bases is found to be due to the presence of oxygen
combined with one or other of a peculiar set of metals. Ammonia is,
however, a violent outstanding exception, such as here alluded to,
being a compound of azote and hydrogen: but there are almost certain
indications that this exception is not a real one, but assumes that
appearance in consequence of some modifying cause not understood.

(156.) 7th, If we can either find produced by nature, or produce
designedly for ourselves, two instances which agree _exactly_ in all
but one particular, and differ in that one, its influence in producing
the phenomenon, if it have any, _must_ thereby be rendered sensible.
If that particular be present in one instance and wanting altogether
in the other, the production or non-production of the phenomenon will
decide whether it be or be not the only cause: still more evidently,
if it be present _contrariwise_ in the two cases, and the effect be
thereby reversed. But if its total presence or absence only produces
a change in the _degree_ or intensity of the phenomenon, we can then
only conclude that it acts as a concurrent cause or condition with
some other to be sought elsewhere. In nature, it is comparatively
rare to find instances pointedly differing in one circumstance and
agreeing in every other; but when we call experiment to our aid, it
is easy to produce them; and this is, in fact, the grand application
of _experiments of enquiry_ in physical researches. They become more
valuable, and their results clearer, in proportion as they possess this
quality (of agreeing exactly in all their circumstances but one), since
the question put to nature becomes thereby more pointed, and its answer
more decisive.

(157.) 8th, If we cannot obtain a complete negative or opposition of
the circumstance whose influence we would ascertain, we must endeavour
to find cases where it varies considerably in degree. If _this_ cannot
be done, we may perhaps be able to weaken or exalt its influence by
the introduction of some fresh circumstance, which, abstractedly
considered, seems _likely_ to produce this effect, and thus obtain
indirect evidence of its influence. But then we are always to remember,
that the evidence so obtained _is_ indirect, and that the new
circumstance introduced _may_ have a direct influence of its own, or
may exercise a modifying one on some _other_ circumstance.

(158.) 9th, Complicated phenomena, in which several causes concurring,
opposing, or quite independent of each other, operate at once, so as to
produce a compound effect, may be simplified by subducting the effect
of all the known causes, as well as the nature of the case permits,
either by deductive reasoning or by appeal to experience, and thus
leaving, as it were, a _residual phenomenon_ to be explained. It is by
this process, in fact, that science, in its present advanced state, is
chiefly promoted. Most of the phenomena which nature presents are very
complicated; and when the effects of all known causes are estimated
with exactness, and subducted, the residual facts are constantly
appearing in the form of phenomena altogether new, and leading to the
most important conclusions.

(159.) For example: the return of the comet predicted by professor
Encke, a great many times in succession, and the general good agreement
of its calculated with its observed place during any one of its periods
of visibility, would lead us to say that its gravitation towards the
sun and planets is the sole and sufficient cause of all the phenomena
of its orbitual motion; but when the effect of this cause is strictly
calculated and subducted from the observed motion, there is found to
remain behind a _residual phenomenon_, which would never have been
otherwise ascertained to exist, which is a small anticipation of the
time of its reappearances or a diminution of its periodic time, which
cannot be accounted for by gravity, and whose cause is therefore to be
enquired into. Such an anticipation would be caused by the resistance
of a medium disseminated through the celestial regions; and as there
are other good reasons for believing this to be a _vera causa_, it has
therefore been ascribed to such a resistance.

(160.) This 9th observation is of such importance in science, that
we shall exemplify it by another instance or two. M. Arago, having
suspended a magnetic needle by a silk thread, and set it in vibration,
observed, that it came much sooner to a state of rest when suspended
over a plate of copper, than when no such plate was beneath it. Now, in
both cases there were two _veræ causæ_ why it _should_ come at length
to rest, viz. the resistance of the air, which opposes, and at length
destroys, all motions performed in it; and the want of perfect mobility
in the silk thread. But the effect of these causes being exactly known
by the observation made in the absence of the copper, and being thus
allowed for and subducted, a _residual_ phenomenon appeared, in the
fact that a retarding influence was exerted by the copper itself;
and this fact, once ascertained, speedily led to the knowledge of
an entirely new and unexpected class of relations. To add one more
instance. If it be true (as M. Fourrier considers it demonstrated to
be) that the celestial regions have a temperature independent of the
sun, not greatly inferior to that at which quicksilver congeals, and
much superior to some degrees of cold which have been artificially
produced, two causes suggest themselves: one is that assigned by the
author above mentioned; the radiation of the stars; another may be
proposed in the ether or elastic medium mentioned in the last section,
which the phenomena of light and the resistance of comets give us
reason to believe fills all space, and which, in analogy to all the
elastic media known, may be supposed to possess a temperature and a
specific heat of its own, which it is capable of communicating to
bodies surrounded by it. Now, if we consider that the heat radiated
by the sun follows the same proportion as its light, and regard it as
reasonable to admit with respect to stellar heat what holds good of
solar; the effect of stellar radiation in maintaining a temperature in
space should be as much inferior to that of the radiation of the sun
as the light of a moonless midnight is to that of an equatorial noon;
that is to say, almost inconceivably smaller. Allowing, then, the full
effect for this cause, there would still remain a great residuum due to
the presence of the ether.

(161.) Many of the new elements of chemistry have been detected in
the investigation of _residual phenomena_. Thus, Arfwedson discovered
lithia by perceiving an _excess of weight_ in the sulphate produced
from a small portion of what he considered as magnesia present in a
mineral he had analysed. It is on this principle, too, that the _small
concentrated residues of great operations_ in the arts are almost
sure to be the lurking places of new chemical ingredients: witness
iodine, brome, selenium, and the new metals accompanying platina in the
experiments of Wollaston and Tennant. It was a happy thought of Glauber
to examine what every body else threw away.

(162.) Finally, we have to observe, that the detection of a _possible_
cause, by the comparison of assembled cases, _must_ lead to one of
two things: either, 1st, The detection of a real cause, and of its
manner of acting, so as to furnish a complete explanation of the facts;
or, 2dly, The establishment of an abstract law of nature, pointing
out two phenomena of a general kind as invariably connected; and
asserting, that where one is, there the other will always be found.
Such invariable connection is itself a phenomenon of a higher order
than any particular fact; and when many such are discovered, we may
again proceed to classify, combine, and examine them, with a view to
the detection of _their_ causes, or the discovery of still more general
laws, and so on without end.

(163.) Let us now exemplify this inductive search for a cause by one
general example: suppose _dew_ were the phenomenon proposed, whose
cause we would know. In the first place, we must separate dew from rain
and the moisture of fogs, and limit the application of the term to
what is really meant, which is, the spontaneous appearance of moisture
on substances exposed in the open air when no rain or _visible_ wet
is falling. Now, here we have analogous phenomena in the moisture
which bedews a cold metal or stone when we breathe upon it; that which
appears on a glass of water fresh from the well in hot weather; that
which appears on the _inside_ of windows when sudden rain or hail
chills the external air; that which runs down our walls when, after
a long frost, a warm moist thaw comes on: all these instances agree
in one point (Rule 2. § 147.), the coldness of the object dewed, in
comparison with the air in contact with it.

(164.) But, in the case of the night dew, is this a _real cause_--is it
a fact that the object dewed _is_ colder than the air? Certainly not,
one would at first be inclined to say; for what is to _make_ it so? But
the analogies are cogent and unanimous; and, therefore, (pursuant to
Rule 3. § 148.) we are not to discard their indications; and, besides,
the experiment is easy: we have only to lay a thermometer in contact
with the dewed substance, and hang one at a little distance above it
out of reach of its influence. The experiment has been therefore made;
the question has been asked, and the answer has been invariably in the
_affirmative_. Whenever an object contracts dew, _it is_ colder than
the air. Here, then, we have _an invariable concomitant_ circumstance:
but is this chill an effect of dew, or its cause? That dews are
accompanied with a chill is a common remark; but vulgar prejudice would
make the cold the _effect_ rather than the cause. We must, therefore,
collect more facts, or, which comes to the same thing, vary the
circumstances; since every instance in which the circumstances differ
is a fresh fact; and, especially, we must note the contrary or negative
cases (Rule 4. § 150.), _i. e._ where no dew is produced.

(165.) Now, 1st, no dew is produced on the surface of _polished
metals_, but it is very copiously on glass, both exposed with their
faces upwards, and in some cases the under side of a horizontal plate
of glass is also dewed; which last circumstance (by Rule 1. § 146.)
excludes the _fall_ of moisture from the sky in an invisible form,
which would naturally suggest itself as a cause. In the cases of
polished metal and polished glass, the contrast shows evidently that
the _substance_ has much to do with the phenomenon; therefore, let
the substance _alone_ be diversified as much as possible, by exposing
polished surfaces of various kinds. This done, _a scale of intensity_
becomes obvious (Rule 5. § 152.). Those polished substances are found
to be most strongly dewed which conduct heat worst; while those which
conduct well resist dew most effectually. Here we encounter a _law_
of the first degree of generality. But, if we expose rough surfaces,
instead of polished, we sometimes find this law interfered with
(Rule 5. § 152.). Thus, roughened iron, especially if painted over
or blackened, becomes dewed sooner than varnished paper: the kind of
_surface_ therefore has a great influence. Expose, then, the _same_
material in very diversified states as to surface (Rule 7. § 156.), and
another scale of intensity becomes at once apparent; those _surfaces_
which _part with their heat_ most readily by radiation are found to
contract dew most copiously: and thus we have detected another law of
the same generality with the former, by a comparison of two classes of
facts, one relating to dew, the other to the radiation of heat from
surfaces. Again, the influence ascertained to exist of _substance_ and
_surface_ leads us to consider that of _texture_: and here, again, we
are presented on trial with remarkable differences, and with a third
_scale of intensity_, pointing out substances of a close firm texture,
such as stones, metals, &c. as unfavourable, but those of a loose one,
as cloth, wool, velvet, eiderdown, cotton, &c. as eminently favourable,
to the contraction of dew: and these are precisely those which are best
adapted for clothing, or for impeding the free passage of heat from
the skin into the air, so as to allow their outer surfaces to be very
cold while they remain warm within.

(166.) Lastly, among the negative instances, (§ 150.) it is observed,
that dew is never copiously deposited in situations much screened
from the open sky, and not at all in _a cloudy night_; but if the
clouds withdraw, even for a few minutes, and leave a clear opening,
a deposition of dew presently begins, and goes on increasing. Here,
then, a cause is distinctly pointed out by its antecedence to the
effect in question (§ 145.). A clear view of the cloudless sky, then,
is an essential condition, or, which comes to the same thing, clouds or
surrounding objects act as _opposing causes_. This is so much the case,
that dew formed in clear intervals will often even evaporate again when
the sky becomes thickly overcast (Rule 4. § 150.).

(167.) When we now come to assemble these partial inductions so as to
raise from them a general conclusion, we consider, 1st, That all the
conclusions we have come to have a reference to that first general
fact--the cooling of the exposed surface of the body dewed below
the temperature of the air. Those surfaces which part with their
heat outwards most readily, and have it supplied from within most
slowly, will, of course, become coldest if there be an opportunity
for their heat to escape, and not be restored to them from without.
Now, a clear sky affords such an opportunity. It is a law well known
to those who are conversant with the nature of heat, that heat is
constantly escaping from _all bodies_ in rays, or by _radiation_, but
is as constantly restored to them by the similar radiation of others
surrounding them. Clouds and surrounding objects therefore act as
opposing causes by replacing the whole or a great part of the heat so
radiated away, which can escape effectually, without being replaced,
only through openings into infinite space. Thus, at length, we arrive
at the general proximate cause of dew, in the cooling of the dewed
surface by radiation faster than its heat can be restored to it, by
communication with the ground, or by counter-radiation; so as to
become colder than the air, and thereby to cause a condensation of its
moisture.

(168.) We have purposely selected this theory of dew, first developed
by the late Dr. Wells, as one of the most beautiful specimens we can
call to mind of inductive experimental enquiry lying within a moderate
compass. It is not possible in so brief a space to do it justice; but
we earnestly recommend his work[43] (a short and very entertaining one)
for perusal to the student of natural philosophy, as a model with which
he will do well to become familiar.

(169.) In the analysis above given, the formation of dew is referred to
two more general phenomena; the radiation of heat, and the condensation
of invisible vapour by cold. The cause of the former is a much higher
enquiry, and may be said, indeed, to be totally unknown; that of the
latter actually forms a most important branch of physical enquiry. In
such a case, when we reason upwards till we reach an ultimate fact, we
regard a phenomenon as fully explained; as we consider the branch of
a tree to terminate when traced to its insertion in the trunk, or a
twig to its junction with the branch; or rather, as a rivulet retains
its importance and its name till lost in some larger tributary, or in
the main river which delivers it into the ocean. This, however, always
supposes that, on a reconsideration of the case, we see clearly how the
admission of such a fact, with all its attendant laws, will perfectly
account for _every particular_--as well those which, in the different
stages of the induction, have led us to a knowledge of it, as those
which we had neglected, or considered less minutely than the rest.
But, had we no previous knowledge of the radiation of heat, this same
induction would have made it known to us, and, duly considered, might
have led to the knowledge of many of its laws.

(170.) In the study of nature, we must not, therefore, be scrupulous
as to _how_ we reach to a knowledge of such general facts: provided
only we verify them carefully when once detected, we must be content
to seize them wherever they are to be found. And this brings us to
consider the _verification_ of inductions.

(171.) If, in our induction, every individual case has actually been
present to our minds, we are sure that it will find itself duly
_represented_ in our final conclusion: but this is impossible for
such cases as were _unknown_ to us, and hardly ever happens even
with all the known cases; for such is the tendency of the human mind
to speculation, that on the least idea of an analogy between a few
phenomena, it leaps forward, as it were, to a cause or law, to the
temporary neglect of all the rest; so that, in fact, almost all our
principal inductions must be regarded as a series of ascents and
descents, and of conclusions from a few cases, verified by trial on
many.

(172.) Whenever, therefore, we think we have been led by induction to
the knowledge of the proximate cause of a phenomenon or of a law of
nature, our next business is to examine deliberately and _seriatim_
all the cases we have collected of its occurrence, in order to satisfy
ourselves that they are explicable by our cause, or fairly included in
the expression of our law: and in case any exception occurs, it must
be carefully noted and set aside for re-examination at a more advanced
period, when, possibly, the cause of exception may appear, and the
exception itself, by allowing for the effect of that cause, be brought
over to the side of our induction; but should exceptions prove numerous
and various in their features, our faith in the conclusion will be
proportionally shaken, and at all events its importance lessened by the
destruction of its universality.

(173.) In the conduct of this verification, we are to consider whether
the cause or law to which we are conducted be one already known and
recognised as a more general one, whose nature is well understood, and
of which the phenomenon in question is but one more case in addition
to those already known, or whether it be one less general, less known,
or altogether new. In the latter case, our verification will suffice,
if it merely shows that all the cases considered are plainly cases in
point. But in the former, the process of verification is of a much
more severe and definite kind. We must trace the action of our cause
with distinctness and precision, as modified by all the circumstances
of each case; we must estimate its effects, and show that nothing
unexplained remains behind; at least, in so far as the presence of
unknown modifying causes is not concerned.

(174.) Now, this is precisely the sort of process in which _residual
phenomena_ (such as spoken of in art. 158.) may be expected to occur.
If our induction be really a valid and a comprehensive one, _whatever_
remains unexplained in the comparison of its conclusion with particular
cases, under all their circumstances, _is_ such a phenomenon, and comes
in its turn to be a subject of inductive reasoning to discover its
cause or laws. It is thus that we may be said to witness facts with
the eyes of reason; and it is thus that we are continually attaining a
knowledge of new phenomena and new laws which lie beneath the surface
of things, and give rise to the creation of fresh branches of science
more and more remote from common observation.

(175.) Physical astronomy affords numerous and splendid instances of
this. The law, for example, which asserts that the planets are retained
in their orbits about the sun, and satellites about their primaries,
by an attractive force, decreasing as the square of the distances
increases, comes to be verified in each particular case by deducing
from it the exact motions which, under the circumstances, ought to take
place, and comparing them with fact. This comparison, while it verifies
in general the existence of the law of gravitation as supposed, and
its adequacy to explain all the principal motions of every body in the
system, yet leaves some small deviations in those of the planets, and
some very considerable ones in that of the moon and other satellites,
still unaccounted for; residual phenomena, which still remain to be
traced up to causes. By further examining these, their causes have at
length been ascertained, and found to consist in the mutual actions of
the planets on each other, and the disturbing influence of the sun on
the motions of the satellites.

(176.) But a law of nature has not that degree of generality which
fits it for a stepping-stone to greater inductions, unless it be
_universal_ in its application. We cannot rely on its enabling us to
extend our views beyond the circle of instances from which it was
obtained, unless we have already had experience of its power to do so;
unless it actually _has_ enabled us before trial to say what will take
place in cases analogous to those originally contemplated; unless, in
short, we have studiously placed ourselves in the situation of its
antagonists, and even perversely endeavoured to find exceptions to
it without success. It is in the precise proportion that a law once
obtained endures this extreme severity of trial, that its value and
importance are to be estimated; and our next step in the verification
of an induction must therefore consist in _extending_ its application
to cases not originally contemplated; in studiously varying the
circumstances under which our causes act, with a view to ascertain
whether their effect is general; and in pushing the application of our
laws to extreme cases.

(177.) For example, a fair induction from a great number of facts led
Galileo to conclude that the accelerating power of gravity is the same
on all sorts of bodies, and on great and small masses indifferently;
and this he exemplified by letting bodies of very different natures
and weights fall at the same instant from a high tower, when it was
observed that they struck the ground at the same moment, abating a
certain trifling difference, due, as he justly believed it to be, to
the greater proportional resistance of the air to light than to heavy
bodies. The experiment could not, at that time, be fairly tried with
extremely light substances, such as cork, feathers, cotton, &c. because
of the great resistance experienced by these in their fall; no means
being then known of removing this cause of disturbance. It was not,
therefore, till after the invention of the air-pump that this law could
be put to the severe test of an extreme case. A guinea and a downy
feather were let drop at once from the upper part of a tall exhausted
glass, and struck the bottom at the same moment. Let any one make the
trial _in the air_, and he will perceive the force of an _extreme case_.

(178.) In the verification of a law whose expression is _quantitative_,
not only must its generality be established by the trial of it in as
various circumstances as possible, but every such trial must be one of
precise measurement. And in such cases the means taken for subjecting
it to trial ought to be so devised as to repeat and multiply a great
number of times any deviation (if any exist); so that, let it be ever
so small, it shall at last become sensible.

(179.) For instance, let the law to be verified be, that _the gravity
of every material body is in the direct proportion of its mass_, which
is only another mode of expressing Galileo’s law above mentioned.
The time of falling from any moderate height cannot be measured with
precision enough for our purpose: but if it can be repeated a very
great multitude of times _without any loss or gain_ in the intervals,
and the whole amount of the times of fall so repeated measured by
a clock; and if at the same time the resistance of the air can be
rendered _exactly alike_ for all the bodies tried, we have here
Galileo’s trial in a much more refined state; and it is evident that
almost unlimited exactness may be obtained. Now, all this Newton
accomplished by the simple and elegant contrivance of enclosing in a
hollow pendulum the same weights of a great number of substances the
most different that could be found in all respects, as gold, glass,
wood, water, wheat, &c.[44], and ascertaining the time required for
the pendulum so charged to make a great number of oscillations; in
each of which it is clear the weights had to fall, and be raised again
successively, without loss of time, through the same _identical_
spaces. Thus any difference, however inconsiderable, that might
exist in the time of one such fall and rise would be multiplied and
accumulated till they became sensible. And none having been discovered
by so delicate a process in any case, the law was considered verified
both in respect of generality and exactness. This, however, is nothing
to the verifications afforded by astronomical phenomena, where the
deviations, if any, accumulate for thousands of years instead of a few
hours.

(180.) The surest and best characteristic of a well-founded and
extensive induction, however, is when verifications of it spring up,
as it were, spontaneously, into notice, from quarters where they might
be least expected, or even among instances of that very kind which
were at first considered hostile to them. Evidence of this kind is
irresistible, and compels assent with a weight which scarcely any other
possesses. To give an example: M. Mitscherlich had announced a law to
this effect--_that_ the chemical elements of which all bodies consist
are susceptible of being classified in distinct groups, which he termed
_isomorphous_ groups; and _that_ these groups are so related, that
when similar combinations are formed of individuals belonging to two,
three, or more of them, such combinations will crystallize in the same
geometrical forms. To this curious and important law there appeared
a remarkable exception. According to professor Mitscherlich, the
arsenic and phosphoric acids _are_ similar combinations coming under
the meaning of his law, and their combinations with soda and water,
forming the salts known to chemists under the names of arseniate and
phosphate of soda, ought, if the law were general, to crystallize in
identical shapes. The fact, however, was understood to be otherwise.
But lately, Mr. Clarke, a British chemist, having examined the two
salts attentively, ascertained the fact that their compositions
deviate essentially from that similarity which M. Mitscherlich’s law
requires; and that, therefore, the exception in question disappears.
This was something: but, pursuing the subject further, the same
ingenious enquirer happily succeeded in producing a _new_ phosphate of
soda, differing from that generally known in containing a different
proportion of water, and agreeing in composition exactly with the
arseniate. The crystals of this new salt, when examined, were found by
him to be precisely identical in form with those of the arseniate: thus
verifying, in a most striking and totally unexpected manner, the law in
question, or, as it is called, the law of isomorphism.

(181.) Unexpected and peculiarly striking confirmations of inductive
laws frequently occur in the form of residual phenomena, in the course
of investigations of a widely different nature from those which gave
rise to the inductions themselves. A very elegant example may be cited
in the unexpected confirmation of the law of the developement of heat
in elastic fluids by compression, which is afforded by the phenomena
of sound. The enquiry into the cause of sound had led to conclusions
respecting its mode of propagation, from which its velocity in the air
could be precisely calculated. The calculations were performed; but,
when compared with fact, though the agreement was quite sufficient
to show the general correctness of the cause and mode of propagation
assigned, _yet_ the _whole_ velocity could not be shown to arise from
this theory. There was still a _residual_ velocity to be accounted
for, which placed dynamical philosophers for a long time in a great
dilemma. At length Laplace struck on the happy idea, that this might
arise from the _heat_ developed in the act of that condensation which
necessarily takes place at every vibration by which sound is conveyed.
The matter was subjected to exact calculation, and the result was
at once the complete explanation of the residual phenomenon, and a
striking confirmation of the general law of the developement of heat by
compression, under circumstances beyond artificial imitation.

(182.) In extending our inductions to cases not originally
contemplated, there is one step which always strikes the mind with
peculiar force, and with such a sensation of novelty and surprise,
as often gives it a weight beyond its due philosophic value. It is
the transition from the little to the great, and _vice versâ_, but
especially the former. It is so beautiful to see, for instance, an
experiment performed in a watch-glass, or before a blowpipe, succeed,
in a great manufactory, on many tons of matter, or, in the bosom of
a volcano, upon millions of cubic fathoms of lava, that we almost
forget that these great masses are made up of watch-glassfuls, and
blowpipe-beads. We see the enormous intervals between the stars and
planets of the heavens, which afford room for innumerable processes
to be carried on, for light and heat to circulate, and for curious
and complicated motions to go forward among them: we look more
attentively, and we see sidereal systems, probably not less vast and
complicated than our own, crowded apparently into a small space (from
the effect of their distance from us), and forming groups resembling
bodies of a substantial appearance, having form and outline: yet we
recoil with incredulous surprise when we are asked _why_ we cannot
conceive the atoms of a grain of sand to be as remote from each other
(proportionally to their sizes) as the stars of the firmament; and
why there may not be going on, in that little microcosm, processes
as complicated and wonderful as those of the great world around us.
Yet the student who makes any progress in natural philosophy will
encounter numberless cases in which this transfer of ideas from the one
extreme of magnitude to the other will be called for: he will find,
for instance, the phenomena of the propagation of winds referred to
the same laws which regulate the propagation of motions through the
smallest masses of air; those of lightning assimilated to the mere
communication of an electric spark, and those of earthquakes to the
tremors of a stretched wire: in short, he must lay his account to
finding the distinction of great and little altogether annihilated in
nature: and it is well for man that such is the case, and that the same
laws, which he can discover and verify in his own circumscribed sphere
of power, should prove available to him when he comes to apply them on
the greatest scale; since it is thus only that he is enabled to become
an exciting cause in operations of any considerable magnitude, and to
vindicate his importance in creation.

(183.) But the business of induction does not end here: its final
result must be followed out into all its consequences, and applied to
all those cases which seem even remotely to bear upon the subject of
enquiry. Every new addition to our stock of causes becomes a means
of fresh attack with new vantage ground upon all those unexplained
parts of former phenomena which have resisted previous efforts. It
can hardly be pressed forcibly enough on the attention of the student
of nature, that there is scarcely any natural phenomenon which can be
fully and completely explained in all its circumstances, without a
union of several, perhaps of all, the sciences. The great phenomena of
astronomy, indeed, may be considered exceptions; but this is merely
because their scale is so vast that one only of the most widely
extending forces of nature takes the lead, and all those agents whose
sphere of action is limited to narrower bounds, and which determine
the production of phenomena nearer at hand, are thrown into the back
ground, and become merged and lost in comparative insignificance. But
in the more intimate phenomena which surround us it is far otherwise.
Into what a complication of different branches of science are we not
led by the consideration of such a phenomenon as rain, for instance,
or flame, or a thousand others, which are constantly going on before
our eyes? Hence, it is hardly possible to arrive at the knowledge of
a law of any degree of generality in any branch of science, but it
immediately furnishes us with a means of extending our knowledge of
innumerable others, the most remote from the point we set out from; so
that, when once embarked in any physical research, it is impossible for
any one to predict where it may ultimately lead him.

(184.) This remark rather belongs to the inverse or _deductive_
process, by which we pursue laws into their remote consequences.
But it is very important to observe, that the successful process of
scientific enquiry demands continually the alternate use of both
the _inductive_ and _deductive_ method. The path by which we rise to
knowledge must be made smooth and beaten in its lower steps, and often
ascended and descended, before we can scale our way to any eminence,
much less climb to the summit. The achievement is too great for a
single effort; stations must be established, and communications kept
open with all below. To quit metaphor; there is nothing so instructive,
or so likely to lead to the acquisition of general views, as this
pursuit of the consequences of a law once arrived at into every subject
where it may seem likely to have an influence. The discovery of a
new law of nature, a new ultimate fact, or one that even temporarily
puts on that appearance, is like the discovery of a new element in
chemistry. Thus, selenium was hardly discovered by Berzelius in the
vitriol works of Fahlun, when it presently made its appearance in the
sublimates of Stromboli, and the rare and curious products of the
Hungarian mines. And thus it is with every new law, or general fact. It
is hardly announced before its traces are found every where, and every
one is astonished at its having so long remained concealed. And hence
it happens that unexpected lights are shed at length over parts of
science that had been abandoned in despair, and given over to hopeless
obscurity.

(185.) The verification of _quantitative_ laws has been already spoken
of (178.); but their importance in physical science is so very great,
inasmuch as they alone afford a handle to strict mathematical deductive
application, that something ought to be said of the nature of the
inductions by which they are to be arrived at. In their simplest or
least general stages (of which alone we speak at present) they usually
express some numerical relation between two quantities dependent on
each other, either as collateral effects of a common cause, or as the
amount of its effect under given numerical circumstances or _data_.
For example, the law of refraction before noticed (§ 22.) expresses,
by a very simple relation, the amount of angular deviation of a ray
of light from its course, when the _angle_ at which it is inclined to
the refracting surface is known, viz. that the _sine_ of the angle
which the incident ray makes with a perpendicular to the surface is
always to that of the angle made by the refracted ray with the same
perpendicular, in a constant proportion, so long as the refracting
substance is the same. To arrive inductively at laws of this kind,
where one quantity _depends_ on or _varies with_ another, all that is
required is a series of careful and exact measures in every different
state of the _datum_ and _quæsitum_. Here, however, the mathematical
form of the law being of the highest importance, the greatest attention
must be given to the _extreme cases_ as well as to all those points
where the one quantity changes rapidly with a small change of the
other.[45] The results must be set down in a table in which the _datum_
gradually increases in magnitude from the lowest to the highest limit
of which it is susceptible. It will depend then entirely on our
habit of treating mathematical subjects, how far we may be able to
include such a table in the distinct statement of a mathematical law.
The discovery of such laws is often remarkably facilitated by the
contemplation of a class of phenomena to be noticed further on, under
the head of Collective Instances, (see § 194.) in which the nature of
the mathematical expression in which the law sought is comprehended, is
pointed out by the figure of some curve brought under inspection by a
proper mode of experimenting.

(186.) After all, unless our induction embraces a series of cases which
absolutely include the whole scale of variation of which the quantities
in question admit, the mathematical expression so obtained cannot be
depended upon as the true one, and if the scale actually embraced be
small, the extension of laws so derived to extreme cases will in all
probability be exceedingly fallacious. For example, air is an elastic
fluid, and as such, if enclosed in a confined space and squeezed, its
bulk diminishes: now, from a great number of trials made in cases where
the air has been compressed into a half, a third, &c. even as far
as a fiftieth of its bulk, or less, it has been concluded that “the
density of air is proportional to the compressing force,” or the bulk
it occupies _inversely_ as that force; and when the air is rarefied
by taking off part of its natural pressure, the same is found to be
the case, within very extensive limits. Yet it is impossible that this
should be, strictly or mathematically speaking, the true law; for, if
it were so, there could be no limit to the condensation of air, while
yet we have the strongest analogies to show that long before it had
reached any very enormous pitch the air would be reduced into a liquid,
and even, perhaps, if pressed yet more violently, into a solid form.

(187.) Laws thus derived, by the direct process of including in
mathematical formulæ the results of a greater or less number of
measurements, are called “empirical laws.” A good example of such a
law is that given by Dr. Young (Phil. Trans. 1826,) for the decrement
of life, or the law of mortality. Empirical laws in this state are
evidently _unverified inductions_, and are to be received and reasoned
on with the utmost reserve. No confidence can ever be placed in them
beyond the limits of the data from which they are derived; and even
within those limits they require a special and severe scrutiny to
examine _how nearly_ they do represent the observed facts; that is to
say, whether, in the comparison of their results with the observed
quantities, the differences are such as may fairly be attributed to
error of observation. When so carefully examined, they become, however,
most valuable; and frequently, when afterwards verified theoretically
by a deductive process (as will be explained in our next chapter),
turn out to be rigorous laws of nature, and afford the noblest and
most convincing supports of which theories themselves are susceptible.
The finest instances of this kind are the great laws of the planetary
motions deduced by Kepler, entirely from a comparison of observations
with each other, with no assistance from theory. These laws, viz. that
the planets move in ellipses round the sun; that each describes about
the sun’s centre equal areas in equal times; and that in the orbits of
different planets the squares of the periodical times are proportional
to the cubes of the distances; were the results of inconceivable
labour of calculation and comparison: but they amply repaid the
labour bestowed on them, by affording afterwards the most conclusive
and unanswerable proofs of the Newtonian system. On the other hand,
when empirical laws are unduly relied on beyond the limits of the
observations from which they were deduced, there is no more fertile
source of fatal mistakes. The formulæ which have been empirically
deduced for the elasticity of steam (till very recently), and those
for the resistance of fluids, and other similar subjects, have almost
invariably failed to support the theoretical structures which have been
erected on them.

(188.) It is a remarkable and happy fact, that the shortest and most
direct of all inductions should be that which has led at once, or by
very few steps, to the highest of all natural laws,--we mean those of
motion and force. Nothing can be more simple, precise, and general,
than the enunciation of these laws; and, as we have once before
observed, their application to particular facts in the descending or
deductive method is limited by nothing but the limited extent of our
mathematics. It would seem, then, that dynamical science were taken
thenceforward out of the pale of induction, and transformed into a
matter of absolute _à priori_ reasoning, as much as geometry; and so
it would be, were our mathematics perfect, and all the _data_ known.
Unhappily, the first is so far from being the case, that in many
of the most interesting branches of dynamical enquiry they leave
us completely at a loss. In what relates to the motions of fluids,
for instance, this is severely felt. We can include our problems,
it is true, in algebraical equations, and we can demonstrate that
they _contain_ the solutions; but the equations themselves are so
intractable, and present such insuperable difficulties, that they often
leave us quite as much in the dark as before. But even were these
difficulties overcome, recourse to experience must still be had, to
establish the _data_ on which particular applications are to depend;
and although mathematical analysis affords very powerful means of
_representing_ in general terms the data of any proposed case, and
_afterwards_, by comparison of its results with fact, determining
_what_ those data must be to explain the observed phenomena, still,
in any mode of considering the matter, an appeal to experience in
every particular instance of application is unavoidable, even when
the general principles are regarded as sufficiently established
without it. Now, in all such cases of difficulty we must recur to our
inductive processes, and regard the branches of dynamical science where
this takes place as purely experimental. By this we gain an immense
advantage, viz. that in all those points of them where the abstract
dynamical principles _do_ afford distinct conclusions, we obtain
verifications for our inductions of the highest and finest possible
kind. When we work our way up inductively to one of these results, we
cannot help feeling the strongest assurance of the validity of the
induction.

(189.) The necessity of this appeal to experiment in every thing
relating to the motions of fluids on the large scale has long been
felt. Newton himself, who laid the first foundations of hydrodynamical
science (so this branch of dynamics is called), distinctly perceived
it, and set the example of laborious and exact experiments on their
resistance to motion, and other particulars. Venturi, Bernoulli, and
many others, have applied the method of experiment to the motions
of fluids in pipes and canals; and recently the brothers Weber have
published an elaborate and excellent experimental enquiry into the
phenomena of waves. One of the greatest and most successful attempts,
however, to bring an important, and till then very obscure, branch
of dynamical enquiry back to the dominion of experiment, has been
made by Chladni and Savart in the case of sound and vibratory motion
in general; and it is greatly to be wished that the example may be
followed in many others hardly less abstruse and impracticable when
theoretically treated. In such cases the inductive and deductive
methods of enquiry may be said to go hand in hand, the one verifying
the conclusions deduced by the other; and the combination of experiment
and theory, which may thus be brought to bear in such cases, forms
an engine of discovery infinitely more powerful than either taken
separately. This state of any department of science is perhaps of
all others the most interesting, and that which promises the most to
research.

(190.) It can hardly be expected that we should terminate this division
of our subject without some mention of the “prerogatives of instances”
of Bacon, by which he understands characteristic phenomena, selected
from the great miscellaneous mass of facts which occur in nature,
and which, by their number, indistinctness, and complication, tend
rather to confuse than to direct the mind in its search for causes
and general heads of induction. Phenomena so selected on account of
some peculiarly forcible way in which they strike the reason, and
impress us with a kind of sense of causation, or a particular aptitude
for generalization, he considers, and justly, as holding a kind of
prerogative dignity, and claiming our first and especial attention in
physical enquiries.

(191.) We have already observed that, in forming inductions, it will
most commonly happen that we are led to our conclusions by the especial
force of some two or three strongly impressive facts, rather than by
affording the whole mass of cases a regular consideration; and hence
the need of cautious verification. Indeed, so strong is this propensity
of the human mind, that there is hardly a more common thing than to
find persons ready to assign a cause for every thing they see, and, in
so doing, to join things the most incongruous, by analogies the most
fanciful. This being the case, it is evidently of great importance
that these first ready impulses of the mind should be made on the
contemplation of the cases most likely to lead to good inductions.
The misfortune, however, is, in natural philosophy, that the choice
does not rest with us. We must take the instances as nature presents
them. Even if we are furnished with a list of them in tabular order,
we must understand and compare them with each other, before we can
tell which _are_ the instances thus deservedly entitled to the highest
consideration. And, after all, after much labour in vain, and groping
in the dark, accident or casual observation will present a case which
strikes us at once with a full insight into a subject, before we can
even have time to determine to what class its _prerogative_ belongs.
For example, the laws of crystallography were obscure, and its causes
still more so, till Haüy fortunately dropped a beautiful crystal of
calcareous spar on a stone pavement, and broke it. In piecing together
the fragments, he observed their facets not to correspond with those of
the crystal in its entire state, but to belong to another form; and,
following out the hint offered by a “_glaring instance_” thus casually
obtruded on his notice, he discovered the beautiful laws of the
cleavage, and the primitive forms of minerals.

(192.) It has always appeared to us, we must confess, that the help
which the classification of instances, under their different titles of
prerogative, affords to inductions, however just such classification
may be in itself, is yet more apparent than real. The force of the
instance must be felt in the mind, before it can be referred to
its place in the system; and, before it can be either referred or
appretiated, it must be known; and when it _is_ appretiated, we are
ready enough to interweave it in our web of induction, without greatly
troubling ourselves with enquiring whence it derives the weight we
acknowledge it to have in our decisions. However, since much importance
is usually attached to this part of Bacon’s work, we shall here give a
few examples to illustrate the nature of some of his principal cases.
One, of what he calls “glaring instances,” has just been mentioned.
In these, the _nature_ or cause enquired into, (which in this case
is the cause of the assumption of a peculiar external form, or the
internal _structure_ of a crystal,) “stands naked and alone, and this
in an eminent manner, or in the highest degree of its power.” No doubt,
such instances as these are highly instructive; but the difficulty in
physics is to find such, not to perceive their force when found.

(193.) The contrary of glaring are “clandestine instances,” where
“the nature sought is exhibited in its weakest and most imperfect
state.” Of this, Bacon himself has given an admirable example in the
cohesion of fluids, as a _clandestine instance_ of the “_nature_ or
quality of consistence, or solidity.” Yet here, again, the same acute
discrimination which enabled Bacon to perceive the analogy which
connects fluids with solids, through the common property of cohesive
attraction, would, at the same time, have enabled him to draw from it,
if properly supported, every consequence necessary to forming just
notions of the cohesive force; nor does its reference to the class of
clandestine instances at all assist in bringing forward and maturing
the final results. When, however, the final result is obtained,--when
our induction is complete, and we would verify it,--this class of
instances is of great use, being, in fact, frequently no other than
that of _extreme cases_, such as we have already spoken of (in §
177.); which, by placing our conclusions, as it were, in violent
circumstances, try their temper, and bring their vigour to the test.

(194.) Bacon’s “collective instances” (_instantiæ unionis_), are no
other than general facts, or laws of some degree of generality, and
are themselves the results of induction. But there is a species of
collective instance which Bacon does not seem to have contemplated, of
a peculiarly instructive character; and that is, where particular cases
are offered to our observation in such numbers at once as to make the
induction of their law a matter of ocular inspection. For example, the
parabolic form assumed by a jet of water spouted from a round hole,
is a _collective instance_ of the velocities and directions of the
motions of all the particles which compose it _seen at once_, and which
thus leads us, without trouble, to recognize the law of the motion of
a projectile. Again, the beautiful figures exhibited by sand strewed
on regular plates of glass or metal set in vibration, are _collective
instances_ of an infinite number of points which remain at rest while
the remainder of the plate vibrates; and in consequence afford us,
as it were, a sight of the law which regulates their arrangement
and sequence throughout the whole surface. The beautifully coloured
lemniscates seen around the optic axes of crystals exposed to polarized
light afford a superb example of the same kind, pointing at once to
the general mathematical expression of the law which regulates their
production.[46] Of such collective instances as these, it is easy to
see the importance, and its reason. They lead us to a general law by an
induction which offers itself spontaneously, and thus furnish advanced
points in our enquiries; and when we start from these, already “a
thousand steps are lost.”

(195.) A fine example of a collective instance is that of the system
of Jupiter or Saturn with its satellites. We have here, in miniature,
and seen at one view, a system similar to that of the planets about
the sun; of which, from the circumstance of our being involved in it,
and unfavourably situated for seeing it otherwise than in detail, we
are incapacitated from forming a general idea but by slow progressive
efforts of reason. Accordingly, the contemplation of the _circumjovial
planets_ (as they were called) most materially assisted in securing the
admission of the Copernican system.

(196.) Of “Crucial instances” we have also already spoken, as affording
the readiest and securest means of eliminating extraneous causes, and
deciding between rival hypotheses. Owing to the disposition of the
mind to form hypotheses, and to prejudge cases, it constantly happens
that, among all the possible suppositions which may occur, two or three
principal ones occupy us, to the exclusion of the rest; or it may
be that, if we have been less precipitate, out of a great multitude
rejected for obvious inapplicability to some one or other case, two or
three of better claims remain for decision; and this such instances
enable us to do. One of the instances cited by Bacon in illustration of
his crucial class is very remarkable, being neither more nor less than
the proposal of a direct experiment to determine whether the tendency
of heavy bodies downwards is a result of some peculiar mechanism in
themselves, or of the attraction of the earth “by the corporeal mass
thereof, as by a collection of bodies of the same nature.” If it be so,
he says, “it will follow that the nearer all bodies approach to the
earth, the stronger and with the greater force and velocity they will
tend to it; but the farther they are, the weaker and slower:” and his
experiment consists in comparing the effect of a spring and a weight
in keeping up the motions of two “clocks,” regulated together, and
removed alternately to the tops of high buildings and into the deepest
mines. By _clocks_ he could not have meant pendulum clocks, which were
not then known, (the first made in England was in 1662,) _fly_-clocks,
so that the comparison, though too coarse, was not contrary to sound
mechanical principles. In short, its principle was the comparison of
the effect of a spring with that of a weight, in producing certain
motions in certain times, on heights and in mines. Now, this is the
very same thing that has really been done in the recent experiments
of professors Airy and Whewell in Dolcoath mine: a pendulum (a weight
moved by gravity) has been compared with a chronometer balance, moved
and regulated by a spring. In his 37th aphorism, Bacon also speaks of
gravity as an incorporeal power, acting at a distance, and _requiring
time for its transmission_; a consideration which occurred at a later
period to Laplace, in one of his most delicate investigations.

(197.) A well chosen and strongly marked crucial instance is,
sometimes, of the highest importance; when two theories, which run
parallel to each other (as is sometimes the case) in their explanation
of great classes of phenomena, at length come to be placed at issue
upon a single fact. A beautiful instance of this will be cited in the
next section. We may add to the examples above given of such instances,
that of the application of chemical tests, which are almost universally
crucial experiments.

(198.) Bacon’s “travelling instances” are those in which the _nature_
or quality under investigation “travels,” or varies in degree; and thus
(according to § 152.) afford an indication of a cause by a gradation
of intensity in the effect. One of his instances is very happy, being
that of “paper, which is white when dry, but proves less so when wet,
and comes nearer to the state of transparency upon the exclusion of the
air, and admission of water.” In reading this, and many other instances
in the Novum Organum, one would almost suppose (had it been written)
that its author had taken them from Newton’s Optics.

(199.) The travelling instances, as well as what Bacon terms “frontier
instances,” are cases in which we are enabled to trace that general
law which seems to pervade all nature--the law, as it is termed, of
continuity, and which is expressed in the well known sentence, “Natura
non agit per saltum.” The pursuit of this law into cases where its
application is not at first sight obvious, has proved a fertile source
of physical discovery, and led us to the knowledge of an analogy and
intimate connection of phenomena between which at first we should never
have expected to find any.

(200.) For example, the transparency of gold leaf, which permits a
bluish-green light to pass through it, is a frontier instance between
the transparency of pellucid bodies and the opacity of metals, and it
prevents a breach of the law of continuity between transparent and
opake bodies, by exhibiting a body of the class generally regarded
the most opake in nature, as still possessed of some slight degree
of transparency. It thus proves that the quality of opacity is not a
_contrary_ or _antagonist_ quality to that of transparency, but only
its extreme lowest degree.



CHAP. VII.

  OF THE HIGHER DEGREES OF INDUCTIVE GENERALIZATION, AND OF THE
    FORMATION AND VERIFICATION OF THEORIES.


(201.) As particular inductions and laws of the first degree of
generality are obtained from the consideration of individual facts,
so Theories result from a consideration of these laws, and of the
proximate causes brought into view in the previous process, regarded
all together as constituting a new set of phenomena, the creatures
of reason rather than of sense, and each representing under general
language innumerable particular facts. In raising these higher
inductions, therefore, more scope is given to the exercise of pure
reason than in slowly groping out our first results. The mind is more
disencumbered of matter, and moves as it were in its own element. What
is now before it, it perceives more intimately, and less through the
medium of sense, or at least not in the same manner as when actually at
work on the immediate objects of sense. But it must not be therefore
supposed that, in the formation of theories, we are abandoned to
the unrestrained exercise of imagination, or at liberty to lay down
arbitrary principles, or assume the existence of mere fanciful causes.
The liberty of speculation which we possess in the domains of theory is
not like the wild licence of the slave broke loose from his fetters,
but rather like that of the freeman who has learned the lessons of
self-restraint in the school of just subordination. The ultimate
objects we pursue in the highest theories are the same as those of the
lowest inductions; and the means by which we can most securely attain
them bear a close analogy to those which we have found successful in
such inferior cases.

(202.) The immediate object we propose to ourselves in physical
theories is the analysis of phenomena, and the knowledge of the hidden
processes of nature in their production, so far as they can be traced
by us. An important part of this knowledge consists in a discovery
of the actual structure or mechanism of the universe and its parts,
through which, and by which, those processes are executed; and of the
agents which are concerned in their performance. Now, the mechanism of
nature is for the most part either on too large or too small a scale
to be immediately cognizable by our senses; and her agents in like
manner elude direct observation, and become known to us only by their
effects. It is in vain therefore that we desire to become witnesses to
the processes carried on with such means, and to be admitted into the
secret recesses and laboratories where they are effected. Microscopes
have been constructed which magnify more than a thousand times in
_linear_ dimension, so that the smallest visible grain of sand may
be enlarged to the appearance of one a thousand million times more
bulky; yet the only impression we receive by viewing it through such
a magnifier is, that it reminds us of some vast fragment of a rock,
while the intimate structure on which depend its colour, its hardness,
and its chemical properties, remains still concealed: we do not seem
to have made even an approach to a closer analysis of it by any such
scrutiny.

(203.) On the other hand, the mechanism of the great system of which
our planet forms a part escapes immediate observation by the immensity
of its scale, nay, even by the slowness of its evolutions. The motion
of the minute hand of a watch can hardly be perceived without the
closest attention, and that of the hour hand not at all. But what are
these, in respect of the impression of slowness they produce in our
minds, compared with a revolving movement which takes a whole year, or
twelve, thirty, or eighty years to complete, as is the case with the
planets in their revolutions round the sun. Yet no sooner do we come
to reflect on the linear dimensions of these orbs, (which however we
do not _see_, nor can we measure them but by a long, circuitous, and
difficult process,) than we are lost in astonishment at the swiftness
of the very motions which before seemed so slow.[47] The motion of the
sails of a windmill offers (on a small scale) an illustrative case. At
a distance the rotation seems slow and steady--but when we stand close
to one of the sails in its sweep, we are surprised at the swiftness
with which it rushes by us.

(204.) Again, the agents employed by nature to act on material
structures are invisible, and only to be traced by the effects they
produce. Heat dilates matter with an irresistible force; but what heat
is, remains yet a problem. A current of electricity passing along a
wire moves a magnetized needle at a distance; but except from this
effect we perceive no difference between the condition of the wire
when it conveys and when it does not convey the stream: and we apply
the terms current, or stream, to the electricity only because in some
of its relations it reminds us of something we have observed in a
stream of air or water. In like manner we see that the moon circulates
about the earth; and because we believe it to be a solid mass, and
have never seen one solid substance revolve round another within our
reach to handle and examine unless retained by a force or united by a
tie, we conclude that there _is_ a force, and a mode of connection,
between the moon and the earth; though, what that mode can be, we have
no conception, nor can imagine _how_ such a force can be exerted at a
distance, and with empty space, or at most an invisible fluid, between.
(See § 148.)

(205.) Yet are we not to despair, since we see regular and beautiful
results brought about in human works by means which nobody would, at
first sight, think could have any thing to do with them. A sheet of
blank paper is placed upon a frame, and shoved forwards, and after
winding its way successively over and under half a dozen rollers, and
performing many other strange evolutions, comes out printed on both
sides. And, after all, the acting cause in this process is nothing
more than a few gallons of water boiled in an iron vessel, at a
distance from the scene of operations. But _why_ the water so boiled
should be capable of producing the active energy which sets the whole
apparatus in motion is, and will probably long remain, a secret to us.

(206.) This, however, does not at all prevent our having a very perfect
comprehension of the whole subsequent process. We might frequent
printing-houses, and form a theory of printing, and having worked our
way up to the point where the mechanical action commenced (the boiler
of the steam-engine), and verified it by taking to pieces, and putting
together again, the train of wheels and the presses, and by sound
theoretical examination of all the transfers of motion from one part to
another; we should, at length, pronounce our theory good, and declare
that we understood printing thoroughly. Nay, we might even go away and
apply the principles of mechanism we had learned in this enquiry to
other widely different purposes; construct other machines, and put them
in motion by the same moving power, and all without arriving at any
correct idea as to the ultimate source of the force employed. But, if
we were inclined to theorize farther, we might do so; and it is easy
to imagine how two theorists might form very different _hypotheses_ as
to the origin of the power which alternately raised and depressed the
piston-rod of the engine. One, for example, might maintain that the
boiler (whose contents we will suppose that neither theorist has been
permitted to examine) was the den of some powerful unknown animal, and
he would not be without plausible analogies in the warmth, the supply
of fuel and water, the breathing noises, the smoke, and above all, the
mechanical power exerted. He would say (not without a show of reason),
that where there is a positive and wonderful effect, and many strong
analogies, such as materials consumed, and all the usual signs of life
maintained, we are not to deny the existence of animal life because
we know no animal that consumes such food. Nay, he might observe with
truth, that the fuel actually consists of the chemical ingredients
which constitute the chief food of all animals, &c.; while, on the
other hand, his brother theorist, who caught a glimpse of the fire,
and detected the peculiar sounds of ebullition, might acquire a better
notion of the case, and form a theory more in consonance with fact.

(207.) Now, nothing is more common in physics than to find two, or even
many, _theories_ maintained as to the origin of a natural phenomenon.
For instance, in the case of heat itself, one considers it as a really
existing material fluid, of such exceeding subtlety as to penetrate
all bodies, and even to be capable of combining with them chemically;
while another regards it as nothing but a rapid vibratory or rotatory
motion in the ultimate particles of the bodies heated; and produces
a singularly ingenious train of mechanical reasoning to show, that
there is nothing contradictory to sound dynamical principles in such
a doctrine. Thus, again, with light: one considers it as consisting
in actual particles darted forth from luminous bodies, and acted
upon in their progress by forces of extreme intensity residing in the
substances on which they strike; another, in the vibratory motion of
the particles of luminous bodies, communicated to a peculiar subtle and
highly elastic ethereal medium, filling all space, and conveyed through
it into our eyes, as sounds are to our ears, by the undulations of the
air.

(208.) Now, are we to be deterred from framing hypotheses and
constructing theories, because we meet with such dilemmas, and
find ourselves frequently beyond our depth? Undoubtedly not. _Est
quodam prodire tenus si non datur ultra._ Hypotheses, with respect
to theories, are what presumed proximate causes are with respect to
particular inductions: they afford us motives for searching into
analogies; grounds of citation to bring before us all the cases which
seem to bear upon them, for examination. A well imagined hypothesis,
if it have been suggested by a fair inductive consideration of general
laws, can hardly fail at least of enabling us to generalize a step
farther, and group together several such laws under a more universal
expression. But this is taking a very limited view of the value and
importance of hypotheses: it may happen (and it has happened in the
case of the undulatory doctrine of light) that such a weight of analogy
and probability may become accumulated on the side of an hypothesis,
that we are compelled to admit one of two things; either that it is
an actual statement of what really passes in nature, or that the
reality, whatever it be, must run so close a parallel with it, as to
admit of some mode of expression common to both, at least in so far
as the phenomena actually known are concerned. Now, this is a very
great step, not only for its own sake, as leading us to a high point in
philosophical speculation, but for its applications; because whatever
conclusions we deduce from an hypothesis so supported must have at
least a strong presumption in their favour: and we may be thus led to
the trial of many curious experiments, and to the imagining of many
useful and important contrivances, which we should never otherwise have
thought of, and which, at all events, if verified in practice, are real
additions to our stock of knowledge and to the arts of life.

(209.) In framing a theory which shall render a rational account of
any natural phenomenon, we have _first_ to consider the agents on
which it depends, or the causes to which we regard it as ultimately
referable. These agents are not to be arbitrarily assumed; they
must be such as we have good inductive grounds to believe do exist
in nature, and do perform a part in phenomena analogous to those we
would render an account of; or such, whose presence in the actual
case can be demonstrated by unequivocal signs. They must be _veræ
causæ_, in short, which we can not only show to exist and to act,
but the laws of whose action we can derive independently, by direct
induction, from experiments purposely instituted; or at least make
such suppositions respecting them as shall not be contrary to our
experience, and which will remain to be verified by the coincidence of
the conclusions we shall deduce from them, with facts. For example,
in the theory of gravitation we suppose an agent,--_viz._ force, or
mechanical power,--to act on _any_ material body which is placed in
the presence of _any_ other, and to urge the two mutually towards each
other. This is a _vera causa_; for heavy bodies (that is, all bodies,
but some more, some less,) tend to, or endeavour to reach, the earth,
and require the exertion of force to counteract this endeavour, or
to keep them up. Now, that which opposes and neutralizes force _is_
force. And again, a plumb-line, which, when allowed to hang freely,
always hangs perpendicularly; is found to hang observably aside from
the perpendicular when in the neighbourhood of a considerable mountain;
thereby proving that a force is exerted upon it, which draws it towards
the mountain. Moreover, since it is a fact that the moon does circulate
about the earth, it must be drawn towards the earth by a force; for if
there were no force acting upon it, it would go on in a straight line
without turning aside to circulate in an orbit, and would, therefore,
soon go away and be lost in space. This force, then, which we call the
_force_ of gravity, is a real cause.

(210.) We have next to consider the laws which regulate the action of
these our primary agents; and these we can only arrive at in three
ways: 1st, By inductive reasoning; that is, by examining all the
cases in which we know them to be exercised, inferring, as well as
circumstances will permit, its amount or intensity in each particular
case, and then piecing together, as it were, these _disjecta membra_,
generalizing from them, and so arriving at the laws desired; 2dly,
By forming at once a bold hypothesis, particularizing the law,
and trying the truth of it by following out its consequences and
comparing them with facts; or, 3dly, By a process partaking of both
these, and combining the advantages of both without their defects,
viz. by assuming indeed the laws we would discover, but so generally
expressed, that they shall include an unlimited variety of particular
laws;--following out the consequences of this assumption, by the
application of such general principles as the case admits;--comparing
them in succession with all the particular cases within our knowledge;
and, lastly, _on this comparison_, so modifying and restricting the
general enunciation of our laws as to _make the results agree_.

(211.) All these three processes for the discovery of those general
elementary laws on which the higher theories are grounded are
applicable with different advantage in different circumstances.
We might exemplify their successive application to the case of
gravitation: but as this would rather lead into a disquisition too
particular for the objects of this discourse, and carry us too much
into the domain of technical mathematics, we shall content ourselves
with remarking, that the method last mentioned is that which
mathematicians (especially such as have a considerable command of
those general modes of representing and reasoning on quantity, which
constitute the higher analysis,) find the most universally applicable,
and the most efficacious; and that it is applicable with especial
advantage in cases where subordinate inductions of the kind described
in the last section have already led to laws of a certain generality
admitting of mathematical expression. Such a case, for instance,
is the elliptic motion of a planet, which is a general proposition
including the statement of an infinite number of particular _places_,
in which the laws of its motion allow it to be some time or other
found, and for which, of course, the law of force must be so assumed as
to account.

(212.) With regard to the first process of the three above enumerated,
it is in fact an induction of the kind described in § 185.; and all
the remarks we there made on that kind of induction apply to it in
this stage. The direct assumption of a particular hypothesis has been
occasionally practised very successfully. As examples, we may mention
Coulomb’s and Poisson’s theories of electricity and magnetism, in
both which, phenomena of a very complicated and interesting nature
are referred to the actions of attractive and repulsive forces,
following a law similar in its expression to the law of gravitation.
But the difficulty and labour, which, in the greater theories, always
attends the pursuit of a fundamental law into its remote consequences,
effectually precludes this method from being commonly resorted to as
a means of discovery, unless we have some good reason, from analogy
or otherwise, for believing that the attempt will prove successful,
or have been first led by partial inductions to particular laws which
naturally point it out for trial.

(213.) In this case the law assumes all the characters of a general
phenomenon resulting from an induction of particulars, but not yet
verified by comparison with _all_ the particulars, nor extended to all
that it is capable of including. (See § 171.) It is the verification
of such inductions which constitutes theory in its largest sense, and
which embraces an estimation of the influence of all such circumstances
as may modify the effect of the cause whose laws of action we have
arrived at and would verify. To return to our example: particular
inductions drawn from the motions of the several planets about the
sun, and of the satellites round their primaries, &c. having led us
to the general conception of an attractive force exerted by every
particle of matter in the universe on every other according to the law
to which we attach the name of gravitation; when we would verify this
induction, we must set out with assuming this law, considering the
whole system as subjected to its influence and implicitly obeying it,
and nothing interfering with its action; we then, for the first time,
perceive a train of modifying circumstances which had not occurred to
us when reasoning upwards from particulars to obtain the fundamental
law; we perceive that _all the planets_ must attract _each other_,
must therefore draw each other out of the orbits which they would
have if acted on only by the sun; and as this was never contemplated
in the inductive process, its validity becomes a question, which can
only be determined by ascertaining precisely how great a deviation
this new class of mutual actions will produce. To do this is no easy
task, or rather, it is the most difficult task which the genius of
man has ever yet accomplished: still, it _has_ been accomplished by
the mere application of the general laws of dynamics; and the result
(undoubtedly a most beautiful and satisfactory one) is, that all
those observed deviations in the motions of our system which stood
out as exceptions (§ 154.), or were noticed as residual phenomena and
reserved for further enquiry (§ 158.), in that imperfect view of the
subject which we got in the subordinate process by which we rose to
our general conclusion, prove to be the immediate consequences of the
above-mentioned mutual actions. As such, they are neither exceptions
nor residual facts, but fulfilments of general rules, and essential
features in the statement of the case, _without_ which our induction
would be invalid, and the law of gravitation positively untrue.

(214.) In the theory of gravitation, the law is all in all, applying
itself at once to the materials, and directly producing the result.
But in many other cases we have to consider not merely the laws
which regulate the actions of our ultimate causes, but a system of
mechanism, or a structure of parts, through the intervention of which
their effects become sensible to us. Thus, in the delicate and curious
electro-dynamic theory of Ampere, the mutual attraction or repulsion
of two magnets is referred to a more universal phenomenon, the mutual
action of electric currents, according to a certain fundamental law.
But, in order to bring the case of a magnet within the range of this
law, he is obliged to make a supposition of a peculiar structure or
mechanism, which constitutes a body a magnet, viz. that around each
particle of the body there shall be constantly circulating, in a
certain stated direction, a small current of electric fluid.

(215.) This, we may say, is too complex; it is artificial, and cannot
be granted: yet, if the admission of this or any other structure
tenfold more artificial and complicated will enable any one to present
in a general point of view a great number of particular facts,--to make
them a part of one system, and enable us to reason from the known to
the unknown, and actually to _predict facts before trial_,--we would
ask, why should it _not_ be granted? When we examine those instances
of nature’s workmanship which we can take to pieces and understand,
we find them in the highest degree artificial in our own sense of the
word. Take, for example, the structure of an eye, or of the skeleton of
an animal,--what complexity and what artifice! In the one, a _pellucid
muscle_; a lens formed with elliptical surfaces; a circular aperture
capable of enlargement or contraction without loss of form. In the
other, a framework of the most curious carpentry; in which occurs
not a single straight line, nor any known geometrical curve, yet all
evidently systematic, and constructed by rules which defy our research.
Or examine a crystallized mineral, which we can in some measure
dissect, and thus obtain direct evidence of an internal structure.
Neither artifice nor complication are here wanting; and though it
is easy to assert that these appearances are, after all, produced
by something which would be very simple, if we did but know it, it
is plain that the same might be _said_ of a steam-engine executing
the most complicated movements, previous to any investigation of its
nature, or any knowledge of the source of its power.

(216.) In estimating, however, the value of a theory, we are not to
look, _in the first instance_, to the question, whether it establishes
satisfactorily, or not, a particular process or mechanism; for of
this, after all, we can never obtain more than that indirect evidence
which consists in its leading to the same results. What, in the actual
state of science, is far more important for us to know, is whether our
theory truly represent _all_ the facts, and include _all_ the laws, to
which observation and induction lead. A theory which did this would,
no doubt, go a great way to establish any hypothesis of mechanism or
structure, which might form an essential part of it: but this is very
far from being the case, except in a few limited instances; and, till
it is so, to lay any great stress on hypotheses of the kind, except in
as much as they serve as a scaffold for the erection of general laws,
is to “quite mistake the scaffold for the pile.” Regarded in this
light, hypotheses have often an eminent use: and a facility in framing
them, if attended with an equal facility in laying them aside when
they have served their turn, is one of the most valuable qualities a
philosopher can possess; while, on the other hand, a bigoted adherence
to them, or indeed to peculiar views of any kind, in opposition to the
tenor of facts as they arise, is the bane of all philosophy.

(217.) There is no doubt, however, that the safest course, when it
can be followed, is to rise by inductions carried on among laws, as
among facts, from law to law, perceiving, as we go on, how laws which
we have looked upon as unconnected become particular cases, either
one of the other, or all of one still more general, and, at length,
blend altogether in the point of view from which we learn to regard
them. An example will illustrate what we mean. It is a general law,
that all hot bodies throw out or _radiate_ heat in all directions, (by
which we mean, not that heat is an actual substance darted out from hot
bodies, but only that the laws of the transmission of heat to distant
objects are similar to those which would regulate the distribution
of particles thrown forth in all directions,) and that other colder
bodies placed in their neighbourhood become hot, _as if_ they received
the heat so radiated. Again, all solid bodies which become heated in
one part _conduct_, or diffuse, the heat from that part through their
whole substance. Here we have two modes of communicating heat,--by
radiation, and by conduction; and both these have their peculiar,
and, to all appearance, very different laws. Now, let us bring a hot
and a cold body (of the same substance) gradually nearer and nearer
together,--as they approach, the heat will be communicated from the hot
to the cold one by the _laws of radiation_; and from the nearer to the
farther part of the colder one, as it gradually grows warm, by _those
of conduction_. Let their distance be diminished till they just lightly
touch. How does the heat _now_ pass from one to the other? Doubtless,
by radiation; for it may be proved, that in such a contact there is yet
an interval. Let them then be _forced_ together, and it will seem clear
that it must now be by _conduction_. Yet their _interval_ must diminish
gradually, as the force by which they are pressed together increases,
till they actually cohere, and form one. The law of continuity, then,
of which we have before spoken (§ 199.), forbids us to suppose that
the intimate nature of the process of communication is changed in this
transition from light to violent contact, and from that to actual
union. If so, we might ask, at what point does the change happen?
Especially since it is also demonstrable, that the particles of the
most solid body are not, really, in contact. _Therefore_, the laws of
conduction and radiation have a mutual dependence, and the former are
only extreme cases of the latter. If, then, we would rightly understand
what passes, or what is the process of nature in the slow communication
of heat through the substance of a solid, we must ground our enquiries
upon what takes place at a distance, and then urge the laws to which we
have arrived, up to their extreme case.

(218.) When two theories run parallel to each other, and each explains
a great many facts in common with the other, any experiment which
affords a crucial instance to decide between them, or by which one or
other must fall, is of great importance. In thus verifying theories,
since they are grounded on general laws, we may appeal, not merely
to particular cases, but to whole classes of facts; and we therefore
have a great range among the individuals of these for the selection
of some particular effect which ought to take place oppositely in the
event of one of the two suppositions at issue being right and the other
wrong. A curious example is given by M. Fresnel, as decisive, in his
mind, of the question between the two great opinions on the nature
of light, which, since the time of Newton and Huyghens, have divided
philosophers. (See § 207.) When two very clean glasses are laid one
on the other, if they be not perfectly flat, but one or both in an
almost imperceptible degree convex or prominent, beautiful and vivid
colours will be seen between them; and if these be viewed through a
red glass, their appearance will be that of alternate dark and bright
stripes. These stripes are formed _between_ the two surfaces in
apparent contact, as any one may satisfy himself by using, instead of
a flat _plate_ of glass for the upper one, a triangular-shaped piece,
called a prism, like a three-cornered stick, and looking through the
inclined side of it next the eye, by which arrangement the reflection
of light from the upper surface is prevented from intermixing with that
from the surfaces in contact. Now, the coloured stripes thus produced
are explicable on both theories, and are appealed to by both as strong
confirmatory facts; but there is a difference in one circumstance
according as one or the other theory is employed to explain them.
In the case of the Huyghenian doctrine, the intervals between the
bright stripes ought to appear _absolutely black_; in the other,
_half bright_, when so viewed through a prism. This curious case of
difference was tried as soon as the opposing consequences of the two
theories were noted by M. Fresnel, and the result is stated by him to
be decisive in favour of that theory which makes light to consist in
the vibrations of an elastic medium.

(219.) Theories are best arrived at by the consideration of general
laws; but most securely verified by comparing them with particular
facts, because this serves as a verification of the whole train
of induction, from the lowest term to the highest. But then, the
comparison must be made with facts purposely selected so as to include
every variety of case, not omitting extreme ones, and in sufficient
number to afford every reasonable probability of detecting error. A
single numerical coincidence in a final conclusion, however striking
the coincidence or important the subject, is not sufficient. Newton’s
theory of sound, for example, leads to a numerical expression for the
actual velocity of sound, differing but little from that afforded by
the correct theory afterwards explained by Lagrange, and (when certain
considerations not contemplated by him are allowed for) agreeing with
fact; yet this coincidence is no verification of Newton’s view of the
general subject of sound, which is defective in an essential point,
as the great geometer last named has very satisfactorily shown. This
example is sufficient to inspire caution in resting the verification of
theories upon any thing but a very extensive comparison with a great
mass of observed facts.

(220.) But, on the other hand, when a theory will bear the test
of such extensive comparison, it matters little how it has been
originally framed. However strange and, at first sight, inadmissible
its postulates may appear, or however singular it may seem that
such postulates should have been fixed upon,--if they only lead
us, by legitimate reasonings, to conclusions in exact accordance
with numerous observations purposely made under such a variety of
circumstances as fairly to embrace the whole range of the phenomena
which the theory is intended to account for, we cannot refuse to admit
them; or if we still hesitate to regard them as demonstrated truths, we
cannot, at least, object to receive them as temporary substitutes for
such truths, until the latter shall become known. If they suffice to
explain all the phenomena known, it becomes highly improbable that they
will not explain more; and if all their conclusions we have tried have
proved correct, it is probable that others yet untried will be found so
too; so that _in rejecting them altogether, we should reject all the
discoveries to which they may lead_.

(221.) In all theories which profess to give a true account of the
process of nature in the production of any class of phenomena, by
referring them to general laws, or to the action of general causes,
through a train of modifying circumstances; before we can apply those
laws, or trace the action of those causes in any assigned case, we
require to know the circumstances: we must have data whereon to ground
their application. Now, these can be learned only from observation;
and it may seem to be arguing in a vicious circle to have recourse
to observation for any part of those theoretical conclusions, by
whose comparison with fact the theory itself is to be tried. The
consideration of an example will enable us to remove this difficulty.
The most general law which has yet been discovered in chemistry is
this, that all the elementary substances in nature are susceptible of
entering into combination with each other only in fixed or _definite
proportions_ by weight, and not arbitrarily; so that when any two
substances are put together with a view to unite them, if their weights
are not in some certain determinate proportion, a complete combination
will not take place, but some part of one or the other ingredient will
remain over and above, and uncombined. Suppose, now, we have found a
substance having all the outward characters of a homogeneous or unmixed
body, but which, on analysis, we discover to consist of sulphur, and
lead in the proportion of 20 parts of the former to 130 of the latter
ingredient; and we would know whether this is to be regarded as a
verification of the law of definite proportions or an exception to
it. The question is reduced to this, whether the proportion 20 to 130
be or be not _that_ fixed and definite proportion, (or one of them,
if there be more than one proportion possible,) in which, according
to the law in question, sulphur and lead can combine; now, this can
never be decided by merely looking at the law in all its generality.
It is clear, that when particularized by restricting its expression
to sulphur and lead, the law should state _what are_ those particular
fixed proportions in which these bodies can combine. That is to say,
there must be certain data or numbers, by which these are distinguished
from all other bodies in nature, and which require to be known before
we can apply the general law to the particular case. To determine such
data, observation must be consulted; and if we were to have recourse
to that of the combination of the two substances in question with each
other, no doubt there would be ground for the logical objection of
a vicious circle: but this is not done; the determination of these
numerical data is derived from experiments purposely made on a great
variety of different combinations, among which that under consideration
does not of necessity occur, and all these being found, independently
of each other, to agree in giving the same results, they are therefore
safely assumed as part of the system. Thus, the law of definite
proportions, when applied to the actual state of nature, requires two
separate statements, the one announcing the general law of combination,
the other particularizing the numbers appropriate to the several
elements of which natural bodies consist, or the data of nature. Among
these data, if arranged in a list, there will be found opposite to the
element sulphur the number 16, and opposite to lead, 104[48]; and since
20 is to 130 in the exact proportion of 16 to 104, it appears that the
combination in question affords a satisfactory verification of the law.

(222.) The great importance of physical data of this description,
and the advantage of having them well determined, will be obvious,
if we consider, that a list of them, when taken in combination with
the general law, affords the means of determining at once the exact
proportion of the ingredients of all natural compounds, if we only know
the place they hold in the system. In chemistry, the number of admitted
elements is between fifty and sixty, and new ones are added continually
as the science advances. Now, the moment the number corresponding to
any new substance added to the list is determined, we have, in fact,
ascertained all the proportions in which it can enter into combination
with all the others, so that a careful experiment made with the object
of determining this number is, in fact, equivalent to as many different
experiments as there are binary, ternary, or yet more complicated
combinations capable of existing, into which the new substance may
enter, as an ingredient.

(223.) The importance of obtaining exact physical data can scarcely
be too much insisted on, for without them the most elaborate theories
are little better than mere inapplicable forms of words. It would be
of little consequence to be informed, abstractedly, that the sun and
planets attract each other, with forces proportional to their masses,
and inversely as the squares of their distances: but, as soon as we
know the data of our system, as soon as we have an accurate statement
(no matter how obtained) of the distances, masses, and actual motions
of the several bodies which compose it, we need no more to enable us to
predict all the movements of its several parts, and the changes that
will happen in it for thousands of years to come; and even to extend
our views backwards into time, and recover from the past, phenomena,
which no observation has noted, and no history recorded, and which yet
(it is possible) may have left indelible traces of their existence in
their influence on the state of nature in our own globe, and those of
the other planets.

(224.) The proof, too, that our data _are_ correctly assumed, is
involved in the general verification of the whole theory, of which,
when once assumed, they form a part; and the same comparison with
observation which enables us to decide on the truth of the abstract
principle, enables us, at the same time, to ascertain whether we
have fixed the values of our data in accordance with the actual
state of nature. If not, it becomes an important question, whether
the assumed values can be corrected, so as to bring the results of
theory to agree with facts? Thus it happens, that as theories approach
to their perfection, a more and more exact determination of data
becomes requisite. Deviations from observed fact, which, in a first
or approximative verification, may be disregarded as trifling, become
important when a high degree of precision is attained. A difference
between the calculated and observed places of a planet, which would
have been disregarded by Kepler in his verification of the law of
elliptic motion, would now be considered fatal to the theory of
gravity, unless it could be shown to arise from an erroneous assumption
of some of the numerical data of our system.

(225.) The observations most appropriate for the ready and exact
determination of physical data are, therefore, those which it is most
necessary to have performed with exactness and perseverance. Hence
it is, that their performance, in many cases, becomes a national
concern, and observatories are erected and maintained, and expeditions
despatched to distant regions, at an expense which, to a superficial
view, would appear most disproportioned to their objects. But it
may very reasonably be asked why the direct assistance afforded by
governments to the execution of continued series of observations
adapted to this especial end should continue to be, as it has hitherto
almost exclusively been, confined to astronomy.

(226.) Physical data intended to be employed as elements of calculation
in extensive theories, require to be known with a much greater degree
of exactness than any single observation possesses, not only on account
of their dignity and importance, as affording the means of representing
an indefinite multitude of facts; but because, in the variety of
combinations that may arise, or in the changes that circumstances may
undergo, cases will occur when any trifling error in one of the data
may become enormously magnified in the final result to be compared
with observation. Thus, in the case of an eclipse of the sun, when
the moon enters very obliquely upon the sun’s disc, a trifling error
in the diameter of either the sun or moon may make a great one in the
time when the eclipse shall be announced to commence. It ought to
be remarked, that these are, of all others, the conjunctures where
observations are most available for the determination of data; for,
by the same rule that a small change in the data will, in such cases,
produce a great one in the thing to be observed; so, _vice versâ_, any
moderate amount of error, committed in an observation undertaken for
ascertaining its value, can produce but a very trifling one in the
_reverse_ calculation from which the data come to be determined by
observation. This remark extends to every description of physical data
in every department of science, and is never to be overlooked when the
object in view is the determination of data with the last degree of
precision.

(227.) But how, it may be asked, are we to ascertain _by_ observation,
data more precise than observation itself? How are we to conclude the
value of that which we do not see, with greater certainty than that
of quantities which we actually see and measure? It is the number of
observations which may be brought to bear on the determination of data
that enables us to do this. Whatever error we may commit in a single
determination, it is highly improbable that we should always err the
same way, so that, when we come to take an average of a great number of
determinations, (unless there be some constant cause which gives a bias
one way or the other,) we cannot fail, at length, to obtain a very near
approximation to the truth, and, even allowing a bias, to come much
nearer to it than can fairly be expected from any single observation,
liable to be influenced by the same bias.

(228.) This useful and valuable property of the average of a great
many observations, that it brings us nearer to the truth than any
single observation can be relied on as doing, renders it the most
constant resource in all physical enquiries where accuracy is desired.
And it is surprising what a rapid effect, in equalizing fluctuations
and destroying deviations, a moderate multiplication of individual
observations has. A better example can hardly be taken than the average
height of the quicksilver in the common barometer, which measures
the pressure of the air, and whose fluctuations are proverbial.
Nevertheless, if we only observe it regularly every day, and, at the
end of each month, take an average of the observed heights, we shall
find the fluctuations surprisingly diminished in amount; and if we
go on for a whole year, or for many years in succession, the annual
averages will be found to agree with still greater exactness. This
equalizing power of averages, by destroying all such fluctuations as
are irregular or accidental, frequently enables us to obtain evidence
of fluctuations really regular, periodic in their recurrence, and
so much smaller in their amount than the accidental ones, that, but
for this mode of proceeding, they never would have become apparent.
Thus, if the height of the barometer be observed four times a day,
constantly, for a few months, and the averages taken, it will be seen
that a regular _daily_ fluctuation, of very small amount, takes place,
the quicksilver rising and falling twice in the four-and-twenty hours.
It is by such observations that we are enabled to ascertain--what no
single measure (unless by a fortunate coincidence), could give us any
idea, and never any certain knowledge of--the true _sea level_ at any
part of the coast, or the height at which the water of the ocean would
stand, if perfectly undisturbed by winds, waves, or tides: a subject of
very great importance, and upon which it would be highly desirable to
possess an extensive series of observations, at a great many points on
the coasts of the principal continents and islands over the whole globe.

(229.) In all cases where there is a direct and simple relation between
the phenomenon observed and a single _datum_ on which it depends,
every single observation will give a value of this quantity, and the
average of all (under certain restrictions) will be its exact value. We
say, under certain restrictions; for, if the circumstances under which
the observations are made be not alike, they may not all be equally
favourable to exactness, and it would be doing injustice to those most
advantageous, to class them with the rest. In such cases as these,
as well as in cases where the _data_ are numerous and complicated
together, so as not to admit of single, separate determination (a
thing of continual occurrence), we have to enter into very nice, and
often not a little intricate, considerations respecting the _probable_
accuracy of our results, or the limits of error within which it is
_probable_ they lie. In so doing we are obliged to have recourse to
a refined and curious branch of mathematical enquiry, called the
doctrine of probabilities, the object of which (as its name imports)
is to reduce our estimation of the probability of any conclusion to
calculation, so as to be able to give more than a mere guess at the
degree of reliance which ought to be placed in it.

(230.) To give some general idea of the considerations which such
computations involve, let us imagine a person firing with a pistol
at a wafer on a wall ten yards distant: we might, in a general way,
take it for granted, that he would hit the wall, but not the wafer,
at the first shot; but if we would form any thing like a probable
conjecture of _how near_ he would come to it, we must first have an
idea of his skill. No better way of judging could be devised than
by letting him fire a hundred shots at it, and marking where they
all struck. Suppose this done,--suppose the wafer has been hit once
or twice, that a certain number of balls have hit the wall within an
inch of it, a certain number between one and two inches, and so on,
and that one or two have been some feet wide of the mark. Still the
question arises, what estimate are we thence to form of his skill? how
_near_ (or nearer) may we, after this experience, safely, or at least
not unfairly, bet that he will come to the mark the next subsequent
shot? This the laws of probability enable us on such data to say.
Again, suppose, _before_ we were allowed to measure the distances,
the wafer were to have been taken away, and we were called upon, on
the mere evidence of the marks on the wall, to say where it had been
placed; it is clear that no reasoning would enable any one to say with
certainty; yet there is assuredly one place which we may fix on with
greater probability of being right than any other. Now, this is a very
similar case to that of an observer--an astronomer for example--who
would determine the exact place of a heavenly body. He points to it
his telescope, and obtains a series of results disagreeing among
themselves, but yet all agreeing within certain limits, and only a
comparatively small number of them deviating considerably from the mean
of all; and from these he is called upon to say, definitively, what he
shall consider to have been the most probable place of his star at the
moment. Just so in the calculation of physical _data_; where no two
results agree exactly, and where all come within limits, some wide,
some close, what have we to guide us when we would make up our minds
what to conclude respecting them? It is evident that any system of
calculation that can be shown to lead of necessity to the most probable
conclusion where certainty is not to be had must be valuable. However,
as this doctrine is one of the most difficult and delicate among the
applications of mathematics to natural philosophy, this slight mention
of it must suffice at present.

(231.) In the foregoing pages we have endeavoured to explain the spirit
of the methods to which, since the revival of philosophy, natural
science has been indebted for the great and splendid advances it has
made. What we have all along most earnestly desired to impress on the
student is, that natural philosophy is essentially united in all its
departments, through all which one spirit reigns and one method of
enquiry applies. It cannot, however, be studied as a whole, without
subdivision into parts; and, in the remainder of this discourse, we
shall therefore take a summary view of the progress which has been made
in the different branches into which it may be most advantageously
so subdivided, and endeavour to give a general idea of the nature of
each, and of its relations to the rest. In the course of this, we shall
have frequent opportunity to point out the influence of those general
principles we have above endeavoured to explain, on the progress of
discovery. But this we shall only do as cases arise, without entering
into any regular analysis of the history of each department with that
view. Such an analysis would, indeed, be a most useful and valuable
work, but would far exceed our present limits. We are not, however,
without a hope that this great desideratum in science will, ere long,
be supplied from a quarter every way calculated to do it justice.



                               PART III.

         OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES,
                      AND THEIR MUTUAL RELATIONS.



CHAPTER I.

OF THE PHENOMENA OF FORCE, AND OF THE CONSTITUTION OF NATURAL BODIES.


(232.) Natural History may be considered in two very different lights:
either, 1st, as a collection of facts and objects presented by nature,
from the examination, analysis, and combination of which we acquire
whatever knowledge we are capable of attaining both of the order of
nature, and of the agents she employs for producing her ends, and from
which, therefore, all sciences arise; or, 2dly, as an assemblage of
phenomena to be explained; of effects to be deduced from causes; and of
materials prepared to our hands, for the application of our principles
to useful purposes. Natural history, therefore, considered in the
one or the other of these points of view, is either the beginning or
the end of physical science. As it offers to us, in a confused and
interwoven mass, the elements of all our knowledge, our business is to
disentangle, to arrange, and to present them in a separate and distinct
state: and to this end we are called upon to resolve the important but
complicated problem,--Given the effect, or assemblage of effects, to
find the causes. The principles on which this enquiry relies are those
which constitute the relation of cause and effect, as it exists with
reference to our minds; and their rules and mode of application have
been attempted to be sketched out, (though in far less detail than the
intrinsic interest of the subject, both in a logical and practical
point of view, would demand,) in the foregoing pages. It remains
now to bring together, in a summary statement, the results of the
general examination of nature, so far as it has been prosecuted to the
discovery of natural agents, and the mode in which they act.

(233.) The first great agent which the analysis of natural phenomena
offers to our consideration, more frequently and prominently than
any other, is force. Its effects are either, 1st, to counteract the
exertion of opposing force, and thereby to maintain _equilibrium_; or,
2dly, to produce _motion_ in matter.

(234.) Matter, or that, whatever it be, of which all the objects in
nature which manifest themselves directly to our senses consist,
presents us with two general qualities, which at first sight appear
to stand in contradiction to each other--activity and inertness. Its
activity is proved by its power of spontaneously setting other matter
in motion, and of itself obeying their mutual impulse, and moving
under the influence of its own and other force; inertness, in refusing
to move unless obliged to do so by a force impressed externally, or
mutually exerted between itself and other matter, and by persisting in
its state of motion or rest unless disturbed by some external cause.
Yet in reality this contradiction is only apparent. Force being the
cause, and motion the effect produced by it on matter, to say that
matter is inert, or has _inertia_, as it is termed, is only to say
that the cause is expended in producing its effect, and that the
same cause cannot (without renewal) produce double or triple its own
proper effect. In this point of view, equilibrium may be conceived as
a continual production of two opposite effects, each undoing at every
instant what the other has done.

(235.) However, if this should appear too metaphysical, at all events
this difference of effects gives rise to two great divisions of the
science of force, which are commonly known by the names of STATICS and
DYNAMICS; the latter term, which is general, and has been used by us
before in its general sense, being usually confined to the doctrine
of motion, as produced and modified by force. Each of these great
divisions again branches out into distinct subdivisions, according as
we consider the equilibrium or motion of matter in the three distinct
states in which it is presented to us in nature, the solid, liquid, and
aëriform state, to which, perhaps, ought to be added the _viscous_,
as a state intermediate between that of solidity and fluidity, the
consideration of which, though very obscure and difficult, offers a
high degree of interest on a variety of accounts.


_Statics and Dynamics._

(236.) The principles have been definitively fixed by Galileo and his
successors, down to Newton, on a basis of sound induction; and as they
are perfectly general, and apply to every case, they are competent,
as we have already before observed, to the solution of every problem
that can occur in the deductive processes, by which phenomena are
to be explained, or effects calculated. Hence, they include every
question that can arise respecting the motions and rest of the smallest
particles of matter, as well as of the largest masses. But the mode of
reasoning from these general principles differs materially, whether
we consider them as applied to masses of matter of a sensible size,
or to those excessively minute, and perhaps indivisible, molecules of
which such masses are composed. The investigations which relate to the
latter subject are extremely intricate, as they necessarily involve the
consideration of the hypotheses we may form respecting the intimate
constitution of the several sorts of bodies above enumerated.

(237.) On the other hand, those which respect the equilibrium and
motions of sensible masses of matter are happily capable of being
so managed as to render unnecessary the adoption of any particular
hypothesis of structure. Thus, in reasoning respecting the application
of forces to a solid mass, we suppose its parts indissolubly and
unalterably connected; it matters not by what tie, provided this
condition be satisfied, that one point of it cannot be moved without
setting all the rest in motion, so that the relative situation of the
parts one among another be not changed. This is the abstract notion
of a solid which the mechanician employs in his reasonings. And their
conclusions will apply to natural bodies, of course, only so far as
they conform to such a definition. In strictness of speaking, however,
there are no bodies which absolutely conform to it. No substance is
known whose parts are absolutely incapable of yielding one among
another; but the amount by which they do yield is so excessively
small as to be demonstrably incapable, in most cases, of having any
influence on the results: and in those where it has such influence, an
especial investigation of its amount can always be made. This gives
rise to two subdivisions of the application of mechanical reasonings
to solid masses. Those which refer to the action of forces on flexible
or elastic, and on inflexible or rigid, bodies, comprehending under
the latter all such whose resistance to flexure or fracture is so
very great as to permit our adoption of the language and ideas of the
extreme case without fear of material error.

(238.) In like manner, when we reason respecting the action of forces
on a fluid mass, all we have occasion to assume is, that its parts
are freely moveable one among the other. If, besides this, we choose
to regard a fluid as incompressible, and deduce conclusions on this
supposition, they will hold good only so far as there may be found
such fluids in nature. Now, in strictness, there are none such; but,
practically speaking, in the greater number of cases their resistance
to compression is so very great that the result of the reasoning so
carried on is not sensibly vitiated; and, in the remaining cases,
the same general principles enable us to enter on a special enquiry
directed to this point: and hence the division of fluids, in mechanical
language, into compressible and incompressible, the latter being only
the extreme or limiting case of the former.

(239.) As we propose here, however, only to consider what is the actual
constitution of nature, we shall regard all bodies, as they really
are, more or less flexible and yielding. We know for certain, that
the space which any material body appears to occupy is not entirely
filled by it; because there is none which by the application of a
sufficient force may not be _compressed_ or forced into a smaller
space, and which, either wholly, as in air or liquids, or in part, as
in the greater number of solids, will not recover its former dimensions
when the force is taken off. In the case of air, this condensation
may be urged to almost any extent; and not only does a mass of air
so condensed completely recover its original bulk, when the applied
pressure is removed, but if that ordinary pressure under which it
exists at the earth’s surface (and which arises from the weight of
the atmosphere) be also removed by an air-pump, it will still further
dilate itself without limit so far as we have yet been able to try
it. Hence we are led to the conclusion that the particles of air are
mutually elastic, and have a _tendency to recede from one another_,
which can only be counteracted by _force_, and therefore is itself a
force of the repulsive kind. Nevertheless, as air is heavy, and as
gravitation is a universal property of matter, there is no doubt that
this repulsive tendency must have a limit, and that there is a distance
to which, if the particles of the air could be removed from each other,
their mutual repulsion would cease, and an attraction take its place.
This limit is probably attained at some very great height above the
earth’s surface, beyond which, of course, its atmosphere cannot extend.

(240.) What, however, we can only conclude by this or similar reasoning
respecting air, we see distinctly in liquids. They are all, though
in a small degree, compressible, and recover their former dimensions
completely when the pressure is removed; but they cannot be dilated (by
mechanical means), and have no tendency, while they remain liquids, to
enlarge themselves beyond a certain limit, and therefore they assume a
determinate _surface_ while at rest, and their parts actually resist
further separation with a considerable force, thus giving rise to the
phenomenon of the _cohesion of liquids_.

(241.) Both in air and in liquids, however, the most perfect freedom
of motion of the parts among each other subsists, which could hardly
be the case if they were not separate and independent of each other.
And from this, combined with the foregoing considerations, it has been
concluded that they do not actually touch, but are kept asunder at
determinate distances from each other, by the constant action of the
two forces of attraction and repulsion, which are supposed to balance
and counteract each other at the ordinary distances of the particles,
but to prevail, the one, or the other, according as they are forcibly
urged together or pulled asunder.

(242.) In solids, however, the case is very different. The mutual free
motion of their parts _inter se_ is powerfully impeded, and in some
almost destroyed. In some, a slow and gradual change of figure may be
produced to a great extent, by pressure or blows, as for instance in
the metals, clay, butter, &c.; in others, fracture is the consequence
of any attempt to change the figure by violence beyond a certain very
small limit. In solids, then, it is evident, that the consideration of
their intimate structure has a very great influence in modifying the
general results of the action of such attractive and repulsive forces
as may be assumed to account for the phenomena they present; yet the
general facts that their parts _cohere_ with a certain energy, and that
they resist displacement or intrusion on the part of other bodies,
are sufficient to demonstrate at least the existence of such forces,
whatever obscurity may subsist as to their mode of action.

(243.) This division of bodies into airs, liquids, and solids, gives
rise, then, to three distinct branches of mechanical science, in each
of which the general principles of equilibrium and motion have their
peculiar mode of application; viz. pneumatics, hydrostatics, and what
might, without impropriety, be termed stereostatics.


_Pneumatics._

(244.) Pneumatics relates to the equilibrium or movements of aërial
fluids under all circumstances of pressure, density, and elasticity.
The weight of the air, and its pressure on all the bodies on the
earth’s surface, were quite unknown to the ancients, and only first
perceived by Galileo, on the occasion of a sucking-pump refusing to
draw water above a certain height. Before his time it had always been
supposed that water rose by suction in a pipe, in consequence of a
certain natural _abhorrence of a vacuum_ or empty space, which obliged
the water to enter by way of supplying the place of the air sucked out.
But if any such abhorrence existed, and had the force of an _acting
cause_, which could urge water a single foot into a pipe, there is no
reason why the same principle should not carry it up two, three, or
any number of feet; none why it should suddenly stop short at a certain
height, and refuse to rise higher, however violent the suction might
be, nay, even fall back, if purposely forced up too high.

(245.) Galileo, however, at first contented himself with the
conclusion, that the natural abhorrence of a vacuum was not strong
enough to sustain the water more than about thirty-two feet above
its level; and, although the true cause of the phenomenon at length
occurred to him, in the pressure of the air on the general surface,
it was not satisfactorily demonstrated till his pupil, Torricelli,
conceived the happy idea of instituting an experiment on a small
scale by the use of a much heavier liquid, mercury, instead of water,
and, in place of sucking out the air from above, employing the much
more effectual method of filling a long glass tube with mercury, and
inverting it into a basin of the same metal. It was then at once seen,
as by a _glaring instance_, that the maintenance of the mercury in the
tube (which is nothing else than the common barometer) was the effect
of a perfectly definite external cause, while its fluctuations from day
to day, with the varying state of the atmosphere, strongly corroborated
the notion of its being due to the pressure of the external air on the
surface of the mercury in the reservoir.

(246.) The discovery of Torricelli was, however, at first much
misconceived, and even disputed, till the question was finally decided
by appeal to a _crucial instance_, one of the first, if not the very
first on record in physics, and for which we are indebted to the
celebrated Pascal. His acuteness perceived that if the weight of the
incumbent air be the direct cause of the elevation of the mercury,
it must be measured by the amount of that elevation, and therefore
that, by carrying a barometer up a high mountain, and so ascending
into the atmosphere _above_ a large portion of the incumbent air, the
pressure, as well as the length of the column sustained by it, must
be diminished; while, on the other hand, if the phenomenon were due
to the cause originally assigned, no difference could be expected to
take place, whether the observation were made on a mountain or on the
plain. Perhaps the decisive effect of the experiment which he caused
to be instituted for the purpose, on the Puy de Dôme, a high mountain
in Auvergne, while it convinced every one of the truth of Torricelli’s
views, tended more powerfully than any thing which had previously been
done in science to confirm, in the minds of men, that disposition to
experimental verification which had scarcely yet taken full and secure
root.

(247.) Immediately on this discovery followed that of the air-pump,
by Otto von Guericke of Magdeburgh, whose aim seems to have been to
decide the question, whether a vacuum could or could not exist, by
endeavouring to make one. The imperfection of his mechanism enabled
him only to diminish the aërial contents of his receivers, not
entirely to empty them; but the curious effects produced by even a
partial exhaustion of air speedily excited attention, and induced our
illustrious countryman, Robert Boyle, to the prosecution of those
experiments which terminated in his hands, and in those of Hauksbee,
Hooke, Mariotte, and others, in a satisfactory knowledge of the
general law of the equilibrium of the air under the influence of
greater or less pressures. These discoveries have since been extended
to all the various descriptions of aërial fluids which chemistry has
shown to exist, and to maintain their aëriform state under artificial
pressure, and even to those which may be produced from liquids reduced
to a state of vapour by heat, so long as they retain that state.

(248.) The manner in which the observed law of equilibrium of an
elastic fluid, like air, may be considered to originate in the mutual
repulsion of its particles, has been investigated by Newton, and
the actual statement of the law itself, as announced by Mariotte,
“that the density of the air, or the quantity of it contained in the
same space, is, _cæteris paribus_, proportional to the pressure it
supports,” has recently been verified within very extensive limits by
direct experiment, by a committee of the Royal Academy of Paris. This
law contains the principle of solution of every dynamical question
that can occur relative to the equilibrium of elastic fluids, and is
therefore to be regarded as one of the highest _axioms_ in the science
of pneumatics.


_Hydrostatics._

(249.) The principles of the equilibrium of liquids, understanding
by this word such fluids as do not, though quite at liberty, attempt
to dilate themselves beyond a certain point, are at once few and
simple. The first steps towards a knowledge of them were made by
Archimedes, who established the general fact, that a solid immersed in
a liquid loses a portion of its weight equal to that of the liquid it
displaces. It seems very astonishing, after this, that it should not
have been at once concluded that the weight thus said to be _lost_ is
only _counteracted_ by the upward pressure of the liquid, and that,
therefore, a portion of any liquid, surrounded on all sides by a liquid
of the same kind, does really exert its weight in keeping its place.
Yet the prejudice that “liquids do not gravitate in their natural
place” kept its ground, and was only dispelled with the mass of error
and absurdity which the introduction of a rational and experimental
philosophy by Galileo swept away.

(250.) The hydrostatical law of _the equal pressure of liquids in all
directions_, with its train of curious and important consequences, is
an immediate conclusion from the perfect mobility of their parts among
one another, in consequence of which each of them tends to recede from
an excess of pressure on one side, and thus bears upon the rest, and
distributes the pressure among its neighbours. In this form it was
laid down by Newton, and has proved one of the most useful and fertile
principles of physico-mathematical reasoning on the equilibrium of
fluid masses, as affording a means of tracing the action of a force
applied at any point of a liquid through its whole extent. It applies,
too, without any modification, to expansible fluids as well as to
liquids; and, in the applications of geometry to this subject, enables
us to dispense with any minute and intricate enquiries as to the mode
in which individual particles act on each other.

(251.) In a practical point of view, this law is remarkable for the
directness of its application to useful purposes. The immediate and
perfect distribution of a pressure applied on any one part, however
small, of a fluid surface through the whole mass, enables us to
communicate _at one instant_ the same pressure to any number of such
parts by merely increasing the surface of the fluid, which may be done
by enlarging the containing vessel; and if the vessel be so constructed
that a large portion of its surface shall be moveable together, the
pressures on all the similar parts of this portion will be united into
one consentient force, which may thus be increased to any extent we
please. The hydraulic press, invented by Bramah, (or rather applied by
him after a much more ancient inventor, Stevin,) is constructed on this
principle. A small quantity of water is driven by sufficient pressure
into a vessel _already full_, and provided with a moveable surface or
piston of great size. Under such circumstances something must give way;
the great surface of the piston accumulates the pressure on it to such
an extent that nothing can resist its violence. Thus, trees are torn
up by the roots; piles extracted from the earth; woollen and cotton
goods compressed into the most portable dimensions; and even hay, for
military service, reduced to such a state of coercion as to be easily
packed on board transports.

(252.) Liquids differ from aëriform fluids by their _cohesion_, which
may be regarded as a kind of approach to a solid state, and was so
regarded by Bacon (193.). Indeed, there can be little doubt that
the solid, liquid, and aëriform states of bodies are merely stages
in a progress of gradual transition from one extreme to the other;
and that, however strongly marked the distinctions between them may
appear, they will ultimately turn out to be separated by no sudden or
violent line of demarcation, but shade into each other by insensible
gradations. The late experiments of Baron Cagnard de la Tour may be
regarded as a first step towards the full demonstration of this (199.).
But the cohesion of liquids is not, like that of solids, so modified
by their structure in other respects as to destroy the mobility of
their parts one among another (unless in those cases of nearer approach
to the solid state which obtain in viscid or gummy liquids). On the
contrary, the two qualities co-exist, and give rise to a number of
curious and intricate phenomena.

(253.) One of the most remarkable of these is capillary attraction,
or capillarity as it is sometimes called. Every body has remarked the
adhesion of water to glass. The elevation of the general surface of
the liquid where it is in contact with the containing vessel; the form
of a drop suspended at the under side of a solid: these are instances
of capillary attraction. If a small glass tube with a bore as fine as
a hair be immersed in water, the water will be observed to rise in
it to a certain height, and to assume a concave surface at its upper
extremity. The attraction of the glass on the water, and the cohesion
of the parts of the water to each other, are no doubt the joint causes
of this curious effect; but the mode of action is at once obscure and
complex; and although the researches of Laplace and Young have thrown
great light on it, further investigation seems necessary before we can
be said distinctly to understand it.

(254.) As the capillarity and cohesion of the parts of liquids shows
them to possess the power of mutual attraction, so their elasticity
demonstrates that they also possess that of repulsion when forcibly
brought nearer than their natural state. From the extremely small
extent to which the compression of liquids can be carried by any force
we can employ, compared with that of air, we must conclude that this
repulsion is much more violent in the former than in the latter, but
counteracted also by a more powerful force of attraction. So much more
powerful, indeed, is the resistance of liquids to compression, that
they were usually regarded as incompressible; an opinion corroborated
by a celebrated experiment made at Florence, in which water was forced
through the pores (as it was said) of a golden ball. More recent
experiments by Canton, and since by Perkins, Oërsted, and others,
have demonstrated however the contrary, and assigned the amount of
compression.

(255.) The consideration of the motions of fluids, whether liquid
or expansible, is infinitely more complicated than that of their
equilibrium. When their motions are slow, it is reasonable to suppose
that the law of the equable distribution of pressure obtains; but in
very rapid displacements of their parts one among the other, it is not
easy to see how such an equable distribution can be accomplished, and
some phenomena exist which seem to indicate a contrary conclusion.

(256.) Independent of this, there are difficulties of an almost
insuperable nature to the regular deductive application of the general
principles of mechanics to this subject, which arise from the excessive
intricacy of the pure mathematical enquiries to which its investigation
leads. It was Newton who set the example of a first attempt to draw
any conclusions respecting the motion of fluid masses by direct
reasoning from dynamical principles, and thus laid the foundation of
HYDRODYNAMICS; but it was not till the time of D’Alembert that the
method of reducing any question respecting the motions of fluids under
the action of forces to strict mathematical investigation could be said
to be completely understood. But the cases even now in which this mode
of treating such questions can be applied with full satisfaction are
few in comparison of those in which the experimental method of enquiry
as already observed (189.) is preferable. Such, for example, is that
of the resistance of fluids to bodies moving through them; a knowledge
of which is of great importance in naval architecture and in gunnery,
where the resistance of the air acts to an enormous extent. Such,
too, among the practical subjects which depend mainly on this branch
of science, are the use of sails in navigation; the construction of
windmills, and water-wheels; the transmission of water through pipes
and channels; the construction of docks and harbours, &c.


_Nature of Solids in general._

(257.) The intimate constitution of solids is, in all probability, very
complicated, and we cannot be said to know much of it. By some recent
delicate experiments on the dimensions of wires violently strained, it
has been shown that they are to a certain small extent capable of being
dilated by tension, as they are also of being compressed by pressure,
but within limits even narrower than those of liquids. Usually, when
strained too far, they break, and refuse to re-unite; or, if compressed
too forcibly, take a permanent contraction of dimension. Thus, wood
may be indented by a blow, and metals rendered denser and heavier by
hammering or rolling. There is a certain degree of confusion prevalent
in ordinary language about the hardness, elasticity, and other similar
qualities, of solids, which it may be well to remove. Hardness is that
disposition of a solid which renders it difficult to displace its
parts among themselves. Thus, steel is harder than iron; and diamond
almost infinitely harder than any other substance in nature: but the
compressibility of steel, or the extent to which it will yield to a
given pressure and recover itself, is not much less than that of soft
iron, and that of ice is very nearly the same with that of water.

(258.) Again, we call Indian rubber a very elastic body, and so it is;
but in a different sense from steel. Its parts admit of great mutual
displacement without permanent dislocation; however distorted, it
recovers its figure readily, but with a small force. Yet, if Indian
rubber were to be enclosed in a space that it just filled, so as not to
permit its parts to yield laterally, doubtless it would resist actual
compression with great violence. Here, then, we have an instance
of two kinds of elasticity in one substance; a feebler effort of
recovery from distorted figure, and a more violent one from a state
of altered dimension. Both, however, originate in the same causes,
and are referable to the same principles; the former being in fact
only a modified case of the latter, as the effort of a steel spring,
when bent, to recover its former shape, is referable to the same
forces which give to steel its hardness and strength to resist actual
compression and fracture.

(259.) The toughness of a solid, or that quality by which it will
endure heavy blows without breaking, is again distinct from hardness
though often confounded with it. It consists in a certain yielding of
parts with a powerful general cohesion, and is compatible with various
degrees of elasticity. Malleability is again another quality of solids,
especially metals, quite distinct from toughness, and depends on their
capability of being deprived of their figure without an effort to
recover it and without fracture.

(260.) Tenacity, again, is a property of solids more directly depending
on the cohesion of their parts than toughness. It consists in their
power of resisting separation by a strain steadily applied, while the
quality of toughness is materially influenced by their disposition
to communicate through their substance the jarring effect of a
blow. Accordingly, the tenacity of a solid is a direct measure of
the cohesive attraction of its parts, and is the best proof of the
existence of such a power.


_Crystallography._

(261.) It cannot be supposed that these and many other tangible
qualities, as they may be called, should subsist in solids without
a corresponding mechanism in their internal structure. That they
have such a mechanism, and that a very curious and intricate one,
the phenomena of crystallography sufficiently show. This interesting
and beautiful department of natural science is of comparatively very
modern date. That many natural substances affected certain forms must
have been known from the earliest times. Pliny appears to have been
acquainted with this fact, at least in some instances, as he describes
the forms of quartz and diamond. But till the time of Linnæus no
material attention seems to have been bestowed on the subject. He,
however, observed, and described with care, the crystalline forms
of a variety of substances, and even regarded them as so definite a
character of the solids which assumed them, that he supposed every
particular form to be generated by a particular salt. Romé de l’Isle
pursued the study of the crystalline forms of bodies yet farther. He
first ascertained the important fact of the constancy of the angles
at which their faces meet; and observing further that many of them
appear in several different shapes, first conceived the idea that these
shapes might be reducible to one, appropriated in a peculiar manner to
each _substance_, and modified by strict geometrical laws. Bergmann,
reasoning on a fact imparted to him by his pupil Gahn, made a yet
greater step, and showed how at least one species of crystal might
be built up of thin laminæ ranged in a certain order, and following
certain rules of superposition. He failed, however, in deducing just
and general conclusions from this remark, which, correctly viewed, is
the foundation of the most important law of crystallography, that which
connects the primitive form with other forms capable of being exhibited
by the same substance, by a certain fixed relation. An idea may be
formed of what is meant by this sort of connection of one form with
another, by considering a pointed pyramid built up of cubic stones,
disposed in layers, each of which separately is a square plate of the
thickness of a single stone. These layers, laid horizontally one on the
other, and decreasing regularly in size from the bottom to the top,
produce a pyramidal form with a rough or channeled surface; and if the
layers are so extremely thin that the channels cease to be visible to
the eye, the pyramid will seem smooth and perfect.

(262.) Very shortly after this, and without knowledge of what had been
done by Gahn and Bergmann, the Abbé Haüy, instructed by the accidental
fracture of a fine group of crystals, made the remark noticed already
(in 67.), and reasoning on it with more caution and success, and
pursuing it into all its detail, developed the general laws which
regulate the superposition of the layers of particles of which he
supposes all crystals to be built up, and which enable us, from knowing
their primitive forms, to discover, previous to trial, what other
forms they are capable of assuming; and which, according to this idea,
are called derivative or secondary forms. Mohs and others have since
imagined processes and systems by which the derivation of forms from
each other is facilitated, and have corrected some errors of over-hasty
generalization into which their predecessors had fallen, as well as
advanced, by an extraordinary diligence of research, our knowledge of
the forms which the various substances which occur in nature and art
actually do assume.

(263.) In what manner a variety in point of external form may originate
in a variety of figures in the ultimate particles of which a solid
is composed, may very readily be imagined by considering what would
happen if the bricks of which an edifice is constructed had all a
certain _leaning_ or bias in one direction out of the perpendicular.
Suppose every brick, for instance, when laid flat on its face, with
its longer edges north and south, had its eastern and western faces
upright, but its northern and southern ones leaning southwards at a
certain inclination the same for each brick; a house built of such
bricks would lean the same way, if the bricks fitted well together.
If, _besides this_, the eastern and western faces of the bricks,
instead of being truly upright, had an inclination eastward, the house
would have a similar one, and all its four corners, instead of being
upright, would lean to the south-east. Suppose, instead of a house, a
pyramid were built of such oblique bricks, with the sides of its base
directed to the four points of the compass; then its point, instead
of being situated vertically over the centre of its base, would stand
perpendicularly over some point to the south-east of that centre, and
the pyramid itself would have its sides facing the south and the east,
more highly inclined to the horizon than those towards the north and
west.

(264.) Whatever conception we may form of the manner in which the
particles of a crystal cohere and form masses, it is next to impossible
to divest ourselves of the idea of a determinate figure common to them
all. Any other supposition, indeed, would be incompatible with that
exact similarity in all other respects which the phenomena of chemistry
may be considered as having demonstrated. However, it must be borne in
mind that this idea, plausible as it may appear, is yet in some degree
hypothetical, and that the laws of crystallography, as determined from
inductive observation, are quite independent of any supposition of the
kind, or even of the existence of such things as ultimate particles or
atoms at all.

(265.) Still, that peculiar internal constitution of solid bodies,
whatever it be, which is indicated by the assumption of determinate
figures, by their splitting easier in some directions than in others,
and by their presenting glittering plane surfaces when broken into
fragments, cannot but have an important influence on all their
relations to external agents, as well as to their internal movements
and the mutual actions of their parts on one another. Accordingly, the
division of bodies into crystallized and uncrystallized, or imperfectly
crystallized, is one of the most universal importance; and almost all
the phenomena produced by those more intimate natural causes which
act within small limits, and as it were on the immediate mechanism
of solid substances, are remarkably modified by their crystalline
structure. Thus, in transparent solids, the course taken by the rays
of light, in traversing them, as well as the properties impressed upon
them in so doing, are intimately connected with this structure. The
recent experiments of M. Savart, too, have proved that this is also the
case with their power of resistance to external force, on which depends
their elasticity. Crystallized substances, according to the results of
these experiments, resist compression with different degrees of elastic
force, according to the direction in which it is attempted to compress
them; and all the phenomena dependent on their elasticity are affected
by this cause, especially those which relate to their vibratory
movements and their conveyance of sound.

(266.) There can be little doubt that modifications, similarly
depending on the internal structure of crystals, will be traced through
every department of physics. In that interesting one which relates
to the action of heat in expanding the dimensions of substances, a
beginning has already been made by Professor Mitscherlich. It had long
been known that all substances are dilated by heat, and no exception
to this law has been found, so long as we regard the _bulk_ of the
heated body. Thus, an iron rod when hot is both longer and thicker than
when cold; and the difference of dimension, though but trifling in
itself, is yet capable of being made sensible, and is of considerable
consequence in engineering. Thus, too, the quicksilver in a common
thermometer occupies a larger space when hot than when cold; and being
confined by the glass ball, (which also expands, but _not so much in
proportion_,) it is forced to rise in the tube. These and similar facts
had long been known; and accurate measures of the total amount of
dilatation of a variety of different bodies, under similar accessions
of heat, had been obtained and registered in tables. But no one had
suspected the important fact, that this expansion in crystallized
bodies takes place under totally different circumstances from what
obtains in uncrystallized ones. M. Mitscherlich has lately shown that
such substances expand differently in different directions, and has
even produced a case in which expansion in one direction is actually
accompanied with contraction in another. This step, the most important
beyond a doubt which has yet been made in pyrometry, can however only
be regarded as the first in a series of researches which will occupy
the next generation, and which promises to afford an abundant harvest
of new facts, as well as the elucidation of some of the most obscure
and interesting points in the doctrine of heat.

(267.) From what has been said, it is clear that if we look upon solid
bodies as collections of particles or atoms, held together and kept
in their places by the perpetual action of attractive and repulsive
forces, we cannot suppose these forces, at least in crystallized
substances, to act alike in all directions. Hence arises the conception
of _polarity_, of which we see an instance, on a great scale, in the
magnetic needle, but which, under modified forms, there is nothing to
prevent us from conceiving to act among the ultimate atoms of solid
or even fluid bodies, and to produce all the phenomena which they
exhibit in their crystallized state, either when acting on each other,
or on light, heat, &c. It is not difficult, if we give the reins to
imagination, to conceive how attractive and repulsive atoms, bound
together by some unknown tie, may form little machines or compound
particles, which shall have many of the properties which we refer to
polarity; and accordingly many ingenious suppositions have been made to
that effect: but in the actual state of science it is certainly safest
to wave these hypotheses, without however absolutely rejecting them,
and regard the _polarity of matter_ as one of the ultimate phenomena to
which the analysis of nature leads us, and of which it is our business
fully to investigate the laws, before we endeavour to ascertain its
causes, or trace the mechanism by which it is produced.

(268.) The mutual attractions and repulsions of the particles of
matter, then, and their polarity, whether regarded as an original or a
derivative property, are the forces which, acting with great energy,
and within very confined limits, we must look to as the principles on
which the intimate constitution of all bodies and many of their mutual
actions depend. These are what are understood by the general term of
_molecular forces_. Molecular attraction has been attempted to be
confounded by some with the general attraction of gravity, which all
matter exerts on all other matter; but this idea is refuted by the
plainest facts.



CHAP. II.

OF THE COMMUNICATION OF MOTION THROUGH BODIES.--OF SOUND AND LIGHT.


(269.) The propagation of motion through all substances, whether of a
single impulse, as a blow or thrust, or of one frequently and regularly
repeated, such as a jarring or vibratory movement, depends wholly on
these molecular forces; and it is on such propagation that sound and
very probably light depend. To conceive the manner in which a motion
may be conveyed from one part of a substance to another, whether solid
or fluid, we may attend to what takes place when a wave is made to
run along a stretched string, or the surface of still water. Every
part of the string, or water, is in succession moved from its place,
and agitated with a motion similar to that of the original impulse,
leaving its place and returning to it, and when one part ceases to move
the next receives as it were the impression, and forwards it onward.
This may seem a slow and circuitous process in description; but when
sound, for example, is conveyed through the air, we are to consider,
1st, that the air, the substance actually in motion, is extremely light
and acted upon by a very powerful elasticity, so that the force which
propagates the motion, or by which the particles adjacent act on, and
urge forward, each other, is very great, compared with the quantity of
materials set in motion by it: and the same is true, even in a greater
degree, in liquids and solids; for in these the elastic forces are even
greater, in proportion to the weight, than in air.

(270.) A general notion of the mode in which sounds are conveyed
through the air was not altogether deficient among the ancients; but
it is to Newton that we owe the first attempt to analyze the process,
and show correctly what takes place in the communication of motion
from particle to particle. Reasoning on the properties of the air as
an elastic body, he showed the effect of an impulse on any portion of
it to consist in a condensation of the air immediately adjacent in the
direction of the impulse, which then, re-acting by its spring, drives
back the portion which had advanced to its original place, and at the
same time urges forward the portion before it, in the direction of the
impulse, so that every particle alternately advances and retreats.
But, in pursuing this idea into its details, Newton fell into some
errors which were pointed out by Cramer, though their origin was not
traced, nor the reasoning corrected, till the subject was resumed by
Lagrange and Euler; nor is this any impeachment of the penetration of
our immortal countryman. The mathematical theory of the propagation
of sound, and of vibratory and undulatory motions in general, is
one of the utmost intricacy; and, in spite of every exertion on the
part of the most expert geometers, continues to this day to give
continual occasion for fresh researches; while phenomena are constantly
presenting themselves, which show how far we are from being able to
deduce all the particulars, even of cases comparatively simple, by any
direct reasoning from first principles.

(271.) Whenever an impulse of any kind is conveyed by the air, to our
ears, it produces the impression of sound; but when such an impulse
is regularly and uniformly repeated in extremely rapid succession, it
gives us that of a musical note, the pitch of the note depending on
the rapidity of the succession (see art. 153.). The sense of harmony,
too, depends on the periodical recurrence of coincident impulses on the
ear, and affords, perhaps, the only instance of a sensation for whose
pleasing impression a distinct and intelligible reason can be assigned.

(272.) Acoustics, then, or the science of sound, is a very considerable
branch of physics, and one which has been cultivated from the earliest
ages. Even Pythagoras and Aristotle were not ignorant of the general
mode of its transmission through the air, and of the nature of harmony;
but as a branch of science, independent of its delightful application
in the art of music, it could be hardly said to exist, till its nature
and laws became a matter of experimental enquiry to Bacon and Galileo,
Mersenne and Wallis; and of mathematical investigation to Newton, and
his illustrious successors, Lagrange and Euler. From that time its
progress, as a branch both of mathematical and experimental science,
has been constant and accelerated. A curious and beautiful method of
observation, due to Chladni, consists in the happy device of strewing
sand over the surfaces of bodies in a state of sonorous vibration,
and marking the figures it assumes. This has made their motions
susceptible of ocular examination, and has been lately much improved
on, and varied in its application, by M. Savart, to whom we also owe a
succession of instructive researches on every point connected with the
subject of sound, which may rank among the finest specimens of modern
experimental enquiry. But the subject is far from being exhausted; and,
indeed, there are few branches of physics which promise at once so much
amusing interest, and such important consequences, in its bearings on
other subjects, and especially, through the medium of strong analogies,
on that of light.


_Light and Vision._

(273.) The nature of light has always been involved in considerable
doubt and mystery. The ancients could scarcely be said to have any
opinion on the subject, unless, indeed, it could be considered such
to affirm that distant bodies could not be put into communication
without an intermedium; and that, therefore, there must be _something_
between the eye and the thing seen. What that something is, however,
they could only form crude and vague conjectures. One supposed that
the eyes themselves emit rays or emanations of some unknown kind, by
which distant objects are as it were felt; a singularly unfortunate
idea, since it gives no reason why objects should not be equally
well seen in the dark--no account, in short, of the part performed
by _light_ in vision. Others imagined that all visible objects are
constantly throwing out from them, in all directions, some sort of
resemblances or spectral forms of themselves, which, when received by
the eyes, produce an impression of the objects. Vague and clumsy as
this hypothesis obviously is, it assigns to the object a power, and to
light a diffusive propagation in all directions, which are, the one and
the other, independent of our eyes, and therefore goes to separate the
phenomena of _light_ from those of _vision_.

(274.) The hypothesis of Newton is a refinement and improvement on
this idea. Instead of spectra or resemblances, he supposes luminous
objects actually to dart out from them in all directions, particles,
of inconceivable minuteness (as indeed they must be, having such
an enormous velocity (see 17.), not to dash in pieces every thing
they strike upon). These particles he supposes to be acted upon by
attractive and repulsive forces, residing in all material bodies, the
latter extending to some very small distance beyond their surfaces; and
by the action of these forces to be turned aside from their natural
straight-lined course, without ever coming in actual contact with the
particles themselves of the bodies on which they fall, but either being
turned back and _reflected_ by the repulsive forces before they reach
them, or penetrating between their intervals, as a bird may be supposed
to fly through the branches of a forest, and undergoing all their
actions, to take at quitting them a direction finally determined by
the position of the surface at which they emerge with respect to their
course.

(275.) This hypothesis, which was discussed and reasoned upon by Newton
in a manner worthy of himself, affords, by the application of the
same dynamical laws which he had applied with so much success to the
explanation of the planetary motions, not merely a plausible, but a
perfectly reasonable and fair explanation of all the _usual_ phenomena
of light known in his time. His own beautiful discoveries, too, of
the different refrangibilities of the differently coloured rays,
were perfectly well represented in this theory, by simply admitting
a difference of velocity in the particles, which produce in the eye
the sensations of different colours. And had the properties of light
remained confined to these, there would have been no occasion to have
resorted to any other mode of conceiving it.

(276.) A very different hypothesis had, however, been suggested about
the same period by Huyghens, who supposed light to be produced in the
same manner with sound, by the communication of a vibratory motion
from the luminous body to a highly elastic fluid, which he imagined
as filling all space, and as being less condensed within the limits
of space occupied by matter, and that to a greater or less extent,
according to the nature of the occupying substance. Thus, in place of
any thing actually thrown off, he substituted waves, or vibrations,
propagated in all directions from luminous bodies, through this medium,
or ether, as he called it. Huyghens, being himself a consummate
mathematician, was enabled to trace many of the consequences of this
hypothesis, and to show that the ordinary laws of reflection and
refraction were represented or accounted for by it, as well as by
Newton’s. But the hypothesis of Huyghens has not been fully successful
in accounting for what may be considered the chief of all optical
facts, the production of colours in the ordinary refraction of
light by a prism, of which the theory of Newton gives a complete and
elegant explanation; and the discovery of which by him marks one of
the greatest epochs in the annals of experimental science. This, which
has been often urged in objection to it, remains still, if not quite
unanswered, at least only imperfectly removed.

(277.) Other phenomena, however, were not wanting to afford a further
trial of the _explanatory powers_ of either hypothesis. The diffraction
or inflection of light, discovered by Grimaldi, a Jesuit of Bologna,
seemed to indicate that the rays of light were turned aside from their
straight course by merely passing near bodies of every description.
These phenomena, which are very curious and beautiful, were minutely
examined by Newton, and referred by him to the action of repulsive
forces extending to a sensible distance from the surfaces of bodies;
and his explanation, so far as the facts known to him are concerned,
appears as satisfactory as could reasonably be then expected; and much
more so than any thing which could at that time be produced on the side
of the hypothesis of Huyghens, which, in fact, seemed incapable of
giving any account whatever of them.

(278.) Another class of delicate and splendid optical phenomena, which
had begun to attract attention somewhat previous to Newton’s time,
seemed to leave both hypotheses equally at a loss. These were the
colours exhibited by very thin films, either of a liquid (such as a
soap-bubble), or of air, as when two glasses are laid together with
only air between them. These colours were examined by Newton with a
minuteness and care altogether unexampled in experimental philosophy
at that time, and with which few researches undertaken since will bear
to stand in competition. Their result was a theory of a very singular
nature, which he grounded on an hypothesis of what he termed _fits of
easy transmission and reflection_; and which supposed each ray of light
to pass in its progress periodically through a succession of states
such as would alternately dispose it to penetrate or be reflected back
from the surface of a body on which it might fall. The simplest way
in which the reader may conceive this hypothesis, is to regard every
particle of light as a sort of little magnet revolving rapidly about
its own centre while it advances in its course, and thus alternately
presenting its attractive and repulsive pole, so that when it arrives
at the surface of a body with its repulsive pole foremost, it is
repelled and reflected; and when the contrary, attracted, so as to
enter the surface. Newton, however, very cautiously avoided announcing
his theory in this or any similar form, confining himself entirely to
general language. In consequence, it has been confidently asserted
by all his followers, that the doctrine of fits of easy reflection
and transmission, as laid down by him, is substantially nothing more
than a statement of facts. Were it so, it is clear that any other
theory which should offer a just account of the same phenomena must
ultimately involve and coincide with that of Newton. But this, as we
shall presently see, is not the case; and this instance ought to serve
to make us extremely cautious how we employ, in stating physical laws
derived from experiment, language which involves any thing in the
slightest degree theoretical, if we would present the laws themselves
in a form which no future research shall modify or subvert.

(279.) A third class of optical phenomena, which were likewise
discovered while Newton was yet engaged in his optical researches, was
that exhibited by doubly refracting crystals. In what the phenomenon of
double refraction consists, we have already had occasion to explain.
The fact itself was first noticed by Erasmus Bartolin in the crystal
called Iceland spar; and was studied with attention by Huyghens, who
ascertained its laws, and referred it with remarkable ingenuity and
success to his theory of light, by the additional hypothesis of such
a constitution of his ethereal medium within the crystal as should
enable it to convey an impulse faster in one direction than another:
as if, for example’s sake, we should suppose a sound conveyed through
the air with different degrees of rapidity in a vertical and horizontal
direction.

(280.) Some remarkable facts accompanying the double refraction
produced by Iceland spar, which Bartolin, Huyghens, and Newton, had
observed, led the latter to conceive the singular idea that a ray of
light after its emergence from such a crystal acquires _sides_, that
is to say, distinct relations to surrounding space, which it carries
with it through its whole subsequent course, and which give rise to all
those curious and complicated phenomena which are now known under the
name of the _polarization of light_. These results, however, appeared
so extraordinary, and offered so little handle for further enquiry,
that their examination dropped, as if by common consent; Newton himself
resting content with urging strongly the apparent incompatibility of
these properties with the Huyghenian doctrine, but without making any
attempt to explain them by his own.

(281.) From the period of Newton’s optical discoveries to the
commencement of the present century, no great accession to our
knowledge of the nature of light was made, if we except one, which,
from its invaluable practical application, must ever hold a prominent
place in the annals both of art and science: we mean, the discovery
of the principle of the achromatic telescope, which originated in a
discussion between the celebrated geometer Euler, Klingenstierna, an
eminent Swedish philosopher, and our own countryman, the admirable
optician Dollond, on the occasion of certain abstract theoretical
investigations of the former, which led him to speculate on its
_possibility_, and which ultimately terminated in its complete and
happy _execution_ by the latter; a memorable case in science, though
not a singular one, where the speculative geometer in his chamber,
apart from the world, and existing among abstractions, has originated
views of the noblest practical application.[49]

(282.) The explanation which our knowledge of optical laws affords of
the mechanism of the eye, and the process by which vision is performed,
is as complete and satisfactory as that of hearing by the propagation
of motion through the air. The camera obscura, invented by Baptista
Porta in 1560, gave the first idea how the actual images of external
objects might be conveyed into the eye, but it was not till after a
considerable interval that Kepler, the immortal discoverer of those
great laws which regulate the periods and motions of the planets,
pointed out distinctly the offices performed by the several parts
of the eye in the act of vision. From this to the invention of the
telescope and microscope there would seem but a small step, but it is
to accident rather than design that it is due; and its re-invention
by Galileo, on a mere description of its effects, may serve, among
a thousand similar instances, to show that inestimable practical
applications lie open to us, if we can only once bring ourselves
to conceive their possibility, a lesson which the invention of the
achromatic telescope itself, as we have above related it, not less
strongly exemplifies.

(283.) The little instrument with which Galileo’s splendid discoveries
were made was hardly superior in power to an ordinary finder of the
present day; but it was rapidly improved on, and in the hands of
Huyghens attained to gigantic dimensions and very great power. It was
to obviate the necessity of the enormous length required for these
telescopes, and yet secure the same power, that Gregory and Newton
devised the reflecting telescope, which has since become a much
more powerful instrument than its original inventors probably ever
contemplated.

(284.) The telescope, as it exists at present, with the improvements
in its structure and execution which modern artists have effected, must
assuredly be ranked among the highest and most refined productions of
human art; that in which man has been able to approximate most closely
to the workmanship of nature, and which has conferred upon him, if
not another sense, at least an exaltation of one already possessed
by him that merits almost to be regarded as a new one. Nor does it
appear yet to have reached its ultimate perfection, to which indeed
it is difficult to assign any bounds, when we take into consideration
the wonderful progress which workmanship of every kind is making,
and the delicacy, far superior to that of former times, with which
materials may now be wrought, as well as the ingenious inventions and
combinations which every year is bringing forth for accomplishing the
same ends by means hitherto unattempted.[50]

(285.) After a long torpor, the knowledge of the properties of light
began to make fresh progress about the end of the last century,
advancing with an accelerated rapidity, which has continued unabated
to the present time. The example was set by our late admirable and
lamented countryman, Dr. Wollaston, who re-examined and verified
the laws of double refraction in Iceland spar announced by Huyghens.
Attention being thus drawn to the subject, the geometry of Laplace
soon found a means of explaining at least one portion of the mystery
of this singular phenomenon, by the Newtonian theory of light, applied
under certain supposed conditions; and the reasoning which led him to
the result (at that time quite unexpected), may justly be regarded as
one of his happiest efforts. The prosecution of the subject, which had
now acquired a high degree of interest, was encouraged by the offer
of a prize on the part of the French Academy of Sciences; and it was
in a memoir which received this honourable reward on that occasion,
in 1810, that Malus, a retired officer of engineers in the French
army, announced the great discovery of the _polarization of light_ by
ordinary reflection at the surface of a transparent body.

(286.) Malus found that when a beam of light is reflected from the
surface of such a body at a certain angle, it acquires precisely the
same singular property which is impressed upon it in the act of double
refraction, and which Newton had before expressed by saying that it
possessed _sides_. This was the first circumstance which pointed out a
connection between that hitherto mysterious phenomenon and any of the
ordinary modifications of light; and it proved ultimately the means of
bringing the whole within the limits, if not of a complete explanation,
at least of a highly plausible theoretical representation. So true is,
in science, the remark of Bacon, that no natural phenomenon can be
adequately studied _in itself alone_, but, to be understood, must be
considered _as it stands connected with all nature_.

(287.) The new class of phenomena thus disclosed were immediately
studied with diligence and success, both abroad by Malus and Arago, and
at home by our countryman Dr. Brewster, and their laws investigated
with a care proportioned to their importance; when another and
apparently still more extraordinary class of phenomena presented
itself in the production of the most vivid and beautiful colours
(every way resembling those observed by Newton in thin films of air
or liquids, only infinitely more developed and striking,) in certain
transparent crystallized substances, when divided into flat plates in
particular directions, and exposed in a beam of polarized light. The
attentive examination of these colours by Wollaston, Biot, and Arago,
but more especially by Brewster, speedily led to the disclosure of a
series of optical phenomena so various, so brilliant, and evidently
so closely connected with the most important points relating to the
intimate structure of crystallized bodies, as to excite the highest
interest,--that sort of interest which is raised when we feel we are
on the eve of some extraordinary discovery, and expect every moment
that some leading fact will turn up, which will throw light on all that
appears obscure, and reduce into order all that seems anomalous.

(288.) This expectation was not disappointed. So long before the time
we are speaking of as the first year of the present century, our
illustrious countryman, the late Dr. Thomas Young, had established a
principle in optics, which, regarded as a physical law, has hardly its
equal for beauty, simplicity, and extent of application, in the whole
circle of science. Considering the manner in which the vibrations of
two musical sounds arriving at once at the ear affect the sense with
an impression of sound or silence according as they conspire or oppose
each other’s effects, he was led to the idea that the same ought to
hold good with light as with sound, if the theory which makes light
analogous to sound be the true one; and that, therefore, two rays of
light, setting off from the same origin, at the same instant, and
arriving at the same place by different routes, ought to strengthen
or wholly or partially destroy each other’s effects according to
the difference in length of the routes described by them. That two
lights should in any circumstances combine to produce darkness may
be considered strange, but is _literally true_; and it had even been
noticed long ago as a singular and unaccountable fact by Grimaldi, in
his experiments on the inflection of light. The experimental means by
which Dr. Young confirmed this principle, which is known in optics
by the name of the _interference_ of the rays of light, were as
simple and satisfactory as the principle itself is beautiful; but the
verifications of it, drawn from the explanation it affords of phenomena
apparently the most remote, are still more so. Newton’s colours of thin
films were the first phenomena to which its author applied it with full
success. Its next remarkable application was to those of diffraction,
of which, in the hands of M. Fresnel, a late eminent French geometer,
it also furnished a complete explanation, and that, too, in cases to
which Newton’s hypothesis could not apparently be made to apply, and
through a complication of circumstances which might afford a very
severe test of any hypothesis.

(289.) A simple and beautiful experiment on the interferences of
polarized light due to Fresnel and Arago enabled them to bring Dr.
Young’s law to bear on the colours produced by crystallized plates in a
polarized beam, and by so doing afforded a key to all the intricacies
of these magnificent but complex phenomena. Nothing now was wanting to
a rational theory of double refraction but to frame an hypothesis of
some mode in which light might be conceived to be propagated through
the elastic medium supposed to convey it in such a way as not to be
contradictory to any of the facts, nor to the general laws of dynamics.
This essential idea, without which every thing that had been before
done would have been incomplete, was also furnished by Dr. Young, who,
with a sagacity which would have done honour to Newton himself, had
declared, that to accommodate the doctrine of Huyghens to the phenomena
of polarized light it is necessary to conceive the mode of propagation
of a luminous impulse through the ether, differently from that of a
sonorous one through the air. In the latter, the particles of the air
_advance_ and _recede_; in the former, those of the ether must be
supposed to _tremble laterally_.

(290.) Taking this as the groundwork of his reasoning, Fresnel
succeeded in erecting on it a theory of polarization and double
refraction, so happy in its adaptation to facts, and in the coincidence
with experience of results deduced from it by the most intricate
analysis, that it is difficult to conceive it unfounded. If it be
so, it is at least the most curiously artificial system that science
has yet witnessed; and whether it be so or not, so long as it serves
to group together in one comprehensive point of view a mass of facts
almost infinite in number and variety, to reason from one to another,
and to establish analogies and relations between them; on whatever
hypothesis it may be founded, or whatever arbitrary assumptions it
may make respecting structures and modes of action, it can never be
regarded as other than a most real and important accession to our
knowledge.

(291.) Still, it is by no means impossible that the Newtonian theory of
light, if cultivated with equal diligence with the Huyghenian, might
lead to an equally plausible explanation of phenomena now regarded
as beyond its reach. M. Biot is the author of the hypothesis we have
already mentioned of a rotatory motion of the particles of light about
their axes. He has employed it only for a very limited purpose; but
it might doubtless be carried much farther; and by admitting only the
regular emission of the luminous particles at equal intervals of time,
and in similar states of motion from the shining body, which does not
seem a very forced supposition, all the phenomena of interference at
least would be readily enough explained without the admission of an
ether.

(292.) The optical examination of crystallized substances affords
one among many fine examples of the elucidation which every branch
of science is capable of affording to every other. The indefatigable
researches of Dr. Brewster and others have shown that the phenomena
exhibited by polarized light in its transmission through crystals
afford a certain indication of the most important points relating to
the structure of the crystals themselves, and thus become most valuable
characters by which to recognise their internal constitution. It was
Newton who first showed of what importance as a physical character,--as
the indication of other properties,--the action of a body on light
might become; but the characters afforded by the use of polarized light
as an instrument of experimental enquiry are so marked and intimate,
that they may almost be said to have furnished us with a kind of
intellectual sense, by which we are enabled to scrutinize the internal
arrangement of those wonderful structures which Nature builds up by
her refined and invisible architecture, with a delicacy eluding our
conception, yet with a symmetry and beauty which we are never weary
of admiring. In this point of view the science of optics has rendered
to mineralogy and crystallography services not less important than to
astronomy by the invention of the telescope, or to natural history by
that of the microscope; while the relations which have been discovered
to exist between the optical properties of bodies and their crystalline
forms, and even their chemical habitudes, have afforded numerous
and beautiful instances of general laws concluded from laborious and
painful induction, and curiously exemplifying the simplicity of nature
as it emerges slowly from an entangled mass of particulars in which, at
first, neither order nor connection can be traced.



CHAP. III.

OF COSMICAL PHENOMENA.


_Astronomy and Celestial Mechanics._

(293.) Astronomy, as has been observed in the former part of this
discourse, as a science of observation, had made considerable progress
among the ancients: indeed, it was the only branch of physical science
which could be regarded as having been cultivated by them with any
degree of assiduity or real success. The Chaldean and Egyptian records
had furnished materials from which the motions of the sun and moon
could be calculated with sufficient exactness for the prediction of
eclipses; and some remarkable cycles, or periods of years in which
the lunar eclipses return in very nearly the same order, had been
ascertained by observation. Considering the extreme imperfection of
their means of measuring time and space, this was, perhaps, as much
as could have been expected at that early period, and it was followed
up for a while in a philosophical spirit of just speculation, which,
if continued, could hardly have failed to lead to sound and important
conclusions.

(294.) Unfortunately, however, the philosophy of Aristotle laid it
down as a principle, that the celestial motions were regulated by laws
proper to themselves, and bearing no affinity to those which prevail
on earth. By thus drawing a broad and impassable line of separation
between celestial and terrestrial mechanics, it placed the former
altogether out of the pale of experimental research, while it at the
same time impeded the progress of the latter by the assumption of
principles respecting natural and unnatural motions, hastily adopted
from the most superficial and cursory remark, undeserving even the
name of observation. Astronomy, therefore, continued for ages a
science of mere record, in which theory had no part, except in so
far as it attempted to conciliate the inequalities of the celestial
motions with that assumed law of uniform circular revolution which
was alone considered consistent with the perfection of the heavenly
mechanism. Hence arose an unwieldy, if not self-contradictory, mass
of hypothetical motions of sun, moon, and planets, in circles, whose
centres were carried round in other circles, and these again in others
without end,--“cycle on epicycle, orb on orb,”--till at length, as
observation grew more exact, and fresh epicycles were continually
added, the absurdity of so cumbrous a mechanism became too palpable to
be borne. Doubts were expressed, to which the sarcasm of a monarch[51]
gave a currency they might not have obtained in a period when men
scarcely dared trust themselves to think; and at length Copernicus,
promulgating his own, or reviving the Pythagorean doctrine, which
places the sun in the centre of our system, gave to astronomy a
simplicity which, contrasted with the complication of the preceding
views, at once commanded assent.

(295.) An elegant writer[52], whom we have before had occasion to
quote, has briefly and neatly accounted for the confused notions which
so long prevailed respecting the constitution of our system, and the
difficulty experienced in acquiring a true notion of the disposition
of its parts. “We see it,” he observes, “not in _plan_, but in
_section_.” The reason of this is, that our point of observation lies
in its general plane, but the notion we aim at forming of it is not
that of its section, but of its plan. This is as if we should attempt
to read a book, or make out the countries on a map, with the eye on a
level with the paper. We can only judge directly of the distances of
objects by their sizes, or rather of their change of distance by their
change of size; neither have we any means of ascertaining, otherwise
than indirectly, even their positions, one among the other, from their
apparent places as seen by us. Now, the variations in apparent size
of the sun and moon are too small to admit of exact measure without
the use of the telescope, and the bodies of the planets cannot even be
distinguished as having any distinct size with the naked eye.

(296.) The Copernican system once admitted, however, this difficulty
of conception, at least, is effectually got over, and it becomes
a mere problem of geometry and calculation to determine, from the
observed places of a planet, its real orbit about the sun, and the
other circumstances of its motion. This Kepler accomplished for the
orbit of Mars, which he ascertained to be an ellipse having the sun
in one of its foci; and the same law, being extended by inductive
analogy to all the planets, was found to be verified in the case of
each. This with the other remarkable laws which are usually cited in
physical astronomy by the name of Kepler’s laws, constitute undoubtedly
the most important and beautiful system of geometrical relations which
have ever been discovered by a mere inductive process, independent of
any consideration of a theoretical kind. They comprise within them a
compendium of the motions of all the planets, and enable us to assign
their places in their orbits at any instant of time past or to come
(disregarding their mutual perturbations), provided certain purely
geometrical problems can be numerically resolved.

(297.) It was not, however, till long after Kepler’s time that the
real importance of these laws could be felt. Regarded in themselves,
they offered, it is true, a fine example of regular and harmonious
disposition in the greatest of all the works of creation, and a
striking contrast to the cumbersome mechanism of the cycles and
epicycles which preceded them; but there their utility seemed to
terminate, and, indeed, Kepler was reproached, and not without a
semblance of reason, with having rendered the actual calculation of
the places of the planets more difficult than before, the resources of
geometry being then inadequate to resolve the problems to which the
strict application of his laws gave rise.

(298.) The first result of the invention of the telescope and its
application to astronomical purposes, by Galileo, was the discovery
of Jupiter’s disc and satellites,--of a system offering a beautiful
miniature of that greater one of which it forms a portion, and
presenting to the eye of sense, at a single glance, that disposition of
parts which in the planetary system itself is discerned only by the eye
of reason and imagination (see 195.). Kepler had the satisfaction of
seeing it ascertained, that the law which he had discovered to connect
the times of revolution of the planets with their distances from the
sun, holds good also when applied to the periods of circulation of
these little attendants round the centre of their principal; thus
demonstrating it to be something more than a mere empirical rule, and
to depend on the intimate nature of planetary motion itself.

(299.) It had been objected to the doctrine of Copernicus, that, were
it true, Venus should appear sometimes horned like the moon. To this
he answered by admitting the conclusion, and averring that, should we
ever be able to see its actual shape, it _would_ appear so. It is easy
to imagine with what force the application would strike every mind when
the telescope confirmed this prediction, and showed the planet just as
both the philosopher and his objectors had agreed it ought to appear.
The history of science affords perhaps only one instance analogous to
this. When Dr. Hutton expounded his theory of the consolidation of
rocks by the application of heat, at a great depth below the bed of
the ocean, and especially of that of marble by actual fusion; it was
objected that, whatever might be the case with others, with calcareous
or marble rocks, at least, it was impossible to grant such a cause
of consolidation, since heat decomposes their substance and converts
it into quicklime, by driving off the carbonic acid, and leaving a
substance perfectly infusible, and incapable even of agglutination
by heat. To this he replied, that the pressure under which the heat
was applied would prevent the escape of the carbonic acid; and that
being retained, it might be expected to give that fusibility to the
compound which the simple quicklime wanted. The next generation saw
this anticipation converted into an observed fact, and verified by the
direct experiments of Sir James Hall, who actually succeeded in melting
marble, by retaining its carbonic acid under violent pressure.

(300.) Kepler, among a number of vague and even wild speculations on
the causes of the motions whose laws he had developed so beautifully
and with so much patient labour, had obtained a glimpse of the general
law of the inertia of matter, as applicable to the great masses of the
heavenly bodies as well as to those with which we are conversant on
the earth. After Kepler, Galileo, while he gave the finishing blow to
the Aristotelian dogmas which erected a barrier between the laws of
celestial and terrestrial motion, by his powerful argument and caustic
ridicule, contributed, by his investigations of the laws of falling
bodies and the motions of projectiles, to lay the foundation of a
true system of dynamics, by which motions could be determined from a
knowledge of the forces producing them, and forces from the motions
they produce. Hooke went yet farther, and obtained a view so distinct
of the mode in which the planets might be retained in their orbits
by the sun’s attraction, that, had his mathematical attainments been
equal to his philosophical acumen, and his scientific pursuits been
less various and desultory, it can hardly be doubted that he would have
arrived at a knowledge of the law of gravitation.

(301.) But every thing which had been done towards this great end,
before Newton, could only be regarded as smoothing some first
obstacles, and preparing a state of knowledge, in which powers like his
could be effectually exerted. His wonderful combination of mathematical
skill with physical research enabled him to invent, at pleasure, new
and unheard-of methods of investigating the effects of those causes
which his clear and penetrating mind detected in operation. Whatever
department of science he touched, he may be said to have formed afresh.
Ascending by a series of close-compacted inductive arguments to the
highest axioms of dynamical science, he succeeded in applying them
to the complete explanation of all the great astronomical phenomena,
and many of the minuter and more enigmatical ones. In doing this, he
had every thing to create: the mathematics of his age proved totally
inadequate to grapple with the numerous difficulties which were to
be overcome; but this, so far from discouraging him, served only to
afford new opportunities for the exertion of his genius, which, in the
invention of the method of fluxions, or, as it is now more generally
called, the differential calculus, has supplied a means of discovery,
bearing the same proportion to the methods previously in use, that
the steam-engine does to the mechanical powers employed before its
invention. Of the optical discoveries of Newton we have already spoken;
and if the magnitude of the objects of his astronomical discoveries
excite our admiration of the mental powers which could so familiarly
grasp them, the minuteness of the researches into which he there set
the first example of entering, is no less calculated to produce a
corresponding impression. Whichever way we turn our view, we find
ourselves compelled to bow before his genius, and to assign to the
name of NEWTON a place in our veneration which belongs to no other in
the annals of science. His era marks the accomplished maturity of the
human reason as applied to such objects. Every thing which went before
might be more properly compared to the first imperfect attempts of
childhood, or the essays of inexpert, though promising, adolescence.
Whatever has been since performed, however great in itself, and worthy
of so splendid and auspicious a beginning, has never, in point of
intellectual effort, surpassed that astonishing one which produced the
Principia.

(302.) In this great work, Newton shows all the celestial motions known
in his time to be consequences of the simple law, that every particle
of matter attracts every other particle in the universe with a force
proportional to the product of their masses directly, and the square
of their mutual distance inversely, and is itself attracted with an
equal force. Setting out from this, he explains how an attraction
arises between the great spherical masses of which our system consists,
regulated by a law precisely similar in its expression; how the
elliptic motions of planets about the sun, and of satellites about
their primaries, according to the exact rules inductively arrived at
by Kepler, result as necessary consequences from the same general law
of force; and how the orbits of comets themselves are only particular
cases of planetary movements. Thence proceeding to applications of
greater difficulty, he explains how the perplexing inequalities of
the moon’s motion result from the sun’s disturbing action; how tides
arise from the unequal attraction of the sun as well as of the moon
on the earth, and the ocean which surrounds it; and, lastly, how the
precession of the equinoxes is a necessary consequence of the very same
law.

(303.) The immediate successors of Newton found full occupation
in verifying his discoveries, and in extending and improving the
mathematical methods which it had now become manifest were to prove
the keys to an inexhaustible treasure of knowledge. The simultaneous
but independent discovery of a method of mathematical investigation in
every respect similar to that of Newton, by Leibnitz, while it created
a degree of national jealousy which can now only be regretted, had the
effect of stimulating the continental geometers to its cultivation, and
impressing on it a character more entirely independent of the ancient
geometry, to which Newton was peculiarly attached. It was fortunate
for science that it did so; for it was speedily found that (with one
fine exception on the part of our countryman Maclaurin, followed up,
after a long interval, by the late Professor Robison of Edinburgh, with
equal elegance,) the geometry of Newton was like the bow of Ulysses,
which none but its master could bend; and that, to render his methods
available beyond the points to which he himself carried them, it was
necessary to strip them of every vestige of that antique dress in which
he had delighted to clothe them. This, however, the countrymen of
Newton were very unwilling to do; and they paid the penalty in finding
themselves condemned to the situation of lookers on, while their
continental neighbours both in Germany and France were pushing forward
in the career of mathematico-physical discovery with emulous rapidity.

(304.) The legacy of research which Newton may be said to have left
to his successors was truly immense. To pursue, through all its
intricacies, the consequences of the law of gravitation; to account for
all the inequalities of the planetary movements, and the infinitely
more complicated, and to us more important ones, of the moon; and to
give, what Newton himself certainly never entertained a conception
of, a demonstration of the stability and permanence of the system,
under all the accumulating influence of its internal perturbations;
this labour, and this triumph, were reserved for the succeeding
age, and have been shared in succession by Clairaut, D’Alembert,
Euler, Lagrange and Laplace. Yet so extensive is the subject, and so
difficult and intricate the purely mathematical enquiries to which it
leads, that another century may yet be required to go through with
the task. The recent discoveries of astronomers have supplied matter
for investigation, to the geometers of this and the next generation,
of a difficulty far surpassing any thing that had before occurred.
Five primary planets have been added to our system; four of them
since the commencement of the present century, and these, singularly
deviating from the general analogy of the others, and offering _cases
of difficulty_ in theory, which no one had before contemplated. Yet
even the intricate questions to which these bodies have given rise
seem likely to be surpassed by those which have come into view, with
the discovery of several comets revolving in elliptic orbits, like the
planets, round the sun, in very moderate periods. But the resources of
modern geometry seem, so far from being exhausted, to increase with the
difficulties they have to encounter, and already, among the successors
of Lagrange and Laplace, the present generation has to enumerate a
powerful array of names, which promise to render it not less celebrated
in the annals of physico-mathematical research than that which has just
passed away.

(305.) Meanwhile the positions, figures, and dimensions of all the
planetary orbits, are now well known, and their variations from century
to century in great measure determined; and it has been generally
demonstrated, that all the changes which the mutual actions of the
planets on each other can produce in the course of indefinite ages,
are _periodical_, that is to say, increasing to a certain extent (and
that never a very great one), and then again decreasing; so that the
system can never be destroyed or subverted by the mutual action of its
parts, but keeps constantly oscillating, as it were, round a certain
mean state, from which it can never deviate to any ruinous extent. In
particular the researches of Laplace, Lagrange, and Poisson, have shown
the ultimate invariability of the mean distance of each planet from the
sun, and consequently of its periodic time. Relying on these grand
discoveries, we are enabled to look forward, from the point of time
which we now occupy, many thousands of years into futurity, and predict
the state of our system without fear of material error, but such as
may arise from causes whose existence at present we have no reason to
suppose, or from interference which we have no right to anticipate.

(306.) A correct enumeration and description of the fixed stars in
catalogues, and an exact knowledge of their position, supply the
only effectual means we can have of ascertaining what changes they
are liable to, and what motions, too slow to deprive them of their
usual epithet, _fixed_, yet sufficient to produce a sensible change
in the lapse of ages, may exist among them. Previous to the invention
of the compass, they served as guides to the navigator by night; but
for this purpose, a very moderate knowledge of a few of the principal
ones sufficed. Hipparchus was the first astronomer, who, excited
by the appearance of a new star, conceived the idea of forming a
catalogue of the stars, with a view to its use as an astronomical
record, “by which,” says Pliny, “posterity will be able to discover,
not only whether they are born and die, but also whether they change
their places, and whether they increase or decrease.” His catalogue,
containing more than 1000 stars, was constructed about 128 years before
Christ. It was in the course of the laborious discussion of his own and
former observations of them, undertaken with a view to the formation of
this catalogue, that he first recognised the fact of that slow, general
advance of all the stars eastward, when compared with the place of
the equinox, which is known under the name of the precession of the
equinoxes, and which Newton succeeded in referring to a motion in the
earth’s axis, produced by the attraction of the sun and moon.

(307.) Since Hipparchus, at various periods in the history of
astronomy, catalogues of stars have been formed, among which that
of Ulugh Begh, comprising about 1000 stars, constructed in 1437, is
remarkable as the production of a sovereign prince, working personally
in conjunction with his astronomers; and that of Tycho Brahe,
containing 777 stars, constructed in 1600, as having originated in a
phenomenon similar to that which drew the attention of Hipparchus. In
more recent times, astronomers provided with the finest instruments
their respective eras could supply, and established in observatories,
munificently endowed by the sovereigns and governments of different
European nations, have vied and are still vying with each other,
in extending the number of registered stars, and giving the utmost
possible degree of accuracy to the determination of their places.
Among these, it would be ungrateful not to claim especial notice
for the superb series of observations which, under a succession of
indefatigable and meritorious astronomers, has, for a very long period,
continued to emanate from our own national observatory of Greenwich.

(308.) The distance of the fixed stars is so immense, that every
attempt to assign a limit, _within which_ it _must_ fall, has hitherto
failed. The enquiries of astronomers of all ages have been directed
to ascertain this distance, by taking the dimensions of our own
particular system of sun and planets, or of the earth itself, as the
unit of a scale on which it might be measured. But although many have
imagined that their observations afforded grounds for the decision
of this interesting point, it has uniformly happened either that the
phenomena on which they relied have proved to be referable to other
causes not previously known, and which the superior accuracy of their
researches has for the first time brought to light; or to errors
arising from instrumental imperfections and unavoidable defects of the
observations themselves.

(309.) The only indication we can expect to obtain of the actual
distance of a star, would consist in an annual change in its apparent
place corresponding to the motion of the earth round the sun, called
its _annual parallax_, and which is nothing more than the measure
of the apparent size of the earth’s orbit as seen from the star.
Many observers have thought they have detected a measurable amount
of this parallax; but as astronomical instruments have advanced in
perfection, the quantity which they have successively assigned to it
has been continually reduced within narrower and narrower limits,
and has invariably been commensurate with the errors to which the
instruments used might fairly be considered liable. The conclusion this
strongly presses on us is, that it is really a quantity too small to
admit of distinct measurement in the present state of our means for
that purpose; and that, therefore, the distance of the stars must be
a magnitude of such an order as the imagination almost shrinks from
contemplating. But this increase in our scale of dimension calls for
a corresponding enlargement of conception in all other respects. The
same reasoning which places the stars at such immeasurable remoteness,
exalts them at the same time into glorious bodies, similar to, and even
far surpassing, our own sun, the centres perhaps of other planetary
systems, or fulfilling purposes of which we can have no idea, from any
analogy in what passes immediately around us.

(310.) The comparison of catalogues, published at different periods,
has given occasion to many curious remarks, respecting changes both
of place and brightness among the stars, to the discovery of variable
ones which lose and recover their lustre periodically, and to that of
the disappearance of several from the heavens so completely as to have
left no vestige discernible even by powerful telescopes. In proportion
as the construction of astronomical and optical instruments has gone on
improving, our knowledge of the contents of the heavens has undergone
a corresponding extension, and, at the same time, attained a degree of
precision which could not have been anticipated in former ages. The
places of all the principal stars in the northern hemisphere, and of a
great many in the southern, are now known to a degree of nicety which
must infallibly detect any real motions that may exist among them,
and has in fact done so, in a great many instances, some of them very
remarkable ones.

(311.) It is only since a comparatively recent date, however, that
any great attention has been bestowed on the smaller stars, among
which there can be no doubt of the most interesting and instructive
phenomena being sooner or later brought to light. The minute
examination of them with powerful telescopes, and with delicate
instruments for the determination of their places, has, indeed, already
produced immense catalogues and masses of observations, in which
thousands of stars invisible to the naked eye are registered; and has
led to the discovery of innumerable important and curious facts, and
disclosed the existence of whole classes of celestial objects, of a
nature so wonderful as to give room for unbounded speculation on the
extent and construction of the universe.

(312.) Among these, perhaps the most remarkable are the revolving
double stars, or stars which, to the naked eye or to inferior
telescopes, appear single; but, if examined with high magnifying
powers, are found to consist of two individuals placed almost close
together, and which, when carefully watched, are (many of them) found
to revolve in regular elliptic orbits about each other; and so far
as we have yet been able to ascertain, to obey the same laws which
regulate the planetary movements. There is nothing calculated to give a
grander idea of the scale on which the sidereal heavens are constructed
than these beautiful systems. When we see such magnificent bodies
united in pairs, undoubtedly by the same bond of mutual gravitation
which holds together our own system, and sweeping over their enormous
orbits, in periods comprehending many centuries, we admit at once that
they must be accomplishing ends in creation which will remain for ever
unknown to man; and that we have here attained a point in science
where the human intellect is compelled to acknowledge its weakness, and
to feel that no conception the wildest imagination can form will bear
the least comparison with the intrinsic greatness of the subject.


_Geology._

(313.) The researches of physical astronomy are confessedly incompetent
to carry us back to the origin of our system, or to a period when
its state was, in any great essential, different from what it is
at present. So far as the causes now in action go, and so far as
our calculations will enable us to estimate their effects, we are
equally unable to perceive in the general phenomena of the planetary
system either the evidence of a beginning, or the prospect of an end.
Geometers, as already stated, have demonstrated that, in the midst of
all the fluctuations which can possibly take place in the elements of
the orbits of the planets, by reason of their mutual attraction, the
general balance of the parts of the system will always be preserved,
and every departure from a mean state periodically compensated. But
neither the researches of the physical astronomer, nor those of
the geologist, give us any ground for regarding our system, or the
globe we inhabit, as of eternal duration. On the contrary, there are
circumstances in the physical constitution of our own planet which at
least obscurely point to an origin and a formation, however remote,
since it has been found that the figure of the earth is not globular
but elliptical, and that its attraction is such as requires us to admit
the interior to be more dense than the exterior, and the density to
increase with some degree of regularity from the surface towards the
centre, and _that_, in layers arranged elliptically round the centre,
circumstances which could scarcely happen without some such successive
deposition of materials as would enable pressure to be propagated with
a certain degree of freedom from one part of the mass to another, even
if we should hesitate to admit a state of primitive fluidity.

(314.) But from such indications nothing distinct can be concluded;
and if we would speculate to any purpose on a former state of our
globe and on the succession of events which from time to time may have
changed the condition and form of its surface, we must confine our
views within limits far more restricted, and to subjects much more
within the reach of our capacity, than either the creation of the world
or its assumption of its present figure. These, indeed, were favourite
speculations with a race of geologists now extinct; but the science
itself has undergone a total change of character, even within the last
half century, and is brought, at length, effectually within the list
of the inductive sciences. Geologists now no longer bewilder their
imaginations with wild theories of the formation of the globe from
chaos, or its passage through a series of hypothetical transformations,
but rather aim at a careful and accurate examination of the records
of its former state, which they find indelibly impressed on the great
features of its actual surface, and to the evidences of former life
and habitation which organised remains imbedded and preserved in its
strata indisputably afford.

(315.) Records of this kind are neither few nor vague; and though the
obsoleteness of their language when we endeavour to interpret it too
minutely, may, and no doubt often does, lead to misapprehension, still
its general meaning is, on the whole, unequivocal and satisfactory.
Such records teach us, in terms too plain to be misunderstood, that
the whole or nearly the whole of our present lands and continents
were formerly at the bottom of the sea, where they received deposits
of materials from the wearing and degradation of other lands not now
existing, and furnished receptacles for the remains of marine animals
and plants inhabiting the ocean above them, as well as for similar
spoils of the land washed down into its bosom.

(316.) These remains are occasionally brought to light; and their
examination has afforded indubitable evidence of the former existence
of a state of animated nature widely different from what now obtains
on the globe, and of a period anterior to that in which it has been
the habitation of man, or rather, indeed, of a series of periods, of
unknown duration, in which both land and sea teemed with forms of
animal and vegetable life, which have successively disappeared and
given place to others, and these again to new races approximating
gradually more and more nearly to those which now inhabit them, and at
length comprehending species which have their counterparts existing.

(317.) These wrecks of a former state of nature, thus wonderfully
preserved (like ancient medals and inscriptions in the ruins of an
empire), afford a sort of rude chronology, by whose aid the successive
depositions of the strata in which they are found may be marked out
in epochs more or less definitely terminated, and each characterized
by some peculiarity which enables us to recognise the deposits of any
period, in whatever part of the world they may be found. And, so far
as has been hitherto investigated, the _order_ of succession in which
these deposits have been formed appears to have been the same in every
part of the globe.

(318.) Many of the strata which thus bear evident marks of having been
deposited at the bottom of the sea, and of course in a horizontal
state, are now found in a position highly inclined to the horizon, and
even occasionally vertical. And they often bear no less evident marks
of violence, in their bending and fracture, the dislocation of parts
which were once contiguous, and the existence of vast collections of
broken fragments which afford every proof of great violence having been
used in accomplishing some at least of the changes which have taken
place.

(319.) Besides the rocks which carry this internal evidence of
submarine deposition, are many which exhibit no such proofs, but on the
contrary hold out every appearance of owing their origin to volcanoes
or to some other mode of igneous action; and in every part of the
world, and among strata of all ages, there occur evidences of such
action so abundant, and on such a scale, as to point out the volcano
and the earthquake as agents which may have been instrumental in the
production of those changes of level, and those violent dislocations
which we perceive to have taken place.

(320.) At all events, in accounting for those changes, geologists
have no longer recourse, as formerly, to causes purely hypothetical,
such as a shifting of the earth’s axis of rotation, bringing the sea
to overflow the land, by a change in the place of the longer and
shorter diameters of the spheroidal figure, nor to tides produced by
the attraction of comets suddenly approaching very near the earth,
nor to any other fanciful and arbitrarily assumed hypotheses; but
rather endeavour to confine themselves to a careful consideration
of causes evidently in action at present, with a view to ascertain
how far they, in the first instance, are capable of accounting for
the facts observed, and thus legitimately bringing into view, as
residual phenomena, those effects which cannot be so accounted for.
When this shall have been in some measure accomplished, we shall be
able to pronounce with greater security than at present respecting the
necessity of admitting a long succession of tremendous and ravaging
catastrophes and cataclysms,--epochs of terrific confusion and violence
which many geologists (perhaps with justice) regard as indispensable to
the explanation of the existing features of the world. We shall learn
to distinguish between the effects which require for their production
the sudden application of convulsive and fracturing efforts, and those,
probably not less extensive, changes which may have been produced by
forces equally or more powerful, but acting with less irregularity,
and so distributed over time as to produce none of those _interregnums_
of chaotic anarchy which we are apt to think (perhaps erroneously)
great disfigurements of an order so beautiful and harmonious as that of
nature.

(321.) But to estimate justly the effects of causes now in action in
geology is no easy task. There is no _à priori_ or deductive process by
which we can estimate the amount of the annual erosion, for instance,
of a continent by the action of meteoric agents, rain, wind, frost,
&c., nor the quantity of destruction produced on its coasts by the
direct violence of the sea, nor the quantity of lava thrown up _per
annum_ by volcanoes over the whole surface of the earth, nor any
similar effect. And to consult experience on all such points is a
slow and painful process if rightly gone into, and a very fallible
one if only partially executed. Much, then, at present must be left
to opinion, and to that sort of clear-judging tact which sometimes
anticipates experience; but this ought not to stand in the way of our
making every possible effort to obtain accurate information on such
points, by which alone geology can be rendered, if not an experimental
science, at least a science of that kind of active observation which
forms the nearest approach to it, where actual experiment is impossible.

(322.) Let us take, for example, the question, “What is the actual
direction in which changes of relative level are taking place between
the existing continents and seas?” If we consult partial experience,
that is, _all_ the information that we possess respecting ancient
sea-marks, soundings, &c., we shall only find ourselves bewildered in
a mass of conflicting, because imperfect, evidence. It is obvious that
the only way to decide the point is to ascertain, by very precise and
careful observations at proper stations on coasts, selected at points
where there exist natural marks not liable to change in the course of
at least a century, the true elevation of such marks above the _mean_
level of the sea, and to multiply these stations sufficiently over the
whole globe to be capable of affording real available knowledge. Now,
this is not a very easy operation (considering the accuracy required);
for the _mean_ level of the sea can be determined by no single
observation, any more than the mean height of the barometer at a given
station, being affected both by periodical and accidental fluctuations
due to tides, winds, waves, and currents. Yet if an instrument adapted
for the purpose were constructed, and rendered easily attainable, and
rules for its use carefully drawn up, there is little doubt we should
soon (by the industry of observers scattered over the world) be in
possession of a most valuable mass of information, which could not fail
to afford a point of departure for the next generation, and furnish
ground for the only kind of argument which ever can be conclusive on
such subjects.

(323.) Geology, in the magnitude and sublimity of the objects of
which it treats, undoubtedly ranks, in the scale of the sciences,
next to astronomy; like astronomy, too, its progress depends on the
continual accumulation of observations carried on for ages. But, unlike
astronomy, the observations on which it depends, when the whole extent
of the subject to be explored is taken into consideration, can hardly
yet be said to be more than commenced. Yet, to make up for this, there
is another important difference, that while in the latter science it is
impossible to recall the past or anticipate the future, and observation
is in consequence limited to a single fact in a single moment; in
the former, the records of the past are always present;--they may be
examined and re-examined as often as we please, and require nothing
but diligence and judgment to put us in possession of their whole
contents. Only a very small part of the surface of our globe has,
however, been accurately examined in detail, and of that small portion
we are only able to scratch the mere exterior, for so we must consider
those excavations which we are apt to regard as searching the bowels
of the earth; since the deepest mines which have been sunk penetrate
to a depth hardly surpassing the ten thousandth part of the distance
between its surface and its centre. Of course inductions founded on
such limited examination can only be regarded as provisional, except
in those remarkable cases where the same great formations in the same
order have been recognised in very distant quarters, and without
exception. This, however, cannot long be the case. The spirit with
which the subject has been prosecuted for many years in our own country
has been rewarded with so rich a harvest of surprising and unexpected
discoveries, and has carried the investigation of our island into such
detail, as to have excited a corresponding spirit among our continental
neighbours; while the same zeal which animates our countrymen on their
native shore accompanies them in their sojourns abroad, and has
already begun to supply a fund of information respecting the geology of
our Indian possessions, as well as of every other point where English
intellect and research can penetrate.

(324.) Nothing can be more desirable than that every possible facility
and encouragement should be afforded for such researches, and indeed
to the pursuits of the enlightened resident or traveller in every
department of science, by the representatives of our national authority
wherever our power extends. By these only can our knowledge of the
actual state of the surface of the globe, and that of the animals
and vegetables of the ancient continents and seas, be extended and
perfected, while more complete information than we at present possess
of the habits of those actually existing, and the influence of changes
of climate, food, and circumstances, on them, may be expected to render
material assistance to our speculations respecting those which have
become extinct.



CHAP. IV.

OF THE EXAMINATION OF THE MATERIAL CONSTITUENTS OF THE WORLD.


_Mineralogy._

(325.) The consideration of the history and structure of our globe, and
the examination of the fossil contents of its strata, lead us naturally
to consider the materials of which it consists. The history of these
materials, their properties as objects of philosophical enquiry, and
their application to the useful arts and the embellishments of life,
with the characters by which they can be certainly distinguished one
from another, form the object of mineralogy, taken in its most extended
sense.

(326.) There is no branch of science which presents so many points
of contact with other departments of physical research, and serves
as a connecting link between so many distant points of philosophical
speculation, as this. To the geologist, the chemist, the optician, the
crystallographer, the physician, it offers especially the very elements
of their knowledge, and a field for many of their most curious and
important enquiries. Nor, with the exception of chemistry, is there any
which has undergone more revolutions, or been exhibited in a greater
variety of forms. To the ancients it could scarcely be said to be at
all known, and up to a comparatively recent period, nothing could
be more imperfect than its descriptions, or more inartificial and
unnatural than its classification. The more important minerals in the
arts, indeed, those used for economical purposes and those from which
metals were extracted, had a certain degree of attention paid to them,
for the sake of their utility and commercial value, and the precious
stones for that of ornament. But until their crystalline forms were
attentively observed and shown to be determinate characters on which
dependence could be placed, no mineralogist could give any correct
account of the real distinction between one mineral and another.

(327.) It was only, however, when chemical analysis had acquired
a certain degree of precision and universal applicability that
the importance of mineralogy as a science began to be recognized,
and the connection between the external characters of a stone and
its ingredient constituents brought into distinct notice. Among
these characters, however, none were found to possess that eminent
distinctness which the crystalline form offers; a character, in the
highest degree geometrical, and affording, as might be naturally
supposed, the strongest evidence of its necessary connection with the
intimate constitution of the substance. The full importance of this
character was, however, not felt until its connection with the texture
or cleavage of a mineral was pointed out, and even then it required
numerous and striking instances of the critical discernment of Haüy
and other eminent mineralogists in predicting from the measurements
of the angles of crystals which had been confounded together that
differences would be found to exist in their chemical composition, all
which proved fully justified in their result before the essential value
of this character was acknowledged. This was no doubt in great measure
owing to the high importance set by the German mineralogists on those
external characters of touch, sight, weight, colour, and other sensible
qualities, which are little susceptible, with the exception of weight,
of exact determination, and which are subject to material variations
in different specimens of the same mineral. By degrees, however, the
necessity of ascribing great weight to a character so definite was
admitted, especially when it was considered that the same step which
pointed out the intimate connection of external form with internal
structure furnished the mineralogist with the means of reducing all
the forms of which a mineral is susceptible under one general type, or
primitive form, and afforded grounds for an elegant theoretical account
of the assumption of definite figures _ab initio_.

(328.) A simple and elegant invention of Dr. Wollaston, the reflecting
goniometer, gave a fresh impulse to that view of mineralogy which makes
the crystalline form the essential or leading character, by putting
it in the power of every one, by the examination of even the smallest
portion of a broken crystal, to ascertain and verify that essential
character on which the identity of a mineral in the system of Haüy
was made to depend. The application of so ready and exact a method
speedily led to important results, and to a still nicer discrimination
of mineral species than could before be attained; and the confirmation
given to these results by chemical analysis stamped them with a
scientific and decided character which they have retained ever since.

(329.) Meanwhile the progress made in chemical analysis had led to
the important conclusion that every chemical compound susceptible of
assuming the solid state assumed with it a determinate crystalline
form; and the progress of optical science had shown that the
fundamental crystalline form, in the case at least of transparent
bodies, drew with it a series of optical properties no less curious
than important in relation to the affections of light in its passage
through such substances. Thus, in every point of view, additional
importance became added to this character; and the study of the
crystalline forms of bodies in general assumed the form of a separate
and independent branch of science, of which the geometrical forms of
the mineral world constituted only a particular case. Mineralogy,
however, as a branch of natural history, remains still distinct either
from optics or crystallography. The mineralogist is content, and thinks
he has performed his task, if not as a natural historian at least as
a classifier and arranger, if he only gives such a characteristic
description of a mineral as shall effectually distinguish it from every
other, and shall enable any one who may encounter such a body in any
part of the world to impose on it its name, assign it a place in his
system, and turn to his books for a further description of all that
the chemist, the optician, the lapidary, or the artist, may require to
know. Still this is no easy matter: the laborious researches of the
most eminent mineralogists can hardly yet be said to have effectually
accomplished it; and its difficulty may be appreciated by the small
number of simple minerals, or minerals of perfectly definite and
well-marked characters, which have been hitherto made out. Nor can
this indeed be wondered at, when we consider that by far the greater
portion of the rocks and stones which compose the external crust of the
globe consists of nothing more than the accumulated _detritus_ of older
rocks, in which the fragments and powder of an infinite variety of
substances are mingled together, in all sorts of varying proportions,
and in such a way as to defy separation. Many of these rocks, however,
so compounded, occur with sufficient frequency and uniformity of
character to have acquired names and to have been usefully applied;
indeed, in the latter respect, minerals of this description far surpass
all the others. As objects of natural history, therefore, they are well
worthy of attention, however difficult it may be to assign them a place
in any artificial arrangement.

(330.) This paucity of simple minerals, however, is probably rather
apparent than real, and in proportion as the researches of the chemist
and crystallographer shall be extended throughout nature, they will
no doubt become much more numerous. Indeed, in the great laboratories
of nature it can hardly be doubted that almost every kind of chemical
process is going forwards, by which compounds of every description are
continually forming. Accordingly, it is remarked, that the lavas and
ejected scoriæ of volcanoes are receptacles in which mineral products
previously unknown are constantly discovered, and that the primitive
formations, as they are called in geology, which bear no marks of
having been produced by the destruction of others, are also remarkable
for the beauty and distinctness of character of their minerals.

(331.) The great difficulty which has been experienced in attempts to
classify mineral substances by their chemical constituents has arisen
from the observed presence, in some specimens of minerals bearing
that general resemblance in other respects as well as agreement in
form which would seem to entitle them to be considered as alike, of
ingredients foreign to the usual composition of the species, and that
occasionally in so large a proportion as to render it unjustifiable
to refer their occurrence to accidental impurities. These cases, as
well as some anomalies observed in the classification of minerals by
their crystalline forms, which seemed to show that the same substance
might occasionally appear under two distinct forms, as well as some
remarkable coincidences between the forms of substances quite distinct
from each other in a chemical point of view, have within a recent
period given rise to a branch of the science of crystallography of a
very curious and important nature. The _isomorphism_ of certain groups
of chemical elements has already afforded us an example illustrative
of the manner in which inductions sometimes receive unexpected
verifications (see 180.). The laws and relations thus brought to light
are among the most curious and interesting parts of modern science,
and seem likely in their further developement to afford ample scope
for the exercise of chemical and mineralogical research. They have
already afforded innumerable fine examples of that important step in
science by which anomalies disappear, and occasional incongruities
become reconciled under more general expressions of physical laws,
and thus unite in affording support to those very views which they
promised, when first observed, to overset. Nothing, indeed, can be
more striking than to see the very ingredient which every previous
chemist and mineralogist would agree to disregard and reject as a
mere casual impurity brought forward and appealed to in support of a
theory expressly directed to the object of rescuing science from the
imputation of disregarding, under any circumstances, the plain results
of direct experiment.


_Chemistry._

(332.) The laws which concern the intimate constitution of bodies,
not as respects their _structure_ or the manner in which their parts
are put together, but as regards their _materials_ or the ingredients
of which those parts are composed, form the objects of chemistry. A
solid body may be regarded as a fabric, more or less regularly and
artificially constructed, in which the materials and the workmanship
may be separately considered, and in which, though the latter be
ruined and confounded by violence, the former remain unchanged in
their nature, though differently arranged. In liquid or aërial bodies,
too, though there prevails a less degree of difference in point of
structure, and a greater facility of dispersion and dissipation, than
in solids, yet an equal diversity of _materials_ subsists, giving to
them properties differing extremely from each other.

(333.) The inherent activity of matter is proved not only by the
production of motion by the mutual attractions and repulsions of
distant or contiguous masses, but by the changes and apparent
transformations which different substances undergo in their sensible
qualities by mere mixture. If water be added to water, or salt to salt,
the effect is an increase of quantity, but no change of quality. In
this case, the mutual action of the particles is entirely mechanical.
Again, if a blue powder and a yellow one, each perfectly dry, be mixed
and well shaken together, a green powder will be produced; but this
is a mere effect arising in the eye from the intimate mixture of the
yellow and blue light separately and independently reflected from
the minute particles of each; and the proof is had by examining the
mixture with a microscope, when the yellow and blue grains will be seen
separate and each quite unaltered. If the same experiment be tried with
coloured liquids, which are susceptible of mixing without chemical
action, a compound colour is likewise produced, but no examination
with magnifiers is in that case sufficient to detect the ingredients;
the reason obviously being, the excessive minuteness of the parts, and
their perfect intermixture, produced by agitating two liquids together.
From the mixture of two powders, extreme patience would enable any one,
by picking out with a magnifier grain after grain, to separate the
ingredients. But when liquids are mixed, no mechanical separation is
any longer practicable; the particles are so minute as to elude all
search. Yet this does not hinder us from regarding such a compound as
still a mere mixture, and its properties are accordingly intermediate
between those of the liquids mixed. But this is far from being the
case with all liquids. When a solution of potash, for example, and
another of tartaric acid, each perfectly liquid, are mixed together in
proper proportions, a great quantity of a solid saline substance falls
to the bottom of the containing vessel, which is quite different from
either potash or tartaric acid, and the liquid from which it subsided
offers no indications by its taste or other sensible qualities of the
ingredients mixed, but of something totally different from either.
It is evident that this is a phenomenon widely different from that
of mere mixture; there has taken place a great and radical change in
the intimate nature of the ingredients, by which a new substance is
produced which had no existence before. And it has been produced by the
_union_ of the ingredients presented to each other; for when examined
it is found that nothing has been _lost_, the weight of the whole
mixture being the sum of the weights mixed. Yet the potash and tartaric
acid have disappeared entirely, and the weight of the new product is
found to be exactly equal to that of the tartaric acid and potash
employed, taken together, abating a small portion held in solution in
the liquid, which may be obtained however by evaporation. They have
therefore combined, and adhere to one another with a cohesive force
sufficient to form a solid out of a liquid; a force which has thus been
called into action by merely presenting them to each other in a state
of solution.

(334.) It is the business of chemistry to investigate these and similar
changes, or the reverse of such changes, where a single substance is
resolved into two or more others, having different properties from it,
and from each other, and to enquire into all the circumstances which
can influence them; and either determine, modify, or suspend their
accomplishment, whether such influence be exercised by heat or cold, by
time and rest, or by agitation or pressure, or by any of those agents
of which we have acquired a knowledge, such as electricity, light,
magnetism, &c.

(335.) The wonderful and sudden transformations with which chemistry is
conversant, the violent activity often assumed by substances usually
considered the most inert and sluggish, and, above all, the insight
it gives into the nature of innumerable operations which we see daily
carried on around us, have contributed to render it the most popular,
as it is one of the most extensively useful, of the sciences; and
we shall, accordingly, find none which have sprung forward, during
the last century, with such extraordinary vigour, and have had such
extensive influence in promoting corresponding progress in others. One
of the chief causes of its popularity is, perhaps, to be sought for in
this, that it is, of all the sciences, perhaps, the most completely an
experimental one; and even its theories are, for the most part, of that
generally intelligible and readily applicable kind, which demand no
intense concentration of thought, and lead to no profound mathematical
researches. The simple process of inductive generalization, grounded on
the examination of numerous facts, all of them presenting considerable
intrinsic interest, has sufficed, in most instances, to lead, by a
clear and direct road, to its highest laws yet known. But, on the other
hand, these laws, when stated, are not yet fully sufficient to lead us,
except in very limited cases, to a deductive knowledge of particulars
never before examined, at least, not without great caution, and
constant appeal to experiment as a check on our reasoning; so that we
are justified in regarding the _axioms_ of chemistry, the true handles
of deductive reasoning, as still unknown, and, perhaps, likely long
to remain so. This is no fault of its cultivators, who have comprised
in their list the highest and most varied talents and industry, but
of the inherent complexity of the subject, and the infinite multitude
of causes which are concerned in the production of every, even the
simplest, chemical phenomenon.

(336.) The history of chemistry (on which, however, we are not about
to enlarge,) is one of great interest to those who delight to trace
the steps by which mankind advance to the discovery of truth through
a series of mistakes and failures. It may be divided, 1st, into
the period of the alchemists, a lamentable epoch in the annals of
intellectual wandering; 2dly, that of the phlogistic doctrines of
Beccher and Stahl, in which, as if to prove the perversity of the human
mind, of two possible roads the wrong was chosen; and a theory obtained
universal credence on the strength of an induction, valid as such, but
wrongly interpreted, which is negatived, _in every instance_, by an
appeal to the balance. This, too, happened, not by reason of unlucky
coincidences, or individual oversights, but of necessity, and from an
inherent defect of the theory itself, which thus impeded the progress
of the science, as far as a science of experiment can be impeded by
a false theory, by perplexing its cultivators with the appearance of
contradictions in their experiments where none really subsisted, by
destroying all their confidence in the numerical exactness of their
own results, and by involving the subject in a mist of visionary and
hypothetical causes in place of the true acting principles. Thus, in
the combustion of any substance which is incapable of flying away in
fumes, an increase of weight takes place,--the ashes are heavier than
the fuel. Whenever this was observed, however, it was passed carelessly
over as arising from the escape of phlogiston, or the principle of
inflammability, which was considered as being either the element of
fire itself, or in some way combined with it, and thus essentially
_light_. It is now known that the increase of weight is owing to
the absorption of, and combination with, a quantity of a peculiar
ingredient called _oxygen_, from the air, a principle essentially
_heavy_. So far as weight is concerned, it makes no difference whether
a body having weight enters, or one having levity escapes; but there
is this plain difference in a philosophical point of view, that oxygen
is a real producible substance, and phlogiston is no such thing: the
former is a _vera causa_, the latter an hypothetical being, introduced
to account for what the other accounts for much better.

(337.) The third age of chemistry--that which may be called
emphatically modern chemistry--commenced (in 1786) when Lavoisier, by
a series of memorable experiments, extinguished for ever this error,
and placed chemistry in the rank of one of the exact sciences,--a
science of number, weight, and measure. From that epoch to the
present day it has constantly advanced with an accelerated progress,
and at this moment may be regarded as more progressive than ever.
The principal features in this progress may be comprised under the
following general heads:--

   1. The discovery of the proximate, if not the ultimate, elements
        of all bodies, and the enlargement of the list of known
        elements to its present extent of between fifty and sixty
        substances.

   2. The developement of the doctrine of latent heat by Black,
        with its train of important consequences, including the
        scientific theory of the steam-engine.

   3. The establishment of Wenzel’s law of definite proportions on
        his own experiments, and those of Richter, a discovery
        subsequently merged in the more general wording and better
        development of Dalton’s atomic theory.

   4. The precise determination of the atomic weights of the
        different chemical elements, mainly due to the astonishing
        industry of Berzelius, and his unrivalled command of chemical
        resources, as well as to the researches of the other chemists
        of the Swedish and German school.

   5. The assimilation of gases and vapours, by which we are led
        to regard the former, universally, as particular cases of
        the latter, a generalization resulting chiefly from the
        experiments of Faraday on the condensation of the gases,
        and those of Gay-Lussac and Dalton, on the laws of their
        expansion by heat compared with that of vapours.

   6. The establishment of the laws of the combination of gases and
        vapours by definite volumes, by Gay-Lussac.

   7. The discovery of the chemical effects of electricity, and
        the decomposing agency of the Voltaic pile, by Nicholson
        and Carlisle; the investigation of the laws of such
        decompositions, by Berzelius and Hisinger: the decomposition
        of the alkalies by Davy, and the consequent introduction into
        chemistry of new and powerful agents in their metallic bases.

   8. The application of chemical analysis to all the objects of
        organized and unorganized nature, and the discovery of
        the ultimate constituents of all, and the proximate ones
        of organic matter, and the recognisance of the important
        distinctions which appear to divide these great classes of
        bodies from each other.

   9. The applications of chemistry to innumerable processes in the
        arts, and among other useful purposes to the discovery of the
        essential medical principles in vegetables, and to important
        medicaments in the mineral kingdom.

  10. The establishment of the intimate connection between
        chemical composition and crystalline form, by Haüy
        and Vauquelin, with the successive rectifications the
        statement of that connection has undergone in the hands of
        Mitscherlich, Rose, and others, with the progress of chemical
        and crystallographical knowledge.

(338.) To pursue these several heads into detail would lead us into
a treatise on chemistry; but a few remarks on one or two of them, as
they bear upon the general principles of all scientific enquiry, will
not be irrelevant. And first, then, with reference to the discovery
of new elements, it will be observed, that philosophical chemistry no
more aims at determining the one essential element out of which all
matter is framed--the one ultimate principle of the universe--than
astronomy at discovering the origin of the planetary movements in
the application of a determinate projectile force in a determinate
direction, or geology at ascending to the creation of the earth. There
may be such an element. Some singular relations which have been pointed
out in the atomic weights of bodies seem to suggest to minds fond of
speculation that there is; but philosophical chemistry is content to
wait for some striking fact, which may either occur unexpectedly or
be led to by the slow progress of enlarged views, to disclose to us
its existence. Still, the multiplication of so-considered elementary
bodies has been considered by some as an inconvenience. We confess
we do not coincide with this view. Whatever they be, the obstinacy
with which they resist decomposition shows that they are ingredients
of a very high and primary importance in the economy of nature; and
such as, in any state of science, it would be indispensably necessary
to be perfectly familiar with. Like particular theorems in geometry,
which, though not rising to the highest point of generality, have yet
their several scopes and ranges of extensive application, they must be
well and perfectly understood in all their bearings. Should we ever
arrive at an analysis of these bodies, the chemical properties of the
new elements which will then come into view will be known only by our
knowledge of these, or of other compounds of the same class, which they
may be capable of forming. Not but that such an analysis would be a
most important and indeed triumphant achievement, and change the face
of chemistry; but it would undo nothing that has been done, and render
useless no point of knowledge which we have yet arrived at.

(339.) The atomic theory, or the law of definite proportions, which
is the same thing presented in a form divested of all hypothesis,
after the laws of mechanics, is, perhaps, the most important which
the study of nature has yet disclosed. The extreme simplicity which
characterizes it, and which is itself an indication, not unequivocal,
of its elevated rank in the scale of physical truths, had the effect
of causing it to be announced at once by Mr. Dalton, in its most
general terms, on the contemplation of a few instances[53], without
passing through subordinate stages of painful inductive ascent by the
intermedium of subordinate laws, such as, had the contrary course been
pursued by him, would have been naturally preparatory to it, and such
as would have led others to it by the prosecution of Wenzel’s and
Richter’s researches, had they been duly attended to. This is, in fact,
an example, and a most remarkable one, of the effect of that natural
propensity to generalize and simplify (noticed in 171.), which, if it
occasionally leads to over-hasty conclusions, limited or disproved by
further experience, is yet the legitimate parent of many of our most
valuable and soundest results. Instances like this, where great and,
indeed, immeasurable steps in our knowledge of nature are made at once,
and almost without intellectual effort, are well calculated to raise
our hopes of the future progress of science, and, by pointing out the
simplest and most obvious combinations as those which are actually
found to be agreeable to the harmony of creation, to hold out the
cheering prospect of difficulties diminishing as we advance, instead of
thickening around us in increasing complexity.

(340.) A consequence of this immediate presentation of the law of
definite proportions in its most general form is, that its subordinate
laws--those which limit its generality in particular cases, which
diminish the number of combinations abstractly possible, and restrain
the indiscriminate mixture of elements,--remain to be discovered. Some
such limitations have, in fact, been traced to a certain extent, but by
no means so far as the importance of the subject requires; and we have
here abundant occupation for chemists for some time.

(341.) The determination of the atomic weights of the chemical
elements, like that of other standard physical data, with the utmost
exactness, is in itself a branch of enquiry not only of the greatest
importance, but of extreme difficulty. Independent of the general
reasons for desiring accuracy in this respect, there is one peculiar
to the subject. It has been suggested (by Dr. Prout), and strongly
insisted on (by Dr. Thomson), that all the numbers representing these
weights, constituting a scale of great extent, in which the extremes
already known are in proportion to each other, as 1 to upwards of 200,
are simple even multiples of the least of them. If this be really the
case, it opens views of such importance as to justify any degree of
labour and pains in the verification of the law as a purely inductive
one. But in the actual state of chemical analysis, with all deference
to such high authority, we confess it appears to us to stand in great
need of further confirmation, since it seems doubtful whether such
accuracy has yet been attained as to enable us to answer positively
for a fraction not exceeding the three or four hundredth part of the
whole quantity to be determined: at least the results of the first
experimenters, obtained with the greatest care, differ often by a
greater amount; and this degree of exactness, at least, would be
required to verify the law satisfactorily in the higher parts of the
scale.

(342.) The mere agitation of such a question, however, points out
a class of phenomena in physical science of a remote and singular
kind, and of a very high and refined order, which could never become
known but in an advanced state of science, not only practical, but
theoretical,--we mean, such as consist in observed relations among the
_data_ of physics, which show them to be quantities not _arbitrarily_
assumed, but depending on laws and causes which they may be the means
of at length disclosing. A remarkable instance of such a relation is
the curious law which Bode observed to obtain in the progression of the
magnitudes of the several planetary orbits. This law was interrupted
between Mars and Jupiter, so as to induce him to consider a planet
as wanting in that interval;--a deficiency long afterwards strangely
supplied by the discovery of _four_ new planets in that very interval,
all of whose orbits conform in dimension to the law in question, within
such moderate limits of error as may be due to causes independent of
those on which the law itself ultimately rests.[54]

(343.) Neither is it irrelevant to our subject to remark, that the
progress which has been made in this department of chemistry, and
the considerable exactness actually attainable in chemical analysis,
have been owing, in great measure, to a circumstance which might at
first have been hardly considered likely to exercise much influence
on the progress of a science,--the discovery of platina. Without the
resources placed at the ready disposal of chemists by this invaluable
metal, it is difficult to conceive that the multitude of delicate
analytical experiments which have been required to construct the fabric
of existing knowledge could have ever been performed. This, among many
such lessons, will teach us that the most important uses of natural
objects are not those which offer themselves to us most obviously. The
chief use of the moon for man’s immediate purposes remained unknown to
him for five thousand years from his creation. And, since it cannot but
be that innumerable and most important uses remain to be discovered
among the materials and objects already known to us, as well as among
those which the progress of science must hereafter disclose, we may
hence conceive a well-grounded expectation, not only of constant
increase in the physical resources of mankind, and the consequent
improvement of their condition, but of continual accessions to our
power of penetrating into the arcana of nature, and becoming acquainted
with her highest laws.



CHAP. V.

OF THE IMPONDERABLE FORMS OF MATTER.


_Heat._

(344.) One of the chief agents in chemistry, on whose proper
application and management the success of a great number of its
enquiries depends, and many of whose most important laws are disclosed
to us by phenomena of a chemical nature, is HEAT. Although some of
its effects are continually before our eyes as matters of the most
common occurrence, insomuch that there is scarcely any process in the
useful arts and manufactures which does not call for its intervention,
and although, independent of this high utility, and the proportionate
importance of a knowledge of its nature and laws, it presents in itself
a subject of the most curious speculation; yet there is scarcely
any physical agent of which we have so imperfect a knowledge, whose
intimate nature is more hidden, or whose laws are of such delicate and
difficult investigation.

(345.) The word heat generally implies the sensation which we
experience on approaching a fire; but, in the sense it carries in
physics, it denotes the cause, whatever it be, of that sensation, and
of all the other phenomena which arise on the application of fire,
or of any other heating cause. We should be greatly deceived if we
referred only to sensation as an indication of the presence of this
cause. Many of those things which excite in our organs, and especially
of those of taste, a sensation of heat, owe this property to chemical
stimulants, and not at all to their being actually _hot_. This error
of judgment has produced a corresponding confusion of language, and
hence had actually at one period[55] crept into physical philosophy
a great many illogical and absurd conclusions. Again, there are a
number of chemical agents, which, from their corroding, blackening, and
dissolving, or drying up the parts of some descriptions of bodies, and
producing on them effects not generally unlike (though intrinsically
very different from) those produced by heat, are said, in loose and
vulgar language, to burn them; and this error has even become rooted
into a prejudice, by the fact that some of these agents are capable
of becoming actually and truly _hot_ during their action on moist
substances, by reason of their combination with the water the latter
contain. Thus, quicklime and oil of vitriol both exercise a powerful
corrosive action on animal and vegetable substances, and both become
violently hot by their combination with water. They are, therefore,
set down in vulgar parlance as substances of a hot nature; whereas,
in their relations to the physical cause of heat, they agree with the
generality of bodies similarly constituted.

(346.) The nature of heat has hitherto been chiefly studied under the
general heads of--

  1st, Its sources, or the phenomena which it usually accompanies.

  2d, Its communication from its sources to substances capable of
        receiving it, and from these to others, with a view to
        discover the laws which regulate its distribution through
        space or through the bodies which occupy it.

  3d, Its effects, on our senses, and on the bodies to which it is
        communicated in its various degrees of intensity, by which,
        means are afforded us of measuring these degrees.

  4th, Its intimate relations to the atoms of matter, as exhibited
        in its capability of acquiring a latent state under certain
        circumstances, and of entering into something like chemical
        combinations.

(347.) The most obvious sources of heat are, the sun, fire, animal
life, fermentations, violent chemical actions of all kinds, friction,
percussion, lightning, or the electric discharge, in whatever manner
produced, the sudden condensation of air, and others, so numerous,
and so varied, as to show the extensive and important part it has
to perform in the economy of nature. The discoveries of chemists,
however, have referred most of these to the general head of chemical
combination. Thus, fire, or the combustion of inflammable bodies, is
nothing more than a violent chemical action attending the combination
of their ingredients with the oxygen of the air. Animal heat is, in
like manner, referable to a process bearing no remote analogy to
a slow combustion, by which a portion of carbon, an inflammable
principle existing in the blood, is united with the oxygen of the air
in respiration; and thus carried off from the system: fermentation
is nothing more than a decomposition of chemical elements loosely
united, and their re-union in a more permanent state of combination.
The analogy between the sun and terrestrial fire is so natural as to
have been chosen by Newton to exemplify the irresistible force of an
inference derived from that principle. But the nature of the sun and
the mode in which its wonderful supply of light and heat is maintained
are involved in a mystery which every discovery that has been made
either in chemistry or optics, so far from elucidating, seems only to
render more profound. Friction as a source of heat is well known: we
rub our hands to warm them, and we grease the axles of carriage-wheels
to prevent their setting fire to the wood; an accident which, in
spite of this precaution, does sometimes happen. But the effect of
friction, as a means of producing heat with little or no consumption
of materials, was not fully understood till made the subject of direct
experiment by count Rumford, whose results appear to have established
the extraordinary fact, that an unlimited supply of heat may be derived
by friction from the same materials. Condensation, whether of air by
pressure, or of metals by percussion, is another powerful source of
heat. Thus, iron may be so dexterously hammered as to become red-hot,
and the rapid condensation of a confined portion of air will set tinder
on fire.

(348.) The most violent heats known are produced by the concentration
of the solar rays by burning glasses,--by the combustion of oxygen and
hydrogen gases mixed in the exact proportion in which they combine to
produce water,--and by the discharge of a continued and copious current
of electricity through a small conductor. As these three sources of
heat are independent of each other, and each capable of being brought
into action in a very confined space, there seems no reason why they
might not all three be applied at once at the same point, by which
means, probably, effects would be produced infinitely surpassing any
hitherto witnessed.

(349.) Heat is communicated either by _radiation_ between bodies at a
distance, or by _conduction_ between bodies in contact, or between the
contiguous parts of one and the same body. The laws of the radiation
of heat have been studied with great attention, and have been found
to present strong analogies with that of light in some points, and
singular differences in others. Thus, the heat which accompanies the
sun’s rays comports itself, in all respects, like light; being subject
to similar laws of reflection, refraction, and even of polarization, as
has been shown by Berard. Yet they are not identical with each other;
Sir William Herschel having shown, by decisive experiments, verified by
those of Sir H. Englefield, that there exist in a solar beam both rays
of heat which are not luminous, and rays of light which have no heating
power.

(350.) The heat, radiated by terrestrial fires, and by bodies
_obscurely_ hot, by whatever means they have acquired their heat
(even by exposure to the sun’s rays), differs very materially from
solar heat in their power of penetrating transparent substances. This
singular and important difference was first noticed by Mariotte, and
afterwards made the subject of many curious and interesting experiments
by Scheele, who found that terrestrial heat, or that radiated from
fires or heated bodies, is intercepted and detained by glass or
other transparent bodies, while solar heat is not; and that, being
so detained, it heats them: which the latter, as it passes freely
through them, is incapable of doing. The more recent researches of
Delaroche, however, have shown that this detention is complete only
when the temperature of the source of heat is low; but that, as that
temperature is higher, a portion of the heat radiated acquires a
power of penetrating glass; and that the quantity which does so bears
continually a larger and larger proportion to the whole, as the heat
of the radiant body is more intense. This discovery is very important,
as it establishes a community of nature between solar and terrestrial
heat; while at the same time it leads us to regard the actual
temperature of the sun as far exceeding that of any earthly flame.

(351.) A variety of theories have been framed to account for these
curious phenomena; but the subject stands rather in need of further
elucidation from experiment, and is one which merits, and will probably
amply repay, the labours of those who may hereafter devote their
attention to it. The theory of the radiation of heat, in general, which
seems to agree best with the known phenomena, is that of M. Prevost,
who considers all bodies as constantly radiating out heat in all
directions, and receiving it by a similar means of communication from
others, and thus tending, in any space filled, wholly or in part, with
bodies at various temperatures, to establish an equilibrium or equality
of heat in all parts. The application of this idea to the explanation
of the phenomenon of dew we have already seen (see 167.). The laws
of such radiation, under various circumstances, have been lately
investigated in a beautiful series of experiments on the cooling of
bodies by their own radiation in vacuo, by Messrs. Dulong and Petit,
which offer some of the best examples in science of the inductive
investigation of quantitative laws.

(352.) The communication of heat between bodies in contact, or between
the different parts of the same body, is performed by a process called
conduction. It is, in fact, only a particular case of radiation, as
has been explained above (217.); but a case _so_ particular as to
require a separate and independent investigation of its laws. The most
important consideration introduced into the enquiry by this peculiarity
is that of time. The communication of heat by conduction is performed,
for the most part, with extreme slowness, while that performed by
direct radiation is probably not less rapid than the propagation
of light itself. The analysis of the delicate and difficult points
which arise in the investigation of this subject in its reduction
to direct geometrical treatment has been executed with admirable
success by the late Baron Fourrier, whose recent lamented death has
deprived science of an ornament it could ill spare, thinned as its
ranks have been within the last few years. This acute philosopher and
profound mathematician has developed, in a series of elaborate memoirs
presented to the French Institute, the laws of the communication of
heat through the interior of solid masses, placed under the influence
of any external heating and cooling causes, and has in particular
applied his results to the conditions on which the maintenance of the
actual observed temperature on the earth’s surface depends; to the
possible influence of a supposed central heat on our climates; and to
the determination of the actual amount of the heat, derived to us from
the sun, or at least that portion of it on which the difference of the
seasons depends.

(353.) The principal effects of heat are the sensations of warmth or
cold consequent on its entry or egress into or out of our bodies; the
dilatation it causes in the dimensions of all substances in which it is
accumulated; the changes of state it produces in the melting of solids,
and the conversion of them and of liquids into vapour; and the chemical
changes it performs by actual decompositions effected in the intimate
molecules of various substances, especially those of which vegetables
and animals are composed; to which we may add, the production of
electric phenomena under certain circumstances in the contact of
metals, and the developement of electric polarity in crystallised
substances.

(354.) Cold has been considered by some as a positive quality, the
effect of a cause antagonist to that of heat; but this idea seems
now (with perhaps a single exception) to be universally abandoned.
The sensation of cold is as easily explicable by the passage of heat
outwards through the surface of the body as that of heat by its ingress
from without; and the experiments cited in proof of a radiation of
cold are all perfectly explained by Prevost’s theory of reciprocal
interchange. It is remarkable, however, how very limited our means
of producing intense cold are, compared with those we possess of
effecting the accumulation of heat in bodies. This is one of the
strongest arguments adducible in favour of the doctrines of those who
maintain the possibility of exhausting the heat of a body altogether,
and leaving it in a state absolutely devoid of it. But we ought to
consider, that the known methods of generating heat chiefly turn on the
production of chemical combinations: we may easily conceive, therefore,
that, to obtain equally powerful corresponding frigorific effects, we
ought to possess the means of effecting a disunion equally extensive
and rapid between such elements, actually combined, as have already
produced heat by their union. This, however, we can only accomplish by
engaging them in combinations still more energetic, that is to say,
in which we may reasonably expect more heat to be produced by the new
combination than would be destroyed or abstracted by the proposed
decomposition. Chemistry, however, (unaided by electric agency,)
affords no means of suddenly breaking the union of two elements, and
presenting _both_ in an uncombined state. A certain analogy to such
disunion, however, and its consequences, may be traced in the sudden
expansion of condensed gases from a liquid state into vapour, which is
the most powerful source of cold known.

(355.) The dilatation of bodies by heat forms the subject of that
branch of science called pyrometry. There is no body but is capable
of being penetrated by heat, though some with greater, others with
less rapidity; and being so penetrated, all bodies (with a very few
exceptions, and those depending on very peculiar circumstances,) are
dilated by it in bulk, though with a great diversity in the amount
of dilatation produced by the same degree of heat. Of the several
forms of natural bodies, gases and vapours are observed to be most
dilatable; liquids next, and solids least of all. The dilatation of
solids has been made a subject of repeated and careful measurement by
several experimenters; among whom, Smeaton, Lavoisier, and Laplace, are
the principal. The remarkable discovery of the unequal dilatation of
crystallised bodies by Mitscherlich has already been spoken of. (266.)
That of gases and vapours was examined about the same time by Dalton
and Gay-Lussac, who both arrived independently at the conclusion of an
equal dilatability subsisting in them all, which constitutes one of the
most remarkable points in their history.

(356.) The dilatation of air by heat affords, perhaps, the most
unexceptionable means known of measuring degrees of heat. The
thermometer, as originally constructed by Cornelius Drebell, was an
air thermometer. Those now in common use measure accessions of heat
not by the degree of dilatation of air but of mercury. It has been
shown, by the researches of Dulong and Petit, that its indications
coincide exactly with that of the air-thermometer in moderate
temperatures; though at very elevated ones they exhibit a sensible,
and even considerable, deviation. By this instrument, which owes its
present convenience and utility to the happy idea of Newton, who first
thought of fixing determinate points on its scale, we are enabled
to estimate, or at least identify, the degrees of heat; and thereby
to investigate with accuracy the laws of its communication and its
other properties. Were we sure that equal additions of heat produced
equal increments of dimension in any substance, the indications of a
thermometer would afford a true and secure _measure_ of the quantity
present; but this is so far from being the case, that we are nearly in
total ignorance on this important point; a circumstance which throws
the greatest difficulty in the way of all theoretical reasoning, and
even of experimental enquiry. The laws of the dilatation of liquids, in
consequence of this deficiency of necessary preliminary knowledge, are
still involved in great obscurity, notwithstanding the pains which have
been bestowed on them by the elaborate experiments and calculations of
Gilpin, Blagden, Deluc, Dalton, Gay-Lussac, and Biot.

(357.) The most striking and important of the effects of heat consist,
however, in the liquefaction of solid substances, and the conversion of
the liquids so produced into vapour. There is no solid substance known
which, by a sufficiently intense heat, may not be melted, and finally
dissipated in vapour; and this analogy is so extensive and cogent,
that we cannot but suppose that all those bodies which are liquid
under ordinary circumstances, owe their liquidity to heat, and would
freeze or become solid if their heat could be sufficiently reduced.
In many we see this to be the case in ordinary winters; for some,
severe frosts are requisite; others freeze only with the most intense
artificial colds; and some have hitherto resisted all our endeavours;
yet the number of these last is few, and they will probably cease to be
exceptions as our means of producing cold become enlarged.

(358.) A similar analogy leads us to conclude that all aëriform
fluids are merely liquids kept in the state of vapour by heat. Many
of them have been actually condensed into the liquid state by cold
accompanied with violent pressure; and as our means of applying these
causes of condensation have improved, more and more refractory ones
have successively yielded. Hence we are fairly entitled to extend our
conclusion to those which we have not yet been able to succeed with;
and thus we are led to regard it as a general fact, that the liquid and
aëriform or vaporous states are entirely dependent on _heat_; that were
it not for this cause, there would be nothing but solids in nature; and
that, on the other hand, nothing but a sufficient intensity of heat is
requisite to destroy the cohesion of every substance, and reduce all
bodies, first to liquids, and then into vapour.

(359.) But solids, themselves, by the abstraction of heat shrink in
dimension, and at the same time become harder, and more brittle;
yielding less to pressure, and permitting less separation between
their parts by tension. These facts, coupled with the greater
compressibility of liquids, and the still greater of gases, strongly
induce us to believe that it is heat, and heat alone, which holds
the particles of all bodies at that distance from each other which
is necessary to allow of compression; which in fact gives them
their elasticity, and acts as the antagonist force to their mutual
attraction, which would otherwise draw them into actual contact, and
retain them in a state of absolute immobility and impenetrability.
Thus we learn to regard heat as one of the great maintaining powers of
the universe, and to attach to all its laws and relations a degree of
importance which may justly entitle them to the most assiduous enquiry.

(360.) It was first ascertained by Dr. Black that when heat produces
the liquefaction of a solid, or the conversion of a liquid into vapour,
the liquid or the vapour resulting is no _hotter_ than the solid or
liquid from which it was produced, though a great deal of heat has been
expended in producing this effect, and has actually entered into the
substance.

(361.) Hence he drew the conclusion that it has become _latent_, and
continues to exist in the product, maintaining it in its new state,
without increasing its temperature. He further proved, that when the
vapour condenses, or the liquid freezes, this latent heat is again
given out from it. This great discovery, with its natural and hardly
less important concomitant, that of the difference of specific heats in
different bodies, or the different quantities of heat they require to
raise their temperature equally, are the chief reasons for regarding
heat as a material substance in a more decided manner than light, with
which in its radiant state it holds so close an analogy.

(362.) The subject of latent heat has been far less attentively
studied than its great practical importance would appear to demand,
when we consider that it is to this part of physical science that the
theory of the steam-engine is mainly referable, and that material
improvements may not unreasonably be expected in that wonderful
instrument, from a more extended knowledge than we possess of the
latent heats of different vapours. This is not the case, however,
with the subject of specific heat, which was followed up immediately
after its first promulgation with diligence by Irvine; and, after a
brief interval, by Lavoisier and Laplace, as well as by our countryman
Crawfurd, who determined the specific heats of many substances, both
solid and liquid. After a considerable period of inactivity, the
subject was again resumed by Delaroche and Berard, and subsequently
by Dulong and Petit: the result of whose investigations has been the
inductive establishment of one of those simple and elegant physical
laws which carry with them, if not their own evidence, at least their
own recommendation to our belief, as being in unison with every thing
we know of the harmony of nature. The law to which we allude is
this:--that the atoms of all the simple chemical elements have exactly
the same capacity for heat, or are all equally heated or cooled by
equal accessions or abstractions of heat. It is only among laws like
this that we can expect to find a clew capable of guiding us to a
knowledge of the true nature of heat, and its relations to ponderable
matter.


_Magnetism and Electricity._

(363.) These two subjects, which had long maintained a distinct
existence, and been studied as separate branches of science, are at
length effectually blended. This is, perhaps, the most satisfactory
result which the experimental sciences have ever yet attained. All
the phenomena of magnetic polarity, attraction, and repulsion, have
at length been resolved into one general fact, that two currents of
electricity, moving in the same direction repel, and in contrary
directions attract, each other. The phenomena of the communication
of magnetism and what is called its induced state, alone remain
unaccounted for; but the interesting theory which has been developed
by M. Ampere, under the name of Electro-dynamics, holds out a hope
that this difficulty will also in its turn give way, and the whole
subject be at length completely merged, as far as the consideration of
the acting causes goes, in the more general one of electricity. This,
however, does not prevent magnetism from maintaining its separate
importance as a department of physical enquiry, having its own peculiar
laws and relations of the highest practical interest, which are capable
of being studied quite apart from all consideration of its electrical
origin. And not only so, but to study them with advantage, we must
proceed as if that origin were totally unknown, and, at least up to
a certain point, and that a considerably advanced one, conduct our
enquiries into the subject on the same inductive principles as if this
branch of physics were absolutely independent of all others.

(364.) Iron, and its oxides and alloys, were for a long time the only
substances considered susceptible of magnetism. The loadstone was
even one of the examples produced by Bacon of that class of physical
instances to which he applies the term “Instantiæ monodicæ”--_singular
instances_. And the history of magnetism affords a beautiful comment
on his remark on instances of this sort. “Nor should our enquiries,”
he observes, “into their nature be broken off, till the properties and
qualities found in such things as may be esteemed wonders in nature
are reduced and comprehended under some certain law; so that all
irregularity or singularity may be found to depend upon some common
form, and the wonder only rest in the exact differences, degrees,
or extraordinary concurrence, and not in the species itself.” The
discovery of the magnetism of nickel, which though inferior to that
of iron, is still considerable; that of cobalt, yet feebler, and
that of titanium, which is only barely perceptible, have effectually
broken down the imaginary limit between iron and the other materials
of the world, and established the existence of that general law of
continuity which it is one chief business of philosophy to trace
throughout nature. The more recent discoveries of M. Arago (mentioned
in 160.) have completed this generalization, by showing that there
is no substance but which, under proper circumstances, is capable of
exhibiting unequivocal signs of the magnetic virtue. And to obliterate
all traces of that line of separation which was once so broad, we are
now enabled, by the great discovery of Oërsted, to communicate at and
during pleasure to a coiled wire of any metal indifferently all the
properties of a magnet;--its attraction, repulsion, and polarity; and
_that_ even in a more intense degree than was previously thought to
be possible in the best natural magnets. In short, in this case, and
in this case only, perhaps, in science, have we arrived at that point
which Bacon seems to have understood by the discovery of “forms.” “The
_form_ of any nature,” says he, “is such, that where it is, the given
nature must infallibly be. The form, therefore, is perpetually present
when that nature is present; ascertains it universally, and accompanies
it every where. Again, this form is such, that when removed, the given
nature infallibly vanishes. Lastly, a true form is such as can deduce
a given nature from some essential property, which resides in many
things.”

(365.) Magnetism is remarkable in another important point of view. It
offers a prominent, or “_glaring instance_” of that quality in nature
which is termed _polarity_ (267.), and that under circumstances which
peculiarly adapt it for the study of this quality. It does not appear
that the ancients had any knowledge of this property of the magnet,
though its attraction of iron was well known to them. The first mention
of it in modern times cannot be traced earlier than 1180, though it
was probably known to the Chinese before that time. The polarity of
the magnet consists in this, that if suspended freely, one part of it
will invariably direct itself towards a certain point in the horizon,
the other towards the opposite point; and that, if two magnets, so
suspended, be brought near each other, there will take place a mutual
action, in consequence of which, the positions of both will be
disturbed, in the same manner as would happen if the corresponding
parts of each repelled, and those oppositely directed attracted, each
other; and by properly varying the experiment, it is found that they
really do so. If a small magnet, freely suspended, be brought into
the neighbourhood of a larger one, it will take a position depending
on the position of the _poles_ of the larger one, with respect to its
point of suspension. And it has been ascertained that these and all
other phenomena exhibited by magnets in their mutual attractions and
repulsions are explicable on the supposition of two forces or virtues
lodged in the particles of the magnets, the one predominating at one
end, the other at the other; and such that each particle shall attract
those in which the _opposite_ virtue to its own prevails, and repel
those in which a _similar_ one resides with a force proportional to the
inverse square of their mutual distance.

(366.) The direction in which a magnetic bar, or needle of steel,
freely suspended, places itself, has been ascertained to be different
at different points of the earth’s surface. In some places it points
exactly north and south, in others it deviates from this direction
more or less, and at some actually stands at right angles to it. This
remarkable phenomenon, which is called the variation of the needle,
and which was discovered by Sebastian Cabot in the year 1500, is
accompanied with another called the dip, noticed by Robert Norman in
1576. It consists in a tendency of a needle, nicely balanced on its
centre, when unmagnetized, to _dip_ or point downwards when rendered
magnetic, towards a point below the horizon, and situated within the
earth. By tracing the variation and dip over the whole surface of the
globe, it has been found that these phenomena take place as they would
do if the earth itself were a great magnet, having its poles deeply
situated below the surface,--and, what is very remarkable, possessing
a slow motion within it, in consequence of which neither the variation
nor dip remain constantly the same at the same place. The laws of this
motion are at present unknown; but the discovery of electro-magnetism,
by rendering it almost certain that the earth’s magnetism is merely an
effect of the continual circulation of great quantities of electricity
round it, in a direction generally corresponding with that of its
rotation, have dissipated the greater part of the mystery which hung
over these phenomena; since a variety of causes, both geological and
others, may be imagined which may produce considerable deviations in
the intensity, and partial ones in the direction, of such electric
currents. The unequal distribution of land and sea in the two
hemispheres, by affecting the operation of the sun’s heat in producing
evaporation from the latter, which is probably one of the great sources
of terrestrial electricity, may easily be conceived to modify the
general tendency of such currents, and to produce irregularities in
them, which may render a satisfactory account of whatever still appears
anomalous in the phenomena of terrestrial magnetism. This branch
of science thus becomes connected, on a great scale, with that of
meteorology, one of the most complicated and difficult, but at the same
time interesting, subjects of physical research; one, however, which
has of late begun to be studied with a diligence which promises the
speedy disclosure of relations and laws of which at present we can form
but a very imperfect notion.

(367.) The communication of magnetism from the earth to a magnetic
body, or from one magnetic body to another, is performed by a process
to which the name of induction has been given, and the laws and
properties of such induced magnetism have been studied with much
perseverance and success,--practically, by Gilbert, Boyle, Knight,
Whiston, Cavallo, Canton, Duhamel, Rittenhouse, Scoresby, and others;
and theoretically, by Æpinus, Coulomb, and Poisson, and in our own
country by Messrs. Barlow and Christie, who have investigated with
great care the curious phenomena which take place when masses of iron
are presented successively, in different positions, by rotation on
an axis, to the influence of the earth’s magnetism. The magnetism of
crystallized bodies (partly from the extreme rarity of such as are
susceptible of any considerable magnetic virtue) has not hitherto been
at all examined, but would probably afford very curious results.

(368.) To electricity the views of the physical enquirer now turn
from almost every quarter, as to one of those universal powers which
Nature seems to employ in her most important and secret operations.
This wonderful agent, which we see in intense activity in lightning,
and in a feebler and more diffused form traversing the upper regions
of the atmosphere in the northern lights, is present, probably in
immense abundance, in every form of matter which surrounds us, but
becomes sensible only when disturbed by excitements of peculiar
kinds. The most effectual of these is friction, which we have already
observed to be a powerful source of heat. Everybody is familiar
with the crackling sparks which fly from a cat’s back when stroked.
These, by proper management, may be accumulated in bodies suitably
disposed to receive them, and, although then no longer visible, give
evidence of their existence by the exhibition of a vast variety of
extraordinary phenomena,--producing attractions and repulsions in
bodies at a distance,--admitting of being transferred by contact, or
by sudden and violent transilience of the interval of separation, from
one body to another, under the form of sparks and flashes;--traversing
with perfect facility the substance of the densest metals, and a
variety of other bodies called conductors, but being detained by
others, such as glass, and especially _air_, which are thence called
non-conductors,--producing painful shocks and convulsive motions, and
even death itself if in sufficient quantity, in animals through which
they pass, and finally imitating, on a small scale, all the effects of
lightning.

(369.) The study of these phenomena and their laws until a
comparatively recent period occupied the entire attention of
electricians, and constituted the whole of the science of electricity.
It appears, as the result of their enquiries, that all the phenomena in
question are explicable on the supposition that electricity consists
in a rare, subtle, and highly elastic fluid, which in its tendency
to expand and diffuse itself pervades with more or less facility
the substance of conductors, but is obstructed and detained from
expansion more or less completely by non-conductors. It is supposed,
moreover, that this electric fluid possesses a power of attraction
for the particles of all ponderable matter, together with that of a
repulsion for particles of its own kind. Whether it has weight, or is
rather to be regarded as a species of matter distinct from that of
which ponderable bodies consist, is a question of such delicacy, that
no direct experiments have yet enabled us to decide it; but at all
events its _inertia_ compared with its elastic force must be conceived
excessively small, so that it is to be regarded as a fluid in the
highest degree _active_, obeying every impulse, internal or external,
with the greatest promptitude; in short, a fluid whose energies can
only be compared with those of the ethereal medium by which, in the
undulatory doctrine, light is supposed to be conveyed. The properties
of hydrogen gas compared with those of the denser aëriform fluids will,
in some slight degree, aid our conception of the excessive mobility and
penetrating activity of a fluid so constituted. Electricity, however,
must be regarded as differing in some remarkable points from all those
fluids to which we have hitherto been accustomed to apply the epithet
elastic, such as air, gases, and vapours. In these, the repulsive force
of the particles on which their elasticity depends is considered as
extending only to very small distances, so as to affect only those in
the immediate vicinity of each other, while their attractive power, by
which they obey the general gravitation of all matter, extends to any
distance. In electricity, on the other hand, the very reverse must be
admitted. The force by which its particles repel each other extends to
great distances, while its force of adhesion to ponderable matter must
be regarded as limited in its extent to such minute intervals as escape
observation.

(370.) The conception of a single fluid of this kind, which when
accumulated in excess in bodies tends constantly to escape, and seek
a restoration of equilibrium by communicating itself to any others
where there may be a deficiency, is that which occurs most naturally
to the mind, and was accordingly maintained by Franklin, to whom the
science of electricity is under great obligations for those decisive
experiments which informed us respecting the true nature of lightning.
The same theory was afterwards advocated by Æpinus, who first showed
how the laws of equilibrium of such a fluid might be reduced to strict
mathematical investigation. But there are phenomena accompanying its
transfer from body to body and the state of equilibrium it affects
under various circumstances, which appear to require the admission of
_two distinct fluids_ antagonist to each other, each attracting the
other, and repelling itself; but each, alike, susceptible of adhesion
to material substances, and of transfer more or less rapid from
particle to particle of them. These fluids in the natural undisturbed
state are conceived to exist in a state of combination and mutual
saturation; but this combination may be broken, and either of them
separately accumulated in a body to any amount without the other,
provided its escape be properly obstructed by surrounding it with
non-conductors. When so accumulated, its repulsion for its own kind
and attraction of the opposite species in neighbouring bodies tends
to disturb the natural equilibrium of the two fluids present in them,
and to produce phenomena of a peculiar description, which are termed
_induced_ electricity. Curious and artificial as this theory may
appear, there has hitherto been produced no phenomenon of which it
will not afford at least a plausible, and in by far the majority of
cases a very satisfactory, explanation. It has one character which is
extremely valuable in any theory, that of admitting the application of
strict mathematical reasoning to the conclusions we would draw from
it. Without this, indeed, it is scarcely possible that any theory
should ever be fairly brought to the test by a comparison with facts.
Accordingly, the mathematical theory of electrical equilibrium,
and the laws of the distribution of the electric fluids over the
surfaces of bodies in which they are accumulated, have been made the
subject of elaborate geometrical investigation by the most expert
mathematicians, and have attained a degree of extent and elegance
which places this branch of science in a very high rank in the scale
of mathematico-physical enquiry. These researches are grounded on
the assumption of a law of attraction and repulsion similar to those
of gravity and magnetism, and which by the general accordance of the
results with facts, as well as by experiments instituted for the
express purpose of ascertaining the laws in question, are regarded as
sufficiently demonstrated.

(371.) The most obscure part of the subject is no doubt the original
mode of disturbance of electrical equilibrium, by which electricity is
excited in the first instance, either by friction or by any other of
those causes which have been ascertained to produce such an effect:
analogies, it is true, are not wanting[56]; but it must be allowed that
hitherto nothing decisive has been offered on the subject; and that
conjectural modes of action have in this instance too often usurped the
place of those to which a careful examination of facts alone can lead
us.

(372.) Philosophers had long been familiar with the effects of
electricity above referred to, and with those which it produces in
its sudden and violent transfer from one body to another, in rending
and shattering the parts of the substances through which it passes,
and where in great quantity, producing all the effect of intense
heat, igniting, fusing, and volatilizing metals, and setting fire to
inflammable bodies; even its occasional influence in destroying or
altering the polarity of the magnetic needle had been noticed: but as
heat was known to be produced by mechanical violence, and as magnetism
was also known to be greatly affected by the same cause, these effects
were referred rather to that cause than to any thing in the peculiar
nature of the electric matter, and regarded rather as an indirect
consequence of its mode of action than as connected with its intimate
nature. In short, electricity seemed destined to furnish another in
addition to many instances of subjects insulated from the rest of
philosophy, and capable of being studied only in its own internal
relations, when the great discoveries of Galvani and Volta placed a new
power at the command of the experimenter, by whose means those effects
which had before been crowded within an inappreciable instant could
be developed in detail and studied at leisure; and those forces which
had previously exhibited themselves only in a state of uncontrollable
intensity were tamed down, as it were, and made to distribute their
efficacy over an indefinite time, and to regulate their action at the
will of the operator. It was then soon ascertained that electricity
in the act of its passage along conductors, produces a variety of
wonderful effects, which had never been previously suspected; and these
of such a nature, as to afford points of contact with several other
branches of physical enquiry, and to throw new and unexpected lights on
some of the most obscure operations of nature.

(373.) The history of this grand discovery affords a fine illustration
of the advantage to be derived in physical enquiry from a close and
careful attention to any phenomenon, however apparently trifling,
which may at the moment of observation appear inexplicable on received
principles. The convulsive motions of a dead frog in the neighbourhood
of an electric discharge, which originally drew Galvani’s attention to
the subject, had been noticed by others nearly a century before his
time, but attracted no further remark than as indicating a peculiar
sensibility to electrical excitement depending on that remnant of
vitality which is not extinguished in the organic frame of an animal
by the deprivation of actual life. Galvani was not so satisfied. He
analysed the phenomenon; and in investigating all the circumstances
connected with it was led to the observation of a peculiar electrical
excitement which took place when a circuit was formed of three distinct
parts, a muscle, a nerve, and a metallic conductor, each placed in
contact with the other two, and which was manifested by a convulsive
motion produced in the muscle. To this phenomenon he gave the name of
animal electricity, an unfortunate epithet, since it tended to restrict
enquiry into its nature to the class of phenomena in which it first
became apparent. But this circumstance, which in a less enquiring age
of science might have exercised a fatal influence on the progress of
knowledge, proved happily no obstacle to the further developement of
its principles, the subject being immediately taken up with a kind
of prophetic ardour by Volta, who at once generalized the phenomena,
rejecting the physiological considerations introduced by Galvani, as
foreign to the enquiry, and regarding the contraction of the muscles
as merely a delicate means of detecting the production of electrical
excitements too feeble to be rendered sensible by any other means.
It was thus that he arrived at the knowledge of a general fact, that
of the disturbance of electrical equilibrium by the mere contact of
different bodies, and the circulation of a current of electricity in
one constant direction, through a circuit composed of three different
conductors. To increase the intensity of the very minute and delicate
effect thus observed became his next aim, nor did his enquiry terminate
till it had placed him in possession of that most wonderful of all
human inventions, the pile which bears his name, through the medium of
a series of well conducted and logically combined experiments, which
has rarely, if ever, been surpassed in the annals of physical research.

(374.) Though the original pile of Volta was feeble compared to those
gigantic combinations which were afterwards produced, it sufficed,
however, to exhibit electricity under a very different aspect from any
thing which had gone before, and to bring into view those peculiar
modifications in its action which Dr. Wollaston was the first to
render a satisfactory account of, by referring them to an increase
of _quantity_, accompanied with a diminution of _intensity_ in the
supply afforded. The discovery had not long been made public, and
the instrument in the hands of chemists and electricians, before it
was ascertained that the electric current, transmitted by it through
conducting liquids, produces in them chemical decompositions. This
capital discovery appears to have been made, in the first instance, by
Messrs. Nicholson and Carlisle, who observed the decomposition of water
so produced. It was speedily followed up by the still more important
one of Berzelius and Hisinger, who ascertained it as a general law,
that, in all the decompositions so effected, the acids and oxygen
become transferred to, and accumulated around, the positive,--and
hydrogen, metals, and alkalies round the negative, pole of a Voltaic
circuit; being transferred in an invisible, and, as it were, a latent
or torpid state, by the action of the electric current, through
considerable spaces, and even through large quantities of water or
other liquids, again to re-appear with all their properties at their
appropriate resting-places.

(375.) It was in this state of things that the subject was taken up
by Davy, who, seeing that the strongest chemical affinities were thus
readily subverted by the decomposing action of the pile, conceived
the happy idea of bringing to bear the intense power of the enormous
batteries of the Royal Institution on those substances which, though
strongly suspected to be compounds, had resisted all attempts to
decompose them--the alkalies and earths. They yielded to the force
applied, and a total revolution was thus effected in chemistry; not so
much by the introduction of the new elements thus brought to light, as
by the mode of conceiving the nature of chemical affinity, which from
that time has been regarded (as Davy broadly laid it down, in a theory
which was readily adopted by the most eminent chemists, and by none
more readily than by Berzelius himself,) as entirely due to electric
attractions and repulsions, those bodies combining most intimately
whose particles are habitually in a state of the most powerful
electrical antagonism, and dispossessing each other, according to the
amount of their difference in this respect.

(376.) The connection of magnetism and electricity had long been
suspected, and innumerable fruitless trials had been made to determine,
in the affirmative or negative, the question of such connection. The
phenomena of many crystallized minerals which become electric by heat,
and develope opposite electric poles at their two extremities, offered
an analogy so striking to the polarity of the magnet, that it seemed
hardly possible to doubt a closer connection of the two powers. The
developement of a similar polarity in the Voltaic pile pointed strongly
to the same conclusion; and experiments had even been made with a
view to ascertain whether a pile in a state of excitement might not
manifest a disposition to place itself in the magnetic meridian; but
the essential condition had been omitted, that of allowing the pile to
discharge itself freely, a condition which assuredly never would have
occurred of itself to any experimenter. Of all the philosophers who
had speculated on this subject, none had so pertinaciously adhered to
the idea of a necessary connection between the phenomena as Oërsted.
Baffled often, he returned to the attack; and his perseverance was at
length rewarded by the complete disclosure of the wonderful phenomena
of electro-magnetism. There is something in this which reminds us of
the obstinate adherence of Columbus to his notion of the necessary
existence of the New World; and the whole history of this beautiful
discovery may serve to teach us reliance on those general analogies
and parallels between great branches of science by which one strongly
reminds us of another, though no direct connection appears; as an
indication not to be neglected of a community of origin.

(377.) It is highly probable that we are still ignorant of many
interesting features in electrical science, which the study of the
Voltaic circuit will one day disclose. The violent mechanical effects
produced by it on mercury, placed under conducting liquids which have
been referred by Professor Erman to a modified form of capillary
attraction, but which a careful and extended view of the phenomena
have led others[57] to regard in a very different light, as pointing
out a primary action of a dynamical rather than a statical character,
deserve, in this point of view, a further investigation; and the
curious relations of electricity to heat, as exhibited in the phenomena
of what has been called thermo-electricity, promise an ample supply of
new information.

(378.) Among the remarkable effects of electricity disclosed by the
researches of Galvani and Volta, perhaps the most so consisted in its
influence on the nervous system of animals. The origin of muscular
motion is one of those profound mysteries of nature which we can
scarcely venture to hope will ever be fully explained. Physiologists,
however, had long entertained a general conception of the conveyance
of some subtle fluid or spirit from the brain to the muscles of
animals along the nerves; and the discovery of the rapid transmission
of electricity along conductors, with the violent effects produced by
shocks, transmitted through the body, on the nervous system, would
very naturally lead to the idea that this nervous fluid, if it had
any real existence, might be no other than the electrical. But until
the discoveries of Galvani and Volta, this could only be looked upon
as a vague conjecture. The character of a _vera causa_ was wanting to
give it any degree of rational plausibility, since no reason could
be imagined for the disturbance of the electrical equilibrium in the
animal frame, composed as it is entirely of conductors, or rather, it
seemed contrary to the then known laws of electrical communication
to suppose any such. Yet one strange and surprising phenomenon might
be adduced indicative of the possibility of such disturbance, viz.
the powerful shock given by the torpedo and other fishes of the same
kind, which presented so many analogies with those arising from
electricity, that they could hardly be referred to a different source,
though _besides_ the shock neither spark nor any other indication of
electrical tension could be detected in them.

(379.) The benumbing effect of the torpedo had been ascertained to
depend on certain singularly constructed organs composed of membranous
columns, filled from end to end with laminæ, separated from each other
by a fluid: but of its mode of action no satisfactory account could be
given; nor was there any thing in its construction, and still less in
the nature of its materials, to give the least ground for supposing
it an electrical apparatus. But the pile of Volta supplied at once
the analogies both of structure and of effect, so as to leave little
doubt of the electrical nature of the apparatus, or of the power, a
most wonderful one certainly, of the animal, to determine, by an effort
of its will, that concurrence of conditions on which its activity
depends. This remained, as it probably ever will remain, mysterious
and inexplicable; but the principle once established, that there
exists in the animal economy a power of determining the developement
of electric excitement, capable of being transmitted along the nerves,
and it being ascertained, by numerous and decisive experiments, that
the transmission of Voltaic electricity along the nerves of even
a dead animal is sufficient to produce the most violent muscular
action, it became an easy step to refer the origin of muscular motion
in the living frame to a similar cause; and to look to the brain, a
wonderfully constituted organ, for which no mode of action possessing
the least plausibility had ever been devised, as the source of the
required electrical power.[58]

(380.) It is not our intention, however, to enter into any further
consideration of physiological subjects. They form, it is true, a
most important and deeply interesting province of philosophical
enquiry; but the view that we have taken of physical science has
rather been directed to the study of inanimate nature, than to that of
the mysterious phenomena of organization and life, which constitute
the object of physiology. The history of the animal and vegetable
productions of the globe, as affording objects and materials for the
convenience and use of man, and as dependent on and indicative of the
general laws which determine the distribution of heat, moisture, and
other natural agents, over its surface, and the revolutions it has
undergone, are of course intimately connected with our subject, and
will, therefore, naturally afford room for some remarks, but not such
as will long detain the reader’s attention.

(381.) In _zoology_, the connection of peculiar modes of life and
food, with peculiarities of structure, has given rise to systems of
classification at once obvious and natural; and the great progress
which has been made in comparative anatomy has enabled us to trace
a graduated scale of organization almost through the whole chain of
animal being; a scale not without its intervals, but which every
successive discovery of animals heretofore unknown has tended to fill
up. The wonders disclosed by microscopic observation have opened to
us a new world, in which we discover, with astonishment, the extremes
of minuteness and complexity of structure united; while, on the other
hand, the examination of the fossil remains of a former state of
creation has demonstrated the existence of animals far surpassing in
magnitude those now living, and brought to light many forms of being
which have nothing analogous to them at present, and many others
which afford important connecting links between existing genera. And,
on the other hand, the researches of the comparative anatomist and
conchologist have thrown the greatest light on the studies of the
geologist, and enabled him to discern, through the obscure medium of a
few relics, scattered here and there through a stratum, circumstances
connected with the formation of the stratum itself which he could have
recognised by no other indication. This is one among many striking
instances of the unexpected lights which sciences, however apparently
remote, may throw upon each other.

(382.) To _botany_ many of the same remarks apply. Its artificial
systems of classification, however convenient, have not prevented
botanists from endeavouring to group together the objects of their
science in natural classes having a community of character more
intimate than those which determine their place in the Linnean or any
similar system; a community of character extending over the whole
habit and properties of the individuals compared. The important
chemical discoveries which have been lately made of peculiar proximate
principles which, in an especial manner, characterize certain
families of plants, hold out the prospect of a greatly increased
field of interesting knowledge in this direction, and not only
interesting, but in a high degree important, when it is considered
that the principles thus brought into view are, for the most part,
very powerful medicines, and are, in fact, the essential ingredients
on which the medical virtues of the plants depend. The law of the
distribution of the generic forms of plants over the globe, too, has,
within a comparatively recent period, become an object of study to the
naturalist; and its connection with the laws of climate constitutes one
of the most interesting and important branches of natural-historical
enquiry, and one on which great light remains to be thrown by future
researches. It is this which constitutes the chief connecting link
between botany and geology, and renders a knowledge of the vegetable
fossils, of any portion of the earth’s surface, indispensable to the
formation of a correct judgment of the circumstances under which it
existed in its ancient state. Fossil botany is accordingly cultivated
with great and increasing ardour; and the subterraneous “Flora” of a
geological formation is, in many instances, studied with a degree of
care and precision little inferior to that which its surface exhibits.



CHAP. VI.

  OF THE CAUSES OF THE ACTUAL RAPID ADVANCE OF THE PHYSICAL SCIENCES
    COMPARED WITH THEIR PROGRESS AT AN EARLIER PERIOD.


(383.) There is no more extraordinary contrast than that presented by
the slow progress of the physical sciences, from the earliest ages
of the world to the close of the sixteenth century, and the rapid
developement they have since experienced. In the former period of
their history, we find only small additions to the stock of knowledge,
made at long intervals of time; during which a total indifference
on the part of the mass of mankind to the study of nature operated
to effect an almost complete oblivion of former discoveries, or,
at best, permitted them to linger on record, rather as literary
curiosities, than as possessing, in themselves, any intrinsic interest
and importance. A few enquiring individuals, from age to age, might
perceive their value, and might feel that irrepressible thirst after
knowledge which, in minds of the highest order, supplies the absence
both of external stimulus and opportunity. But the total want of a
right direction given to enquiry, and of a clear perception of the
objects to be aimed at, and the advantages to be gained by systematic
and connected research, together with the general apathy of society
to speculations remote from the ordinary affairs of life, and
studiously kept involved in learned mystery, effectually prevented
these occasional impulses from overcoming the inertia of ignorance, and
impressing any regular and steady progress on science. Its objects,
indeed, were confined in a region too sublime for vulgar comprehension.
An earthquake, a comet, or a fiery meteor, would now and then call the
attention of the whole world, and produce from all quarters a plentiful
supply of crude and fanciful conjectures on their causes; but it was
never supposed that sciences could exist among common objects, have a
place among mechanical arts, or find worthy matter of speculation in
the mine or the laboratory. Yet it cannot be supposed, that all the
indications of nature continually passed unremarked, or that much good
observation and shrewd reasoning on it failed to perish unrecorded,
before the invention of printing enabled every one to make his ideas
known to all the world. The moment this took place, however, the sparks
of information from time to time struck out, instead of glimmering
for a moment, and dying away in oblivion, began to accumulate into a
genial glow, and the flame was at length kindled which was speedily to
acquire the strength and rapid spread of a conflagration. The universal
excitement in the minds of men throughout Europe, which the first
out-break of modern science produced, has been already spoken of. But
even the most sanguine anticipators could scarcely have looked forward
to that steady, unintermitted progress which it has since maintained,
nor to that rapid succession of great discoveries which has kept up
the interest of the first impulse still vigorous and undiminished. It
may truly, indeed, be said, that there is scarcely a single branch of
physical enquiry which is either stationary, or which has not been,
for many years past, in a constant state of advance, and in which the
progress is not, at this moment, going on with accelerated rapidity.

(384.) Among the causes of this happy and desirable state of things,
no doubt we are to look, in the first instance, to that great
increase in wealth and civilization which has at once afforded the
necessary leisure and diffused the taste for intellectual pursuits
among numbers of mankind, which have long been and still continue
steadily progressive in every principal European state, and which the
increase and fresh establishment of civilized communities in every
distant region are rapidly spreading over the whole globe. It is not,
however, merely the increased number of cultivators of science, but
their enlarged opportunities, that we have here to consider, which, in
all those numerous departments of natural research that require local
information, is in fact the most important consideration of all. To
this cause we must trace the great extension which has of late years
been conferred on every branch of natural history, and the immense
contributions which have been made, and are daily making, to the
departments of zoology and botany, in all their ramifications. It is
obvious, too, that all the information that can possibly be procured,
and reported, by the most enlightened and active travellers, must fall
infinitely short of what is to be obtained by individuals actually
resident upon the spot. Travellers, indeed, may make collections,
may snatch a few hasty observations, may note, for instance, the
distribution of geological formations in a few detached points, and now
and then witness remarkable local phenomena; but the resident alone can
make continued series of regular observations, such as the scientific
determination of climates, tides, magnetic variations, and innumerable
other objects of that kind, requires; can alone mark all the details
of geological structure, and refer each stratum, by a careful and long
continued observation of its fossil contents, to its true epoch; can
alone note the habits of the animals of his country, and the limits
of its vegetation, or obtain a satisfactory knowledge of its mineral
contents, with a thousand other particulars essential to that complete
acquaintance with our globe as a whole, which is beginning to be
understood by the extensive designation of physical geography. Besides
which, ought not to be omitted multiplied opportunities of observing
and recording those extraordinary phenomena of nature which offer an
intense interest, from the rarity of their occurrence as well as the
instruction they are calculated to afford. To what, then, may we not
look forward, when a spirit of scientific enquiry shall have spread
through those vast regions in which the process of civilization, its
sure precursor, is actually commenced and in active progress? And what
may we not expect from the exertions of powerful minds called into
action under circumstances totally different from any which have yet
existed in the world, and over an extent of territory far surpassing
that which has hitherto produced the whole harvest of human intellect?
In proportion as the number of those who are engaged on each department
of physical enquiry increases, and the geographical extent over which
they are spread is enlarged, a proportionately increased facility
of communication and interchange of knowledge becomes essential to
the prosecution of their researches with full advantage. Not only
is this desirable, to prevent a number of individuals from making
the same discoveries at the same moment, which (besides the waste of
valuable time) has always been a fertile source of jealousies and
misunderstandings, by which great evils have been entailed on science;
but because methods of observation are continually undergoing new
improvements, or acquiring new facilities, a knowledge of which, it is
for the general interest of science, should be diffused as widely and
as rapidly as possible. By this means, too, a sense of common interest,
of mutual assistance, and a feeling of sympathy in a common pursuit,
are generated, which proves a powerful stimulus to exertion; and, on
the other hand, means are thereby afforded of detecting and pointing
out mistakes before it is too late for their rectification.

(385.) Perhaps it may be truly remarked, that, next to the
establishment of institutions having either the promotion of science
in general, or, what is still more practically efficacious in its
present advanced state, that of particular departments of physical
enquiry, for their express objects, nothing has exercised so powerful
an influence on the progress of modern science as the publication
of monthly and quarterly scientific journals, of which there is now
scarcely a nation in Europe which does not produce several. The quick
and universal circulation of these, places observers of all countries
on the same level of perfect intimacy with each other’s objects and
methods, while the abstracts they from time to time (if well conducted)
contain of the most important researches of the day consigned to the
more ponderous tomes of academical collections, serve to direct the
course of general observation, as well as to hold out, in the most
conspicuous manner, models for emulative imitation. In looking forward
to what may hereafter be expected from this cause of improvement, we
are not to forget the powerful effect which must in future be produced
by the spread of elementary works and digests of what is actually known
in each particular branch of science. Nothing can be more discouraging
to one engaged in active research, than the impression that all he
is doing may, very likely, be labour taken in vain; that it may,
perhaps, have been already done, and much better done, than, with his
opportunities, or his resources, he can hope to perform it; and, on the
other hand, nothing can be more exciting than the contrary impression.
Thus, by giving a connected view of what has been done, and what
remains to be accomplished in every branch, those digests and bodies
of science, which from time to time appear, have, in fact, a very
important weight in determining its future progress, quite independent
of the quantity of information they communicate. With respect to
elementary treatises, it is needless to point out their utility, or
to dwell on the influence which their actual abundance, contrasted
with their past remarkable deficiency, is likely to exercise over the
future. It is only by condensing, simplifying, and arranging, in the
most lucid possible manner, the acquired knowledge of past generations,
that those to come can be enabled to avail themselves to the full of
the advanced point from which they will start.

(386.) One of the means by which an advanced state of physical science
contributes greatly to accelerate and secure its further progress,
is the exact knowledge acquired of physical data, or those normal
quantities which we have more than once spoken of in the preceding
pages (222.); a knowledge which enables us not only to appretiate
the accuracy of experiments, but even to correct their results. As
there is no surer criterion of the state of science in any age than
the degree of care bestowed, and discernment exhibited, in the choice
of such data, so as to afford the simplest possible grounds for the
application of theories, and the degree of accuracy attained in their
determination, so there is scarcely any thing by which science can be
more truly benefited than by researches directed expressly to this
object, and to the construction of tables exhibiting the true numerical
relations of the elements of theories, and the actual state of nature,
in all its different branches. It is only by such determinations that
we can ascertain what changes are slowly and imperceptibly taking place
in the existing order of things; and the more accurate they are, the
_sooner_ will this knowledge be acquired. What might we not now have
known of the motions of the (so-called) fixed stars, had the ancients
possessed the means of observation we now possess, and employed them
as we employ them now?

(387.) In any enumeration of causes which have contributed to
the recent rapid advancement of science, we must not forget the
very important one of improved and constantly improving means of
observation, both in instruments adapted for the exact measurement of
quantity, and in the general convenience and well-judged adaptation
to its purposes, of every description of scientific apparatus. In
the actual state of science there are few observations which can
be productive of any great advantage but such as afford accurate
measurement; and an increased refinement in this respect is constantly
called for. The degree of delicacy actually attained, we will not say
in the most elaborate works of the highest art, but in such ordinary
apparatus as every observer may now command, is such as could not have
been arrived at unless in a state of the mechanical arts, which in
its turn (such is the mutual re-action of cause and effect) requires
for its existence a very advanced state of science. What an important
influence may be exercised over the progress of a single branch of
science by the invention of a ready and convenient mode of executing a
definite measurement, and the construction and common introduction of
an instrument adapted for it cannot be better exemplified than by the
instance of the reflecting goniometer. This simple, cheap, and portable
little instrument, has changed the face of mineralogy, and given it all
the characters of one of the exact sciences.

(388.) Our means of perceiving and measuring minute quantities, in the
important relations of weight, space, and time, seem already to have
been carried to a point which it is hardly conceivable they should
surpass. Balances have been constructed which have rendered sensible
the millionth part of the whole quantity weighed; and to turn with the
thousandth part of a grain is the performance of balances pretending
to no very extraordinary degree of merit. The elegant invention of
the sphærometer, by substituting the sense of touch for that of sight
in the measurement of minute objects, permits the determination of
their dimensions with a degree of precision which is fully adequate
to the nicest purposes of scientific enquiry. By its aid an inch may
be readily subdivided into ten or even twenty thousand parts; and the
lever of contact, an instrument in use among the German opticians,
enables us to appretiate quantities of space even yet smaller. For
the subdivision of time, too, the perfection of modern mechanism has
furnished resources which leave very little to be desired. By the
aid of clocks and chronometers, as they are now constructed, a few
tenths of a second is all the error that need be apprehended in the
subdivision of a day; and for the further subdivision of smaller
portions of time, instruments have been imagined which admit of
almost unlimited precision, and permit us to appreciate intervals to
the nicety of the hundredth, or even the thousandth part of a single
second.[59] When the precision attainable by such means is contrasted
with what could be procured a few generations ago, by the rude and
clumsy workmanship of even the early part of the last century, it will
be no matter of astonishment that the sciences which depend on exact
measurements should have made a proportional progress. Nor will any
degree of nicety in physical determinations appear beyond our reach, if
we consider the inexhaustible resources which science itself furnishes,
in rendering the quantities actually to be determined by measure great
multiples of the elements required for the purposes of theory, so as to
diminish in the same proportion the influence of any errors which may
be committed on the final results.

(389.) Great, indeed, as have been of late the improvements in the
construction of instruments, both as to what regards convenience and
accuracy, it is to the discovery of improved _methods_ of observation
that the chief progress of those parts of science which depend on
exact determinations is owing. The balance of torsion, the ingenious
invention of Cavendish and Coulomb, may be cited as an example of what
we mean. By its aid we are enabled not merely to render sensible,
but to subject to precise measurement and subdivision, degrees of
force infinitely too feeble to affect the nicest balance of the usual
construction, even were it possible to bring them to act on it. The
galvanometer, too, affords another example of the same kind, in an
instrument whose range of utility lies among electric forces which we
have no other means of rendering sensible, much less of estimating
with exactness. In determinations of quantities less minute in
themselves, the methods devised by Messrs. Arago and Fresnel, for the
measurement of the refractive powers of transparent media by means of
the phenomenon of diffraction, may be cited as affording a degree of
precision limited only by the wishes of the observer, and the time and
patience he is willing to devote to his observation. And in respect of
the direction of observations to points from which real information
is to be obtained, and positive conclusions drawn, the hygrometer of
Daniell may be cited as an elegant example of the introduction into
general use of an instrument substituting an indication founded on
strict principles for one perfectly arbitrary.

(390.) In speculating on the future prospects of physical science,
we should not be justified in leaving out of consideration the
probability, or rather certainty, of the occasional occurrence of those
happy accidents which have had so powerful an influence on the past;
occasions, where a fortunate combination opportunely noticed may admit
us in an instant to the knowledge of principles of which no suspicion
might occur but for some such casual notice. Boyle has entitled one of
his essays thus remarkably,--“_Of Man’s great Ignorance of the Uses
of natural Things; or that there is no one Thing in Nature whereof
the Uses to human Life are yet thoroughly understood_.”[60] The whole
history of the arts since Boyle’s time has been one continued comment
on this text; and if we regard among the uses of the works of nature,
_that_, assuredly the noblest of all, which leads us to a knowledge
of the Author of nature through the contemplation of the wonderful
means by which he has wrought out his purposes in his works, the
sciences have not been behind hand in affording their testimony to its
truth. Nor are we to suppose that the field is in the slightest degree
narrowed, or the chances in favour of such fortunate discoveries at all
decreased, by those which have already taken place: on the contrary,
they have been incalculably extended. It is true that the ordinary
phenomena which pass before our eyes have been minutely examined, and
those more striking and obvious principles which occur to superficial
observation have been noticed and embodied in our systems of science;
but, not to mention that by far the greater part of natural phenomena
remain yet unexplained, every new discovery in science brings into
view whole classes of facts which would never otherwise have fallen
under our notice at all, and establishes relations which afford to
the philosophic mind a constantly extending field of speculation,
in ranging over which it is next to impossible that he should not
encounter new and unexpected principles. How infinitely greater, for
instance, are the mere chances of discovery in chemistry among the
innumerable combinations with which the modern chemist is familiar,
than at a period when two or three imaginary elements, and some ten
or twenty substances, whose properties were known with an approach to
distinctness, formed the narrow circle within which his ideas had to
revolve? How many are the instances where a new substance, or a new
property, introduced into familiar use, by being thus brought into
relation with all our actual elements of knowledge, has become the
means of developing properties and principles among the most common
objects, which could never have otherwise been discovered? Had not
platina (to take an instance) been an object of the most ordinary
occurrence in a laboratory, would a suspicion have ever occurred that
a lamp could be constructed to burn without flame; and should we have
ever arrived at a knowledge of those curious phenomena and products of
semi-combustion which this beautiful experiment discloses?

(391.) Finally, when we look back on what has been accomplished in
science, and compare it with what remains to be done, it is hardly
possible to avoid being strongly impressed with the idea that we have
been and are still executing the labour by which succeeding generations
are to profit.[61] In a few instances only have we arrived at those
general axiomatic laws which admit of direct deductive inference,
and place the solutions of physical phenomena before us as so many
problems, whose principles of solution we fully possess, and which
require nothing but acuteness of reasoning to pursue even into their
farthest recesses. In fewer still have we reached that command of
abstract reasoning itself which is necessary for the accomplishment of
so arduous a task. Science, therefore, in relation to our faculties,
still remains boundless and unexplored, and, after the lapse of a
century and a half from the æra of Newton’s discoveries, during which
every department of it has been cultivated with a zeal and energy which
have assuredly met their full return, we remain in the situation in
which he figured himself,--standing on the shore of a wide ocean, from
whose beach we may have culled some of those innumerable beautiful
productions it casts up with lavish prodigality, but whose acquisition
can be regarded as no diminution of the treasures that remain.

(392.) But this consideration, so far from repressing our efforts, or
rendering us hopeless of attaining any thing intrinsically great, ought
rather to excite us to fresh enterprise, by the prospect of assured
and ample recompense from that inexhaustible store which only awaits
our continued endeavours. “It is no detraction from human capacity to
suppose it incapable of infinite exertion, or of exhausting an infinite
subject.”[62] In whatever state of knowledge we may conceive man to
be placed, his progress towards a yet higher state need never fear a
check, but must continue till the last existence of society.

(393.) It is in this respect an advantageous view of science, which
refers all its advances to the discovery of general laws, and to
the inclusion of what is already known in generalizations of still
higher orders; inasmuch as this view of the subject represents it, as
it really is, essentially incomplete, and incapable of being fully
embodied in any system, or embraced by any single mind. Yet it must be
recollected that, so far as our experience has hitherto gone, every
advance towards generality has at the same time been a step towards
simplification. It is only when we are wandering and lost in the mazes
of particulars, or entangled in fruitless attempts to work our way
downwards in the thorny paths of applications, to which our reasoning
powers are incompetent, that nature appears complicated:--the moment we
contemplate it as it is, and attain a position from which we can take a
commanding view, though but of a small part of its plan, we never fail
to recognise that sublime simplicity on which the mind rests satisfied
that it has attained the truth.



INDEX.


  Acoustics cultivated by Pythagoras and Aristotle, page 248.

  Æpinus, his laws of equilibrium of electricity, 332.

  Aëriform fluids, liquids kept in a state of vapour, 321.

  Agricola, George, his knowledge of mineralogy and metallurgy, 112.

  Air, compressibility and elasticity of; limitation to the repulsive
        tendency of, 226.
    Weight of, unknown to the ancients, 228.
    First perceived by Galileo, 228.
    Proved by a crucial instance, 229.
    Equilibrium of, established, 231.
    Dilatation of, by heat, 319.

  Air-pump, discovery of, 230.

  Airy, his experiments in Dolcoath mine, 187.

  Alchemists, advantages derived from, 11.

  Algebra, 19.

  Ampere, his electro-dynamic theory, 202.
    Utility of, 203, 324.

  Analysis of force, 86.
    Of motion, 87.
    Of complex phenomena, 88.

  Anaxagoras, philosophy of, 107.

  Animal electricity, 337.

  Arago, M., his experiment with a magnetic needle and a plate of
        copper, 157.

  Archimedes, his practical application of science, 72.
    His knowledge of hydrostatics, 231.

  Arfwedson, his discovery of lithia, 158.

  Aristotle, his knowledge of natural history, 109.
    His works condemned, and subsequently studied with avidity, 111.
    His philosophy overturned by the discoveries of Copernicus, Kepler,
        and Galileo, 113.

  Arithmetic, 19.

  Art, empirical and scientific, differences between, 71.
    Remarks on the language, terms, or signs, used in treating of
        it, 70.

  Assurances, life, utility and abuses of, 58.

  Astronomy, cause of the slow progress of our knowledge of, 78.
    Theory and practical observations distinct in, 132.
    An extensive acquaintance with science and every branch of knowledge
        necessary to make a perfect observer in, 132.
    Five primary planets added to our system, 274.
    Positions, figures, and dimensions of all the planetary orbits now
        well known, 275.

  Atomic theory, 305.
    Advantage of, 306.

  Atomic weights of chemical elements, 306.

  Attraction, capillary, or capillarity, investigated by Laplace and
        Young, 234.


  Bacon, celebrated in England for his knowledge of science, 72.
    Benefits conferred on Natural Philosophy by him, 104.
    His Novum Organum, 105.
    His reform in philosophy proves the paramount importance of
        induction, 114.
    His prerogative of facts, 181.
    Illustrated by the fracture of a crystallized substance, 183.
    His collective instances, 184.
    Importance of, 185.
    His experiment on the weight of bodies, 186.
    Travelling instances of, frontier instances of, 188.
    His difference between liquids and aëriform fluids, 233.

  Bartolin, Erasmus, first discovers the phenomena exhibited by doubly
        refracting crystals, 254.

  Beccher, phlogistic doctrines of, 300.

  Bergmann, his advancement in crystallography, 239.

  Bernoulli, experiments of, in hydrodynamical science, 181.

  Biot, his hypothesis of a rotatory motion of the particles of light
        about their axes, 262.

  Black, Dr., his discovery of latent heat, 322.

  Bode, his curious law observed in the progression of the magnitudes of
        the several planetary orbits, 308.

  Bodies, natural constitution of, 221.
    Division of, into crystallized and uncrystallized, 242.

  Bones, dry, a magazine of nutriment, 65.

  Borda, his invention for subdivision, 128.

  Botany, general utility of, 345.

  Boyle, Robert, his enthusiasm in the pursuit of science, 115.
    His improvement on the air-pump, 230.

  Brain, hypothesis of its being an electric pile, 343.

  Bramah’s press, principle and utility of, 233.

  Brewster, Dr., his improvement on lenses for lighthouses, 56.
    His researches prove that the phenomena exhibited by polarized
        light, in its transmission through crystals, afford a certain
        indication of the most important points relating to the
        structure of crystals themselves, 263.


  Cabot, Sebastian, his discovery of the variation of the needle, 327.

  Cagnard, Baron de la Tour, utility of his experiments, 234.

  Causes and consequences directors of the will of man, 6.

  Causes, proximate, discovery of, called by Newton _veræ causæ_, 144.

  Celestial mechanics, 265.

  Chaldean records, 265.

  Chemistry furnishes causes of sudden action, also fulminating
        compositions, 62.
    Analogy of the complex phenomena of, with those of physics, 92.
    Benefits arising from the analysis of, 94.
    Axioms of, analogous to those of geometry, 95.
    Many of the new elements of, detected in the investigation of
        residual phenomena, 158.
    The most general law of, 209.
    Illustration of, 210.
    Between fifty and sixty elements in, 211.
    Objects of, 296.
    General heads of the principal improvements in, 302.
    Remarks on those general heads, 304.

  Chemistry, Stahlian, cause of the mistakes and confusions of, 123.

  Chladni, experiments of, in dynamical science, 181.

  Chlorine, disinfectant powers of, 56.

  Clarke, Dr., his experiments on the arseniate and phosphate
        of soda, 170.
    His success in producing a new phosphate of soda, 171.

  Climate, change of, in large tracts of the globe, alleged
        cause of, 145.

  Coals, power of a bushel of, properly consumed, 59.
    Quantity consumed in London, 60.

  Cohesion, an ultimate phenomenon, 90.

  Cold, qualities of, 318.

  Compass, mariner’s, 55.

  Condensation, a source of heat, 313.

  Conduction of heat, laws of, 205.

  Copernicus, effect of his discoveries on the Aristotelian
        philosophy, 113.
    Objections to his astronomical doctrines, 269.

  Crystallography, laws of, 123, 239.
    A determinate figure supposed to be common to all the particles of a
        crystal, 242.


  D’Alembert, his improvements in hydrodynamics, 236.

  Dalton, his announcement of the atomic theory, 305.
    His examination of gases and vapours, 319.

  Davy, Sir H., brings the voltaic pile to bear upon the earths and
        alkalies, 339.

  Deduction, utility of, 174.

  De l’Isle, Romé, his study of crystalline bodies, 239.

  Dew, causes of, investigated, 159.
    Effects of, on different substances, 160.
    Objects capable of contracting it, 161.
    A cloudless sky favourable to its production, 162.
    General proximate cause of, 163.

  Drummond, lieutenant, his improvement on lenses for lamps of
        lighthouses, 56.

  Dynamics, importance of, 96, 223.


  Earth, the orbit of,--diminution of its eccentricity round
        the sun, 147.

  Economy, political, 73.

  Egypt, great pyramid of, height, weight, and ground occupied by
        it, 60.
    Accuracy of the astronomical records of, 265.

  Elasticity, an ultimate phenomenon, 90.

  Electricity may be the cause of magnetism, 93.
    Universality of, 329.
    Effects of, 330.
    Activity of, 331.
    Equilibrium of, 332.
    Productive of chemical decomposition, 338.

  Empirical laws, 178.
    Evils resulting from, 179.

  Encke, professor, his prediction of the return of the comet so many
        times in succession, 156.

  Englefield, sir H., his analysis of a solar beam, 314.

  Equilibrium maintained by force, 222.

  Erman, professor, his opinion of the effects of the voltaic
        circuit, 340.

  Euler, his improvement on Newton’s theory of sound, 247.

  Experience, source of our knowledge of nature’s laws, 76.

  Experiment, a means of acquiring experience, 76.
    Utility of, 151.


  Facts, the observation of, 118.

  Faujas de St. Fond, imaginary craters of, 131.

  Fluids, laws of the motion of, 181.
    Compressibility of, 225.
    Consideration of the motions of, more complicated than that of
        equilibrium, 235.

  Force, analysis of, 86.
    The cause of motion, 149.
    Phenomena of, 221.
    Molecular forces, 245.

  Fourier, baron, his opinion that the celestial regions have a
        temperature, independent of the sun, not greatly inferior
        to that at which quicksilver congeals, 157.
    His analysis of the laws of conduction and radiation of heat, 317.

  Franklin, Dr., his experiments on electricity, 332.

  Fresnel, M., his mathematical explanation of the phenomena of double
        refraction, 32.
    His improvement on lenses for lamps of lighthouses, 56.
    His opinions on the nature of light, 207.
    His experiments on the interference of polarized light, 261.
    His theory of polarization, 262.

  Friction, a source of heat, 313.


  Galileo, celebrity of, for his knowledge of science, 72.
    His exposition of the Aristotelian philosophy, 110.
    His refutation of Aristotle’s dogmas respecting motion, his
        persecution in consequence of it, 113.
    His knowledge of the accelerating power of gravity, 168.
    His knowledge of the weight of the atmosphere, 228.

  Galvani, utility of his discoveries in electricity, 335.
    His application of it to animals, 336.

  Gay-Lussac, his examination of gases and vapours, 319.

  Generalization, inductive, 1, 90.

  Geology, 281.
    Its rank as a science, 287.

  Geometry, axioms of, an appeal to experience, not corporeal, but
        mental, 95.

  Gilbert, Dr., of Colchester, his knowledge of magnetism and
        electricity, 112.

  Gravitation, law of, a physical axiom of a very high and universal
        kind, 98.
    Influence of, decreases in the inverse ratio of the square of the
        distance, 123.

  Greece, philosophers of, their extraordinary success in abstract
        reasoning, and their careless consideration of external
        nature, 105.
    Their general character, 106.
    Philosophy of, 108.

  Grimaldi, a jesuit of Bologna, his discovery of diffraction, or
        inflection of light, 252.

  Guinea and feather experiment, 168.

  Gunpowder, invention of, 55.
    A mechanical agent, 62.


  Haarlem lake, draining of, 61.

  Harmony, sense of, 248.

  Head, captain, anecdote of, 84.

  Heat, 193.
    Radiation and conduction of, 205.
    One of the chief agents in chemistry, 310.
    Our ignorance of the nature of, 310.
    Abuse of the sense of the term, 311.
    The general heads under which it is studied, 312.
    Its most obvious sources, 312.
    Animal heat, to what process referable, 313.
    Radiation and conduction of, 314.
    Solar heat differs from terrestrial fires, or hot bodies, 315.
    Principal effects of, 317.
    The antagonist to mutual attraction, 322.
    Latent heat, 322.
    Specific heat, 323.

  Herschel, sir William, his analysis of a solar beam, 314.

  Hipparchus, his catalogue of stars, 276.

  Holland drained of water by windmills, 61.

  Hooke almost the rival of Newton, 116.

  Huel Towan, steam-engine at, 59.

  Huyghens, his doctrine of light, 207.
    Ascertains the laws of double refraction, 254.

  Hydrostatics, first step towards a knowledge of, made by
        Archimedes, 231.
    Law of the equal pressure of liquids, 232.
    General applicability of, 232.

  Hypothesis, not to be deterred from framing them, 196.
    Conditions on which they should be framed, 197.
    Illustrated by the laws of gravitation, 198.
    Use and abuse of, 204.


  Induction, different ways of carrying it on, 102.
    Steps by which it is arrived at on a legitimate and extensive
        scale, 118.
    First stage of, 144.
    Verification of, 164.
    Instanced in astronomy, 166.
    Must be followed into all its consequences, and applied to all those
        cases which seem even remotely to bear upon the subject of
        enquiry, 173.
    Nature of the inductions by which quantitative laws are arrived
        at, 176.
    Necessity of induction embracing a series of cases which absolutely
        include the whole scale of variation of which the quantities
        in question admit, 177.

  Induced electricity, 333.

  Inertia, 223.

  Iodine, discovery of, 50.
    Efficacy of, in curing goître, 51.

  Isomorphism, law of, 170.


  Kepler, effect of his discoveries on the Aristotelian philosophy, 113.
    Nature of his laws of the planetary system, 178.
    Proofs of the Newtonian system, 179.

  Knowledge, physical facts illustrative of the utility of, 45.
    Diffusion of, how to take advantage of in the investigation of
        nature, 138.


  Lagrange, his improvements on Newton’s theory of sound, 247.
    His astronomical researches, 275.

  Lamp, safety, 55.

  Laplace, his explanation of the residual velocity of sound and
        confirmation of the general law of the developement of heat
        by compression, 172.
    His astronomical research, 275.
    His experiments on the dilatation of bodies by heat, 319.
    His study of specific heat, 323.
    Latent heat, 323.

  Laws, inductive, 171.
    General, 198.
    How applicable, 199.
    Illustrated by the planetary system, 201.
    Empirical laws, 178.

  Lavoisier, his improvements in chemical science, 302.
    Experiments on dilatation of bodies by heat, 319.
    His investigation on specific heat, 323.

  Light, refraction of, 30.
    Double refraction of, 31.
    Polarization of, 254.

  Light and vision, ignorance of the ancients respecting, 249.

  Lighthouse, 56.

  Lightning, how to judge philosophically of it, 120.
    Returning stroke of, 121.

  Liquids, cohesion, attraction and repulsion of the particles of, 227.
    Differ from aëriform fluids by their cohesion, 233.
    The Florentine experiment on; experiments by Canton, Perkins,
        Oërsted, and others on, 235.
    Obscurity of the laws of dilatation of, 320.

  Linnæus, his knowledge of crystalline substances, 239.

  Logic, 19.

  Lyell’s Principles of Geology, extract from, 146.


  Magnetism may be caused by electricity, 93.
    Offers a “glaring instance” of polarity, 326.
    Experiments illustrative of, 327.

  Malus, a French officer of engineers, discovers the polarization of
        light, 132, 258.

  Man, regarded as a creature of instinct, 1.
    Of reason and speculation, 3.
    His will determined by causes and consequences, 6.
    Advantages to, from the study of science, 7.
    His necessity to study the laws of nature illustrated, 66.
    Happiness and the opposite state of man in the aggregate, 67.
    Advantages conferred on, by the augmentation of physical
        resources, 68.
    Advantages from intellectual resources, 69.

  Mariotte, his law of equilibrium of an elastic fluid recently verified
        by the Royal Academy of Paris, 231.
    His difference between solar and other heat, 315.

  Matter, indestructibility of; Divided by grinding, 40.
    By fire, 41.
    Dilated by heat, 193.
    Inertia of, 202.
    Polarity of, one of the ultimate phenomena to which the analysis of
        nature leads us, 245.
    Inherent activity of, 297.
    Causes of the polarity of, 299.
    Imponderable forms of, 310.

  Measure, the standard, difficulty of preserving it unaltered, 128.
    How to be assisted in measurement, 129.
    Our conclusions from, should be conditional, 130.

  Menai Bridge, weight and height of, 60.

  Mechanics, practical, 63.

  Mètre, the French, 126.

  Microscopes, power of, 191.

  Millstones, method of making in France, 48.

  Mind, its transition from the little to the great, and _vice versâ_,
        illustrated, 172.

  Mineralogy unknown to the ancients, 79.
    Prejudiced by the rage for nomenclature, 139.
    Benefited by the progress of chemical analysis, 293.

  Minerals, simple, apparent paucity of, 294.
    Difficulty in classing them, 295.

  Mitscherlich, his law of isomorphism, 170.
    His experiments on the expansion of substances by heat, 243.

  Motion, 87.
    Simplicity and precision of the laws of, 179.


  Nature, laws of, 37.
    Immutability of, 42.
    Harmony of, and advantage of studying them, 43.
    Prove the impossibility of attaining the declared object of the
        alchemist. How they serve mankind generally, 44.
    Illustrated by mining, 45.
    Economy derived from a knowledge of, 65.
    How to be regarded, 100, 101.

  Nature, objects of, an enumeration and nomenclature of, useful in the
        study of, 135.
    Mechanism of, on too large or too small a scale to be immediately
        cognisable by our senses, 191.

  Newton, his proof of Galileo’s laws of gravitation by an experiment
        with a hollow glass pendulum, 160.
    His foundation to hydrodynamical science, 181.
    Fixes the division between statics and dynamics, 223.
    His investigation of the law of equilibrium of elastic fluids, 231.
    His law of hydrostatics, 232.
    His foundation of hydrodynamics 236.
    His analysis of sound, 247.
    Hypothesis of light, 250.
    Examination of a soap-bubble, 252.
    His hypothesis of fits of easy transmission and reflection, 253.
    His combination of mathematical skill with physical research, 271.
    His Principia, 272.
    His successors; his geometry, 273.

  Nomenclature, importance of, to science, 136.
    More a consequence than a cause of extended knowledge, 138.
    Prejudicial to mineralogy, 139.

  Norman, Robert, his discovery of the dip of the needle, 327.

  Numerical precision, necessity of, in science, 122.


  Objects, and their mutual actions, subjects of contemplation, 118.

  Observation, a means of acquiring experience, 76.
    Passive and active, 77.
    Recorded observation, 120.
    Necessity of, to acquire precise physical data, 215.
    Illustrated by the barometer, 216.

  Oërsted, his discoveries in electricity and magnetism, 132.
    Of electro-magnetism, 340.

  Opacity, 189.

  Otto von Guericke of Magdeburgh, his invention of the air-pump, 230.


  Paracelsus, power of his chemical remedies; his use of mercury,
        opium, and tartar, 112.

  Pascal, his crucial instances proving the weight of air, 229.

  Pendulum, 126.

  Phenomena, analysis of, illustrated by musical sounds, the sensation
        of taste, 85.
    The ultimate and inward process of nature in the production of, 86.
    Analysis of complex phenomena, 88.
    Ultimate phenomena, 90.
    How the analysis of, is useful, 97.
    A transient phenomenon, how to judge of, 122.
    Method of explaining one when it presents itself, 148.
    How to discover the cause of one, 150.
    Two, or many, theories, maintained as the origin of, in
        physics, 195.
    Cosmical phenomena, 265.

  Philosophy, natural, unfounded objections to the study of, 7.
    Advantages derivable from the study of, 10.
    Pleasure and happiness, the consequences of the study of, 15.

  Phlogistic doctrines of Beccher and Stahl, 300.

  Physical data, necessity of, 209.
    Great importance of, 211.
    Illustrated by the erection of observatories, 213.
    Necessity of an exact knowledge of, 214.
    More precise than the observations by which we acquire them, 215.

  Physics, axioms of; analysis of, 102.

  Planets, circumjovial, 186.

  Platina, discovery of, 308.

  Pliny, his knowledge of quartz and diamond, 239.

  Pneumatics, 228.

  Political economy, 73.

  Prejudices of opinion and sense, 80.
    Conditions on which such are injurious, 81.
    Illustrated by the division of the rays of light, by the moon at the
        horizon, and by ventriloquism, 82.
    By the transition of the hand from heat to cold, 83.

  Prevost, M., his theory of heat, 316.
    His theory of reciprocal interchanges, a proof of the radiation
        of cold, 318.

  Printing, the art of, 193.
    Performed by steam, 194.

  Probabilities, doctrine of, 217.
    Illustrated by shooting at a wafer, 218.

  Prout, Dr., his opinion of the atomic weights, 307.

  Pyrometry, 319.

  Pythagoras, philosophy of, 107.


  Quinine, sulphate of, comparative comfort and health resulting from
        the use of, 56.


  Radiation of heat, laws of, 205.

  Repulsion in fluids and solids, 227.

  Rules, general, for guiding and facilitating our search among a great
        mass of assembled facts, 151.

  Rumford, count, experiments of, on gunpowder, 62.


  Savart, M., his experiments on solids, 243.
    His researches on sound, 249.

  Science, abstract, a preparation for the study of physics, 19.
    Not indispensable to the study of physical laws, 25.
    Instances illustrative of, 27.

  Science, physical, nature and objects, immediate and collateral, as
        regarded in itself and in its application to the practical
        purposes of life, and its influence on society, 35.
    State of, previous to the age of Galileo and Bacon, 104.
    Causes of the rapid advance of, compared with the progress at an
        earlier period, 347.

  Science, natural, cause and effect, the ultimate relations of, 76.

  Sciences and Arts, remarks on the language, terms, or signs used in
        treating of them, 70.
    Receive an impulse by the Baconian philosophy, 114.

  Sensation, cause of, 91.

  Senses, inadequate to give us direct information for the exact
        comparison of quantity, 124.
    Substitutes for the inefficiency of, 125.

  Seringapatam, method of breaking blocks from the quarries of, 47.

  Shells found in rocks at a great height above the sea, supposed
        cause of, 145.

  Smeaton, his experiments on bodies dilated by heat, 319.

  Solids, transparent, exhibit periodical colours when exposed to
        polarized light, 99.
    Influence of, on the Mind, 101.

  Solids in general, nature of, 236.
    Constitution of, complicated, 237.
    Toughness of, distinct from hardness; tenacity of, 238.
    Become liquefied by the addition of heat, 321.

  Sounds, musical, illustrative of the analysis of phenomena, 85.
    Means of having a knowledge of, 89.
    Propagation of, through the air, 246.
    Newton’s analysis of, 247.

  Standard measurement, necessity of, 125.
    Laws of nature used as such, illustrated by the rotation of the
        earth, 126.

  Substances all subject to dilatation by the addition of heat, 243.

  Sun, the character of the heat of, 315.


  Thales, philosophy of, 107.

  Theories, how to estimate the value of, 204.
    Best arrived at by the consideration of general laws, 208.
    Explanatory of the phenomena of nature; on what their application
        ought to be grounded, 209.

  Thomson, Dr., his opinion of the atomic weights, 307.

  Thermometer, air, 319.

  Thermo-electricity, 341.

  Time, division of, 126, 127.

  Torricelli, pupil of Galileo, his experiments proving the weight of
        atmosphere, 229.

  Torpedo, shock of, 341, 342.


  Ulugh Begh, his catalogue of stars, 277.


  Vaccination, success of, as a preventive to small-pox, 52.

  Vision and light, ignorance of the ancients respecting, 249.

  Volta, his discoveries in electricity, 335.
    Electric pile of, 337.

  Voltaic circuit, 338.


  Water, effects of the power of, 61.

  Whewell, his experiments, 187.

  Wells, Dr., his theory of dew, 163.

  Wind, effects of the power of, 61.

  Wire steel, magnetized masks of, used by needle-makers, 57.

  Wollaston, Dr., his verification of the laws of double refraction in
        Iceland spar, 258.
    His invention of the goniometer, 292.

  World, the materials of the, 290.


  Young, Dr., his experiments on the interference of the rays of
        light, 260.


  Zoology, fossil, 344.


THE END.


  LONDON
  PRINTED BY SPOTTISWOODE AND CO.
  NEW-STREET SQUARE.



FOOTNOTES


[1] Hooke’s Posthumous Works. Lond. 1705.--p. 472 and p. 458.

[2] Wealth of Nations, book i. chap. i. p. 15.

[3] On this subject, we cannot forbear citing a passage from one of
the most profound but at the same time popular writers of our time, on
a subject unconnected it is true with our own, but bearing strongly
on the point before us. “But, if science be manifestly incomplete,
and yet of the highest importance, it would surely be most unwise
to restrain enquiry, conducted on just principles, even where the
immediate practical utility of it was not visible. In mathematics,
chemistry, and every branch of natural philosophy, how many are the
enquiries necessary for their improvement and completion, which, taken
separately, do not appear to lead to any specifically advantageous
purpose! how many useful inventions, and how much valuable and
improving knowledge, would have been lost, if a rational curiosity,
and a mere love of information, had not generally been allowed to be a
sufficient motive for the search after truth!”--Malthus’s Principles of
Political Economy, p. 16.

[4] Λογος, _ratio_, reason.

[5] Λογος, _verbum_, a word.

[6] It were much to be wished that navigators would be more cautious in
laying themselves open to a similar censure. On looking hastily over
a map of the world we see three Melville Islands, two King George’s
Sounds, and Cape Blancos innumerable.

[7] Young. Lectures on Nat. Phil. ii. 627. See also Phil. Trans. 1801-2.

[8] Captain Basil Hall, R. N.

[9] We must caution our readers who would assure themselves of it by
trial, that it is an experiment of some delicacy, and not to be made
without several precautions to ensure success. For these we must refer
to our original authority (Fresnel. Mémoire sur la Diffraction de la
Lumiere, p. 124.); and the principles on which they depend will of
course be detailed in that volume of the Cabinet Cyclopædia which is
devoted to the subject of LIGHT.

[10] Little reels used in cotton mills to twist the thread.

[11] Such a block would weigh between four and five hundred thousand
pounds. See Dr. Kennedy’s “Account of the Erection of a Granite Obelisk
of a Single Stone about Seventy Feet high, at Seringapatam.”--_Ed.
Phil. Trans._ vol. ix, p. 312.

[12] Dr. Coindet of Geneva.

[13] Journal of a Voyage to the South Seas, &c. &c. under the Command
of Commodore George Anson, in 1740-1744, by Pascoe Thomas, Lond. 1745,
So tremendous were the ravages of scurvy, that, in the year 1726,
admiral Hosier sailed with seven ships of the line to the West Indies,
and buried his ships’ companies twice, and died himself in consequence
of a broken heart. Dr. Johnson, in the year 1778, could describe a
sea-life in such terms as these:--“As to the sailor, when you look down
from the quarter deck to the space below, you see the utmost extremity
of human misery, such crowding, such filth, such stench!”--“A ship is
a prison with the chance of being drowned--it is worse--worse in every
respect--worse room, worse air, worse food--worse company!” Smollet,
who had personal experience of the horrors of a seafaring life in those
days, gives a lively picture of them in his Roderick Random.

[14] Lemon juice was known to be a remedy for scurvy far superior
to all others 200 years ago, as appears by the writings of Woodall.
His work is entitled “The Surgeon’s Mate, or Military and Domestic
Medicine. By John Woodall, Master in Surgery London, 1636,” p. 165. In
1600, Commodore Lancaster sailed from England with three other ships
for the Cape of Good Hope, on the 2d of April, and arrived in Saldanha
Bay on the 1st of August, the commodore’s own ship being in perfect
health, from the administration of three table-spoonsfull of lemon
juice every morning to each of his men, whereas the other ships were so
sickly as to be unmanageable for want of hands, and the commander was
obliged to send men on board to take in their sails and hoist out their
boats. (Purchas’s Pilgrim, vol. i. p. 149.) A Fellow of the college,
and an eminent practitioner, in 1753 published a tract on sea scurvy,
in which he adverts to the superior virtue of this medicine; and Mr. A.
Baird, surgeon of the Hector sloop of war, states, that from what he
had seen of its effects on board of that ship, he “thinks he shall not
be accused of presumption in pronouncing it, if properly administered,
a _most infallible remedy_, both in the cure and prevention of
scurvy.” (Vide Trotter’s Medicina Nautica.) The precautions adopted
by captain Cook in his celebrated voyages, had fully demonstrated by
their complete success the practicability of keeping scurvy under in
the longest voyages, but a uniform system of prevention throughout the
service was still deficient.

It is to the representations of Dr. Blair and sir Gilbert Blane, in
their capacity of commissioners of the board for sick and wounded
seamen, in 1795, we believe, that its _systematic introduction into
nautical diet_, by a general order of the admiralty, is owing. The
effect of this wise measure (taken, of course, in conjunction with the
general causes of improved health,) may be estimated from the following
facts:--In 1780, the number of cases of scurvy received into Haslar
hospital was 1457; in 1806 _one_ only, and in 1807 _one_. There are now
many surgeons in the navy who have never seen the disease.

[15] Throughout France the conductor is recognised as a most
valuable and useful instrument; and in those parts of Germany where
thunder-storms are still more common and tremendous they are become
nearly universal. In Munich there is hardly a modern house unprovided
with them, and of a much better construction than ours--several copper
wires twisted into a rope.

[16] We have been informed by an eminent physician in Rome, (Dr.
Morichini) that a vast quantity of the sulphate of quinine is
manufactured there and consumed in the Campagna, with an evident effect
in mitigating the severity of the malarious complaints which affect its
inhabitants.

[17] Dr. Johnson, Memoirs of the Medical Society, vol. v.

[18] The engine at Huel Towan. See Mr. Henwood’s Statement “of the
performance of steam-engines in Cornwall for April, May, and June,
1829.” Brewster’s Journal, Oct. 1829.--The _highest_ monthly average of
this engine extends to 79 millions of pounds.

[19] However, this is not quite a fair statement; a man’s daily labour
is about 4 lbs. of coals. The extreme toil of this ascent arises from
other obvious causes than the mere height.

[20] Its surface is about 40,000 acres, and medium depth about 20 feet.
It was proposed to drain it by running embankments across it, and thus
cutting it up into more manageable portions to be drained by windmills.

[21] No one doubts the _practicability_ of the undertaking. Eight or
nine thousand chaldrons of coals duly burnt would evacuate the whole
contents. But many doubt whether it would be profitable, and some,
considering that a few hundreds of fishermen who gain their livelihood
on its waters would be dispossessed, deny that it would be _desirable_.

[22] “Experiments to determine the Force of fired Gunpowder.” Phil.
Trans. vol. lxxxvii. p. 254. et seq.

[23] See a very ingenious application of this kind in Mr. Babbage’s
article on Diving in the Encyc. Metrop.--Others will readily suggest
themselves. For instance, the ballast in reserve of a balloon might
consist of materials capable of evolving great quantities of hydrogen
gas in proportion to their weight, should such be found.

[24] The sulphuric. Bracconot, Annales de Chimie, vol. xii. p. 184.

[25] D’Arcet, Annales de l’Industrie, Fevrier, 1829.

[26] See Dr. Prout’s account of the experiments of professor Autenrieth
of Tubingen. Phil. Trans. 1827, p. 381. This discovery, which renders
famine next to _impossible_, deserves a higher degree of celebrity than
it has obtained.

[27] Greenwich.

[28] Maskelyne’s.

[29] Thomson’s First Principles of Chemistry, vol. ii. p. 68.

[30] Galileo exposes unsparingly the Aristotelian style of reasoning.
The reader may take the following from him as a specimen of its
quality. The object is to prove the immutability and incorruptibility
of the heavens; and thus it is done:--

    I. Mutation is either generation or corruption.

   II. Generation and corruption only happen between contraries.

  III. The motions of contraries are contrary.

   IV. The celestial motions are circular.

    V. Circular motions have no contraries.

      α. Because there can be but three simple motions.
             1. To a centre.
             2. Round a centre.
             3. From a centre.

      β. Of three things, one only can be contrary to one.

      γ. But a motion to a centre is manifestly the contrary to a
          motion from a centre.

      δ. Therefore a motion _round_ a centre (_i. e._ a circular
          motion) remains without a contrary.

   VI. _Therefore_ celestial motions have no contraries--_therefore_
         among celestial _things_ there are no contraries--_therefore_
         the heavens are eternal, immutable, incorruptible, and so forth.

It is evident that all this string of nonsense depends on the excessive
vagueness of the notions of generation, corruption, contrariety, &c. on
which the changes are rung.--_See_ GALILEO, _Systema Cosmicum_, Dial.
i. p. 30.

[31] Macquer justly observes, that the alchemists would have rendered
essential service to chemistry had they only related their unsuccessful
experiments as clearly as they have obscurely related those which they
pretend to have been successful.--_Macquer’s Dictionary of Chemistry_,
i. x.

[32] Paracelsus performed most of these cures by mercury and opium,
the use of which latter drug he had learned in Turkey. Of mercurial
preparations the physicians of his time were ignorant, and of opium
they were afraid, as being “cold in the fourth degree.” Tartar was
likewise a great favourite of Paracelsus, who imposed on it that name,
“because it contains the water, the salt, the oil, and the acid, which
burn the patient as hell does:” in short, a kind of counterbalance to
his opium.

[33] See the Life of Galileo Galilei, by Mr. Drinkwater, with
Illustrations of the Advancement of Experimental Philosophy.

[34] The temporary star in Cassiopeia observed by Cornelius Gemma, in
1572, was so bright as to be seen at noon-day. That in Serpentarius,
first seen by Kepler in 1604, exceeded in brilliancy all the other
stars and planets.

[35] Edinburgh Phil. Journ. 1819, vol. i. p. 8.

[36] The abstract principle of repetition in matters of measurement
(viz. juxta-position of units without error) is applicable to a great
variety of cases in which quantities are required to be determined to
minute nicety. In chemistry, in determining the standard atomic weights
of bodies, it seems easily and completely applicable, by a process
which will suggest itself at once to every chemist, and seems the only
thing wanting to place the exactness of chemical determinations on a
par with astronomical measurements.

[37] Accurate and _perfectly_ authentic copies of the yard and pound,
executed in platina, and hermetically sealed in glass, should be
deposited deep in the interior of the massive stone-work of some great
public building, whence they could only be rescued with a degree
of difficulty sufficient to preclude their being disturbed unless
on some very high and urgent occasion. The fact should be publicly
recorded, and its memory preserved by an inscription. Indeed, how much
valuable and useful information of the actual existing state of arts
and knowledge at any period might be transmitted to posterity in a
distinct, tangible, and imperishable form, if, instead of the absurd
and useless deposition of a few coins and medals under the foundations
of buildings, specimens of ingenious implements or condensed statements
of scientific truths, or processes in arts and manufactures, were
substituted. Will books infallibly preserve to a remote posterity all
that we may desire should be hereafter known of ourselves and our
discoveries, or all that posterity would wish to know? and may not a
useless ceremony be thus transformed into an act of enrolment in a
perpetual archive of what we most prize, and acknowledge to be most
valuable?

[38] In the system alluded to, the name of quartz is assigned to
iolite and obsidian; that of mica to plumbago, chlorite, and uranite;
sulphur, to orpiment and realgar, &c. See Mohs’s System of Mineralogy,
translated by Haidinger.

[39] The following passage, from Lindley’s Synopsis of the British
Flora, characterises justly the respective merits, in a philosophical
point of view, of natural and artificial systems of classification
in general, though limited in its expression to his own immediate
science:--“After all that has been effected, or is likely to be
accomplished hereafter, there will always be more difficulty in
acquiring a knowledge of the natural system of botany than of the
Linnæan. The latter skims only the surface of things, and leaves the
student in the fancied possession of a sort of information which it is
easy enough to obtain, but which is of little value when acquired: the
former requires a minute investigation of every part and every property
known to exist in plants; but when understood has conveyed to the mind
a store of real information, of the utmost use to man in every station
of life. Whatever the difficulties may be of becoming acquainted with
plants according to this method, they are inseparable from botany,
which cannot be usefully studied without encountering them.” Schiller
has some beautiful lines on this, entitled “Menschliches Wissen” (or
Human Knowledge); Gedichte, vol. i. p. 72. Leipzig, 1800.

[40] Lyell’s Principles of Geology, vol. i. Fourrier, Mém. de l’Acad.
des Sciences, tom. vii. p. 592. “L’établissement et le progrès des
sociétés humaines, l’action des forces naturelles, peuvent changer
notablement, et dans de vastes contrées, l’état de la surface du sol,
la distribution des eaux, et les grands mouvemens de l’air. De tels
effets sont propres à faire varier, dans le cours de plusieurs siècles,
le dégré de la chaleur moyenne; car les expressions analytiques
comprennent des coefficiens qui se rapportent à l’état superficiel,
et qui influent beaucoup sur la valeur de la température.” In this
enumeration, by M. Fourrier, of causes which may vary the general
relation of the surface of extensive continents to heat, it is but
justice to Mr. Lyell to observe, that the gradual shifting of the
_places_ of the continents themselves on the surface of the globe,
by the abrading action of the sea on the one hand, and the elevating
agency of subterranean forces on the other, does not expressly occur
and cannot be fairly included in the general sense of the passage,
which confines itself to the consideration of such changes as may take
place on the existing surface of the land.

[41] The reader will find this subject further developed in a paper
lately communicated to the Geological Society.

[42] Phil. Trans. 1824.

[43] Wells on Dew.

[44] Principia, book iii. prop. 6.

[45] A very curious instance of the pursuit of a law completely
empirical into an extreme case is to be found in Newton’s rule for
the dilatation of his coloured rings seen between glasses at great
obliquities. Optics, book ii. part i. obs. 7.

[46] See Phil. Trans. 1819.

[47] “When we are told that Saturn moves in his orbit more than 22,000
miles an hour, we fancy the motion to be swift; but when we find that
he is more than three hours moving his own diameter, we must then think
it, as it really is, slow.” Thirty Letters on various Subjects, by
William Jackson, 1795.

[48] Thomson’s First Principles of Chemistry.

[49] There seems no doubt, however, that an achromatic telescope had
been constructed by a private amateur, a Mr. Hall, some time before
either Euler or Dollond ever thought of it.

[50] We allude to the recently invented achromatic combinations of
Messrs. Barlow and Rogers, and the dense glasses of which Mr. Faraday
has recently explained the manufacture in a memoir full of the most
beautiful examples of delicate and successful chemical manipulation,
and which promise to give rise to a new era in optical practice, by
which the next generation at least may benefit. See Phil. Trans. 1830.

[51] Alphonso of Castile, 1252.

[52] Jackson, Letters on Various Subjects, &c.

[53] Thomson’s First Principles of Chemistry, Introduction.

[54] The progress of astronomical discovery has since shown that this
law cannot be relied on (1851).

[55] Novum Organum, part ii. table 2. (24), (30), &c. on the form or
nature of heat.

[56] We will mention one which we do not remember to have seen
noticed elsewhere in the case of a disturbance of the equilibrium of
heat produced by means purely mechanical, and by a process depending
entirely on a certain order and sequence of events, and the operation
of known causes. Suppose a quantity of air enclosed in a metallic
reservoir, of some good conductor of heat, and suddenly compressed by
a piston. After giving time for the heat developed by the condensation
to be communicated from the air to the metal which will be thereby
more or less raised in temperature _above_ the surrounding atmosphere,
let the piston be suddenly retracted and the air restored to its
original volume in an instant. The whole apparatus is now precisely in
its initial situation, as to the disposition of its material parts,
and the whole quantity of heat it contains remains unchanged. But it
is evident that the distribution of this heat within it is now very
different from what it was before; for the air in its sudden expansion
cannot re-absorb in an instant of time all the heat it had parted with
to the metal: it will, therefore, have a temperature _below_ that of
the general atmosphere, while the metal yet retains one above it. Thus,
a subversion of the equilibrium of temperature has been _bonâ fide_
effected. Heat has been driven from the air into the metal, while every
thing else remains unchanged.

We have here a means by which, it is evident, heat may be obtained, to
any extent, from the air, without fuel. For if, in place of withdrawing
the piston and letting the _same_ air expand, within the reservoir, it
be allowed to escape so suddenly as not to re-absorb the heat given
off, and fresh air be then admitted and the process repeated, any
quantity of air may thus be _drained_ of its heat.

[57] See Phil. Trans. 1824.

[58] If the brain be an electric pile, constantly in action, it may be
conceived to discharge itself at regular intervals, when the tension
of the electricity developed reaches a certain point, along the nerves
which communicate with the heart, and thus to excite the pulsations of
that organ. This idea is forcibly suggested by a view of that elegant
apparatus, the dry pile of Deluc; in which the successive accumulations
of electricity are carried off by a suspended ball, which is kept by
the discharges in a state of regular pulsation for any length of time.
We have witnessed the action of such a pile maintained in this way for
whole years in the study of the above-named eminent philosopher. The
same idea of the cause of the pulsation of the heart appears to have
occurred to Dr. Arnott; and is mentioned in his useful and excellent
work on physics, to which however, we are not indebted for the
suggestion, it having occurred to us independently many years ago.

[59] See a description of a contrivance of this kind by Dr. Young,
Lectures, vol. i. p. 191.

[60] Boyle’s Works, folio, vol. iii. Essay x. p. 185.

[61] Jackson, The Four Ages, p. 52. London: Cadell and Davies, 1798.
8vo.

[62] Jackson, The Four Ages, p. 90.



Transcriber’s Notes


Cover created by Transcriber and placed in the Public Domain.

Punctuation, hyphenation, and spelling were made consistent when a
predominant preference was found in this book; otherwise they were not
changed.

Simple typographical errors were corrected; occasional unbalanced
quotation marks retained.

Ambiguous hyphens at the ends of lines were retained.

Spelling of non-English words was not reviewed.

Text uses both “appreciate” and “appretiate”; both retained.

Index not checked for proper alphabetization or correct page references.





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