Title: Six Lectures on Light - Delivered In The United States In 1872-1873
Author: Tyndall, John, 1820-1893
Language: English
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SIX LECTURES ON LIGHT

DELIVERED IN THE UNITED STATES
IN
1872-1873

BY

JOHN TYNDALL, D.C.L., LL,D., F.R.S.

LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE
ROYAL INSTITUTION OF GREAT BRITAIN



[Illustration: Sir Thomas Laurence PRA Pinx

Henry Adlarc. Sc.

Signature: Thomas Young]


London: Longmans & Co.

_SIXTH IMPRESSION_

LONGMANS, GREEN, AND CO.

39 PATERNOSTER ROW, LONDON

NEW YORK AND BOMBAY

1906



PREFACE TO THE FOURTH EDITION.


In these Lectures I have sought to render clear a difficult but
profoundly interesting subject. My aim has been not only to describe
and illustrate in a familiar manner the principal laws and phenomena
of light, but to point out the origin, and show the application, of
the theoretic conceptions which underlie and unite the whole, and
without which no real interpretation is possible.

The Lectures, as stated on the title-page, were delivered in the
United States in 1872-3. I still retain a vivid and grateful
remembrance of the cordiality with which they were received.

My scope and object are briefly indicated in the 'Summary and
Conclusion,' which, as recommended in a former edition, might be, not
unfitly, read as an introduction to the volume.

J.T.

ALP LUSGEN: _October_ 1885.



CONTENTS.


LECTURE I.

  Introductory
  Uses of Experiment
  Early Scientific Notions
  Sciences of Observation
  Knowledge of the Ancients regarding Light
  Defects of the Eye
  Our Instruments
  Rectilineal Propagation of Light
  Law of Incidence and Reflection
  Sterility of the Middle Ages
  Refraction
  Discovery of Snell
  Partial and Total Reflection
  Velocity of Light
  Roemer, Bradley, Foucault, and Fizeau
  Principle of Least Action
  Descartes and the Rainbow
  Newton's Experiments on the Composition of Solar Light
  His Mistake regarding Achromatism
  Synthesis of White Light
  Yellow and Blue Lights produce White by their Mixture
  Colours of Natural Bodies
  Absorption
  Mixture of Pigments contrasted with Mixture of Lights


LECTURE II.

  Origin of Physical Theories
  Scope of the Imagination
  Newton and the Emission Theory
  Verification of Physical Theories
  The Luminiferous Ether
  Wave-theory of Light
  Thomas Young
  Fresnel and Arago
  Conception of Wave-motion
  Interference of Waves
  Constitution of Sound-waves
  Analogies of Sound and Light
  Illustrations of Wave-motion
  Interference of Sound Waves
  Optical Illustrations
  Pitch and Colour
  Lengths of the Waves of Light and Rates of Vibration of the
    Ether-particles
  Interference of Light
  Phenomena which first suggested the Undulatory Theory
  Boyle and Hooke
  The Colours of thin Plates
  The Soap-bubble
  Newton's Rings
  Theory of 'Fits'
  Its Explanation of the Rings
  Overthrow of the Theory
  Diffraction of Light
  Colours produced by Diffraction
  Colours of Mother-of-Pearl.


LECTURE III.

  Relation of Theories to Experience
  Origin of the Notion of the Attraction of Gravitation
  Notion of Polarity, how generated
  Atomic Polarity
  Structural Arrangements due to Polarity
  Architecture of Crystals considered as an Introduction to their
    Action upon Light
  Notion of Atomic Polarity applied to Crystalline Structure
  Experimental Illustrations
  Crystallization of Water
  Expansion by Heat and by Cold
  Deportment of Water considered and explained
  Bearings of Crystallization on Optical Phenomena
  Refraction
  Double Refraction
  Polarization
  Action of Tourmaline
  Character of the Beams emergent from Iceland Spar
  Polarization by ordinary Refraction and Reflection
  Depolarization.


LECTURE IV.

  Chromatic Phenomena produced by Crystals in Polarized Light
  The Nicol Prism
  Polarizer and Analyzer
  Action of Thick and Thin Plates of Selenite
  Colours dependent on Thickness
  Resolution of Polarized Beam into two others by the Selenite
  One of them more retarded than the other
  Recompounding of the two Systems of Waves by the Analyzer
  Interference thus rendered possible
  Consequent Production of Colours
  Action of Bodies mechanically strained or pressed
  Action of Sonorous Vibrations
  Action of Glass strained or pressed by Heat
  Circular Polarization
  Chromatic Phenomena produced by Quartz
  The Magnetization of Light
  Rings surrounding the Axes of Crystals
  Biaxal and Uniaxal Crystals
  Grasp of the Undulatory Theory
  The Colour and Polarization of Sky-light
  Generation of Artificial Skies.


LECTURE V.

  Range of Vision not commensurate with Range of Radiation
  The Ultra-violet Rays
  Fluorescence
  The rendering of invisible Rays visible
  Vision not the only Sense appealed to by the Solar and Electric Beam
  Heat of Beam
  Combustion by Total Beam at the Foci of Mirrors and Lenses
  Combustion through Ice-lens
  Ignition of Diamond
  Search for the Rays here effective
  Sir William Herschel's Discovery of dark Solar Rays
  Invisible Rays the Basis of the Visible
  Detachment by a Ray-filter of the Invisible Rays from the Visible
  Combustion at Dark Foci
  Conversion of Heat-rays into Light-rays
  Calorescence
  Part played in Nature by Dark Rays
  Identity of Light and Radiant Heat
  Invisible Images
  Reflection, Refraction, Plane Polarization, Depolarization,
    Circular Polarization, Double Refraction, and Magnetization of
    Radiant Heat


LECTURE VI.

  Principles of Spectrum Analysis
  Prismatic Analysis of the Light of Incandescent Vapours
  Discontinuous Spectra
  Spectrum Bands proved by Bunsen and Kirchhoff to be characteristic
    of the Vapour
  Discovery of Rubidium, Cæsium, and Thallium
  Relation of Emission to Absorption
  The Lines of Fraunhofer
  Their Explanation by Kirchhoff
  Solar Chemistry involved in this Explanation
  Foucault's Experiment
  Principles of Absorption
  Analogy of Sound and Light
  Experimental Demonstration of this Analogy
  Recent Applications of the Spectroscope
  Summary and Conclusion


APPENDIX.

On the Spectra of Polarized Light

Measurement of the Waves of Light

INDEX



ON LIGHT



LECTURE I.

  INTRODUCTORY
  USES OF EXPERIMENT
  EARLY SCIENTIFIC NOTIONS
  SCIENCES OF OBSERVATION
  KNOWLEDGE OF THE ANCIENTS REGARDING LIGHT
  DEFECTS OF THE EYE
  OUR INSTRUMENTS
  RECTILINEAL PROPAGATION OF LIGHT
  LAW OF INCIDENCE AND REFLECTION
  STERILITY OF THE MIDDLE AGES
  REFRACTION
  DISCOVERY OF SNELL
  PARTIAL AND TOTAL REFLECTION
  VELOCITY OF LIGHT
  ROEMER, BRADLEY, FOUCAULT, AND FIZEAU
  PRINCIPLE OF LEAST ACTION
  DESCARTES AND THE RAINBOW
  NEWTON'S EXPERIMENTS ON THE COMPOSITION OF SOLAR LIGHT
  HIS MISTAKE AS REGARDS ACHROMATISM
  SYNTHESIS OF WHITE LIGHT
  YELLOW AND BLUE LIGHTS PRODUCE WHITE BY THEIR MIXTURE
  COLOURS OF NATURAL BODIES
  ABSORPTION
  MIXTURE OF PIGMENTS CONTRASTED WITH MIXTURE OF LIGHTS.


§ 1. _Introduction_.

Some twelve years ago I published, in England, a little book entitled
the 'Glaciers of the Alps,' and, a couple of years subsequently, a
second book, entitled 'Heat a Mode of Motion.' These volumes were
followed by others, written with equal plainness, and with a similar
aim, that aim being to develop and deepen sympathy between science and
the world outside of science. I agreed with thoughtful men[1] who
deemed it good for neither world to be isolated from the other, or
unsympathetic towards the other, and, to lessen this isolation, at
least in one department of science, I swerved, for a time, from those
original researches which have been the real pursuit and pleasure of
my life.

The works here referred to were, for the most part, republished by the
Messrs. Appleton of New York,[2] under the auspices of a man who is
untiring in his efforts to diffuse sound scientific knowledge among
the people of the United States; whose energy, ability, and
single-mindedness, in the prosecution of an arduous task, have won for
him the sympathy and support of many of us in 'the old country.' I
allude to Professor Youmans. Quite as rapidly as in England, the aim
of these works was understood and appreciated in the United States,
and they brought me from this side of the Atlantic innumerable
evidences of good-will. Year after year invitations reached me[3] to
visit America, and last year (1871) I was honoured with a request so
cordial, signed by five-and-twenty names, so distinguished in science,
in literature, and in administrative position, that I at once resolved
to respond to it by braving not only the disquieting oscillations of
the Atlantic, but the far more disquieting ordeal of appearing in
person before the people of the United States.

This invitation, conveyed to me by my accomplished friend Professor
Lesley, of Philadelphia, and preceded by a letter of the same purport
from your scientific Nestor, the celebrated Joseph Henry, of
Washington, desired that I should lecture in some of the principal
cities of the Union. This I agreed to do, though much in the dark as
to a suitable subject. In answer to my inquiries, however, I was given
to understand that a course of lectures, showing the uses of
experiment in the cultivation of Natural Knowledge, would materially
promote scientific education in this country. And though such lectures
involved the selection of weighty and delicate instruments, and their
transfer from place to place, I determined to meet the wishes of my
friends, as far as the time and means at my disposal would allow.


§ 2. _Subject of the Course. Source of Light employed._

Experiments have two great uses--a use in discovery, and a use in
tuition. They were long ago defined as the investigator's language
addressed to Nature, to which she sends intelligible replies. These
replies, however, usually reach the questioner in whispers too feeble
for the public ear. But after the investigator comes the teacher,
whose function it is so to exalt and modify the experiments of his
predecessor, as to render them fit for public presentation. This
secondary function I shall endeavour, in the present instance, to
fulfil.

Taking a single department of natural philosophy as my subject, I
propose, by means of it, to illustrate the growth of scientific
knowledge under the guidance of experiment. I wish, in the first
place, to make you acquainted with certain elementary phenomena; then
to point out to you how the theoretical principles by which phenomena
are explained take root in the human mind, and finally to apply these
principles to the whole body of knowledge covered by the lectures. The
science of optics lends itself particularly well to this mode of
treatment, and on it, therefore, I propose to draw for the materials
of the present course. It will be best to begin with the few simple
facts regarding light which were known to the ancients, and to pass
from them, in historic gradation, to the more abstruse discoveries of
modern times.

All our notions of Nature, however exalted or however grotesque, have
their foundation in experience. The notion of personal volition in
Nature had this basis. In the fury and the serenity of natural
phenomena the savage saw the transcript of his own varying moods, and
he accordingly ascribed these phenomena to beings of like passions
with himself, but vastly transcending him in power. Thus the notion of
_causality_--the assumption that natural things did not come of
themselves, but had unseen antecedents--lay at the root of even the
savage's interpretation of Nature. Out of this bias of the human mind
to seek for the causes of phenomena all science has sprung.

We will not now go back to man's first intellectual gropings; much
less shall we enter upon the thorny discussion as to how the groping
man arose. We will take him at that stage of his development, when he
became possessed of the apparatus of thought and the power of using
it. For a time--and that historically a long one--he was limited to
mere observation, accepting what Nature offered, and confining
intellectual action to it alone. The apparent motions of sun and stars
first drew towards them the questionings of the intellect, and
accordingly astronomy was the first science developed. Slowly, and
with difficulty, the notion of natural forces took root in the human
mind. Slowly, and with difficulty, the science of mechanics had to
grow out of this notion; and slowly at last came the full application
of mechanical principles to the motions of the heavenly bodies. We
trace the progress of astronomy through Hipparchus and Ptolemy; and,
after a long halt, through Copernicus, Galileo, Tycho Brahe, and
Kepler; while from the high table-land of thought occupied by these
men, Newton shoots upwards like a peak, overlooking all others from
his dominant elevation.

But other objects than the motions of the stars attracted the
attention of the ancient world. Light was a familiar phenomenon, and
from the earliest times we find men's minds busy with the attempt to
render some account of it. But without _experiment_, which belongs to
a later stage of scientific development, little progress could be here
made. The ancients, accordingly, were far less successful in dealing
with light than in dealing with solar and stellar motions. Still they
did make some progress. They satisfied themselves that light moved in
straight lines; they knew also that light was reflected from polished
surfaces, and that the angle of incidence was equal to the angle of
reflection. These two results of ancient scientific curiosity
constitute the starting-point of our present course of lectures.

But in the first place it will be useful to say a few words regarding
the source of light to be employed in our experiments. The rusting of
iron is, to all intents and purposes, the slow burning of iron. It
develops heat, and, if the heat be preserved, a high temperature may
be thus attained. The destruction of the first Atlantic cable was
probably due to heat developed in this way. Other metals are still
more combustible than iron. You may ignite strips of zinc in a candle
flame, and cause them to burn almost like strips of paper. But we must
now expand our definition of combustion, and include under this term,
not only combustion in air, but also combustion in liquids. Water, for
example, contains a store of oxygen, which may unite with, and
consume, a metal immersed in it; it is from this kind of combustion
that we are to derive the heat and light employed in our present
course.

The generation of this light and of this heat merits a moment's
attention. Before you is an instrument--a small voltaic battery--in
which zinc is immersed in a suitable liquid. An attractive force is at
this moment exerted between the metal and the oxygen of the liquid;
actual combination, however, being in the first instance avoided.
Uniting the two ends of the battery by a thick wire, the attraction is
satisfied, the oxygen unites with the metal, zinc is consumed, and
heat, as usual, is the result of the combustion. A power which, for
want of a better name, we call an electric current, passes at the same
time through the wire.

Cutting the thick wire in two, let the severed ends be united by a
thin one. It glows with a white heat. Whence comes that heat? The
question is well worthy of an answer. Suppose in the first instance,
when the thick wire is employed, that we permit the action to continue
until 100 grains of zinc are consumed, the amount of heat generated in
the battery would be capable of accurate numerical expression. Let
the action then continue, with the thin wire glowing, until 100 grains
of zinc are consumed. Will the amount of heat generated in the battery
be the same as before? No; it will be less by the precise amount
generated in the thin wire outside the battery. In fact, by adding the
internal heat to the external, we obtain for the combustion of 100
grains of zinc a total which never varies. We have here a beautiful
example of that law of constancy as regards natural energies, the
establishment of which is the greatest achievement of modern science.
By this arrangement, then, we are able to burn our zinc at one place,
and to exhibit the effects of its combustion at another. In New York,
for example, we may have our grate and fuel; but the heat and light of
our fire may be made to appear at San Francisco.

[Illustration: Fig. 1.]

Removing the thin wire and attaching to the severed ends of the thick
one two rods of coke we obtain, on bringing the rods together (as in
fig. 1), a small star of light. Now, the light to be employed in our
lectures is a simple exaggeration of this star. Instead of being
produced by ten cells, it is produced by fifty. Placed in a suitable
camera, provided with a suitable lens, this powerful source will give
us all the light necessary for our experiments.

And here, in passing, I am reminded of the common delusion that the
works of Nature, the human eye included, are theoretically perfect.
The eye has grown for ages _towards_ perfection; but ages of
perfecting may be still before it. Looking at the dazzling light from
our large battery, I see a luminous globe, but entirely fail to see
the shape of the coke-points whence the light issues. The cause may be
thus made clear: On the screen before you is projected an image of the
carbon points, the _whole_ of the glass lens in front of the camera
being employed to form the image. It is not sharp, but surrounded by a
halo which nearly obliterates the carbons. This arises from an
imperfection of the glass lens, called its _spherical aberration_,
which is due to the fact that the circumferential and central rays
have not the same focus. The human eye labours under a similar defect,
and from this, and other causes, it arises that when the naked light
from fifty cells is looked at the blur of light upon the retina is
sufficient to destroy the definition of the retinal image of the
carbons. A long list of indictments might indeed be brought against
the eye--its opacity, its want of symmetry, its lack of achromatism,
its partial blindness. All these taken together caused Helmholt to say
that, if any optician sent him an instrument so defective, he would be
justified in sending it back with the severest censure. But the eye is
not to be judged from the standpoint of theory. It is not perfect,
but is on its way to perfection. As a practical instrument, and taking
the adjustments by which its defects are neutralized into account, it
must ever remain a marvel to the reflecting mind.


§ 3. _Rectilineal Propagation of Light. Elementary Experiments. Law of
Reflection._

The ancients were aware of the rectilineal propagation of light. They
knew that an opaque body, placed between the eye and a point of light,
intercepted the light of the point. Possibly the terms 'ray' and
'beam' may have been suggested by those straight spokes of light
which, in certain states of the atmosphere, dart from the sun at his
rising and his setting. The rectilineal propagation of light may be
illustrated by permitting the solar light to enter, through a small
aperture in a window-shutter, a dark room in which a little smoke has
been diffused. In pure _air_ you cannot see the beam, but in smoky air
you can, because the light, which passes unseen through the air, is
scattered and revealed by the smoke particles, among which the beam
pursues a straight course.

The following instructive experiment depends on the rectilineal
propagation of light. Make a small hole in a closed window-shutter,
before which stands a house or a tree, and place within the darkened
room a white screen at some distance from the orifice. Every straight
ray proceeding from the house, or tree, stamps its colour upon the
screen, and the sum of all the rays will, therefore, be an image of
the object. But, as the rays cross each other at the orifice, the
image is inverted. At present we may illustrate and expand the
subject thus: In front of our camera is a large opening (L, fig. 2),
from which the lens has been removed, and which is closed at present
by a sheet of tin-foil. Pricking by means of a common sewing-needle a
small aperture in the tin-foil, an inverted image of the carbon-points
starts forth upon the screen. A dozen apertures will give a dozen
images, a hundred a hundred, a thousand a thousand. But, as the
apertures come closer to each other, that is to say, as the tin-foil
between the apertures vanishes, the images overlap more and more.
Removing the tin-foil altogether, the screen becomes uniformly
illuminated. Hence the light upon the screen may be regarded as the
overlapping of innumerable images of the carbon-points. In like manner
the light upon every white wall, on a cloudless day, may be regarded
as produced by the superposition of innumerable images of the sun.

[Illustration: Fig. 2.]

The law that the angle of incidence is equal to the angle of
reflection has a bearing upon theory, to be subsequently mentioned,
which renders its simple illustration here desirable. A straight lath
(pointing to the figure 5 on the arc in fig. 3) is fixed as an index
perpendicular to a small looking-glass (M), capable of rotation. We
begin by receiving a beam of light upon the glass which is reflected
back along the line of its incidence. The index being then turned, the
mirror turns with it, and at each side of the index the incident and
the reflected beams (L _o_, _o_ R) track themselves through the dust
of the room. The mere inspection of the two angles enclosed between
the index and the two beams suffices to show their equality; while if
the graduated arc be consulted, the arc from 5 to _m_ is found
accurately equal to the arc from 5 to _n_. The complete expression of
the law of reflection is, not only that the angles of incidence and
reflection are equal, but that the incident and reflected rays always
lie in a plane perpendicular to the reflecting surface.

[Illustration: Fig. 3.]

This simple apparatus enables us to illustrate another law of great
practical importance, namely, that when a mirror rotates, the angular
velocity of a beam reflected from it is twice that of the reflecting
mirror. A simple experiment will make this plain. The arc (_m n_, fig.
3) before you is divided into ten equal parts, and when the incident
beam and the index cross the zero of the graduation, both the incident
and reflected beams are horizontal. Moving the index of the mirror to
1, the reflected beam cuts the arc at 2; moving the index to 2, the
arc is cut at 4; moving the index to 3, the arc is cut at 6; moving
the index at 4, the arc is cut at 8; finally, moving the index to 5,
the arc is cut at 10 (as in the figure). In every case the reflected
beam moves through twice the angle passed over by the mirror.

One of the principal problems of science is to help the senses of man,
by carrying them into regions which could never be attained without
that help. Thus we arm the eye with the telescope when we want to
sound the depths of space, and with the microscope when we want to
explore motion and structure in their infinitesimal dimensions. Now,
this law of angular reflection, coupled with the fact that a beam of
light possesses no weight, gives us the means of magnifying small
motions to an extraordinary degree. Thus, by attaching mirrors to his
suspended magnets, and by watching the images of divided scales
reflected from the mirrors, the celebrated Gauss was able to detect
the slightest thrill of variation on the part of the earth's magnetic
force. By a similar arrangement the feeble attractions and repulsions
of the diamagnetic force have been made manifest. The minute
elongation of a bar of metal, by the mere warmth of the hand, may be
so magnified by this method, as to cause the index-beam to move
through 20 or 30 feet. The lengthening of a bar of iron when it is
magnetized may be also thus demonstrated. Helmholtz long ago employed
this method of rendering evident to his students the classical
experiments of Du Bois Raymond on animal electricity; while in Sir
William Thomson's reflecting galvanometer the principle receives one
of its latest and most important applications.


§ 4. _The Refraction of Light. Total Reflection._

For more than a thousand years no step was taken in optics beyond this
law of reflection. The men of the Middle Ages, in fact, endeavoured,
on the one hand, to develop the laws of the universe _à priori_ out of
their own consciousness, while many of them were so occupied with the
concerns of a future world that they looked with a lofty scorn on all
things pertaining to this one. Speaking of the natural philosophers of
his time, Eusebius says, 'It is not through ignorance of the things
admired by them, but through contempt of their useless labour, that we
think little of these matters, turning our souls to the exercise of
better things.' So also Lactantius--'To search for the causes of
things; to inquire whether the sun be as large as he seems; whether
the moon is convex or concave; whether the stars are fixed in the sky,
or float freely in the air; of what size and of what material are the
heavens; whether they be at rest or in motion; what is the magnitude
of the earth; on what foundations is it suspended or balanced;--to
dispute and conjecture upon such matters is just as if we chose to
discuss what we think of a city in a remote country, of which we never
heard but the name.'

As regards the refraction of light, the course of real inquiry was
resumed in 1100 by an Arabian philosopher named Alhazen. Then it was
taken up in succession by Roger Bacon, Vitellio, and Kepler. One of
the most important occupations of science is the determination, by
precise measurements, of the quantitative relations of phenomena; the
value of such measurements depending greatly upon the skill and
conscientiousness of the man who makes them. Vitellio appears to have
been both skilful and conscientious, while Kepler's habit was to
rummage through the observations of his predecessors, to look at them
in all lights, and thus distil from them the principles which united
them. He had done this with the astronomical measurements of Tycho
Brahe, and had extracted from them the celebrated 'laws of Kepler.' He
did it also with Vitellio's measurements of refraction. But in this
case he was not successful. The principle, though a simple one,
escaped him, and it was first discovered by Willebrord Snell, about
the year 1621.

Less with the view of dwelling upon the phenomenon itself than of
introducing it in a form which will render subsequently intelligible
to you the play of theoretic thought in Newton's mind, the fact of
refraction may be here demonstrated. I will not do this by drawing the
course of the beam with chalk on a black board, but by causing it to
mark its own white track before you. A shallow circular vessel (RIG,
fig. 4), half filled with water, rendered slightly turbid by the
admixture of a little milk, or the precipitation of a little mastic,
is placed with its glass front vertical. By means of a small plane
reflector (M), and through a slit (I) in the hoop surrounding the
vessel, a beam of light is admitted in any required direction. It
impinges upon the water (at O), enters it, and tracks itself through
the liquid in a sharp bright band (O G). Meanwhile the beam passes
unseen through the air above the water, for the air is not competent
to scatter the light. A puff of smoke into this space at once reveals
the track of the incident-beam. If the incidence be vertical, the beam
is unrefracted. If oblique, its refraction at the common surface of
air and water (at O) is rendered clearly visible. It is also seen that
_reflection_ (along O R) accompanies refraction, the beam dividing
itself at the point of incidence into a refracted and a reflected
portion.[4]

[Illustration: Fig. 4.]

The law by which Snell connected together all the measurements
executed up to his time, is this: Let A B C D (fig. 5) represent the
outline of our circular vessel, A C being the water-line. When the
beam is incident along B E, which is perpendicular to A C, there is no
refraction. When it is incident along _m_ E, there is refraction: it
is bent at E and strikes the circle at _n_. When it is incident along
_m'_ E there is also refraction at E, the beam striking the point
_n'_. From the ends of the two incident beams, let the perpendiculars
_m_ _o_, _m'_ _o'_ be drawn upon B D, and from the ends of the
refracted beams let the perpendiculars _p_ _n_, _p'_ _n'_ be also
drawn. Measure the lengths of _o m_ and of _p_ _n_, and divide the one
by the other. You obtain a certain quotient. In like manner divide
_m'_ _o'_ by the corresponding perpendicular _p'_ _n'_; you obtain
precisely the same quotient. Snell, in fact, found this quotient to be
_a constant quantity_ for each particular substance, though it varied
in amount from one substance to another. He called the quotient the
_index of refraction_.

[Illustration Fig. 5]

In all cases where the light is incident from air upon the surface of
a solid or a liquid, or, to speak more generally, when the incidence
is from a less highly refracting to a more highly refracting medium,
the reflection is _partial_. In this case the most powerfully
reflecting substances either transmit or absorb a portion of the
incident light. At a perpendicular incidence water reflects only 18
rays out of every 1,000; glass reflects only 25 rays, while mercury
reflects 666 When the rays strike the surface obliquely the reflection
is augmented. At an incidence of 40°, for example, water reflects 22
rays, at 60° it reflects 65 rays, at 80° 333 rays; while at an
incidence of 89½°, where the light almost grazes the surface, it
reflects 721 rays out of every 1,000. Thus, as the obliquity
increases, the reflection from water approaches, and finally quite
overtakes, the perpendicular reflection from mercury; but at no
incidence, however great, when the incidence is from air, is the
reflection from water, mercury, or any other substance, _total_.

Still, total reflection may occur, and with a view to understanding
its subsequent application in the Nicol's prism, it is necessary to
state when it occurs. This leads me to the enunciation of a principle
which underlies all optical phenomena--the principle of
reversibility.[5] In the case of refraction, for instance, when the
ray passes obliquely from air into water, it is bent _towards_ the
perpendicular; when it passes from water to air, it is bent _from_ the
perpendicular, and accurately reverses its course. Thus in fig. 5, if
_m_ E _n_ be the track of a ray in passing from air into water, _n_ E
_m_ will be its track in passing from water into air. Let us push this
principle to its consequences. Supposing the light, instead of being
incident along _m_ E or _m'_ E, were incident as close as possible
along C E (fig. 6); suppose, in other words, that it just grazes the
surface before entering the water. After refraction it will pursue
say the course E _n_''. Conversely, if the light start from _n_'', and
be incident at E, it will, on escaping into the air, just graze the
surface of the water. The question now arises, what will occur
supposing the ray from the water to follow the course _n_''' E, which
lies beyond _n_'' E? The answer is, it will not quit the water at all,
but will be _totally_ reflected (along E _x_). At the under surface of
the water, moreover, the law is just the same as at its upper surface,
the angle of incidence (D E _n_''') being equal to the angle of
reflection (D E _x_).

[Illustration: Fig. 6]

Total reflection may be thus simply illustrated:--Place a shilling in
a drinking-glass, and tilt the glass so that the light from the
shilling shall fall with the necessary obliquity upon the water
surface above it. Look upwards through the water towards that surface,
and you see the image of the shilling shining there as brightly as the
shilling itself. Thrust the closed end of an empty test-tube into
water, and incline the tube. When the inclination is sufficient,
horizontal light falling upon the tube cannot enter the air within it,
but is totally reflected upward: when looked down upon, such a tube
looks quite as bright as burnished silver. Pour a little water into
the tube; as the liquid rises, total reflection is abolished, and with
it the lustre, leaving a gradually diminishing shining zone, which
disappears wholly when the level of the water within the tube reaches
that without it. Any glass tube, with its end stopped water-tight,
will produce this effect, which is both beautiful and instructive.

Total reflection never occurs except in the attempted passage of a ray
from a more refracting to a less refracting medium; but in this case,
when the obliquity is sufficient, it always occurs. The mirage of the
desert, and other phantasmal appearances in the atmosphere, are in
part due to it. When, for example, the sun heats an expanse of sand,
the layer of air in contact with the sand becomes lighter and less
refracting than the air above it: consequently, the rays from a
distant object, striking very obliquely on the surface of the heated
stratum, are sometimes totally reflected upwards, thus producing
images similar to those produced by water. I have seen the image of a
rock called Mont Tombeline distinctly reflected from the heated air of
the strand of Normandy near Avranches; and by such delusive
appearances the thirsty soldiers of the French army in Egypt were
greatly tantalised.

The angle which marks the limit beyond which total reflection takes
place is called the _limiting angle_ (it is marked in fig. 6 by the
strong line E _n_''). It must evidently diminish as the refractive
index increases. For water it is 48½°, for flint glass 38°41', and for
diamond 23°42'. Thus all the light incident from two complete
quadrants, or 180°, in the case of diamond, is condensed into an
angular space of 47°22' (twice 23°42') by refraction. Coupled with its
great refraction, are the great dispersive and great reflective
powers of diamond; hence the extraordinary radiance of the gem, both
as regards white light and prismatic light.


§ 5. _Velocity of Light. Aberration. Principle of least Action._

In 1676 a great impulse was given to optics by astronomy. In that year
Olav Roemer, a learned Dane, was engaged at the Observatory of Paris
in observing the eclipses of Jupiter's moons. The planet, whose
distance from the sun is 475,693,000 miles, has four satellites. We
are now only concerned with the one nearest to the planet. Roemer
watched this moon, saw it move round the planet, plunge into Jupiter's
shadow, behaving like a lamp suddenly extinguished: then at the other
edge of the shadow he saw it reappear, like a lamp suddenly lighted.
The moon thus acted the part of a signal light to the astronomer, and
enabled him to tell exactly its time of revolution. The period between
two successive lightings up of the lunar lamp he found to be 42 hours,
28 minutes, and 35 seconds.

This measurement of time was so accurate, that having determined the
moment when the moon emerged from the shadow, the moment of its
hundredth appearance could also be determined. In fact, it would be
100 times 42 hours, 28 minutes, 35 seconds, after the first
observation.

Roemer's first observation was made when the earth was in the part of
its orbit nearest Jupiter. About six months afterwards, the earth
being then at the opposite side of its orbit, when the little moon
ought to have made its hundredth appearance, it was found unpunctual,
being fully 15 minutes behind its calculated time. Its appearance,
moreover, had been growing gradually later, as the earth retreated
towards the part of its orbit most distant from Jupiter. Roemer
reasoned thus: 'Had I been able to remain at the other side of the
earth's orbit, the moon might have appeared always at the proper
instant; an observer placed there would probably have seen the moon 15
minutes ago, the retardation in my case being due to the fact that the
light requires 15 minutes to travel from the place where my first
observation was made to my present position.'

This flash of genius was immediately succeeded by another. 'If this
surmise be correct,' Roemer reasoned, 'then as I approach Jupiter
along the other side of the earth's orbit, the retardation ought to
become gradually less, and when I reach the place of my first
observation, there ought to be no retardation at all.' He found this
to be the case, and thus not only proved that light required time to
pass through space, but also determined its rate of propagation.

The velocity of light, as determined by Roemer, is 192,500 miles in a
second.

For a time, however, the observations and reasonings of Roemer failed
to produce conviction. They were doubted by Cassini, Fontenelle, and
Hooke. Subsequently came the unexpected corroboration of Roemer by the
English astronomer, Bradley, who noticed that the fixed stars did not
really appear to be fixed, but that they describe little orbits in the
heavens every year. The result perplexed him, but Bradley had a mind
open to suggestion, and capable of seeing, in the smallest fact, a
picture of the largest. He was one day upon the Thames in a boat, and
noticed that as long as his course remained unchanged, the vane upon
his masthead showed the wind to be blowing constantly in the same
direction, but that the wind appeared to vary with every change in the
direction of his boat. 'Here,' as Whewell says, 'was the image of his
case. The boat was the earth, moving in its orbit, and the wind was
the light of a star.'

We may ask, in passing, what, without the faculty which formed the
'image,' would Bradley's wind and vane have been to him? A wind and
vane, and nothing more. You will immediately understand the meaning of
Bradley's discovery. Imagine yourself in a motionless railway-train,
with a shower of rain descending vertically downwards. The moment the
train begins to move, the rain-drops begin to slant, and the quicker
the motion of the train the greater is the obliquity. In a precisely
similar manner the rays from a star, vertically overhead, are caused
to slant by the motion of the earth through space. Knowing the speed
of the train, and the obliquity of the falling rain, the velocity of
the drops may be calculated; and knowing the speed of the earth in her
orbit, and the obliquity of the rays due to this cause, we can
calculate just as easily the velocity of light. Bradley did this, and
the 'aberration of light,' as his discovery is called, enabled him to
assign to it a velocity almost identical with that deduced by Roemer
from a totally different method of observation. Subsequently Fizeau,
and quite recently Cornu, employing not planetary or stellar
distances, but simply the breadth of the city of Paris, determined the
velocity of light: while Foucault--a man of the rarest mechanical
genius--solved the problem without quitting his private room. Owing
to an error in the determination of the earth's distance from the sun,
the velocity assigned to light by both Roemer and Bradley is too
great. With a close approximation to accuracy it may be regarded as
186,000 miles a second.

By Roemer's discovery, the notion entertained by Descartes, and
espoused by Hooke, that light is propagated instantly through space,
was overthrown. But the establishment of its motion through stellar
space led to speculations regarding its velocity in transparent
terrestrial substances. The 'index of refraction' of a ray passing
from air into water is 4/3. Newton assumed these numbers to mean that
the velocity of light in water being 4, its velocity in air is 3; and
he deduced the phenomena of refraction from this assumption. Huyghens
took the opposite and truer view. According to this great man, the
velocity of light in water being 3, its velocity in air is 4; but both
in Newton's time and ours the same great principle determined, and
determines, the course of light in all cases. In passing from point to
point, whatever be the media in its path, or however it may be
refracted or reflected, light takes the course which occupies _least
time_. Thus in fig. 4, taking its velocity in air and in water into
account, the light reaches G from I more rapidly by travelling first
to O, and there changing its course, than if it proceeded straight
from I to G. This is readily comprehended, because, in the latter
case, it would pursue a greater distance through the water, which is
the more retarding medium.


§ 6. _Descartes' Explanation of the Rainbow_.

Snell's law of refraction is one of the corner-stones of optical
science, and its applications to-day are million-fold. Immediately
after its discovery Descartes applied it to the explanation of the
rainbow. A beam of solar light falling obliquely upon a rain-drop is
refracted on entering the drop. It is in part reflected at the back of
the drop, and on emerging it is again refracted. By these two
refractions, and this single reflection, the light is sent to the eye
of an observer facing the drop, and with his back to the sun.

Conceive a line drawn from the sun, through the back of his head, to
the observer's eye and prolonged beyond it. Conceive a second line
drawn from the shower to the eye, and enclosing an angle of 42½° with
the line drawn from the sun. Along this second line a rain-drop when
struck by a sunbeam will send red light to the eye. Every other drop
similarly situated, that is, every drop at an angular distance of 42½°
from the line through the sun and eye, will do the same. A circular
band of red light is thus formed, which may be regarded as the
boundary of the base of a cone, with its apex at the observer's eye.
Because of the magnitude of the sun, the angular width of this red
band will be half a degree.

From the eye of the observer conceive another line to be drawn,
enclosing an angle, not of 42½°, but of 40½°, with the prolongation of
the line drawn from the sun. Along this other line a rain-drop, at its
remote end, when struck by a solar beam, will send violet light to the
eye. All drops at the same angular distance will do the same, and we
shall therefore obtain a band of violet light of the same width as the
red band. These two bands constitute the limiting colours of the
rainbow, and between them the bands corresponding to the other colours
lie.

Thus the line drawn from the eye to the _middle_ of the bow, and the
line drawn through the eye to the sun, always enclose an angle of
about 41°. To account for this was the great difficulty, which
remained unsolved up to the time of Descartes.

Taking a pen in hand, and calculating by means of Snell's law the
track of every ray through a raindrop, Descartes found that, at one
particular angle, the rays, reflected at its back, emerged from the
drop _almost parallel to each other_. They were thus enabled to
preserve their intensity through long atmospheric distances. At all
other angles the rays quitted the drop _divergent_, and through this
divergence became so enfeebled as to be practically lost to the eye.
The angle of parallelism here referred to was that of forty-one
degrees, which observation had proved to be invariably associated with
the rainbow.

From what has been said, it is clear that two observers standing
beside each other, or one above the other, nay, that even the two eyes
of the same observer, do not see exactly the same bow. The position of
the base of the cone changes with that of its apex. And here we have
no difficulty in answering a question often asked--namely, whether a
rainbow is ever seen reflected in water. Seeing two bows, the one in
the heavens, the other in the water, you might be disposed to infer
that the one bears the same relation to the other that a tree upon the
water's edge bears to its reflected image. The rays, however, which
reach an observer's eye after reflection from the water, and which
form a bow in the water, would, were their course from the shower
uninterrupted, converge to a point vertically under the observer, and
as far below the level of the water as his eye is above it. But under
no circumstances could an eye above the water-level and one below it
see the same bow--in other words, the self-same drops of rain cannot
form the reflected bow and the bow seen directly in the heavens. The
reflected bow, therefore, is not, in the usual optical sense of the
term, the _image_ of the bow seen in the sky.


§ 7. _Analysis and Synthesis of Light. Doctrine of Colours_.

In the rainbow a new phenomenon was introduced--the phenomenon of
colour. And here we arrive at one of those points in the history of
science, when great men's labours so intermingle that it is difficult
to assign to each worker his precise meed of honour. Descartes was at
the threshold of the discovery of the composition of solar light; but
for Newton was reserved the enunciation of the true law. He went to
work in this way: Through the closed window-shutter of a room he
pierced an orifice, and allowed a thin sunbeam to pass through it. The
beam stamped a round white image of the sun on the opposite wall of
the room. In the path of this beam Newton placed a prism, expecting to
see the beam refracted, but also expecting to see the image of the
sun, after refraction, still round. To his astonishment, it was drawn
out to an image with a length five times its breadth. It was,
moreover, no longer white, but divided into bands of different
colours. Newton saw immediately that solar light was _composite_, not
simple. His elongated image revealed to him the fact that some
constituents of the light were more deflected by the prism than
others, and he concluded, therefore, that white light was a mixture of
lights of different colours, possessing different degrees of
refrangibility.

Let us reproduce this celebrated experiment. On the screen is now
stamped a luminous disk, which may stand for Newton's image of the
sun. Causing the beam (from the aperture L, fig. 7) which produces the
disk to pass through a lens (E), we form a sharp image of the
aperture. Placing in the track of the beam a prism (P), we obtain
Newton's coloured image, with its red and violet ends, which he called
a _spectrum_. Newton divided the spectrum into seven parts--red,
orange, yellow, green, blue, indigo, violet; which are commonly called
the seven primary or prismatic colours. The drawing out of the white
light into its constituent colours is called _dispersion_.

[Illustration: Fig. 7.]

This was the first _analysis_ of solar light by Newton; but the
scientific mind is fond of verification, and never neglects it where
it is possible. Newton completed his proof by _synthesis_ in this way:
The spectrum now before you is produced by a glass prism. Causing the
decomposed beam to pass through a second similar prism, but so placed
that the colours are refracted back and reblended, the perfectly white
luminous disk is restored.

[Illustration: Fig. 8.]

In this case, refraction and dispersion are simultaneously abolished.
Are they always so? Can we have the one without the other? It was
Newton's conclusion that we could not. Here he erred, and his error,
which he maintained to the end of his life, retarded the progress of
optical discovery. Dollond subsequently proved that by combining two
different kinds of glass, the colours can be extinguished, still
leaving a residue of refraction, and he employed this residue in the
construction of achromatic lenses--lenses yielding no colour--which
Newton thought an impossibility. By setting a water-prism--water
contained in a wedge-shaped vessel with glass sides (B, fig. 8)--in
opposition to a wedge of glass (to the right of B), this point can be
illustrated before you. We have first of all the position (dotted) of
the unrefracted beam marked upon the screen; then we produce the
narrow water-spectrum (W); finally, by introducing a flint-glass
prism, we refract the beam back, until the colour disappears (at A).
The image of the slit is now _white_; but though the dispersion is
abolished, there remains a very sensible amount of refraction.

This is the place to illustrate another point bearing upon the
instrumental means employed in these lectures. Bodies differ widely
from each other as to their powers of refraction and dispersion. Note
the position of the water-spectrum upon the screen. Altering in no
particular the wedge-shaped vessel, but simply substituting for the
water the transparent bisulphide of carbon, you notice how much higher
the beam is thrown, and how much richer is the display of colour. To
augment the size of our spectrum we here employ (at L) a slit, instead
of a circular aperture.[6]

[Illustration: Fig. 9.]

The synthesis of white light may be effected in three ways, all of
which are worthy of attention: Here, in the first instance, we have a
rich spectrum produced by the decomposition of the beam (from L, fig.
9). One face of the prism (P) is protected by a diaphragm (not shown
in the figure), with a longitudinal slit, through which the beam
passes into the prism. It emerges decomposed at the other side. I
permit the colours to pass through a cylindrical lens (C), which so
squeezes them together as to produce upon the screen a sharply defined
rectangular image of the longitudinal slit. In that image the colours
are reblended, and it is perfectly white. Between the prism and the
cylindrical lens may be seen the colours, tracking themselves through
the dust of the room. Cutting off the more refrangible fringe by a
card, the rectangle is seen red: cutting off the less refrangible
fringe, the rectangle is seen blue. By means of a thin glass prism
(W), I deflect one portion of the colours, and leave the residual
portion. On the screen are now two coloured rectangles produced in
this way. These are _complementary_ colours--colours which, by their
union, produce white. Note, that by judicious management, one of these
colours is rendered _yellow_, and the other _blue_. I withdraw the
thin prism; yellow and blue immediately commingle, and we have _white_
as the result of their union. On our way, then, we remove the fallacy,
first exposed by Wünsch, and afterwards independently by Helmholtz,
that the mixture of blue and yellow lights produces green.

Restoring the circular aperture, we obtain once more a spectrum like
that of Newton. By means of a lens, we can gather up these colours,
and build them together, not to an image of the aperture, but to an
image of the carbon-points themselves.

Finally, by means of a rotating disk, on which are spread in sectors
the colours of the spectrum, we blend together the prismatic colours
in the eye itself, and thus produce the impression of whiteness.

Having unravelled the interwoven constituents of white light, we have
next to inquire, What part the constitution so revealed enables this
agent to play in Nature? To it we owe all the phenomena of colour, and
yet not to it alone; for there must be a certain relationship between
the ultimate particles of natural bodies and white light, to enable
them to extract from it the luxury of colour. But the function of
natural bodies is here _selective_, not _creative_. There is no colour
_generated_ by any natural body whatever. Natural bodies have showered
upon them, in the white light of the sun, the sum total of all
possible colours; and their action is limited to the sifting of that
total--the appropriating or absorbing of some of its constituents,
and the rejecting of others. It will fix this subject in your minds if
I say, that it is the portion of light which they reject, and not that
which they appropriate or absorb, that gives bodies their colours.

Let us begin our experimental inquiries here by asking, What is the
meaning of blackness? Pass a black ribbon through the colours of the
spectrum; it quenches all of them. The meaning of blackness is thus
revealed--it is the result of the absorption of all the constituents
of solar light. Pass a red ribbon through the spectrum. In the red
light the ribbon is a vivid red. Why? Because the light that enters
the ribbon is not quenched or absorbed, but in great part sent back to
the eye. Place the same ribbon in the green of the spectrum; it is
black as jet. It absorbs the green light, and renders the space on
which that light falls a space of intense darkness. Place a green
ribbon in the green of the spectrum. It shines vividly with its proper
colour; transfer it to the red, it is black as jet. Here it absorbs
all the light that falls upon it, and offers mere darkness to the eye.

Thus, when white light is employed, the red sifts it by quenching the
green, and the green sifts it by quenching the red, both exhibiting
the residual colour. The process through which natural bodies acquire
their colours is therefore a _negative_ one. The colours are produced
by subtraction, not by addition. This red glass is red because it
destroys all the more refrangible rays of the spectrum. This blue
liquid is blue because it destroys all the less refrangible rays. Both
together are opaque because the light transmitted by the one is
quenched by the other. In this way, by the union of two transparent
substances, we obtain a combination as dark as pitch to solar light.
This other liquid, finally, is purple because it destroys the green
and the yellow, and allows the terminal colours of the spectrum to
pass unimpeded. From the blending of the blue and the red this
gorgeous purple is produced.

One step further for the sake of exactness. The light which falls upon
a body is divided into two portions, one of which is reflected from
the surface of the body; and this is of the same colour as the
incident light. If the incident light be white, the superficially
reflected light will also be white. Solar light, for example,
reflected from the surface of even a black body, is white. The
blackest camphine smoke in a dark room, through which a sunbeam passes
from an aperture in the window-shutter, renders the track of the beam
white, by the light scattered from the surfaces of the soot particles.
The moon appears to us as if

    'Clothed in white samite, mystic, wonderful;'

but were it covered with the blackest velvet it would still hang as a
white orb in the heavens, shining upon our world substantially as it
does now.


§ 8. _Colours of Pigments as distinguished from Colours of Light_.

The second portion of the incident light enters the body, and upon its
treatment there the colour of the body depends. And here a moment may
properly be given to the analysis of the action of pigments upon
light. They are composed of fine particles mixed with a vehicle; but
how intimately soever the particles may be blended, they still remain
particles, separated, it may be, by exceedingly minute distances, but
still separated. To use the scientific phrase, they are not optically
continuous. Now, wherever optical continuity is ruptured we have
reflection of the incident light. It is the multitude of reflections
at the limiting surfaces of the particles that prevents light from
passing through snow, powdered glass, or common salt. The light here
is exhausted in echoes, not extinguished by true absorption. It is the
same kind of reflection that renders the thunder-cloud so impervious
to light. Such a cloud is composed of particles of water, mixed with
particles of air, both separately transparent, but practically opaque
when thus mixed together.

In the case of pigments, then, the light is _reflected_ at the
limiting surfaces of the particles, but it is in part _absorbed_
within the particles. The reflection is necessary to send the light
back to the eye; the absorption is necessary to give the body its
colour. The same remarks apply to flowers. The rose is red, in virtue,
not of the light reflected from its surface, but of light which has
entered its substance, which has been reflected from surfaces within,
and which, in returning _through_ the substance, has had its green
extinguished. A similar process in the case of hard green leaves
extinguishes the red, and sends green light from the body of the
leaves to the eye.

All bodies, even the most transparent, are more or less absorbent of
light. Take the case of water. A glass cell of clear water interposed
in the track of our beam does not perceptibly change any one of the
colours of the spectrum. Still absorption, though insensible, has
here occurred, and to render it sensible we have only to increase the
depth of the water through which the light passes. Instead of a cell
an inch thick, let us take a layer, ten or fifteen feet thick: the
colour of the water is then very evident. By augmenting the thickness
we absorb more of the light, and by making the thickness very great we
absorb the light altogether. Lampblack or pitch can do no more, and
the only difference in this respect between them and water is that a
very small depth in their case suffices to extinguish all the light.
The difference between the highest known transparency and the highest
known opacity is one of degree merely.

If, then, we render water sufficiently deep to quench all the light;
and if from the interior of the water no light reaches the eye, we
have the condition necessary to produce blackness. Looked properly
down upon, there are portions of the Atlantic Ocean to which one would
hardly ascribe a trace of colour: at the most a tint of dark indigo
reaches the eye. The water, in fact, is practically _black_, and this
is an indication both of its depth and purity. But the case is
entirely changed when the ocean contains solid particles in a state of
mechanical suspension, capable of sending the light impinging on them
back to the eye.

Throw, for example, a white pebble, or a white dinner plate, into the
blackest Atlantic water; as it sinks it becomes greener and greener,
and, before it disappears, it reaches a vivid blue green. Break such a
pebble, or plate, into fragments, these will behave like the unbroken
mass: grind the pebble to powder, every particle will yield its
modicum of green; and if the particles be so fine as to remain
suspended in the water, the scattered light will be a uniform green.
Hence the greenness of shoal water. You go to bed with the black water
of the Atlantic around you. You rise in the morning, find it a vivid
green, and correctly infer that you are crossing the Bank of
Newfoundland. Such water is found charged with fine matter in a state
of mechanical suspension. The light from the bottom may sometimes come
into play, but it is not necessary. The subaqueous foam, generated by
the screw or paddle-wheels of a steamer, also sends forth a vivid
green. The foam here furnishes a _reflecting surface_, the water
between the eye and it the _absorbing medium_.

Nothing can be more superb than the green of the Atlantic waves when
the circumstances are favourable to the exhibition of the colour. As
long as a wave remains unbroken no colour appears, but when the foam
just doubles over the crest like an Alpine snow-cornice, under the
cornice we often see a display of the most exquisite green. It is
metallic in its brilliancy. The foam is first illuminated, and it
scatters the light in all directions; the light which passes through
the higher portion of the wave alone reaches the eye, and gives to
that portion its matchless colour. The folding of the wave, producing,
as it does, a series of longitudinal protuberances and furrows which
act like cylindrical lenses, introduces variations in the intensity of
the light, and materially enhances its beauty.

We are now prepared for the further consideration of a point already
adverted to, and regarding which error long found currency. You will
find it stated in many books that blue light and yellow light mixed
together, produce green. But blue and yellow have been just proved to
be complementary colours, producing white by their mixture. The
mixture of blue and yellow _pigments_ undoubtedly produces green, but
the mixture of pigments is a totally different thing from the mixture
of lights.

Helmholtz has revealed the cause of the green produced by a mixture of
blue and yellow pigments. No natural colour is _pure_. A blue liquid,
or a blue powder, permits not only the blue to pass through it, but a
portion of the adjacent green. A yellow powder is transparent not only
to the yellow light, but also in part to the adjacent green. Now, when
blue and yellow are mixed together, the blue cuts off the yellow, the
orange, and the red; the yellow, on the other hand, cuts off the
violet, the indigo, and the blue. Green is the only colour to which
both are transparent, and the consequence is that, when white light
falls upon a mixture of yellow and blue powders, the green alone is
sent back to the eye. You have already seen that the fine blue
ammonia-sulphate of copper transmits a large portion of green, while
cutting off all the less refrangible light. A yellow solution of
picric acid also allows the green to pass, but quenches all the more
refrangible light. What must occur when we send a beam through both
liquids? The experimental answer to this question is now before you:
the green band of the spectrum alone remains upon the screen.

The impurity of natural colours is strikingly illustrated by an
observation recently communicated to me by Mr. Woodbury. On looking
through a blue glass at green leaves in sunshine, he saw the
superficially reflected light blue. The light, on the contrary, which
came from the body of the leaves was crimson. On examination, I found
that the glass employed in this observation transmitted both ends of
the spectrum, the red as well as the blue, and that it quenched the
middle. This furnished an easy explanation of the effect. In the
delicate spring foliage the blue of the solar light is for the most
part absorbed, and a light, mainly yellowish green, but containing a
considerable quantity of red, escapes from the leaf to the eye. On
looking at such foliage through the violet glass, the green and the
yellow are stopped, and the red alone reaches the eye. Thus regarded,
therefore, the leaves appear like faintly blushing roses, and present
a very beautiful appearance. With the blue ammonia-sulphate of copper,
which transmits no red, this effect is not obtained.

As the year advances the crimson gradually hardens to a coppery red;
and in the dark green leaves of old ivy it is almost absent.
Permitting a beam of white light to fall upon fresh leaves in a dark
room, the sudden change from green to red, and from red back to green,
when the violet glass is alternately introduced and withdrawn, is very
surprising. Looked at through the same glass, the meadows in May
appear of a warm purple. With a solution of permanganate of potash,
which, while it quenches the centre of the spectrum, permits its ends
to pass more freely than the violet glass, excellent effects are also
obtained.[7]

This question of absorption, considered with reference to its
molecular mechanism, is one of the most subtle and difficult in
physics. We are not yet in a condition to grapple with it, but we
shall be by-and-by. Meanwhile we may profitably glance back on the web
of relations which these experiments reveal to us. We have, firstly,
in solar light an agent of exceeding complexity, composed of
innumerable constituents, refrangible in different degrees. We find,
secondly, the atoms and molecules of bodies gifted with the power of
sifting solar light in the most various ways, and producing by this
sifting the colours observed in nature and art. To do this they must
possess a molecular structure commensurate in complexity with that of
light itself. Thirdly, we have the human eye and brain, so organized
as to be able to take in and distinguish the multitude of impressions
thus generated. The light, therefore, at starting is complex; to sift
and select it as they do, natural bodies must be complex; while to
take in the impressions thus generated, the human eye and brain,
however we may simplify our conceptions of their action,[8] must be
highly complex.

Whence this triple complexity? If what are called material purposes
were the only end to be served, a much simpler mechanism would be
sufficient. But, instead of simplicity, we have prodigality of
relation and adaptation--and this, apparently, for the sole purpose of
enabling us to see things robed in the splendours of colour. Would it
not seem that Nature harboured the intention of educating us for other
enjoyments than those derivable from meat and drink? At all events,
whatever Nature meant--and it would be mere presumption to dogmatize
as to what she meant--we find ourselves here, as the upshot of her
operations, endowed, not only with capacities to enjoy the materially
useful, but endowed with others of indefinite scope and application,
which deal alone with the beautiful and the true.



LECTURE II.

  ORIGIN OF PHYSICAL THEORIES
  SCOPE OF THE IMAGINATION
  NEWTON AND THE EMISSION THEORY
  VERIFICATION OF PHYSICAL THEORIES
  THE LUMINIFEROUS ETHER
  WAVE THEORY OF LIGHT
  THOMAS YOUNG
  FRESNEL AND ARAGO
  CONCEPTION OF WAVE-MOTION
  INTERFERENCE OF WAVES
  CONSTITUTION OF SOUND-WAVES
  ANALOGIES OF SOUND AND LIGHT
  ILLUSTRATIONS OF WAVE-MOTION
  INTERFERENCE OF SOUND-WAVES
  OPTICAL ILLUSTRATIONS
  PITCH AND COLOUR
  LENGTHS OF THE WAVES OF LIGHT AND RATES OF VIBRATION OF
    THE ETHER-PARTICLES
  INTERFERENCE OF LIGHT
  PHENOMENA WHICH FIRST SUGGESTED THE UNDULATORY THEORY
  BOYLE AND HOOKE
  THE COLOURS OF THIN PLATES
  THE SOAP-BUBBLE
  NEWTON'S RINGS
  THEORY OF 'FITS'
  ITS EXPLANATION OF THE RINGS
  OVER-THROW OF THE THEORY
  DIFFRACTION OF LIGHT
  COLOURS PRODUCED BY DIFFRACTION
  COLOURS OF MOTHER-OF-PEARL.


§ 1. _Origin and Scope of Physical Theories_.

We might vary and extend our experiments on Light indefinitely, and
they certainly would prove us to possess a wonderful mastery over the
phenomena. But the vesture of the agent only would thus be revealed,
not the agent itself. The human mind, however, is so constituted that
it can never rest satisfied with this outward view of natural things.
Brightness and freshness take possession of the mind when it is
crossed by the light of principles, showing the facts of Nature to be
organically connected.

Let us, then, inquire what this thing is that we have been generating,
reflecting, refracting and analyzing.

In doing this, we shall learn that the life of the experimental
philosopher is twofold. He lives, in his vocation, a life of the
senses, using his hands, eyes, and ears in his experiments: but such a
question as that now before us carries him beyond the margin of the
senses. He cannot consider, much less answer, the question, 'What is
light?' without transporting himself to a world which underlies the
sensible one, and out of which all optical phenomena spring. To
realise this subsensible world the mind must possess a certain
pictorial power. It must be able to form definite images of the things
which that world contains; and to say that, if such or such a state of
things exist in the subsensible world, then the phenomena of the
sensible one must, of necessity, grow out of this state of things.
Physical theories are thus formed, the truth of which is inferred from
their power to explain the known and to predict the unknown.

This conception of physical theory implies, as you perceive, the
exercise of the imagination--a word which seems to render many
respectable people, both in the ranks of science and out of them,
uncomfortable. That men in the ranks of science should feel thus is, I
think, a proof that they have suffered themselves to be misled by the
popular definition of a great faculty, instead of observing its
operation in their own minds. Without imagination we cannot take a
step beyond the bourne of the mere animal world, perhaps not even to
the edge of this one. But, in speaking thus of imagination, I do not
mean a riotous power which deals capriciously with facts, but a
well-ordered and disciplined power, whose sole function is to form
such conceptions as the intellect imperatively demands. Imagination,
thus exercised, never really severs itself from the world of fact.
This is the storehouse from which its materials are derived; and the
magic of its art consists, not in creating things anew, but in so
changing the magnitude, position, grouping, and other relations of
sensible things, as to render them fit for the requirements of the
intellect in the subsensible world.[9]

Descartes imagined space to be filled with something that transmitted
light _instantaneously_. Firstly, because, in his experience, no
measurable interval was known to exist between the appearance of a
flash of light, however distant, and its effect upon consciousness;
and secondly, because, as far as his experience went, no physical
power is conveyed from place to place without a vehicle. But his
imagination helped itself farther by illustrations drawn from the
world of fact. 'When,' he says,' one walks in darkness with staff in
hand, the moment the distant end of the staff strikes an obstacle the
hand feels it. This explains what might otherwise be thought strange,
that the light reaches us instantaneously from the sun. I wish thee to
believe that light in the bodies that we call luminous is nothing more
than a very brisk and violent motion, which, by means of the air and
other transparent media, is conveyed to the eye, exactly as the shock
through the walking-stick reaches the hand of a blind man. This is
instantaneous, and would be so even if the intervening distance were
greater than that between earth and heaven. It is therefore no more
necessary that anything material should reach the eye from the
luminous object, than that something should be sent from the ground to
the hand of the blind man when he is conscious of the shock of his
staff.' The celebrated Robert Hooke at first threw doubt upon this
notion of Descartes, but he afterwards substantially espoused it. The
belief in instantaneous transmission was destroyed by the discovery of
Roemer referred to in our last lecture.


§ 2. _The Emission Theory of Light_.

The case of Newton still more forcibly illustrates the position, that
in forming physical theories we draw for our materials upon the world
of fact. Before he began to deal with light, he was intimately
acquainted with the laws of elastic collision, which all of you have
seen more or less perfectly illustrated on a billiard-table. As
regards the collision of sensible elastic masses, Newton knew the
angle of incidence to be equal to the angle of reflection, and he also
knew that experiment, as shown in our last lecture (fig. 3), had
established the same law with regard to light. He thus found in his
previous knowledge the material for theoretic images. He had only to
change the magnitude of conceptions already in his mind to arrive at
the Emission Theory of Light. Newton supposed light to consist of
elastic particles of inconceivable minuteness, shot out with
inconceivable rapidity by luminous bodies. Optical reflection
certainly occurred _as if_ light consisted of such particles, and this
was Newton's justification for introducing them.

But this is not all. In another important particular, also, Newton's
conceptions regarding the nature of light were influenced by his
previous knowledge. He had been pondering over the phenomena of
gravitation, and had made himself at home amid the operations of this
universal power. Perhaps his mind at this time was too freshly and too
deeply imbued with these notions to permit of his forming an
unfettered judgment regarding the nature of light. Be that as it may,
Newton saw in Refraction the result of an attractive force exerted on
the light-particles. He carried his conception out with the most
severe consistency. Dropping vertically downwards towards the earth's
surface, the motion of a body is accelerated as it approaches the
earth. Dropping downwards towards a horizontal surface--say from air
on to glass or water--the velocity of the light-particles, when they
came close to the surface, is, according to Newton, also accelerated.
Approaching such a surface obliquely, he supposed the particles, when
close to it, to be drawn down upon it, as a projectile is deflected by
gravity to the surface of the earth. This deflection was, according to
Newton, the refraction seen in our last lecture (fig. 4). Finally, it
was supposed that differences of colour might be due to differences
in the 'bigness' of the particles. This was the physical theory of
light enunciated and defended by Newton; and you will observe that it
simply consists in the transference of conceptions, born in the world
of the senses, to a subsensible world.

But, though the region of physical theory lies thus behind the world
of senses, the verifications of theory occur in that world. Laying the
theoretic conception at the root of matters, we determine by deduction
what are the phenomena which must of necessity grow out of this root.
If the phenomena thus deduced agree with those of the actual world, it
is a presumption in favour of the theory. If, as new classes of
phenomena arise, they also are found to harmonise with theoretic
deduction, the presumption becomes still stronger. If, finally, the
theory confers prophetic vision upon the investigator, enabling him to
predict the occurrence of phenomena which have never yet been seen,
and if those predictions be found on trial to be rigidly correct, the
persuasion of the truth of the theory becomes overpowering.

Thus working backwards from a limited number of phenomena, the human
mind, by its own expansive force, reaches a conception which covers
them all. There is no more wonderful performance of the intellect than
this; but we can render no account of it. Like the scriptural gift of
the Spirit, no man can tell whence it cometh. The passage from fact to
principle is sometimes slow, sometimes rapid, and at all times a
source of intellectual joy. When rapid, the pleasure is concentrated,
and becomes a kind of ecstasy or intoxication. To any one who has
experienced this pleasure, even in a moderate degree, the action of
Archimedes when he quitted the bath, and ran naked, crying 'Eureka!'
through the streets of Syracuse, becomes intelligible.

How, then, did it fare with the Emission Theory when the deductions
from it were brought face to face with natural phenomena? Tested by
experiment, it was found competent to explain many facts, and with
transcendent ingenuity its author sought to make it account for all.
He so far succeeded, that men so celebrated as Laplace and Malus, who
lived till 1812, and Biot and Brewster, who lived till our own time,
were found among his disciples.


§ 3. _The Undulatory Theory of Light_.

Still, even at an early period of the existence of the Emission
Theory, one or two great men were found espousing a different one.
They furnish another illustration of the law that, in forming
theories, the scientific imagination must draw its materials from the
world of fact and experience. It was known long ago that sound is
conveyed in waves or pulses through the air; and no sooner was this
truth well housed in the mind than it became the basis of a theoretic
conception. It was supposed that light, like sound, might also be the
product of wave-motion. But what, in this case, could be the material
forming the waves? For the waves of sound we have the air of our
atmosphere; but the stretch of imagination which filled all space with
a _luminiferous ether_ trembling with the waves of light was so bold
as to shock cautious minds. In one of my latest conversations with Sir
David Brewster, he said to me that his chief objection to the
undulatory theory of light was, that he could not think the Creator
capable of so clumsy a contrivance as the filling of space with ether
to produce light. This, I may say, is very dangerous ground, and the
quarrel of science with Sir David, on this point as with many
estimable persons on other points, is, that they profess to know too
much about the mind of the Creator.

This conception of an ether was advocated, and successfully applied to
various phenomena of optics, by the illustrious astronomer, Huyghens.
He deduced from it the laws of reflection and refraction, and applied
it to explain the double refraction of Iceland spar. The theory was
espoused and defended by the celebrated mathematician, Euler. They
were, however, opposed by Newton, whose authority at the time bore
them down. Or shall we say it was authority merely? Not quite so.
Newton's preponderance was in some degree due to the fact that, though
Huyghens and Euler were right in the main, they did not possess
sufficient data to _prove_ themselves right. No human authority,
however high, can maintain itself against the voice of Nature speaking
through experiment. But the voice of Nature may be an uncertain voice,
through the scantiness of data. This was the case at the period now
referred to, and at such a period, by the authority of Newton, all
antagonists were naturally overborne.

The march of mind is rhythmic, not uniform, and this great Emission
Theory, which held its ground so long, resembled one of those circles
which, according to your countryman Emerson, the intermittent force of
genius periodically draws round the operations of the intellect, but
which are eventually broken through by pressure from behind. In the
year 1773 was born, at Milverton, in Somersetshire, a circle-breaker
of this kind. He was educated for the profession of a physician, but
was too strong to be tied down to professional routine. He devoted
himself to the study of natural philosophy, and became in all its
departments a master. He was also a master of letters. Languages,
ancient and modern, were housed within his brain, and, to use the
words of his epitaph, 'he first penetrated the obscurity which had
veiled for ages the hieroglyphics of Egypt.' It fell to the lot of
this man to discover facts in optics which Newton's theory was
incompetent to explain, and his mind roamed in search of a sufficient
theory. He had made himself acquainted with all the phenomena of
wave-motion; with all the phenomena of sound; working successfully in
this domain as an original discoverer. Thus informed and disciplined,
he was prepared to detect any resemblance which might reveal itself
between the phenomena of light and those of wave-motion. Such
resemblances he did detect; and, spurred on by the discovery, he
pursued his speculations and experiments, until he finally succeeded
in placing on an immovable basis the Undulatory Theory of Light.

The founder of this great theory was Thomas Young, a name, perhaps,
unfamiliar to many of you, but which ought to be familiar to you all.
Permit me, therefore, by a kind of geometrical construction which I
once ventured to employ in London, to give you a notion of the
magnitude of this man. Let Newton stand erect in his age, and Young in
his. Draw a straight line from Newton to Young, tangent to the heads
of both. This line would slope downwards from Newton to Young,
because Newton was certainly the taller man of the two. But the slope
would not be steep, for the difference of stature was not excessive.
The line would form what engineers call a gentle gradient from Newton
to Young. Place underneath this line the biggest man born in the
interval between both. It may be doubted whether he would reach the
line; for if he did he would be taller intellectually than Young, and
there was probably none taller. But I do not want you to rest on
English estimates of Young; the German, Helmholtz, a kindred genius,
thus speaks of him: "His was one of the most profound minds that the
world has ever seen; but he had the misfortune to be too much in
advance of his age. He excited the wonder of his contemporaries, who,
however, were unable to follow him to the heights at which his daring
intellect was accustomed to soar. His most important ideas lay,
therefore, buried and forgotten in the folios of the Royal Society,
until a new generation gradually and painfully made the same
discoveries, and proved the exactness of his assertions and the truth
of his demonstrations."

It is quite true, as Helmholtz says, that Young was in advance of his
age; but something is to be added which illustrates the responsibility
of our public writers. For twenty years this man of genius was
quenched--hidden from the appreciative intellect of his
country-men--deemed in fact a dreamer, through the vigorous sarcasm of
a writer who had then possession of the public ear, and who in the
_Edinburgh Review_ poured ridicule upon Young and his speculations. To
the celebrated Frenchmen Fresnel and Arago he was first indebted for
the restitution of his rights; for they, especially Fresnel,
independently remade and vastly extended his discoveries. To the
students of his works Young has long since appeared in his true light,
but these twenty blank years pushed him from the public mind, which
became in time filled with the fame of Young's colleague at the Royal
Institution, Davy, and afterwards with the fame of Faraday. Carlyle
refers to a remark of Novalis, that a man's self-trust is enormously
increased the moment he finds that others believe in him. If the
opposite remark be true--if it be a fact that public disbelief weakens
a man's force--there is no calculating the amount of damage these
twenty years of neglect may have done to Young's productiveness as an
investigator. It remains to be stated that his assailant was Mr. Henry
Brougham, afterwards Lord Chancellor of England.


§ 4. _Wave-Motion, Interference of Waves, 'Whirlpool Rapids' of
Niagara_.

Our hardest work is now before us. But the capacity for hard work
depends in a great measure on the antecedent winding up of the will; I
would call upon you, therefore, to gird up your loins for coming
labours.

In the earliest writings of the ancients we find the notion that sound
is conveyed by the air. Aristotle gives expression to this notion, and
the great architect Vitruvius compares the waves of sound to waves of
water. But the real mechanism of wave-motion was hidden from the
ancients, and indeed was not made clear until the time of Newton. The
central difficulty of the subject was, to distinguish between the
motion of the wave itself, and the motion of the particles which at
any moment constitute the wave.

Stand upon the seashore and observe the advancing rollers before they
are distorted by the friction of the bottom. Every wave has a back and
a front, and, if you clearly seize the image of the moving wave, you
will see that every particle of water along the front of the wave is
in the act of rising, while every particle along its back is in the
act of sinking. The particles in front reach in succession the crest
of the wave, and as soon as the crest is past they begin to fall. They
then reach the furrow or _sinus_ of the wave, and can sink no farther.
Immediately afterwards they become the front of the succeeding wave,
rise again until they reach the crest, and then sink as before. Thus,
while the waves pass onwards horizontally, the individual particles
are simply lifted up and down vertically. Observe a sea-fowl, or, if
you are a swimmer, abandon yourself to the action of the waves; you
are not carried forward, but simply rocked up and down. The
propagation of a wave is the propagation of a _form_, and not the
transference of the substance which constitutes the wave.

The _length_ of the wave is the distance from crest to crest, while
the distance through which the individual particles oscillate is
called the _amplitude_ of the oscillation. You will notice that in
this description the particles of water are made to vibrate _across_
the line of propagation.[10]

And now we have to take a step forwards, and it is the most important
step of all. You can picture two series of waves proceeding from
different origins through the same water. When, for example, you throw
two stones into still water, the ring-waves proceeding from the two
centres of disturbance intersect each other. Now, no matter how
numerous these waves may be, the law holds good that the motion of
every particle of the water is the algebraic sum of all the motions
imparted to it. If crest coincide with crest and furrow with furrow,
the wave is lifted to a double height above its sinus; if furrow
coincide with crest, the motions are in opposition and their sum is
zero. We have then _still_ water. This action of wave upon wave is
technically called _interference_, a term, to be remembered.

To the eye of a person conversant with these principles, nothing can
be more interesting than the crossing of water ripples. Through their
interference the water-surface is sometimes shivered into the most
beautiful mosaic, trembling rhythmically as if with a kind of visible
music. When waves are skilfully generated in a dish of mercury, a
strong light thrown upon the shining surface, and reflected on to a
screen, reveals the motions of the liquid metal. The shape of the
vessel determines the forms of the figures produced. In a circular
dish, for example, a disturbance at the centre propagates itself as a
series of circular waves, which, after reflection, again meet at the
centre. If the point of disturbance be a little way removed from the
centre, the interference of the direct and reflected waves produces
the magnificent chasing shown in the annexed figure.[11] The light
reflected from such a surface yields a pattern of extraordinary
beauty. When the mercury is slightly struck by a needle-point in a
direction concentric with the surface of the vessel, the lines of
light run round in mazy coils, interlacing and unravelling themselves
in a wonderful manner. When the vessel is square, a splendid
chequer-work is produced by the crossing of the direct and reflected
waves. Thus, in the case of wave-motion, the most ordinary causes give
rise to most exquisite effects. The words of Emerson are perfectly
applicable here:--

[Illustration: Fig. 10.]

    'Thou can'st not wave thy staff in the air,
       Or dip thy paddle in the lake,
     But it carves the brow of beauty there.
       And the ripples in rhymes the oars forsake.'

The most impressive illustration of the action of waves on waves that
I have ever seen occurs near Niagara. For a distance of two miles, or
thereabouts, below the Falls, the river Niagara flows unruffled
through its excavated gorge. The bed subsequently narrows, and the
water quickens its motion. At the place called the 'Whirlpool Rapids,'
I estimated the width of the river at 300 feet, an estimate confirmed
by the dwellers on the spot. When it is remembered that the drainage
of nearly half a continent is compressed into this space, the
impetuosity of the river's escape through this gorge may be imagined.

Two kinds of motion are here obviously active, a motion of translation
and a motion of undulation--the race of the river through its gorge,
and the great waves generated by its collision with the obstacles in
its way. In the middle of the stream, the rush and tossing are most
violent; at all events, the impetuous force of the individual waves is
here most strikingly displayed. Vast pyramidal heaps leap incessantly
from the river, some of them with such energy as to jerk their summits
into the air, where they hang suspended as bundles of liquid pearls,
which, when shone upon by the sun, are of indescribable beauty.

The first impression, and, indeed, the current explanation of these
Rapids is, that the central bed of the river is cumbered with large
boulders, and that the jostling, tossing, and wild leaping of the
waters there are due to its impact against these obstacles. A very
different explanation occurred to me upon the spot. Boulders derived
from the adjacent cliffs visibly cumber the _sides_ of the river.
Against these the water rises and sinks rhythmically but violently,
large waves being thus produced. On the generation of each wave there
is an immediate compounding of the wave-motion with the river-motion.
The ridges, which in still water would proceed in circular curves
round the centre of disturbance, cross the river obliquely, and the
result is, that at the centre waves commingle which have really been
generated at the sides. This crossing of waves may be seen on a small
scale in any gutter after rain; it may also be seen on simply pouring
water from a wide-lipped jug. Where crest and furrow cross each other,
the wave is annulled; where furrow and furrow cross, the river is
ploughed to a greater depth; and where crest and crest aid each other,
we have that astonishing leap of the water which breaks the cohesion
of the crests, and tosses them shattered into the air. The phenomena
observed at the Whirlpool Rapids constitute, in fact, one of the
grandest illustrations of the principle of interference.


§ 5. _Analogies of Sound and Light._

Thomas Young's fundamental discovery in optics was that the principle
of Interference was applicable to light. Long prior to his time an
Italian philosopher, Grimaldi, had stated that under certain
circumstances two thin beams of light, each of which, acting singly,
produced a luminous spot upon a white wall, when caused to act
together, partially quenched each other and darkened the spot. This
was a statement of fundamental significance, but it required the
discoveries and the genius of Young to give it meaning. How he did so
will gradually become clear to you. You know that air is compressible:
that by pressure it can be rendered more dense, and that by
dilatation it can be rendered more rare. Properly agitated, a
tuning-fork now sounds in a manner audible to you all, and most of you
know that the air through which the sound is passing is parcelled out
into spaces in which the air is condensed, followed by other spaces in
which the air is rarefied. These condensations and rarefactions
constitute what we call _waves_ of sound. You can imagine the air of a
room traversed by a series of such waves, and you can imagine a second
series sent through the same air, and so related to the first that
condensation coincides with condensation and rarefaction with
rarefaction. The consequence of this coincidence would be a louder
sound than that produced by either system of waves taken singly. But
you can also imagine a state of things where the condensations of the
one system fall upon the rarefactions of the other system. In this
case (other things being equal) the two systems would completely
neutralize each other. Each of them taken singly produces sound; both
of them taken together produce no sound. Thus by adding sound to sound
we produce silence, as Grimaldi, in his experiment, produced darkness
by adding light to light.

Through his investigations on sound, which were fruitful and profound,
Young approached the study of light. He put meaning into the
observation of Grimaldi, and immensely extended it. With splendid
success he applied the undulatory theory to the explanation of the
colours of thin plates, and to those of striated surfaces. He
discovered and explained classes of colour which had been previously
unnoticed or unknown. On the assumption that light was wave-motion,
all his experiments on interference were accounted for; on the
assumption that light was flying particles, nothing was explained. In
the time of Huyghens and Euler a medium had been assumed for the
transmission of the waves of light; but Newton raised the objection
that, if light consisted of the waves of such a medium, shadows could
not exist. The waves, he contended, would bend round opaque bodies and
produce the motion of light behind them, as sound turns a corner, or
as waves of water wash round a rock. It was proved that the bending
round referred to by Newton actually occurs, but that the inflected
waves abolish each other by their mutual interference. Young also
discerned a fundamental difference between the waves of light and
those of sound. Could you see the air through which sound-waves are
passing, you would observe every individual particle of air
oscillating to and fro, _in the direction of propagation_. Could you
see the luminiferous ether, you would also find every individual
particle making a small excursion to and fro; but here the motion,
like that assigned to the water-particles above referred to, would be
_across_ the line of propagation. The vibrations of the air are
_longitudinal_, those of the ether _transversal_.

The most familiar illustration of the interference of sound-waves is
furnished by the _beats_ produced by two musical sounds slightly out
of unison. When two tuning-forks in perfect unison are agitated
together the two sounds flow without roughness, as if they were but
one. But, by attaching with wax to one of the forks a little weight,
we cause it to vibrate more slowly than its neighbour. Suppose that
one of them performs 101 vibrations in the time required by the other
to perform 100, and suppose that at starting the condensations and
rarefactions of both forks coincide. At the 101st vibration of the
quicker fork they will again coincide, that fork at this point having
gained one whole vibration, or one whole wavelength, upon the other.
But a little reflection will make it clear that, at the 50th
vibration, the two forks condensation where the other tends to produce
a rarefaction; by the united action of the two forks, therefore, the
sound is quenched, and we have a pause of silence. This occurs where
one fork has gained _half a wavelength_ upon the other. At the 101st
vibration, as already stated, we have coincidence, and, therefore,
augmented sound; at the 150th vibration we have again a quenching of
the sound. Here the one fork is _three half-waves_ in advance of the
other. In general terms, the waves conspire when the one series is an
_even_ number of half-wave lengths, and they destroy each other when
the one series is an _odd_ number of half-wave lengths in advance of
the other. With two forks so circumstanced, we obtain those
intermittent shocks of sound separated by pauses of silence, to which
we give the name of beats. By a suitable arrangement, moreover, it is
possible to make one sound wholly extinguish another. Along four
distinct lines, for example, the vibrations of the two prongs of a
tuning-fork completely blot each other out.[12]

The _pitch_ of sound is wholly determined by the rapidity of the
vibration, as the _intensity_ is by the amplitude. What pitch is to
the ear in acoustics, colour is to the eye in the undulatory theory of
light. Though never seen, the lengths of the waves of light have been
determined. Their existence is proved _by their effects_, and from
their effects also their lengths may be accurately deduced. This may,
moreover, be done in many ways, and, when the different determinations
are compared, the strictest harmony is found to exist between them.
This consensus of evidence is one of the strongest points of the
undulatory theory. The shortest waves of the visible spectrum are
those of the extreme violet; the longest, those of the extreme red;
while the other colours are of intermediate pitch or wavelength. The
length of a wave of the extreme red is such, that it would require
39,000 such waves, placed end to end, to cover one inch, while 64,631
of the extreme violet waves would be required to span the same
distance.

Now, the velocity of light, in round numbers, is 186,000 miles per
second. Reducing this to inches, and multiplying the number thus found
by 39,000, we find the number of waves of the extreme red, in 186,000
miles, to be four hundred and sixty millions of millions. _All these
waves enter the eye, and strike the retina at the back of the eye in
one second_. In a similar manner, it may be found that the number of
shocks corresponding to the impression of violet is six hundred and
seventy-eight millions of millions.

All space is filled with matter oscillating at such rates. From every
star waves of these dimensions move, with the velocity of light, like
spherical shells in all directions. And in ether, just as in water,
the motion of every particle is the algebraic sum of all the separate
motions imparted to it. One motion does not blot out the other; or, if
extinction occur at one point, it is strictly atoned for, by augmented
motion, at some other point. Every star declares by its light its
undamaged individuality, as if it alone had sent its thrills through
space.


§ 6. _Interference of Light_.

[Illustration: Fig. 11.]

The principle of interference, as just stated, applies to the waves of
light as it does to the waves of water and the waves of sound. And the
conditions of interference are the same in all three. If two series of
light-waves of the same length start at the same moment from a common
origin (say A, fig. 11), crest coincides with crest, sinus with sinus,
and the two systems blend together to a single system (A _m_ _n_) of
double amplitude. If both series start at the same moment, one of them
being, at starting, a whole wavelength in advance of the other, they
also add themselves together, and we have an augmented luminous
effect. The same occurs when the one system of waves is any _even_
number of semi-undulations in advance of the other. But if the one
system be half a wave-length (as at A' _a_', fig. 12), or any _odd_
number of half wavelengths, in advance, then the crests of the one
fall upon the sinuses of the other; the one system, in fact, tends to
_lift_ the particles of ether at the precise places where the other
tends to _depress_ them; hence, through the joint action of these
opposing forces (indicated by the arrows) the light-ether remains
perfectly still. This stillness of the ether is what we call darkness,
which corresponds with a dead level in the case of water.

[Illustration: Fig. 12.]

It was said in our first lecture, with reference to the colours
produced by absorption, that the function of natural bodies is
selective, not creative; that they extinguish certain constituents of
the white solar light, and appear in the colours of the unextinguished
light. It must at once occur to you that, inasmuch as we have in
interference an agency by which light may be self-extinguished, we may
have in it the conditions for the production of colour. But this would
imply that certain constituents are quenched by interference, while
others are permitted to remain. This is the fact; and it is entirely
due to the difference in the lengths of the waves of light.


§ 7. _Colours of thin Films. Observations of Boyle and Hooke_.

This subject may be illustrated by the phenomena which first suggested
the undulatory theory to the mind of Hooke. These are the colours of
thin transparent films of all kinds, known as the _colours of thin
plates_. In this relation no object in the world possesses a deeper
scientific interest than a common soap-bubble. And here let me say
emerges one of the difficulties which the student of pure science
encounters in the presence of 'practical' communities like those of
America and England; it is not to be expected that such communities
can entertain any profound sympathy with labours which seem so far
removed from the domain of practice as are many of the labours of the
man of science. Imagine Dr. Draper spending his days in blowing
soap-bubbles and in studying their colours! Would you show him the
necessary patience, or grant him the necessary support? And yet be it
remembered it was thus that minds like those of Boyle, Newton and
Hooke were occupied; and that on such experiments has been founded a
theory, the issues of which are incalculable. I see no other way for
you, laymen, than to trust the scientific man with the choice of his
inquiries; he stands before the tribunal of his peers, and by their
verdict on his labours you ought to abide.

Whence, then, are derived the colours of the soap-bubble? Imagine a
beam of white light impinging on the bubble. When it reaches the first
surface of the film, a known fraction of the light is reflected back.
But a large portion of the beam enters the film, reaches its second
surface, and is again in part reflected. The waves from the second
surface thus turn back and hotly pursue the waves from the first
surface. And, if the thickness of the film be such as to cause the
necessary retardation, the two systems of waves interfere with each
other, producing augmented or diminished light, as the case may be.

But, inasmuch as the waves of light are of different lengths, it is
plain that, to produce extinction in the case of the longer waves, a
greater thickness of film is necessary than in the case of the shorter
ones. Different colours, therefore, must appear at different
thicknesses of the film.

Take with you a little bottle of spirit of turpentine, and pour it
into one of your country ponds. You will then see the glowing of those
colours over the surface of the water. On a small scale we produce
them thus: A common tea-tray is filled with water, beneath the surface
of which dips the end of a pipette. A beam of light falls upon the
water, and is reflected by it to the screen. Spirit of turpentine is
poured into the pipette; it descends, issues from the end in minute
drops, which rise in succession to the surface. On reaching it, each
drop spreads suddenly out as a film, and glowing colours immediately
flash forth upon the screen. The colours change as the thickness of
the film changes by evaporation. They are also arranged in zones, in
consequence of the gradual diminution of thickness from the centre
outwards.

Any film whatever will produce these colours. The film of air between
two plates of glass squeezed together, exhibits, as shown by Hooke,
rich fringes of colour. A particularly fine example of these fringes
is now before you. Nor is even air necessary; the rupture of optical
continuity suffices. Smite with an axe the black, transparent
ice--black, because it is pure and of great depth--under the moraine
of a glacier; you readily produce in the interior flaws which no air
can reach, and from these flaws the colours of thin plates sometimes
break like fire. But the source of most historic interest is, as
already stated, the soap-bubble. With one of the mixtures employed by
the eminent blind philosopher, Plateau, in his researches on the
cohesion figures of thin films, we obtain in still air a bubble ten or
twelve inches in diameter. You may look at the bubble itself, or you
may look at its projection upon the screen; rich colours arranged in
zones are, in both cases, exhibited. Rendering the beam parallel, and
permitting it to impinge upon the sides, bottom, and top of the
bubble, gorgeous fans of colour, reflected from the bubble, overspread
the screen, rotating as the beam is carried round. By this experiment
the internal motions of the film are also strikingly displayed.

Not in a moment are great theories elaborated: the facts which demand
them become first prominent; then, to the period of observation
succeeds a period of pondering and of tentative explanation. By such
efforts the human mind is gradually prepared for the final theoretic
illumination. The colours of thin plates, for example, occupied the
attention of Robert Boyle. In his 'Experimental History of Colours' he
contends against the schools which affirmed that colour was 'a
penetrative quality that reaches to the innermost parts of the
object,' adducing opposing facts. 'To give you a first instance,' he
says, 'I shall need but to remind you of what I told you a little
after the beginning of this essay, touching the blue and red and
yellow that may be produced upon a piece of tempered steel; for these
colours, though they be very vivid, yet if you break the steel they
adorn, they will appear to be but superficial.' He then describes, in
phraseology which shows the delight he took in his work, the following
beautiful experiment:--

'We took a quantity of clean lead, and melted it with a strong fire,
and then immediately pouring it out into a clean vessel of convenient
shape and matter (we used one of iron, that the great and sudden heat
might not injure it), and then carefully and nimbly taking off the
scum that floated on the top, we perceived, as we expected, the smooth
and glossy surface of the melted matter to be adorned with a very
glorious colour, which, being as transitory as delightful, did almost
immediately give place to another vivid colour, and that was as
quickly succeeded by a third, and this, as it were, chased away by a
fourth; and so these wonderfully vivid colours successively appeared
and vanished till the metal ceasing to be hot enough to hold any
longer this pleasing spectacle, the colours that chanced to adorn the
surface when the lead thus began to cool remained upon it, but were so
superficial that how little soever we scraped off the surface of the
lead, we did, in such places, scrape off all the colour.' 'These
things,' he adds, 'suggested to me some thoughts or ravings which I
have not now time to acquaint you with.'[13]

He extends his observations to essential oils and spirits of wine,
'which being shaken till they have good store of bubbles, those
bubbles will (if attentively considered) appear adorned with various
and lovely colours, which all immediately vanish upon the
retrogressing of the liquid which affords these bubbles their skins
into the rest of the oil.' He also refers to the colour of glass
films. 'I have seen one that was skilled in fashioning glasses by the
help of a lamp blowing some of them so strongly as to burst them;
whereupon it was found that the tenacity of the metal was such that
before it broke it suffered itself to be reduced into films so
extremely thin that they constantly showed upon their surface the
varying colours of the rainbow.'[14]

Subsequent to Boyle the colours of thin plates occupied the attention
of Robert Hooke, in whose writings we find a dawning of the undulatory
theory of light. He describes with great distinctness the colours
obtained with thin flakes of 'Muscovy glass' (talc), also those
surrounding flaws in crystals where optical continuity is destroyed.
He shows very clearly the dependence of the colour upon the thickness
of the film, and proves by microscopic observation that plates of a
uniform thickness yield uniform colours. 'If,' he says, 'you take any
small piece of the Muscovy glass, and with a needle, or some other
convenient instrument, cleave it oftentimes into thinner and thinner
laminæ, you shall find that until you come to a determinate thinness
of them they shall appear transparent and colourless; but if you
continue to split and divide them further, you shall find at last that
each plate shall appear most lovely tinged or imbued with a
determinate colour. If, further, by any means you so flaw a pretty
thick piece that one part begins to cleave a little from the other,
and between these two there be gotten some pellucid medium, those
laminated or pellucid bodies that fill that space shall exhibit
several rainbows or coloured lines, the colours of which will be
disposed and ranged according to the various thicknesses of the
several parts of the plate.' He then describes fully and clearly the
experiment with pressed glasses already referred to:--

'Take two small pieces of ground and polished looking-glass plate,
each about the bigness of a shilling: take these two dry, and with
your forefingers and thumbs press them very hard and close together,
and you shall find that when they approach each other very near there
will appear several irises or coloured lines, in the same manner
almost as in the Muscovy glass; and you may very easily change any of
the colours of any part of the interposed body by pressing the plates
closer and harder together, or leaving them more lax--that is, a part
which appeared coloured with a red, may presently be tinged with a
yellow, blue, green, purple, or the like. 'Any substance,' he says,
'provided it be thin and transparent, will show these colours.' Like
Boyle, he obtained them with glass films; he also procured them with
bubbles of pitch, rosin, colophony, turpentine, solutions of several
gums, as gum arabic in water, any glutinous liquor, as wort, wine,
spirit of wine, oyl of turpentine, glare of snails, &c.

Hooke's writings show that even in his day the idea that both light
and heat are modes of motion had taken possession of many minds.
'First,' he says, 'that all kind _of fiery burning bodies_ have their
parts in motion I think will be easily granted me. That the spark
struck from a flint and steel is in rapid agitation I have elsewhere
made probable;... that heat argues a motion of the internal parts is
(as I said before) generally granted;... and that in all extremely hot
shining bodies there is a very quick motion that causes light, as well
as a more robust that causes heat, may be argued from the celerity
wherewith the bodies are dissolved. Next, it must be _a vibrative
motion.'_ His reference to the quick motion of light and the more
robust motion of heat is a remarkable stroke of sagacity; but Hooke's
direct insight is better than his reasoning; for the proofs he adduces
that light is 'a vibrating motion' have no particular bearing upon the
question.

Still the Undulatory Theory had undoubtedly dawned upon the mind of
this remarkable man. In endeavouring to account for the colours of
thin plates, he again refers to the relation of colour to thickness:
he dwells upon the fact that the film which shows these colours must
be transparent, proving this by showing that however thin an opaque
body was rendered no colours were produced. 'This,' he says, 'I have
often tried by pressing a small globule of mercury between two smooth
plates of glass, whereby I have reduced that body to a much greater
thinness than was requisite to exhibit the colours with a transparent
body.' Then follows the sagacious remark that to produce the colours
'there must be a considerable reflecting body adjacent to the under or
further side of the lamina or plate: for this I always found, that the
greater that reflection was the more vivid were the appearing colours.
From which observation,' he continues, 'it is most evident, _that the
reflection from the further or under side of the body is the principal
cause of the production of these colours._'

He draws a diagram, correctly representing the reflection at the two
surfaces of the film; but here his clearness ends. He ascribes the
colours to a coalescence or confusion of the two reflecting pulses;
the principal of interference being unknown to him, he could not go
further in the way of explanation.


§ 8. _Newton's Rings. Relation of Colour to Thickness of Film_.

[Illustration: Fig. 13]

In this way, then, by the active operation of different minds, facts
are observed, examined, and the precise conditions of their
appearance determined. All such work in science is the prelude to
other work; and the efforts of Boyle and Hooke cleared the way for the
optical career of Newton. He conquered the difficulty which Hooke had
found insuperable, and determined by accurate measurements the
relation of the thickness of the film to the colour it displays. In
doing this his first care was to obtain a film of variable and
calculable depth. On a plano-convex glass lens (D B E, fig. 13) of
very feeble curvature he laid a plate of glass (A C) with a plane
surface, thus obtaining a film of air of gradually increasing depth
from the point of contact (B) outwards. On looking at the film in
monochromatic light he saw, with the delight attendant on fulfilled
prevision, surrounding the place of contact, a series of bright rings
separated from each other by dark ones, and becoming more closely
packed together as the distance from the point of contact augmented
(as in fig. 14). When he employed red light, his rings had certain
diameters; when he employed blue light, the diameters were less. In
general terms, the more refrangible the light the smaller were the
rings. Causing his glasses to pass through the spectrum from red to
blue, the rings gradually contracted; when the passage was from blue
to red, the rings expanded. This is a beautiful experiment, and
appears to have given Newton the most lively satisfaction. When white
light fell upon, the glasses, inasmuch as the colours were not
superposed, a series _of iris-coloured_ circles was obtained. A
magnified image of _Newton's rings_ is now before you, and, by
employing in succession red, blue, and white light, we obtain all the
effects observed by Newton. You notice that in monochromatic light the
rings run closer and closer together as they recede from the centre.
This is due to the fact that at a distance the film of air thickens
more rapidly than near the centre. When white light is employed, this
closing up of the rings causes the various colours to be superposed,
so that after a certain thickness they are blended together to white
light, the rings then ceasing altogether. It needs but a moment's
reflection to understand that the colours of thin plates, produced by
white light, are never unmixed or monochromatic.

[Illustration: Fig. 14]

Newton compared the tints obtained in this way with the tints of his
soap-bubble, and he calculated the corresponding thickness. How he did
this may be thus made plain to you: Suppose the water of the ocean to
be absolutely smooth; it would then accurately represent the earth's
curved surface. Let a perfectly horizontal plane touch the surface at
any point. Knowing the earth's diameter, any engineer or mathematician
in this room could tell you how far the sea's surface will lie below
this plane, at the distance of a yard, ten yards, a hundred yards, or
a thousand yards from the point of contact of the plane and the sea.
It is common, indeed, in levelling operations, to allow for the
curvature of the earth. Newton's calculation was precisely similar.
His plane glass was a tangent to his curved one. From its refractive
index and focal distance he determined the diameter of the sphere of
which his curved glass formed a segment, he measured the distances of
his rings from the place of contact, and he calculated the depth
between the tangent plane and the curved surface, exactly as the
engineer would calculate the distance between his tangent plane and
the surface of the sea. The wonder is, that, where such infinitesimal
distances are involved, Newton, with the means at his disposal, could
have worked with such marvellous exactitude.

To account for these rings was the greatest optical difficulty that
Newton, ever encountered. He quite appreciated the difficulty. Over
his eagle eye there was no film--no vagueness in his conceptions. At
the very outset his theory was confronted by the question, Why, when a
beam of light is incident on a transparent body, are some of the
light-particles reflected and some transmitted? Is it that there are
two kinds of particles, the one specially fitted for transmission and
the other for reflection? This cannot be the reason; for, if we allow
a beam of light which has been reflected from one piece of glass to
fall upon another, it, as a general rule, is also divided into a
reflected and a transmitted portion. The particles once reflected are
not always reflected, nor are the particles once transmitted always
transmitted. Newton saw all this; he knew he had to explain why it is
that the self-same particle is at one moment reflected and at the next
moment transmitted. It could only he through _some change in the
condition of the particle itself_. The self-same particle, he
affirmed, was affected by 'fits' of easy transmission and reflection.


§ 9. _Theory of 'Fits' applied to Newton's Rings_.

If you are willing to follow me in an attempt to reveal the
speculative groundwork of this theory of fits, the intellectual
discipline will, I think, repay you for the necessary effort of
attention. Newton was chary of stating what he considered to be the
cause of the fits, but there can hardly be a doubt that his mind
rested on a physical cause. Nor can there be a doubt that here, as in
all attempts at theorising, he was compelled to fall back upon
experience for the materials of his theory. Let us attempt to restore
his course of thought and observation. A magnet would furnish him with
the notion of attracted and repelled poles; and he who habitually saw
in the visible an image of the invisible would naturally endow his
light-particles with such poles. Turning their attracted poles towards
a transparent substance, the particles would be sucked in and
transmitted; turning their repelled poles, they would be driven away
or reflected. Thus, by the ascription of poles, the transmission and
reflection of the self-same particle at different times might be
accounted for.

Consider these rings of Newton as seen in pure red light: they are
alternately bright and dark. The film of air corresponding to the
outermost of them is not thicker than an ordinary soap-bubble, and it
becomes thinner on approaching the centre; still Newton, as I have
said, measured the thickness corresponding to every ring, and showed
the difference of thickness between ring and ring. Now, mark the
result. For the sake of convenience, let us call the thickness of the
film of air corresponding to the first dark ring _d_; then Newton
found the distance corresponding to the second dark ring 2 _d_; the
thickness corresponding to the third dark ring 3 _d_; the thickness
corresponding to the tenth dark ring 10 _d_, and so on. Surely there
must be some hidden meaning in this little distance, _d_, which turns
up so constantly? One can imagine the intense interest with which
Newton pondered its meaning. Observe the probable outcome of his
thought. He had endowed his light-particles with poles, but now he is
forced to introduce the notion of _periodic recurrence_. Here his
power of transfer from the sensible to the subsensible would render it
easy for him to suppose the light-particles animated, not only with a
motion of translation, but also with a motion of rotation. Newton's
astronomical knowledge rendered all such conceptions familiar to him.
The earth has such a double motion. In the time occupied in passing
over a million and a half of miles of its orbit--that is, in
twenty-four hours--our planet performs a complete rotation; and in the
time required to pass over the distance _d_, Newton's light-particle
might be supposed to perform a complete rotation. True, the
light-particle is smaller than the planet, and the distance _d_,
instead of being a million and a half of miles, is a little over the
ninety thousandth of an inch. But the two conceptions are, in point of
intellectual quality, identical.

Imagine, then, a particle entering the film of air where it possesses
this precise thickness. To enter the film, its attracted end must be
presented. Within the film it is able to turn _once_ completely round;
at the other side of the film its attracted pole will be again
presented; it will, therefore, enter the glass at the opposite side of
the film _and be lost to the eye_. All round the place of contact,
wherever the film possesses this precise thickness, the light will
equally disappear--we shall therefore have a ring of darkness.

And now observe how well this conception falls in with the law of
proportionality discovered by Newton. When the thickness of the film
is 2 _d_, the particle has time to perform, _two_ complete rotations
within the film; when the thickness is 3 _d, three_ complete
rotations; when 10 _d, ten_ complete rotations are performed. It is
manifest that in each of these cases, on arriving at the second
surface of the film, the attracted pole of the particle will be
presented. It will, therefore, be transmitted; and, because no light
is sent to the eye, we shall have a ring of darkness at each of these
places.

The bright rings follow immediately from the same conception. They
occur between the dark rings, the thicknesses to which they correspond
being also intermediate between those of the dark ones. Take the case
of the first bright ring. The thickness of the film is ½_d_; in this
interval the rotating particle can perform only half a rotation. When,
therefore, it reaches the second surface of the film, its repelled
pole is presented; it is, therefore, driven back and reaches the eye.
At all distances round the centre corresponding to this thickness the
same effect is produced, and the consequence is a ring of brightness.
The other bright rings are similarly accounted for. At the second one,
where the thickness is 1½_d_, a rotation and a half is performed; at
the third, two rotations and a half; and at each of these places the
particles present their repelled poles to the lower surface of the
film. They are therefore sent back to the eye, and produce there the
impression of brightness. This analysis, though involving difficulties
when closely scrutinised, enables us to see how the theory of fits may
have grown into consistency in the mind of Newton.

It has been already stated that the Emission Theory assigned a greater
velocity to light in glass and water than in air or stellar space; and
that on this point it was at direct issue with the theory of
undulation, which makes the velocity in air or stellar space greater
than in glass or water. By an experiment proposed by Arago, and
executed with consummate skill by Foucault and Fizeau, this question
was brought to a crucial test, and decided in favour of the theory of
undulation.

In the present instance also the two theories are at variance. Newton
assumed that the action which produces the alternate bright and dark
rings took place at a _single surface_; that is, the second surface of
the film. The undulatory theory affirms that the rings are caused by
the interference of waves reflected from both surfaces. This also has
been demonstrated by experiment. By a proper arrangement, as we shall
afterwards learn, we may abolish reflection from one of the surfaces
of the film, and when this is done the rings vanish altogether.

Rings of feeble intensity are also formed by _transmitted_ light.
These are referred by the undulatory theory to the interference of
waves which have passed _directly_ through the film, with others which
have suffered _two_ reflections within the film, and are thus
completely accounted for.


§ 10. _The Diffraction of Light_.

Newton's espousal of the Emission Theory is said to have retarded
scientific discovery. It might, however, be questioned whether, in the
long run, the errors of great men have not really their effect in
rendering intellectual progress rhythmical, instead of permitting it
to remain uniform, the 'retardation' in each case being the prelude to
a more impetuous advance. It is confusion and stagnation, rather than
error, that we ought to avoid. Thus, though the undulatory theory was
held back for a time, it gathered strength in the interval, and its
development within the last half century has been so rapid and
triumphant as to leave no rival in the field. We have now to turn to
the investigation of new classes of phenomena, of which it alone can
render a satisfactory account.

Newton, who was familiar with the idea of an ether, and who introduced
it in some of his speculations, objected, as already stated, that if
light consisted of waves shadows could not exist; for that the waves
would bend round the edges of opaque bodies and agitate the ether
behind them. He was right in affirming that this bending ought to
occur, but wrong in supposing that it does not occur. The bending is
real, though in all ordinary cases it is masked by the action of
interference. This inflection of the light receives the name of
_Diffraction_.

To study the phenomena of diffraction it is necessary that our source
of light should be a physical point, or a fine line; for when a
luminous surface is employed, the waves issuing from different points
of the surface obscure and neutralize each other. A _point_ of light
of high intensity is obtained by admitting the parallel rays of the
sun through an aperture in a window-shutter, and concentrating the
beam by a lens of short focus. The small solar image at the focus
constitutes a suitable point of light. The image of the sun formed on
the convex surface of a glass bead, or of a watch-glass blackened
within, though less intense, will also answer. An intense _line_ of
light is obtained by admitting the sunlight through a slit and sending
it through a strong cylindrical lens. The slice of light is contracted
to a physical line at the focus of the lens. A glass tube blackened
within and placed in the light, reflects from its surface a luminous
line which, though less intense, also answers the purpose.

In the experiment now to be described a vertical slit of variable
width is placed in front of the electric lamp, and this slit is looked
at from a distance through another vertical slit, also of variable
aperture, and held in the hand.

The light of the lamp being, in the first place, rendered
monochromatic by placing a pure red glass in front of the slit, when
the eye is placed in the straight line drawn through both slits an
extraordinary appearance (shown in fig. 15) is observed. Firstly, the
slit in front of the lamp is seen as a vivid rectangle of light; but
right and left of it is a long series of rectangles, decreasing in
vividness, and separated from each other by intervals of absolute
darkness.

The breadth of these bands is seen to vary with the width of the slit
held before the eye. When the slit is widened the bands become
narrower, and crowd more losely together; when the slit is narrowed,
the individual bands widen and also retreat from each other, leaving
between them wider spaces of darkness than before.

[Illustration: Fig. 15.]

Leaving everything else unchanged, let a blue glass or a solution of
ammonia-sulphate of copper, which gives a very pure blue, be placed in
the path of the light. A series of blue bands is thus obtained,
exactly like the former in all respects save one; the blue rectangles
are _narrower_, and they are _closer together_ than the red ones.

If we employ colours of intermediate refrangibilities, which we may do
by causing the different colours of a spectrum to shine through the
slit, we obtain bands of colour intermediate in width, and occupying
intermediate positions, between those of the red and blue. The aspect
of the bands in red, green, and violet light is represented in fig.
16. When _white light_, therefore, passes through the slit the various
colours are not superposed, and instead of a series of monochromatic
bands, separated from each other by intervals of darkness, we have a
series of coloured spectra placed side by side. When the distant slit
is illuminated by a candle flame, instead of the more intense electric
light, or when a distant platinum wire raised to a white heat by an
electric current is employed, substantially the same effects are
observed.

[Illustration: Fig. 16.]


§ 11. _Application of the Wave-theory to the Phenomena of
Diffraction_.

Of these and of a multitude of similar effects the Emission Theory is
incompetent to offer any satisfactory explanation. Let us see how they
are accounted for by the Theory of Undulation.

And here, with the view of reaching absolute clearness, I must make an
appeal to that faculty the importance of which I have dwelt upon so
earnestly here and elsewhere--the faculty of imagination. Figure
yourself upon the sea-shore, with a well-formed wave advancing. Take a
line of particles along the front of the wave, all at the same
distance below the crest; they are all rising in the same manner and
at the same rate. Take a similar line of particles on the back of the
wave, they are all falling in the same manner and at the same rate.
Take a line of particles along the crest, they are all in the same
condition as regards the motion of the wave. The same is true for a
line of particles along the furrow of the wave.

The particles referred to in each of these cases respectively, being
in the same condition as regards the motion of the wave, are said to
be in the same _phase_ of vibration. But if you compare a particle on
the front of the wave with one at the back; or, more generally, if you
compare together any two particles not occupying the same position in
the wave, their conditions of motion not being the same, they are said
to be in different phases of vibration. If one of the particles lie
upon the crest, and the other on the furrow of the wave, then, as one
is about to rise and the other about to fall, they are said to be in
_opposite_ phases of vibration.

There is still another point to be cleared up--and it is one of the
utmost importance as regards our present subject. Let O (fig. 17) be a
spot in still water which, when disturbed, produces a series of
circular waves: the disturbance necessary to produce these waves is
simply an oscillation up and down of the water at O. Let _m_ _n_ be
the position of the ridge of one of the waves at any moment, and _m'_
_n'_ its position a second or two afterwards. Now every particle of
water, as the wave passes it, oscillates, as we have learned, up and
down. If, then, this oscillation be a sufficient origin of
wave-motion, each distinct particle of the wave _m_ _n_ ought to give
birth, to a series of circular waves. This is the important point up
to which I wish to lead you. Every particle of the wave _m_ _n_ _does_
act in this way. Taking each particle as a centre, and surrounding it
by a circular wave with a radius equal to the distance between _m_ _n_
and _m'_ _n'_, the coalescence of all these little waves would build
up the large ridge _m'_ _n'_ exactly as we find it built up in nature.
Here, in fact, we resolve the wave-motion into its elements, and
having succeeded in doing this we shall have no great difficulty in
applying our knowledge to optical phenomena.

[Illustration: Fig. 17.]

Now let us return to our slit, and, for the sake of simplicity, we
will first consider the case of monochromatic light. Conceive a series
of waves of ether advancing from the first slit towards the second,
and finally filling the second slit. When each wave passes through the
latter it not only pursues its direct course to the retina, but
diverges right and left, tending to throw into motion the entire mass
of the ether behind the slit. In fact, as already explained, _every
point of the wave which fills the slit is itself a centre of a new
wave system which is transmitted in all directions through the ether
behind the slit_. This is the celebrated principle of Huyghens: we
have now to examine how these secondary waves act upon each other.

[Illustration: Fig. 18.]

Let us first regard the central band of the series. Let AP (fig. 18)
be the width of the aperture held before the eye, grossly exaggerated
of course, and let the dots across the aperture represent ether
particles, all in the same phase of vibration. Let E T represent a
portion of the retina. From O, in the centre of the slit, let a
perpendicular O R be imagined drawn upon the retina. The motion
communicated to the point R will then be the sum of all the motions
emanating in this direction from the ether particles in the slit.
Considering the extreme narrowness of the aperture, we may, without
sensible error, regard all points of the wave A P as equally distant
from R. No one of the partial waves lags sensibly behind the others:
hence, at R, and in its immediate neighbourhood, we have no sensible
reduction of the light by interference. This undiminished light
produces the brilliant central band of the series.

Let us now consider those waves which diverge laterally behind the
second slit. In this case the waves from the two sides of the slit
have, in order to converge upon the retina, to pass over unequal
distances. Let A P (fig. 19) represent, as before, the width of the
second slit. We have now to consider the action of the various parts
of the wave A P upon a point R' of the retina, not situated in the
line joining the two slits.

[Illustration: Fig. 19.]

Let us take the particular case in which the difference of path from
the two marginal points A, P, to the retina is a whole wave-length of
the red light; how must this difference affect the final illumination
of the retina?

Let us fix our attention upon the particular oblique line that passes
through the _centre_ O of the slit to the retina at R'. The difference
of path between the waves which pass along this line and those from
the two margins is, in the case here supposed, half a wavelength. Make
_e_ R' equal to P R', join P and _e_, and draw O _d_ parallel to P e.
A e is then the length of a wave of light, while A _d_ is half a
wave-length. Now the least reflection will make it clear that not only
is there discordance between the central and marginal waves, but that
every line of waves such as _x_ R', on the one side of O R', finds a
line _x_' R' upon the other side of O R', from which its path differs
by half an undulation--with which, therefore, it is in complete
discordance. The consequence is, that the light on the one side of the
central line will completely abolish the light on the other side of
that line, absolute darkness being the result of their coalescence.
The first dark interval of our series of bands is thus accounted for.
It is produced by an obliquity of direction which causes the paths of
the marginal waves to be _a whole wave-length_ different from each
other.

When the difference between the paths of the marginal waves is _half a
wave-length,_ a partial destruction of the light is effected. The
luminous intensity corresponding to this obliquity is a little less
than one-half--accurately 0.4--that of the undiffracted light. If the
paths of the marginal waves be three semi-undulations different from
each other, and if the whole beam be divided into three equal parts,
two of these parts will, for the reasons just given, completely
neutralize each other, the third only being effective. Corresponding,
therefore, to an obliquity which produces a difference of three
semi-undulations in the marginal waves, we have a luminous band, but
one of considerably less intensity than the undiffracted central band.

With a marginal difference of path of four semi-undulations we have a
second extinction of the entire beam, because here the beam can be
divided into four equal parts, every two of which quench each other.
A second space of absolute darkness will therefore correspond to the
obliquity producing this difference. In this way we might proceed
further, the general result being that, whenever the direction of
wave-motion is such as to produce a marginal difference of path of an
_even_ number of semi-undulations, we have complete extinction; while,
when the marginal difference is an _odd_ number of semi-undulations,
we have only partial extinction, a portion of the beam remaining as a
luminous band.

A moment's reflection will make it plain that the wider the slit the
less will be the obliquity of direction needed to produce the
necessary difference of path. With a wide slit, therefore, the bands,
as observed, will be closer together than with a narrow one. It is
also plain that the shorter the wave, the less will be the obliquity
required to produce the necessary retardation. The maxima and minima
of violet light must therefore fall nearer to the centre than the
maxima and minima of red light. The maxima and minima of the other
colours fall between these extremes. In this simple way the undulatory
theory completely accounts for the extraordinary appearance above
referred to.

When a slit and telescope are used, instead of the slit and naked eye,
the effects are magnified and rendered more brilliant. Looking,
moreover, through a properly adjusted telescope with a small circular
aperture in front of it, at a distant point of light, the point is
seen encircled by a series of coloured bands. If monochromatic light
be used, these bands are simply bright and dark, but with white light
the circles display iris-colours. If a slit be shortened so as to form
a square aperture, we have two series of spectra at right angles to
each other. The effects, indeed, are capable of endless variation by
varying the size, shape, and number of the apertures through which the
point of light is observed. Through two square apertures, with their
corners touching each other as at A, Schwerd observed the appearance
shown in fig. 20. Adding two others to them, as at B, he observed the
appearance represented in fig. 21. The position of every band of light
and shade in such figures has been calculated from theory by Fresnel,
Fraunhofer, Herschel, Schwerd, and others, and completely verified by
experiment. Your eyes could not tell you with greater certainty of the
existence of these bands than the theoretic calculation.

[Illustration: Fig. 20.]

The street-lamps at night, looked at through the meshes of a
handkerchief, show diffraction phenomena. The diffraction effects
obtained in looking through a bird's feathers are, as shown by
Schwerd, very brilliant. The iridescence of certain Alpine clouds is
also an effect of diffraction which may be imitated by the
spores of Lycopodium. When shaken over a glass plate these spores
cause a point of light, looked at through the dusted plate, to be
surrounded by coloured circles, which rise to actual splendour when
the light becomes intense. Shaken in the air the spores produce the
same effect. The diffraction phenomena obtained during the artificial
precipitation of clouds from the vapours of various liquids in an
intensely illuminated tube are, as I have elsewhere shewn, exceedingly
fine.

[Illustration: Fig. 21.]

One of the most interesting cases of diffraction by small particles
that ever came before me was that of an artist whose vision was
disturbed by vividly coloured circles. He was in great dread of losing
his sight; assigning as a cause of his increased fear that the circles
were becoming larger and the colours more vivid. I ascribed the
colours to minute particles in the humours of the eye, and ventured to
encourage him by the assurance that the increase of size and vividness
on the part of the circles indicated that the diffracting particles
were becoming _smaller_, and that they might finally be altogether
absorbed. The prediction was verified. It is needless to say one word
on the necessity of optical knowledge in the case of the practical
oculist.

Without breaking ground on the chromatic phenomena presented by
crystals, two other sources of colour may be mentioned here. By
interference in the earth's atmosphere, the light of a star, as shown
by Arago, is self-extinguished, the twinkling of the star and the
changes of colour which it undergoes being due to this cause. Looking
at such a star through an opera-glass, and shaking the glass so as to
cause the image of the star to pass rapidly over the retina, you
produce a row of coloured beads, the spaces between which correspond
to the periods of extinction. Fine scratches drawn upon glass or
polished metal reflect the waves of light from their sides; and some,
being reflected from the opposite sides of the same scratch, interfere
with and quench each other. But the obliquity of reflection which
extinguishes the shorter waves does not extinguish the longer ones,
hence the phenomena of colours. These are called the colours of
_striated surfaces_. They are beautifully illustrated by
mother-of-pearl. This shell is composed of exceedingly thin layers,
which, when cut across by the polishing of the shell, expose their
edges and furnish the necessary small and regular grooves. The most
conclusive proof that the colours are due to the mechanical state of
the surface is to be found in the fact, established by Brewster, that
by stamping the shell carefully upon black sealing-wax, we transfer
the grooves, and produce upon the wax the colours of mother-of-pearl.



LECTURE III.

  RELATION OF THEORIES TO EXPERIENCE
  ORIGIN OF THE NOTION OF THE ATTRACTION OF GRAVITATION
  NOTION OF POLARITY, HOW GENERATED
  ATOMIC POLARITY
  STRUCTURAL ARRANGEMENTS DUE TO POLARITY
  ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION
    TO THEIR ACTION UPON LIGHT
  NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE
  EXPERIMENTAL ILLUSTRATIONS
  CRYSTALLIZATION OF WATER
  EXPANSION BY HEAT AND BY COLD
  DEPORTMENT OF WATER CONSIDERED AND EXPLAINED
  BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA
  REFRACTION
  DOUBLE REFRACTION
  POLARIZATION
  ACTION OF TOURMALINE
  CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR
  POLARIZATION BY ORDINARY REFRACTION AND REFLECTION
  DEPOLARIZATION


§ 1. _Derivation of Theoretic Conceptions from Experience._

One of the objects of our last lecture, and that not the least
important, was to illustrate the manner in which scientific theories
are formed. They, in the first place, take their rise in the desire of
the mind to penetrate to the sources of phenomena. From its
infinitesimal beginnings, in ages long past, this desire has grown and
strengthened into an imperious demand of man's intellectual nature. It
long ago prompted Cæsar to say that he would exchange his victories
for a glimpse of the sources of the Nile; it wrought itself into the
atomic theories of Lucretius; it impelled Darwin to those daring
speculations which of late years have so agitated the public mind. But
in no case, while framing theories, does the imagination _create_ its
materials. It expands, diminishes, moulds, and refines, as the case
may be, materials derived from the world of fact and observation.

This is more evidently the case in a theory like that of light, where
the motions of a subsensible medium, the ether, are presented to the
mind. But no theory escapes the condition. Newton took care not to
encumber the idea of gravitation with unnecessary physical
conceptions; but we know that he indulged in them, though he did not
connect them with his theory. But even the theory, as it stands, did
not enter the mind as a revelation dissevered from the world of
experience. The germ of the conception that the sun and planets are
held together by a force of attraction is to be found in the fact that
a magnet had been previously seen to attract iron. The notion of
matter attracting matter came thus from without, not from within. In
our present lecture the magnetic force must serve as the portal into a
new domain; but in the first place we must master its elementary
phenomena.

The general facts of magnetism are most simply illustrated by a
magnetized bar of steel, commonly called a bar magnet. Placing such a
magnet upright upon a table, and bringing a magnetic needle near its
bottom, one end of the needle is observed to retreat from the magnet,
while the other as promptly approaches. The needle is held quivering
there by some invisible influence exerted upon it. Raising the needle
along the magnet, but still avoiding contact, the rapidity of its
oscillations decreases, because the force acting upon it becomes
weaker. At the centre the oscillations cease. Above the centre, the
end of the needle which had been previously drawn towards the magnet
retreats, and the opposite end approaches. As we ascend higher, the
oscillations become more violent, because the force becomes stronger.
At the upper end of the magnet, as at the lower, the force reaches a
maximum; but all the lower half of the magnet, from E to S (fig. 22),
attracts one end of the needle, while all the upper half, from E to N,
attracts the opposite end. This _doubleness_ of the magnetic force is
called _polarity_, and the points near the ends of the magnet in which
the forces seem concentrated are called its _poles_.

[Illustration: Fig. 22.]

What, then, will occur if we break this magnet in two at the centre E?
Shall we obtain two magnets, each with a single pole? No; each half is
in itself a perfect magnet, possessing two poles. This may be proved
by breaking something of less value than the magnet--the steel of a
lady's stays, for example, hardened and magnetized. It acts like the
magnet. When broken, each half acts like the whole; and when these
parts are again broken, we have still the perfect magnet, possessing,
as in the first instance, two poles. Push your breaking to its utmost
sensible limit--you cannot stop there. The bias derived from
observation will infallibly carry you beyond the bourne of the senses,
and compel you to regard this thing that we call magnetic polarity as
resident in the ultimate particles of the steel. You come to the
conclusion that each molecule of the magnet is endowed with this polar
force.

Like all other forces, this force of magnetism is amenable to
mechanical laws; and, knowing the direction and magnitude of the
force, we can predict its action. Placing a small magnetic needle near
a bar magnet, it takes a determinate position. That position might be
deduced theoretically from the mutual action of the poles. Moving the
needle round the magnet, for each point of the surrounding space there
is a definite direction of the needle and no other. A needle of iron
will answer as well as the magnetic needle; for the needle of iron is
magnetized by the magnet, and acts exactly like a steel needle
independently magnetized.

If we place two or more needles of iron near the magnet, the action
becomes more complex, for then the needles are not only acted on by
the magnet, but they act upon each other. And if we pass to smaller
masses of iron--to iron filings, for example--we find that they act
substantially as the needles, arranging themselves in definite forms,
in obedience to the magnetic action.

Placing a sheet of paper or glass over a bar magnet and showering iron
filings upon the paper, I notice a tendency of the filings to arrange
themselves in determinate lines. They cannot freely follow this
tendency, for they are hampered by the friction against the paper.
They are helped by tapping the paper; each tap releasing them for a
moment, and enabling them to follow their tendencies. But this is an
experiment which can only be seen by myself. To enable you all to see
it, I take a pair of small magnets and by a simple optical arrangement
throw the magnified images of the magnets upon the screen. Scattering
iron filings over the glass plate to which the small magnets are
attached, and tapping the plate, you see the arrangement of the iron
filings in those magnetic curves which have been so long familiar to
scientific men (fig. 23).

[Illustration: Fig. 23.

N is the nozzle of the lamp; M a plane mirror, reflecting the beam
upwards. At P the magnets and iron filings are placed; L is a lens
which forms an image of the magnets and filings; and R is a totally
reflecting prism, which casts the image G upon the screen.]

(By a very ingenious device, Professor Mayer, of Hoboken, has
succeeded in fixing and photographing the magnetic curves. I am
indebted to his kindness for the annexed beautiful illustration, fig.
24.)

The aspect of these curves so fascinated Faraday that the greater
portion of his intellectual life was devoted to pondering over them.
He invested the space through which they run with a kind of
materiality; and the probability is that the progress of science, by
connecting the phenomena of magnetism with the luminiferous ether,
will prove these 'lines of force,' as Faraday loved to call them, to
represent a condition of this mysterious substratum of all radiant
action.

It is not, however, the magnetic curves, as such, but their
relationship to theoretic conceptions, that we have now to consider.
By the action of the bar magnet upon the needle we obtain the notion
of a polar force; by the breaking of the strip of magnetized steel we
attain the notion that polarity can attach itself to the ultimate
particles of matter. The experiment with the iron filings introduces a
new idea into the mind; the idea, namely, of _structural arrangement_.
Every pair of filings possesses four poles, two of which are
attractive and two repulsive. The attractive poles approach, the
repulsive poles retreat; the consequence being a certain definite
arrangement of the particles with reference to each other.


§ 2. _Theory of Crystallization._

Now this idea of structure, as produced by polar force, opens a way
for the intellect into an entirely new region, and the reason you
are asked to accompany me into this region is, that our next inquiry
relates to the action of crystals upon light. Prior to speaking of
this action, I wish you to realise intellectually the process of
crystalline architecture. Look then into a granite quarry, and spend a
few minutes in examining the rock. It is not of perfectly uniform
texture. It is rather an agglomeration of pieces, which, on
examination, present curiously defined forms. You have there what
mineralogists call quartz, you have felspar, you have mica. In a
mineralogical cabinet, where these substances are preserved
separately, you will obtain some notion of their forms. You will see
there, also, specimens of beryl, topaz, emerald, tourmaline, heavy
spar, fluor-spar, Iceland spar--possibly a full-formed diamond, as it
quitted the hand of Nature, not yet having got into the hands of the
lapidary.

[Illustration: Fig. 24.]

These crystals, you will observe, are put together according to law;
they are not chance productions; and, if you care to examine them more
minutely, you will find their architecture capable of being to some
extent revealed. They often split in certain directions before a
knife-edge, exposing smooth and shining surfaces, which are called
planes of cleavage; and by following these planes you sometimes reach
an internal form, disguised beneath the external form of the crystal.
Ponder these beautiful edifices of a hidden builder. You cannot help
asking yourself how they were built; and familiar as you now are with
the notion of a polar force, and the ability of that force to produce
structural arrangement, your inevitable answer will be, that those
crystals are built by the play of polar forces with which their
molecules are endowed. In virtue of these forces, molecule lays
itself to molecule in a perfectly definite way, the final visible form
of the crystal depending upon this play of its ultimate particles.

Everywhere in Nature we observe this tendency to run into definite
forms, and nothing is easier than to give scope to this tendency by
artificial arrangements. Dissolve nitre in water, and allow the water
slowly to evaporate; the nitre remains and the solution soon becomes
so concentrated that the liquid condition can no longer be preserved.
The nitre-molecules approach each other, and come at length within the
range of their polar forces. They arrange themselves in obedience to
these forces, a minute crystal of nitre being at first produced. On
this crystal the molecules continue to deposit themselves from the
surrounding liquid. The crystal grows, and finally we have large
prisms of nitre, each of a perfectly definite shape. Alum crystallizes
with the utmost ease in this fashion. The resultant crystal is,
however, different in shape from that of nitre, because the poles of
the molecules are differently disposed. When they are _nursed_ with
proper care, crystals of these substances may be caused to grow to a
great size.

The condition of perfect crystallization is, that the crystallizing
force shall act with deliberation. There should be no hurry in its
operations; but every molecule ought to be permitted, without
disturbance from its neighbours, to exercise its own rights. If the
crystallization be too sudden, the regularity disappears. Water may be
saturated with sulphate of soda, dissolved when the water is hot, and
afterwards permitted to cool. When cold the solution is
supersaturated; that is to say, more solid matter is contained in it
than corresponds to its temperature. Still the molecules show no sign
of building themselves together.

This is a very remarkable, though a very common fact. The molecules in
the centre of the liquid are so hampered by the action of their
neighbours that freedom to follow their own tendencies is denied to
them. Fix your mind's eye upon a molecule within the mass. It wishes
to unite with its neighbour to the right, but it wishes equally to
unite with its neighbour to the left; the one tendency neutralizes the
other and it unites with neither. But, if a crystal of sulphate of
soda be dropped into the solution, the molecular indecision ceases. On
the crystal the adjacent molecules will immediately precipitate
themselves; on these again others will be precipitated, and this act
of precipitation will continue from the top of the flask to the
bottom, until the solution has, as far as possible, assumed the solid
form. The crystals here produced are small, and confusedly arranged.
The process has been too hasty to admit of the pure and orderly action
of the crystallizing force. It typifies the state of a nation in which
natural and healthy change is resisted, until society becomes, as it
were, supersaturated with the desire for change, the change being then
effected through confusion and revolution.

Let me illustrate the action of the crystallizing force by two
examples of it: Nitre might be employed, but another well-known
substance enables me to make the experiment in a better form. The
substance is common sal-ammoniac, or chloride of ammonium, dissolved
in water. Cleansing perfectly a glass plate, the solution of the
chloride is poured over the glass, to which when the plate is set on
edge, a thin film of the liquid adheres. Warming the glass slightly,
evaporation is promoted, but by evaporation the water only is removed.
The plate is then placed in a solar microscope, and an image of the
film is thrown upon a white screen. The warmth of the illuminating
beam adds itself to that already imparted to the glass plate, so that
after a moment or two the dissolved salt can no longer exist in the
liquid condition. Molecule then closes with molecule, and you have a
most impressive display of crystallizing energy overspreading the
whole screen. You may produce something similar if you breathe upon
the frost ferns which overspread your window-panes in winter, and then
observe through a pocket lens the subsequent recongelation of the
film.

In this case the crystallizing force is hampered by the adhesion of
the film to the glass; nevertheless, the play of power is strikingly
beautiful. Sometimes the crystals start from the edge of the film and
run through it from that edge; for, the crystallization being once
started, the molecules throw themselves by preference on the crystals
already formed. Sometimes the crystals start from definite nuclei in
the centre of the film, every small crystalline particle which rests
in the film furnishing a starting-point. Throughout the process you
notice one feature which is perfectly unalterable, and that is,
angular magnitude. The spiculæ branch from the trunk, and from these
branches others shoot; but the angles enclosed by the spiculæ are
unalterable. In like manner you may find alum-crystals,
quartz-crystals, and all other crystals, distorted in shape. They are
thus far at the mercy of the accidents of crystallization; but in one
particular they assert their superiority over all such
accidents--_angular magnitude_ is always rigidly preserved.

My second example of the action of crystallizing force is this: By
sending a voltaic current through a liquid, you know that we decompose
the liquid, and if it contains a metal, we liberate this metal by
electrolysis. This small cell contains a solution of acetate of lead,
which is chosen for our present purpose, because lead lends itself
freely to this crystallizing power. Into the cell are dipped two very
thin platinum wires, and these are connected by other wires with a
small voltaic battery. On sending the voltaic current through the
solution, the lead will be slowly severed from the atoms with which it
is now combined; it will be liberated upon one of the wires, and at
the moment of its liberation it will obey the polar forces of its
atoms, and produce crystalline forms of exquisite beauty. They are now
before you, sprouting like ferns from the wire, appearing indeed like
vegetable growths rendered so rapid as to be plainly visible to the
naked eye. On reversing the current, these wonderful lead-fronds will
dissolve, while from the other wire filaments of lead dart through the
liquid. In a moment or two the growth of the lead-trees recommences,
but they now cover the other wire.

In the process of crystallization, Nature first reveals herself as a
builder. Where do her operations stop? Does she continue by the play
of the same forces to form the vegetable, and afterwards the animal?
Whatever the answer to these questions may be, trust me that the
notions of the coming generations regarding this mysterious thing,
which some have called 'brute matter,' will be very different from
those of the generations past.

There is hardly a more beautiful and instructive example of this play
of molecular force than that furnished by water. You have seen the
exquisite fern-like forms produced by the crystallization of a film of
water on a cold window-pane.[15] You have also probably noticed the
beautiful rosettes tied together by the crystallizing force during the
descent of a snow-shower on a very calm day. The slopes and summits of
the Alps are loaded in winter with these blossoms of the frost. They
vary infinitely in detail of beauty, but the same angular magnitude is
preserved throughout: an inflexible power binding spears and spiculæ
to the angle of 60 degrees.

The common ice of our lakes is also ruled in its formation by the same
angle. You may sometimes see in freezing water small crystals of
stellar shapes, each star consisting of six rays, with this angle of
60° between every two of them. This structure may be revealed in
ordinary ice. In a sunbeam, or, failing that, in our electric beam, we
have an instrument delicate enough to unlock the frozen molecules,
without disturbing the order of their architecture. Cutting from
clear, sound, regularly frozen ice, a slab parallel to the planes of
freezing, and sending a sunbeam through such a slab, it liquefies
internally at special points, round each point a six-petalled liquid
flower of exquisite beauty being formed. Crowds of such flowers are
thus produced. From an ice-house we sometimes take blocks of ice
presenting misty spaces in the otherwise continuous mass; and when we
inquire into the cause of this mistiness, we find it to be due to
myriads of small six-petalled flowers, into which the ice has been
resolved by the mere heat of conduction.

A moment's further devotion to the crystallization of water will be
well repaid; for the sum of qualities which renders this substance
fitted to play its part in Nature may well excite wonder and stimulate
thought. Like almost all other substances, water is expanded by heat
and contracted by cold. Let this expansion and contraction be first
illustrated:--

A small flask is filled with coloured water, and stopped with a cork.
Through the cork passes a glass tube water-tight, the liquid standing
at a certain height in the tube. The flask and its tube resemble the
bulb and stem of a thermometer. Applying the heat of a spirit-lamp,
the water rises in the tube, and finally trickles over the top.
Expansion by heat is thus illustrated.

Removing the lamp and piling a freezing mixture round the flask, the
liquid column falls, thus showing the contraction of the water by the
cold. But let the freezing mixture continue to act: the falling of the
column continues to a certain point; it then ceases. The top of the
column remains stationary for some seconds, and afterwards begins to
rise. The contraction has ceased, and _expansion by cold_ sets in. Let
the expansion continue till the liquid trickles a second time over the
top of the tube. The freezing mixture has here produced to all
appearance the same effect as the flame. In the case of water,
contraction by cold ceases, and expansion by cold sets in at the
definite temperature of 39° Fahr. Crystallization has virtually here
commenced, the molecules preparing themselves for the subsequent act
of solidification, which occurs at 32°, and in which the expansion
suddenly culminates. In virtue of this expansion, ice, as you know, is
lighter than water in the proportion of 8 to 9.[16]

A molecular problem of great interest is here involved, and I wish now
to place before you, for the satisfaction of your minds, a possible
solution of the problem:--

Consider, then, the ideal case of a number of magnets deprived of
weight, but retaining their polar forces. If we had a mobile liquid of
the specific gravity of steel, we might, by making the magnets float
in it, realize this state of things, for in such a liquid the magnets
would neither sink nor swim. Now, the principle of gravitation
enunciated by Newton is that every particle of matter, of every kind,
attracts every other particle with a force varying inversely as the
square of the distance. In virtue of the attraction of gravity, then,
the magnets, if perfectly free to move, would slowly approach each
other.

But besides the unpolar force of gravity, which belongs to matter in
general, the magnets are endowed with the polar force of magnetism.
For a time, however, the polar forces do not come sensibly into play.
In this condition the magnets resemble our water-molecules at the
temperature say of 50°. But the magnets come at length sufficiently
near each other to enable their poles to interact. From this point the
action ceases to be solely a general attraction of the masses.
Attractions of special points of the masses and repulsions of other
points now come into play; and it is easy to see that the
rearrangement of the magnets consequent upon the introduction of these
new forces may be such as to require a greater amount of room. This, I
take it, is the case with our water-molecules. Like our ideal magnets,
they approach each other for a time _as wholes_. Previous to reaching
the temperature 39° Fahr., the polar forces had doubtless begun to
act, but it is at this temperature that their claim to more room
exactly balances the contraction due to cold. At lower temperatures,
as regards change of volume, the polar forces predominate. But they
carry on a struggle with the force of contraction until the freezing
temperature is attained. The molecules then close up to form solid
crystals, a considerable augmentation of volume being the immediate
consequence.


§ 3. _Ordinary Refraction of Light explained by the Wave Theory_.

We have now to exhibit the bearings of this act of crystallization
upon optical phenomena. According to the undulatory theory, the
velocity of light in water and glass is less than in air. Consider,
then, a small portion of a wave issuing from a point of light so
distant that the minute area may be regarded as practically plane.
Moving vertically downwards, and impinging on a horizontal surface of
glass or water, the wave would go through the medium without change of
direction. As, however, the velocity in glass or water is less than
the velocity in air, the wave would be retarded on passing into the
denser medium.

[Illustration: Fig. 25.]

But suppose the wave, before reaching the glass, to be _oblique_ to
the surface; that end of the wave which first reaches the medium will
be the first retarded by it, the other portions as they enter the
glass being retarded in succession. It is easy to see that this
retardation of the one end of the wave must cause it to swing round
and change its front, so that when the wave has fully entered the
glass its course is oblique to its original direction. According to
the undulatory theory, light is thus _refracted_.

With these considerations to guide us, let us follow the course of a
beam of monochromatic light through our glass prism. The velocity in
air is to its velocity in glass as 3: 2. Let A B C (fig. 25) be the
section of our prism, and _a_ _b_ the section of a plane wave
approaching it in the direction of the arrow. When it reaches _c_ _d_,
one end of the wave is on the point of entering the glass. Following
it still further, it is obvious that while the portion of the wave
still in the air passes over the distance _c_ _e_, the wave in the
glass will have passed over only two-thirds of this distance, or _d_
_f_. The line _e_ _f_ now marks the front of the wave. Immersed wholly
in the glass it pursues its way to _g_ _h_, where the end _g_ of the
wave is on the point of escaping into the air. During the time
required by the end _h_ of the wave to pass over the distance _h_ _k_
to the surface of the prism, the other end _g_, moving more rapidly,
will have reached the point _i_. The wave, therefore, has again
changed its front, so that after its emergence from the prism it will
pass on to _l_ _m_, and subsequently in the direction of the arrow.
The refraction of the beam is thus completely accounted for; and it
is, moreover, based upon actual experiment, which proves that the
ratio of the velocity of light in glass to its velocity in air is that
here mentioned. It is plain that if the change of velocity on entering
the glass were greater, the refraction also would be greater.


§ 4. _Double Refraction of Light explained by the Wave Theory_.

The two elements of rapidity of propagation, both of sound and light,
in any substance whatever, are _elasticity_ and _density_, the speed
increasing with the former and diminishing with the latter. The
enormous velocity of light in stellar space is attainable because the
ether is at the same time of infinitesimal density and of enormous
elasticity. Now the ether surrounds the atoms of all bodies, but it is
not independent of them. In ponderable matter it acts as if its
density were increased without a proportionate increase of elasticity;
and this accounts for the diminished velocity of light in refracting
bodies. We here reach a point of cardinal importance. In virtue of the
crystalline architecture that we have been considering, the ether in
many crystals possesses different densities, and different
elasticities, in different directions; the consequence is, that in
such crystals light is transmitted with different velocities. And as
refraction depends wholly upon the change of velocity on entering the
refracting medium, being greatest where the change of velocity is
greatest, we have in many crystals two different refractions. By such
crystals a beam of light is divided into two. This effect is called
_double refraction_.

In ordinary water, for example, there is nothing in the grouping of
the molecules to interfere with the perfect homogeneity of the ether;
but, when water crystallizes to ice, the case is different. In a plate
of ice the elasticity of the ether in a direction perpendicular to the
surface of freezing is different from what it is parallel to the
surface of freezing; ice is, therefore, a double refracting substance.
Double refraction is displayed in a particularly impressive manner by
Iceland spar, which is crystallized carbonate of lime. The difference
of ethereal density in two directions in this crystal is very great,
the separation of the beam into the two halves being, therefore,
particularly striking.

I am unwilling to quit this subject before raising it to unmistakable
clearness in your minds. The vibrations of light being transversal,
the elasticity concerned in the propagation of any ray is the
elasticity at right angles to the direction of propagation. In Iceland
spar there is one direction round which the crystalline molecules are
symmetrically built. This direction is called the axis of the crystal.
In consequence of this symmetry the elasticity is the same in all
directions perpendicular to the axis, and hence a ray transmitted
along the axis suffers no double refraction. But the elasticity along
the axis is greater than the elasticity at right angles to it.
Consider, then, a system of waves crossing the crystal in a direction
perpendicular to the axis. Two directions of vibration are open to
such waves: the ether particles can vibrate parallel to the axis or
perpendicular to it. _They do both_, and hence immediately divide
themselves into two systems propagated with different velocities.
Double refraction is the necessary consequence.

[Illustration: Fig. 26.]

By means of Iceland spar cut in the proper direction, double
refraction is capable of easy illustration. Causing the beam which
builds the image of our carbon-points to pass through the spar, the
single image is instantly divided into two. Projecting (by the lens E,
fig. 26) an image of the aperture (L) through which the light issues
from the electric lamp, and introducing the spar (P), two luminous
disks (E O) appear immediately upon the screen instead of one.

The two beams into which the spar divides the single incident-beam
have been subjected to the closest examination. They do not behave
alike. One of them obeys the ordinary law of refraction discovered by
Snell, and is, therefore, called the _ordinary ray_: its index of
refraction is 1.654. The other does not obey this law. Its index of
refraction, for example, is not constant, but varies from a maximum of
1.654 to a minimum of 1.483; nor in this case do the incident and
refracted rays always lie in the same plane. It is, therefore, called
the _extraordinary ray_. In calc-spar, as just stated, the ordinary
ray is the most refracted. One consequence of this merits a passing
notice. Pour water and bisulphide of carbon into two cups of the same
depth; the cup that contains the more strongly refracting liquid will
appear shallower than the other. Place a piece of Iceland spar over a
dot of ink; two dots are seen, the one appearing nearer than the other
to the eye. The nearest dot belongs to the most strongly refracted
ray, exactly as the nearest cup-bottom belongs to the most highly
refracting liquid. When you turn the spar round, the extraordinary
image of the dot rotates round the ordinary one, which remains fixed.
This is also the deportment of our two disks upon the screen.


§ 5. _Polarization of Light explained by the Wave Theory_.

The double refraction of Iceland spar was first treated in a work
published by Erasmus Bartholinus, in 1669. Huyghens sought to account
for this phenomenon on the principles of the wave theory, and he
succeeded in doing so. He, moreover, made highly important
observations on the distinctive character of the two beams transmitted
by the spar, admitting, with resigned candour, that he had not solved
the difficulty, and leaving the solution to future times. Newton,
reflecting on the observations of Huyghens, came to the conclusion
that each of the beams transmitted by Iceland spar had two sides; and
from the analogy of this _two-sidedness_ with the _two-endedness_ of a
magnet, wherein consists its polarity, the two beams came subsequently
to be described as _polarized_.

We may begin the study of the polarization of light, with ease and
profit, by means of a crystal of tourmaline. But we must start with a
clear conception of an ordinary beam of light. It has been already
explained that the vibrations of the individual ether-particles are
executed _across_ the line of propagation. In the case of ordinary
light we are to figure the ether-particles as vibrating in all
directions, or azimuths, as it is sometimes expressed, across this
line.

Now, in the case of a plate of tourmaline cut parallel to the axis of
the crystal, a beam of light incident upon the plate is divided into
two, the one vibrating parallel to the axis of the crystal, the other
at right angles to the axis. The grouping of the molecules, and of
the ether associated with the molecules, reduces all the vibrations
incident upon the crystal to these two directions. One of these beams,
namely, that whose vibrations are perpendicular to the axis, is
quenched with exceeding rapidity by the tourmaline. To such vibrations
many specimens of the crystal are highly opaque; so that, after having
passed through a very small thickness of the tourmaline, the light
emerges with all its vibrations reduced to a single plane. In this
condition it is what we call _plane polarized light_.

[Illustration: Fig. 27.]

[Illustration: Fig. 28.]

A moment's reflection will show that, if what is here stated be
correct, on placing a second plate of tourmaline with its axis
parallel to the first, the light will pass through both; but that, if
the axes be crossed, the light that passes through the one plate will
be quenched by the other, a total interception of the light being the
consequence. Let us test this conclusion by experiment. The image of a
plate of tourmaline (_t_ _t_, fig. 27) is now before you. I place
parallel to it another plate (_t'_ _t'_): the green of the crystal is
a little deepened, nothing more; this agrees with our conclusion. By
means of an endless screw, I now turn one of the crystals gradually
round, and you observe that as long as the two plates are oblique to
each other, a certain portion of light gets through; but that when
they are at right angles to each other, the space common to both is a
space of darkness (fig. 28). Our conclusion, arrived at prior to
experiment, is thus verified.

Let us now return to a single plate; and here let me say that it is on
the green light transmitted by the tourmaline that you are to fix your
attention. We have to illustrate the two-sidedness of that green
light, in contrast to the all-sidedness of ordinary light. The white
light surrounding the green image, being ordinary light, is reflected
by a plane glass mirror in all directions; the green light, on the
contrary, is not so reflected. The image of the tourmaline is now
horizontal; reflected upwards, it is still green; reflected sideways,
the image is reduced to blackness, because of the incompetency of the
green light to be reflected in this direction. Making the plate of
tourmaline vertical, and reflecting it as before, it is the light of
the upper image that is quenched; the side image now shows the green.
This is a result of the greatest significance. If the vibrations of
light were longitudinal, like those of sound, you could have no action
of this kind; and this very action compels us to assume that the
vibrations are transversal. Picture the thing clearly. In the one case
the mirror receives, as it were, the impact of the _edges_ of the
waves, the green light being then quenched. In the other case the
_sides_ of the waves strike the mirror, and the green light is
reflected. To render the extinction complete, the light must be
received upon the mirror at a special angle. What this angle is we
shall learn presently.

The quality of two-sidedness conferred upon light by bi-refracting
crystals may also be conferred upon it by ordinary reflection. Malus
made this discovery in 1808, while looking through Iceland spar at the
light of the sun reflected from the windows of the Luxembourg palace
in Paris. I receive upon a plate of window-glass the beam from our
lamp; a great portion of the light reflected from the glass is
polarized. The vibrations of this reflected beam are executed, for the
most part, parallel to the surface of the glass, and when the glass is
held so that the beam shall make an angle of 58° with the
perpendicular to the glass, the _whole_ of the reflected beam is
polarized. It was at this angle that the image of the tourmaline was
completely quenched in our former experiment. It is called _the
polarizing angle_.

Sir David Brewster proved the angle of polarization of a medium to be
that particular angle at which the refracted and reflected rays
inclose a right angle.[17] The polarizing angle augments with the
index of refraction. For water it is 52½°; for glass, as already
stated, 58°; while for diamond it is 68°.

And now let us try to make substantially the experiment of Malus. The
beam from the lamp is received at the proper angle upon a plate of
glass and reflected through the spar. Instead of two images, you see
but one. So that the light, when polarized, as it now is by
reflection, can only get through the spar in one direction, and
consequently can produce but one image. Why is this? In the Iceland
spar as in the tourmaline, all the vibrations of the ordinary light
are reduced to two planes at right angles to each other; but, unlike
the tourmaline, both beams are transmitted with equal facility by the
spar. The two beams, in short, emergent from the spar, are polarized,
their directions of vibration being at right angles to each other.
When, therefore, the light is first polarized by reflection, the
direction of vibration in the spar which coincides with the direction
of vibration of the polarized beam, transmits the beam, and that
direction only. Only one image, therefore, is possible under the
conditions.

You will now observe that such logic as connects our experiments is
simply a transcript of the logic of Nature. On the screen before you
are two disks of light produced by the double refraction of Iceland
spar. They are, as you know, two images of the aperture through which
the light issues from the camera. Placing the tourmaline in front of
the aperture, two images of the crystal will also be obtained; but now
let us reason out beforehand what is to be expected from this
experiment. The light emergent from the tourmaline is polarized.
Placing the crystal with its axis horizontal, the vibrations of its
transmitted light will be horizontal. Now the spar, as already stated,
has two directions of vibration, one of which at the present moment
is vertical, the other horizontal. What are we to conclude? That the
green light will be transmitted along the latter, which is parallel to
the axis of the tourmaline, and not along the former, which is
perpendicular to that axis. Hence we may infer that one image of the
tourmaline will show the ordinary green light of the crystal, while
the other image will be black. Tested by experiment, our reasoning is
verified to the letter (fig. 29).

[Illustration: Fig. 29.]

[Illustration; Fig. 30.]

Let us push our test still further. By means of an endless screw, the
crystal can be turned ninety degrees round. The black image, as I
turn, becomes gradually brighter, and the bright one gradually darker;
at an angle of forty-five degrees both images are equally bright (fig.
30); while, when ninety degrees have been obtained, the axis of the
crystal being then vertical, the bright and black images have changed
places, exactly as reasoning would have led us to suppose (fig. 31).

[Illustration: Fig. 31.]

[Illustration: Fig. 32.]

Considering what has been already said (p. 114) regarding the
reflection of light polarized by transmission through tourmaline, you
will readily foresee what must occur when we receive upon a plate of
glass, held at the polarizing angle, the two beams emergent from our
prism of Iceland spar. I cause both beams to pass side by side through
the air, catch them on a glass plate, and seek to reflect them
upwards. At the polarizing angle one beam only is capable of being
thus reflected. Which? Your prompt answer will be, The beam whose
vibrations are horizontal (fig. 32). I now turn the glass plate and
try to reflect both beams laterally. One of them only is reflected;
that, namely, the vibrations of which are vertical (fig. 33). It is
plain that, by means either of the tourmaline or the reflecting glass,
we can determine in a moment the direction of vibration in any
polarized beam.

[Illustration: Fig. 33.]

As already stated, the whole of a beam of ordinary light reflected
from glass at the polarizing angle is polarized; a word must now be
added regarding the far larger portion of the light which is
_transmitted_ by the glass. The transmitted beam contains a quantity
of polarized light equal to the reflected beam; but this is only a
fraction of the whole transmitted light. By taking two plates of glass
instead of one, we augment the quantity of the transmitted polarized
light; and by taking _a bundle_ of plates, we so increase the quantity
as to render the transmitted beam, for all practical purposes,
_perfectly_ polarized. Indeed, bundles of glass plates are often
employed as a means of furnishing polarized light. It is important to
note that the plane of vibration of this transmitted light is at right
angles to that of the reflected light.

One word more. When the tourmalines are crossed, the space where they
cross each other is black. But we have seen that the least obliquity
on the part of the crystals permits light to get through both. Now
suppose, when the two plates are crossed, that we interpose a third
plate of tourmaline between them, with its axis oblique to both. A
portion of the light transmitted by the first plate will get through
this intermediate one. But, after it has got through, _its plane of
vibration is changed_: it is no longer perpendicular to the axis of
the crystal in front. Hence it will, in part, get through that
crystal. Thus, by pure reasoning, we infer that the interposition of a
third plate of tourmaline will in part abolish the darkness produced
by the perpendicular crossing of the other two plates. I have not a
third plate of tourmaline; but the talc or mica which you employ in
your stoves is a more convenient substance, which acts in the same
way. Between the crossed tourmalines, I introduce a film of this
crystal with its axis oblique to theirs. You see the edge of the film
slowly descending, and, as it descends, light takes the place of
darkness. The darkness, in fact, seems scraped away, as if it were
something material. This effect has been called, naturally but
improperly, _depolarization_. Its proper meaning will be disclosed in
our next lecture.

These experiments and reasonings, if only thoroughly studied and
understood, will form a solid groundwork for the analysis of the
splendid optical phenomena next to be considered.



LECTURE IV.

  CHROMATIC PHENOMENA PRODUCED BY CRYSTALS IN POLARIZED LIGHT
  THE NICOL PRISM
  POLARIZER AND ANALYZER
  ACTION OF THICK AND THIN PLATES OF SELENITE
  COLOURS DEPENDENT ON THICKNESS
  RESOLUTION OF POLARIZED BEAM INTO TWO OTHERS BY THE SELENITE
  ONE OF THEM MORE RETARDED THAN THE OTHER
  RECOMPOUNDING OF THE TWO SYSTEMS OF WAVES BY THE ANALYZER
  INTERFERENCE THUS RENDERED POSSIBLE
  CONSEQUENT PRODUCTION OF COLOURS
  ACTION OF BODIES MECHANICALLY STRAINED OR PRESSED
  ACTION OF SONOROUS VIBRATIONS
  ACTION OF GLASS STRAINED OR PRESSED BY HEAT
  CIRCULAR POLARIZATION
  CHROMATIC PHENOMENA PRODUCED BY QUARTZ
  THE MAGNETIZATION OF LIGHT
  RINGS SURROUNDING THE AXES OF CRYSTALS
  BIAXAL AND UNIAXAL CRYSTALS
  GRASP OF THE UNDULATORY THEORY
  THE COLOUR AND POLARIZATION OF SKY-LIGHT
  GENERATION OF ARTIFICIAL SKIES.


§ 1. _Action of Crystals on Polarized Light: the Nicol Prism._

We have this evening to examine and illustrate the chromatic phenomena
produced by the action of crystals, and double-refracting bodies
generally, upon polarized light, and to apply the Undulatory Theory to
their elucidation. For a long time investigators were compelled to
employ plates of tourmaline for this purpose, and the progress they
made with so defective a means of inquiry is astonishing. But these
men had their hearts in their work, and were on this account enabled
to extract great results from small instrumental appliances. For our
present purpose we need far larger apparatus; and, happily, in these
later times this need has been to a great extent satisfied. We have
seen and examined the two beams emergent from Iceland spar, and have
proved them to be polarized. If, at the sacrifice of half the light,
we could abolish one of these, the other would place at our disposal a
beam of polarized light, incomparably stronger than any attainable
from tourmaline.

The beams, as you know, are refracted differently, and from this, as
made plain in §4, Lecture I., we are able to infer that the one may be
totally reflected, when the other is not. An able optician, named
Nicol, cut a crystal of Iceland spar in two halves in a certain
direction. He polished the severed surfaces, and reunited them by
Canada balsam, the surface of union being so inclined to the beam
traversing the spar that the ordinary ray, which is the most highly
refracted, was totally reflected by the balsam, while the
extraordinary ray was permitted to pass on.

Let _b x, c y_ (fig. 34) represent the section of an elongated rhomb
of Iceland spar cloven from the crystal. Let this rhomb be cut along
the plane _b c_; and the two severed surfaces, after having been
polished, reunited by Canada balsam. We learned, in our first lecture,
that total reflection only takes place when a ray seeks to escape from
a more refracting to a less refracting medium, and that it always,
under these circumstances, takes place when the obliquity is
sufficient. Now the refractive index of Iceland spar is, for the
extraordinary ray less, and for the ordinary greater, than for Canada
balsam. Hence, in passing from the spar to the balsam, the
extraordinary ray passes from a less refracting to a more refracting
medium, where total reflection cannot occur; while the ordinary ray
passes from a more refracting to a less refracting medium, where
total reflection can occur. The requisite obliquity is secured by
making the rhomb of such a length that the plane of which _b c_ is the
section shall be perpendicular, or nearly so, to the two end surfaces
of the rhomb _b x, c y_.

[Illustration: Fig. 34.]

The invention of the Nicol prism was a great step in practical optics,
and quite recently such prisms have been constructed of a size and
purity which enable audiences like the present to witness the
chromatic phenomena of polarized light to a degree altogether
unattainable a short time ago.

(The two prisms employed in these experiments were lent to me by my
lamented friend Mr. William Spottiswoode, and they were manufactured
by Mr. Ahrens, an optician of consummate skill.)


§ 2. _Colours of Films of Selenite in Polarized Light_.

Two Nicol prisms play the same part as the two plates of tourmaline.
Placed with their directions of vibration parallel, the light passes
through both; while when these directions are crossed the light is
quenched. Introducing a film of mica between the prisms, the light, as
in the case of the tourmaline, is restored. But notice, when the film
of mica is _thin_ you have sometimes not only light, but _coloured_
light. Our work for some time to come will consist of the examination
of such colours. With this view, I will take a representative crystal,
one easily dealt with, because it cleaves with great facility--the
crystal gypsum, or selenite, which is crystallized sulphate of lime.
Between the crossed Nicols I place a thick plate of this crystal; like
the mica, it restores the light, but it produces no colour. With my
penknife I take a thin splinter from the crystal and place it between
the prisms; the image of the splinter glows with the richest colours.
Turning the prism in front, these colours gradually fade and
disappear, but, by continuing the rotation until the vibrating
sections of the prisms are parallel to each other, vivid colours again
arise, but these colours are complementary to the former ones.

Some patches of the splinter appear of one colour, some of another.
These differences are due to the different thicknesses of the film. As
in the case of Hooke's thin plates, if the thickness be uniform the
colour is uniform. Here, for instance, is a stellar shape, every
lozenge of the star being a film of gypsum of uniform thickness: each
lozenge, you observe, shows a brilliant and uniform colour. It is
easy, by shaping our films so as to represent flowers or other
objects, to exhibit such objects in hues unattainable by art. Here,
for example, is a specimen of heart's-ease, the colours of which you
might safely defy the artist to reproduce. By turning the front Nicol
90 degrees round, we pass through a colourless phase to a series of
colours complementary to the former ones. This change is still more
strikingly represented by a rose-tree, which is now presented in its
natural hues--a red flower and green leaves; turning the prism 90
degrees round, we obtain a green flower and red leaves. All these
wonderful chromatic effects have definite mechanical causes in the
motions of the ether. The principle of interference duly applied and
interpreted explains them all.


§ 3. _Colours of Crystals in Polarized Light explained by the
Undulatory Theory_.

By this time you have learned that the word 'light' may be used in two
different senses: it may mean the impression made upon consciousness,
or it may mean the physical cause of the impression. It is with this
cause that we have to occupy ourselves at present. The luminiferous
ether is a substance which fills all space, and surrounds the atoms
and molecules of bodies. To this inter-stellar and inter-atomic medium
definite mechanical properties are ascribed, and we deal with it in
our reasonings and calculations as a body possessed of these
properties. In mechanics we have the composition and resolution of
forces and of motions, extending to the composition and resolution of
_vibrations_. We treat the luminiferous ether on mechanical
principles, and, from the composition and resolution of its
vibrations we deduce all the phenomena displayed by crystals in
polarized light.

[Illustration: Fig. 35.]

Let us take, as an example, the crystal of tourmaline, with which we
are now so familiar. Let a vibration cross this crystal oblique to its
axis. Experiment has assured us that a portion of the light will pass
through. The quantity which passes we determine in this way. Let A B
(fig. 35) be the axis of the tourmaline, and let _a_ _b_ represent the
amplitude of an oblique ethereal vibration before it reaches A B. From
_a_ and _b_ let the two perpendiculars _a_ _c_ and _b_ _d_ be drawn
upon the axis: then _c_ _d_ will be the amplitude of the transmitted
vibration.

I shall immediately ask you to follow me while I endeavour to explain
the effects observed when a film of gypsum is placed between the two
Nicol prisms. But, prior to this, it will be desirable to establish
still further the analogy between the action of the prisms and that of
the two plates of tourmaline. The magnified images of these plates,
with their axes at right-angles to each other, are now before you.
Introducing between them a film of selenite, you observe that by
turning the film round it may be placed in a position where it has no
power to abolish the darkness of the superposed portions of the
tourmalines. Why is this? The answer is, that in the gypsum there are
two directions, at right angles to each other, in which alone
vibrations can take place, and that in our present experiment one of
these directions is parallel to one of the axes of the tourmaline, and
the other parallel to the other axis. When this is the case, the film
exercises no sensible action upon the light. But now I turn the film
so as to render its directions of vibration _oblique_ to the two
tourmaline axes; then, you see it exercises the power, demonstrated in
the last lecture, of partially restoring the light.

[Illustration: Fig. 36.]

Let us now mount our Nicol prisms, and cross them as we crossed the
tourmaline. Introducing our film of gypsum between them, you notice
that in one particular position the film has no power whatever over
the field of view. But, when the film is turned a little way round,
the light passes. We have now to understand the mechanism by which
this is effected.

First, then, we have a prism which receives the light from the
electric lamp, and which is called the _polarizer_. Then we have the
plate of gypsum (supposed to be placed at S, fig. 36), and then the
prism in front, which is called the _analyzer_. On its emergence from
the first prism, the light is polarized; and, in the particular case
now before us, its vibrations are executed in a horizontal plane. We
have to examine what occurs when the two directions of vibration in
the interposed gypsum are oblique to the horizon. Draw a rectangular
cross (A B, C D, fig. 37) to represent these two directions. Draw a
line (_a_ _b_) to represent the amplitude of the horizontal vibration
on the emergence of the light from the first Nicol. Let fall from each
end of this line two perpendiculars (_a_ _c_, _a_ _f_, _b_ _d_, _b_
_e_) on the two arms of the cross; then the distances (_c_ _d_, _e_
_f_) between the feet of these perpendiculars represent the amplitudes
of two rectangular vibrations, which are the _components_ of the first
single vibration. Thus the polarized ray, when it enters the gypsum,
is resolved into its two equivalents, which vibrate at right angles to
each other.

[Illustration; Fig. 37.]

In one of these two rectangular directions the ether within the gypsum
is more sluggish than in the other; and, as a consequence, the waves
that follow this direction are more retarded than the others. In both
cases the undulations are shortened when they enter the gypsum, but
in the one case they are more shortened than in the other. You can
readily imagine that in this way the one system of waves may get half
a wave-length, or indeed any number of half wavelengths, in advance of
the other. The possibility of interference here at once flashes upon
the mind. A little consideration, however, will render it evident
that, as long as the vibrations are executed at right angles to each
other, they cannot quench each other, no matter what the retardation
may be. This brings us at once to the part played by the analyzer. Its
sole function is to recompound the two vibrations emergent from the
gypsum. It reduces them to a single plane, where, if one of them be
retarded by the proper amount, extinction will occur.

But here, as in the case of thin films, the different lengths of the
waves of light come into play. Red will require a greater thickness to
produce the retardation necessary for extinction than blue;
consequently when the longer waves have been withdrawn by
interference, the shorter ones remain, the film of gypsum shining with
the colours which the short waves confer. Conversely, when the shorter
waves have been withdrawn, the thickness is such that the longer waves
remain. An elementary consideration suffices to show, that when the
directions of vibration of the prisms and the gypsum enclose an angle
of forty-five degrees, the colours are at their maximum brilliancy.
When the film is turned from this direction, the colours gradually
fade, until, at the point where the directions of vibration in plate
and prisms are parallel, they disappear altogether.

(The best way of obtaining a knowledge of these phenomena is to
construct a model of thin wood or pasteboard, representing the plate
of gypsum, its planes of vibration, and also those of the polarizer
and analyzer. Two parallel pieces of the board are to be separated by
an interval which shall represent the thickness of the film of gypsum.
Between them two other pieces, intersecting each other at a right
angle, are to represent the planes of vibration within the film; while
attached to the two parallel surfaces outside are two other pieces of
board, which represent the planes of vibration of the polarizer and
analyzer. On the two intersecting planes the waves are to be drawn,
showing the resolution of the first polarized beam into two others,
and then the subsequent reduction of the two systems of vibrations to
a common plane by the analyzer. Following out rigidly the interaction
of the two systems of waves, we are taught by such a model that all
the phenomena of colour obtained by the combination of the waves, when
the planes of vibration of the two Nicols are parallel, are displaced
by the _complementary_ phenomena, when the planes of vibration are
perpendicular to each other.)

In considering the next point, we will operate, for the sake of
simplicity, with monochromatic light--with red light, for example,
which is easily obtained pure by red glass. Supposing a certain
thickness of the gypsum produces a retardation of half a wave-length,
twice this thickness will produce a retardation of two half
wave-lengths, three times this thickness a retardation of three half
wave-lengths, and so on. Now, when the Nicols are parallel, the
retardation of half a wave-length, or of any _odd_ number of half
wave-lengths, produces extinction; at all thicknesses, on the other
hand, which correspond to a retardation of an _even_ number of half
wave-lengths, the two beams support each other, when they are brought
to a common plane by the analyzer. Supposing, then, that we take a
plate of a wedge form, which grows gradually thicker from edge to
back, we ought to expect, in red light, a series of recurrent bands of
light and darkness; the dark bands occurring at thicknesses which
produce retardations of one, three, five, etc., half wave-lengths,
while the bright bands occur between the dark ones. Experiment proves
the wedge-shaped film to show these bands. They are also beautifully
shown by a circular film, so worked as to be thinnest at the centre,
and gradually increasing in thickness from the centre outwards. A
splendid series of rings of light and darkness is thus produced.

When, instead of employing red light, we employ blue, the rings are
also seen: but as they occur at thinner portions of the film, they are
smaller than the rings obtained with the red light. The consequence of
employing white light may be now inferred; inasmuch as the red and the
blue fall in different places, we have _iris-coloured_ rings produced
by the white light.

Some of the chromatic effects of irregular crystallization are
beautiful in the extreme. Could I introduce between our two Nicols a
pane of glass covered by those frost-ferns which your cold weather
renders now so frequent, rich colours would be the result. The
beautiful effects of the irregular crystallization of tartaric acid
and other substances on glass plates now presented to you, illustrate
what you might expect from the frosted window-pane. And not only do
crystalline bodies act thus upon light, but almost all bodies that
possess a definite structure do the same. As a general rule, organic
bodies act thus upon light; for their architecture implies an
arrangement of the molecules, and of the ether associated with the
molecules, which involves double refraction. A film of horn, or the
section of a shell, for example, yields very beautiful colours in
polarized light. In a tree, the ether certainly possesses different
degrees of elasticity along and across the fibre; and, were wood
transparent, this peculiarity of molecular structure would infallibly
reveal itself by chromatic phenomena like those that you have seen.


§ 4. _Colours produced by Strain and Pressure._

Not only do natural bodies behave in this way, but it is possible, as
shown by Brewster, to confer, by artificial strain or pressure, a
temporary double refracting structure upon non-crystalline bodies such
as common glass. This is a point worthy of illustration. When I place
a bar of wood across my knee and seek to break it, what is the
mechanical condition of the bar? It bends, and its convex surface is
_strained_ longitudinally; its concave surface, that next my knee, is
longitudinally _pressed_. Both in the strained portion and in the
pressed portion of the wood the ether is thrown into a condition which
would render the wood, were it transparent, double-refracting. For, in
cases like the present, the drawing of the molecules asunder
longitudinally is always accompanied by their approach to each other
laterally; while the longitudinal squeezing is accompanied by lateral
retreat. Each half of the bar of wood exhibits this antithesis, and is
therefore double-refracting.

Let us now repeat this experiment with a bar of glass. Between the
crossed Nicols I introduce such a bar. By the dim residue of light
lingering upon the screen, you see the image of the glass, but it has
no effect upon the light. I simply bend the glass bar with my finger
and thumb, keeping its length oblique to the directions of vibration
in the Nicols. Instantly light flashes out upon the screen. The two
sides of the bar are illuminated, the edges most, for here the strain
and pressure are greatest. In passing from longitudinal strain to
longitudinal pressure, we cross a portion of the glass where neither
is exerted. This is the so-called neutral axis of the bar of glass,
and along it you see a dark band, indicating that the glass along this
axis exercises no action upon the light. By employing the force of a
press, instead of the force of my finger and thumb, the brilliancy of
the light is greatly augmented.

Again, I have here a square of glass which can be inserted into a
press of another kind. Introducing the uncompressed square between the
prisms, its neutrality is declared; but it can hardly be held
sufficiently loosely in the press to prevent its action from
manifesting itself. Already, though the pressure is infinitesimal, you
see spots of light at the points where the press is in contact with
the glass. On turning a screw, the image of the square of glass
flashes out upon the screen. Luminous spaces are seen separated from
each other by dark bands.

Every two adjacent spaces are in opposite mechanical conditions. On
one side of the dark band we have strain, on the other side pressure,
the band marking the neutral axis between both. I now tighten the
vice, and you see colour; tighten still more, and the colours appear
as rich as those presented by crystals. Releasing the vice, the
colours suddenly vanish; tightening suddenly, they reappear. From the
colours of a soap-bubble Newton was able to infer the thickness of the
bubble, thus uniting by the bond of thought apparently incongruous
things. From the colours here presented to you, the magnitude of the
pressure employed might be inferred. Indeed, the late M. Wertheim, of
Paris, invented an instrument for the determination of strains and
pressures, by the colours of polarized light, which exceeded in
accuracy all previous instruments of the kind.

And now we have to push these considerations to a final illustration.
Polarized light may be turned to account in various ways as an
analyzer of molecular condition. It may, for instance, be applied to
reveal the condition of a solid body when it becomes sonorous. A strip
of glass six feet long, two inches wide and a quarter of an inch
thick, is held at the centre between the finger and thumb. On sweeping
a wet woollen rag over one of its halves, you hear an acute sound due
to the vibrations of the glass. What is the condition of the glass
while the sound is heard? This: its two halves lengthen and shorten in
quick succession. Its two ends, therefore, are in a state of quick
vibration; but at the centre the pulses from the two ends alternately
meet and retreat from each other. Between their opposing actions, the
glass at the centre is kept motionless: but, on the other hand, it is
alternately strained and compressed. In fig. 38, A B may be taken to
represent the glass rectangle with its centre condensed; while A' B'
represents the same rectangle with its centre rarefied. The ends of
the strip suffer neither condensation nor rarefaction.

[Illustration: Fig. 38]

If we introduce the strip of glass (_s_ _s'_, fig. 39) between the
crossed Nicols, taking care to keep it oblique to the directions of
vibration of the Nicols, and sweep our wet rubber over the glass, this
is what may be expected to occur: At every moment of compression the
light will flash through; at every moment of strain the light will
also flash through; and these states of strain and pressure will
follow each other so rapidly, that we may expect a permanent luminous
impression to be made upon the eye. By pure reasoning, therefore, we
reach the conclusion that the light will be revived whenever the glass
is sounded. That it is so, experiment testifies: at every sweep of the
rubber (_h_, fig. 39) a fine luminous disk (O) flashes out upon the
screen. The experiment may be varied in this way: Placing in front of
the polarizer a plate of unannealed glass, you have a series of
beautifully coloured rings, intersected by a black cross. Every sweep
of the rubber not only abolishes the rings, but introduces
complementary ones, the black cross being, for the moment, supplanted
by a white one. This is a modification of a beautiful experiment which
we owe to Biot. His apparatus, however, confined the observation of it
to a single person at a time.

[Illustration: Fig. 39.]


§ 5. _Colours of Unannealed Glass_.

Bodies are usually expanded by heat and contracted by cold. If the
heat be applied with perfect uniformity, no local strains or pressures
come into play; but, if one portion of a solid be heated and another
portion not, the expansion of the heated portion introduces strains
and pressures which reveal themselves under the scrutiny of polarized
light. When a square of common window-glass is placed between the
Nicols, you see its dim outline, but it exerts no action on the
polarized light. Held for a moment over the flame of a spirit-lamp, on
reintroducing it between the Nicols, light flashes out upon the
screen. Here, as in the case of mechanical action, you have luminous
spaces of strain divided by dark neutral axes from spaces of pressure.

[Illustration: Fig. 40.]

[Illustration: Fig. 41.]

Let us apply the heat more symmetrically. A small square of glass is
perforated at the centre, and into the orifice a bit of copper wire is
introduced. Placing the square between the prisms, and heating the
wire, the heat passes by conduction to the glass, through which it
spreads from the centre outwards. You immediately see four luminous
quadrants and a dim cross, which becomes gradually blacker, by
comparison with the adjacent brightness. And as, in the case of
pressure, we produced colours, so here also, by the proper application
of heat, gorgeous chromatic effects may be evoked. The condition
necessary to the production of these colours may be rendered permanent
by first heating the glass sufficiently, and then cooling it, so that
the chilled mass shall remain in a state of permanent strain and
pressure. Two or three examples will illustrate this point. Figs. 40
and 41 represent the figures obtained with two pieces of glass thus
prepared; two rectangular pieces of unannealed glass, crossed and
placed between the polarizer and analyzer, exhibit the beautiful iris
fringes represented in fig. 42.

[Illustration: Fig. 42.]


§ 6. _Circular Polarization._

But we have to follow the ether still further into its hiding-places.
Suspended before you is a pendulum, which, when drawn aside and
liberated, oscillates to and fro. If, when the pendulum is passing the
middle point of its excursion, I impart a shock to it tending to drive
it at right angles to its present course, what occurs? The two
impulses compound themselves to a vibration oblique in direction to
the former one, but the pendulum still oscillates in _a plane_. But,
if the rectangular shock be imparted to the pendulum when it is at the
limit of its swing, then the compounding of the two impulses causes
the suspended ball to describe, not a straight line, but an ellipse;
and, if the shock be competent of itself to produce a vibration of the
same amplitude as the first one, the ellipse becomes a circle.

Why do I dwell upon these things? Simply to make known to you the
resemblance of these gross mechanical vibrations to the vibrations of
light. I hold in my hand a plate of quartz cut from the crystal
perpendicular to its axis. The crystal thus cut possesses the
extraordinary power of twisting the plane of vibration of a polarized
ray to an extent dependent on the thickness of the crystal. And the
more refrangible the light the greater is the amount of twisting; so
that, when white light is employed, its constituent colours are thus
drawn asunder. Placing the quartz plate between the polarizer and
analyzer, this vivid red appears; and, turning the analyzer in front
from right to left, the other colours of the spectrum appear in
succession. Specimens of quartz have been found which require the
analyzer to be turned from left to right to obtain the same succession
of colours. Crystals of the first class are therefore called
right-handed, and of the second class, left-handed crystals.

With profound sagacity, Fresnel, to whose genius we mainly owe the
expansion and final triumph of the undulatory theory of light,
reproduced mentally the mechanism of these crystals, and showed their
action to be due to the circumstance that, in them, the waves of
ether so act upon each other as to produce the condition represented
by our rotating pendulum. Instead of being plane polarized, the light
in rock crystal is _circularly polarized_. Two such rays, transmitted
along the axis of the crystal, and rotating in opposite directions,
when brought to interference by the analyzer, are demonstrably
competent to produce all the observed phenomena.


§ 7. _Complementary Colours of Bi-refracting Spar in Circularly
Polarized Light. Proof that Yellow and Blue are Complementary._

I now remove the analyzer, and put in its place the piece of Iceland
spar with which we have already illustrated double refraction. The two
images of the carbon-points are now before you, produced, as you know,
by two beams vibrating at right angles to each other. Introducing a
plate of quartz between the polarizer and the spar, the two images
glow with complementary colours. Employing the image of an aperture
instead of that of the carbon-points, we have two coloured circles. As
the analyzer is caused to rotate, the colours pass through various
changes: but they are always complementary. When the one is red, the
other is green; when the one is yellow, the other is blue. Here we
have it in our power to demonstrate afresh a statement made in our
first lecture, that although the mixture of blue and yellow pigments
produces green, the mixture of blue and yellow lights produces white.
By enlarging our aperture, the two images produced by the spar are
caused to approach each other, and finally to overlap. The one image
is now a vivid yellow, the other a vivid blue, and you notice that
where these colours are superposed we have a pure white. (See fig. 43,
where N is the end of the polarizer, Q the quartz plate, L a lens, and
B the bi-refracting spar. The two images overlap at O, and produce
white by their mixture.)

[Illustration: Fig. 43.]


§ 8. _The Magnetization of Light._

This brings us to a point of our inquiries which, though rarely
illustrated in lectures, is nevertheless so likely to affect
profoundly the future course of scientific thought that I am unwilling
to pass it over without reference. I refer to the experiment which
Faraday, its discoverer, called the 'magnetization of light.' The
arrangement for this celebrated experiment is now before you. We have,
first, our electric lamp, then a Nicol prism, to polarize the beam
emergent from the lamp; then an electro-magnet, then a second Nicol,
and finally our screen. At the present moment the prisms are crossed,
and the screen is dark. I place from pole to pole of the
electro-magnet a cylinder of a peculiar kind of glass, first made by
Faraday, and called Faraday's heavy glass. Through this glass the beam
from the polarizer now passes, being intercepted by the Nicol in
front. On exciting the magnet light instantly appears upon the screen.
By the action of the magnet upon the heavy glass the plane of
vibration is caused to rotate, the light being thus enabled to get
through the analyzer.

The two classes into which quartz-crystals are divided have been
already mentioned. In my hand I hold a compound plate, one half of it
taken from a right-handed, and the other from a left-handed crystal.
Placing the plate in front of the polarizer, I turn one of the Nicols
until the two halves of the plate show a common puce colour. This
yields an exceedingly sensitive means of rendering visible the action
of a magnet upon light. By turning either the polarizer or the
analyzer through the smallest angle, the uniformity of the colour
disappears, and the two halves of the quartz show different colours.
The magnet produces an effect equivalent to this rotation. The
puce-coloured circle is now before you on the screen. (See fig. 44,
where N is the nozzle of the lamp, H the first Nicol, Q the biquartz
plate, L a lens, M the electro-magnet, with the heavy glass across its
perforated poles, and P the second Nicol.) Exciting the magnet, one
half of the image becomes suddenly red, the other half green.
Interrupting the current, the two colours fade away, and the primitive
puce is restored.

The action, moreover, depends upon the polarity of the magnet, or, in
other words, on the direction of the current which surrounds the
magnet. Reversing the current, the red and green reappear, but they
have changed places. The red was formerly to the right, and the green
to the left; the green is now to the right, and the red to the left.
With the most exquisite ingenuity, Faraday analyzed all those actions
and stated their laws. This experiment, however, long remained a
scientific curiosity rather than a fruitful germ. That it would bear
fruit of the highest importance, Faraday felt profoundly convinced,
and present researches are on the way to verify his conviction.

[Illustration: Fig. 44]


§ 9. _Iris-rings surrounding the Axes of Crystals._

A few more words are necessary to complete our knowledge of the
wonderful interaction between ponderable molecules and the ether
interfused among them. Symmetry of molecular arrangement implies
symmetry on the part of the ether; atomic dissymmetry, on the other
hand, involves the dissymmetry of the ether, and, as a consequence,
double refraction. In a certain class of crystals the structure is
homogeneous, and such crystals produce no double refraction. In
certain other crystals the molecules are ranged symmetrically round a
certain line, and not around others. Along the former, therefore, the
ray is undivided, while along all the others we have double
refraction. Ice is a familiar example: its molecules are built with
perfect symmetry around the perpendiculars to the planes of freezing,
and a ray sent through ice in this direction is not doubly refracted;
whereas, in all other directions, it is. Iceland spar is another
example of the same kind: its molecules are built symmetrically round
the line uniting the two blunt angles of the rhomb. In this direction
a ray suffers no double refraction, in all others it does. This
direction of no double refraction is called the _optic axis_ of the
crystal.

Hence, if a plate be cut from a crystal of Iceland spar perpendicular
to the axis, all rays sent across this plate in the direction of the
axis will produce but one image. But, the moment we deviate from the
parallelism with the axis, double refraction sets in. If, therefore, a
beam that has been rendered _conical_ by a converging lens be sent
through the spar so that the central ray of the cone passes along the
axis, this ray only will escape double refraction. Each of the others
will be divided into an ordinary and an extraordinary ray, the one
moving more slowly through the crystal than the other; the one,
therefore, retarded with reference to the other. Here, then, we have
the conditions for interference, when the waves are reduced by the
analyzer to a common plane.

Placing the plate of Iceland spar between the crossed Nicol prisms,
and employing the conical beam, we have upon the screen a beautiful
system of iris-rings surrounding the end of the optic axis, the
circular bands of colour being intersected by a black cross (fig. 45).
The arms of this cross are parallel to the two directions of vibration
in the polarizer and analyzer. It is easy to see that those rays whose
planes of vibration within the spar coincide with the plane of
vibration of _either_ prism, cannot get through _both_. This complete
interception produces the arms of the cross.

[Illustration: Fig. 45.]

With monochromatic light the rings would be simply bright and
black--the bright rings occurring at those thicknesses of the spar
which cause the rays to conspire; the black rings at those thicknesses
which cause them to quench each other. Turning the analyzer 90° round,
we obtain the complementary phenomena. The black cross gives place to
a bright one, and every dark ring is supplanted also by a bright one
(fig. 46). Here, as elsewhere, the different lengths of the
light-waves give rise to iris-colours when white light is employed.

[Illustration: Fig. 46.]

[Illustration: Fig. 47.]

Besides the _regular_ crystals which produce double refraction in no
direction, and the _uniaxal_ crystals which produce it in all
directions but one, Brewster discovered that in a large class of
crystals there are _two_ directions in which double refraction does
not take place. These are called _biaxal_ crystals. When plates of
these crystals, suitably cut, are placed between the polarizer and
analyzer, the axes (A A', fig. 47) are seen surrounded, not by
circles, but by curves of another order and of a perfectly definite
mathematical character. Each band, as proved experimentally by
Herschel, forms a _lemniscata_; but the experimental proof was here,
as in numberless other cases, preceded by the deduction which showed
that, according to the undulatory theory, the bands must possess this
special character.


§ 10. _Power of the Wave Theory_.

I have taken this somewhat wide range over polarization itself, and
over the phenomena exhibited by crystals in polarized light, in order
to give you some notion of the firmness and completeness of the theory
which grasps them all. Starting from the single assumption of
transverse undulations, we first of all determine the wave-lengths,
and find that on them all the phenomena of colour are dependent. The
wavelengths may be determined in many independent ways. Newton
virtually determined them when he measured the periods of his Fits:
the length of a fit, in fact, is that of a quarter of an undulation.
The wave-lengths may be determined by diffraction at the edges of a
slit (as in the Appendix to these Lectures); they may be deduced from
the interference fringes produced by reflection; from the fringes
produced by refraction; also by lines drawn with a diamond upon glass
at measured distances asunder. And when the length determined by these
independent methods are compared together, the strictest agreement is
found to exist between them.

With the wave-lengths once at our disposal, we follow the ether into
the most complicated cases of interaction between it and ordinary
matter, 'the theory is equal to them all. It makes not a single new
physical hypothesis; but out of its original stock of principles it
educes the counterparts of all that observation shows. It accounts
for, explains, simplifies the most entangled cases; corrects known
laws and facts; predicts and discloses unknown ones; becomes the guide
of its former teacher Observation; and, enlightened by mechanical
conceptions, acquires an insight which pierces through shape and
colour to force and cause.'[18]

But, while I have thus endeavoured to illustrate before you the power
of the undulatory theory as a solver of all the difficulties of
optics, do I therefore wish you to close your eyes to any evidence
that may arise against it? By no means. You may urge, and justly urge,
that a hundred years ago another theory was held by the most eminent
men, and that, as the theory then held had to yield, the undulatory
theory may have to yield also. This seems reasonable; but let us
understand the precise value of the argument. In similar language a
person in the time of Newton, or even in our time, might reason thus:
Hipparchus and Ptolemy, and numbers of great men after them, believed
that the earth was the centre of the solar system. But this deep-set
theoretic notion had to give way, and the helio-centric theory may, in
its turn, have to give way also. This is just as reasonable as the
first argument. Wherein consists the strength of the present theory of
gravitation? Solely in its competence to account for all the phenomena
of the solar system. Wherein consists the strength of the theory of
undulation? Solely in its competence to disentangle and explain
phenomena a hundred-fold more complex than those of the solar system.
Accept if you will the scepticism of Mr. Mill[19] regarding the
undulatory theory; but if your scepticism be philosophical, it will
wrap the theory of gravitation in the same or in greater doubt.[20]


§ 11. _The Blue of the Sky_.

I am unwilling to quit these chromatic phenomena without referring to
a source of colour which has often come before me of late in the blue
of your skies at noon, and the deep crimson of your horizon after the
set of sun. I will here summarize and extend what I have elsewhere
said upon this subject. Proofs of the most cogent description could be
adduced to show that the blue light of the firmament is reflected
light. That light comes to us across the direction of the solar rays,
and even against the direction of the solar rays; and this lateral and
opposing rush of wave-motion can only be due to the rebound of the
waves from the air itself, or from something suspended in the air. The
solar light, moreover, is not scattered by the sky in the proportions
which produce white. The sky is blue, which indicates an excess of the
smaller waves. The blueness of the air has been given as a reason for
the blueness of the sky; but then the question arises, How, if the air
be blue, can the light of sunrise and sunset, which travels through
vast distances of air, be yellow, orange, or even red? The passage of
the white solar light through a blue medium could by no possibility
redden the light; the hypothesis of a blue atmosphere is therefore
untenable. In fact, the agent, whatever it be, which sends us the
light of the sky, exercises in so doing a dichroitic action. The light
reflected is blue, the light transmitted is orange or red, A marked
distinction is thus exhibited between reflection from the sky and that
from an ordinary cloud, which exercises no such dichroitic action.

The cloud, in fact, takes no note of size on the part of the waves of
ether, but reflects them all alike. Now the cause of this may be that
the cloud-particles are so large in comparison with the size of the
waves of ether as to scatter them all indifferently. A broad cliff
reflects an Atlantic roller as easily as it reflects a ripple produced
by a sea-bird's wing; and, in the presence of large reflecting
surfaces, the existing differences of magnitude among the waves of
ether may also disappear. But supposing the reflecting particles,
instead of being very large, to be very small, in comparison with the
size of the waves. Then, instead of the whole wave being fronted and
in great part thrown back, a small portion only is shivered off by the
obstacle. Suppose, then, such minute foreign particles to be diffused
in our atmosphere. Waves of all sizes impinge upon them, and at every
collision a portion of the impinging wave is struck off. All the waves
of the spectrum, from the extreme red to the extreme violet, are thus
acted upon; but in what proportions will they be scattered? Largeness
is a thing of relation; and the smaller the wave, the greater is the
relative size of any particle on which the wave impinges, and the
greater also the relative reflection.

A small pebble, placed in the way of the ring-ripples produced by
heavy rain-drops on a tranquil pond, will throw back a large fraction
of each ripple incident upon it, while the fractional part of a larger
wave thrown back by the same pebble might be infinitesimal. Now to
preserve the solar light white, its constituent proportions must not
be altered; but in the scattering of the light by these very small
particles we see that the proportions _are_ altered. The smaller waves
are in excess, and, as a consequence, in the scattered light blue will
be the predominant colour. The other colours of the spectrum must, to
some extent, be associated with the blue: they are not absent, but
deficient. We ought, in fact, to have them all, but in diminishing
proportions, from the violet to the red.

We have thus reasoned our way to the conclusion, that were particles,
small in comparison to the size of the ether waves, sown in our
atmosphere, the light scattered by those particles would be exactly
such as we observe in our azure skies. And, indeed, when this light is
analyzed, all the colours of the spectrum are found in the proportions
indicated by our conclusion.

By its successive collisions with the particles the white light is
more and more robbed of its shorter waves; it therefore loses more and
more of its due proportion of blue. The result may be anticipated. The
transmitted light, where moderate distances are involved, will appear
yellowish. But as the sun sinks towards the horizon the atmospheric
distance increases, and consequently the number of the scattering
particles. They weaken in succession the violet, the indigo, the blue,
and even disturb the proportions of green. The transmitted light under
such circumstances must pass from yellow through orange to red. This
also is exactly what we find in nature. Thus, while the reflected
light gives us, at noon, the deep azure of the Alpine skies, the
transmitted light gives us, at sunset, the warm crimson of the Alpine
snows.

But can small particles be really proved to act in the manner
indicated? No doubt of it. Each one of you can submit the question to
an experimental test. Water will not dissolve resin, but spirit will;
and when spirit which holds resin in solution is dropped into water,
the resin immediately separates in solid particles, which render the
water milky. The coarseness of this precipitate depends on the
quantity of the dissolved resin. Professor Brücke has given us the
proportions which produce particles particularly suited to our present
purpose. One gramme of clean mastic is dissolved in eighty-seven
grammes of absolute alcohol, and the transparent solution is allowed
to drop into a beaker containing clear water briskly stirred. An
exceedingly fine precipitate is thus formed, which declares its
presence by its action upon light. Placing a dark surface behind the
beaker, and permitting the light to fall into it from the top or
front, the medium is seen to be of a very fair sky-blue. A trace of
soap in water gives it a tint of blue. London milk makes an
approximation to the same colour, through the operation of the same
cause: and Helmholtz has irreverently disclosed the fact that a blue
eye is simply a turbid medium.


§ 12. _Artificial Sky_.

But we have it in our power to imitate far more closely the natural
conditions of this problem. We can generate in air artificial skies,
and prove their perfect identity with the natural one, as regards the
exhibition of a number of wholly unexpected phenomena. It has been
recently shown in a great number of instances by myself that waves of
ether issuing from a strong source, such as the sun or the electric
light, are competent to shake asunder the atoms of gaseous molecules.
The apparatus used to illustrate this consists of a glass tube about a
yard in length, and from 2½ to 3 inches internal diameter. The gas or
vapour to be examined is introduced into this tube, and upon it the
condensed beam of the electric lamp is permitted to act. The vapour is
so chosen that one, at least, of its products of decomposition, as
soon as it is formed, shall be _precipitated_ to a kind of cloud. By
graduating the quantity of the vapour, this precipitation may be
rendered of any degree of fineness, forming particles distinguishable
by the naked eye, or particles which are probably far beyond the reach
of our highest microscopic powers. I have no reason to doubt that
particles may be thus obtained whose diameters constitute but a very
small fraction of the length of a wave of violet light.

Now, in all such cases when suitable vapours are employed in a
sufficiently attenuated state, no matter what the vapour may be, the
visible action commences with the formation of a _blue cloud_. Let me
guard myself at the outset against all misconception as to the use of
this term. The blue cloud here referred to is totally invisible in
ordinary daylight. To be seen, it requires to be surrounded by
darkness, _it only_ being illuminated by a powerful beam of light.
This cloud differs in many important particulars from the finest
ordinary clouds, and might justly have assigned to it an intermediate
position between these clouds and true cloudless vapour.

It is possible to make the particles of this _actinic cloud_ grow from
an infinitesimal and altogether ultra-microscopic size to particles of
sensible magnitude; and by means of these in a certain stage of their
growth, we produce a blue which rivals, if it does not transcend, that
of the deepest and purest Italian sky. Introducing into our tube a
quantity of mixed air and nitrite of butyl vapour sufficient to
depress the mercurial column of an air-pump one-twentieth of an inch,
adding a quantity of air and hydrochloric acid sufficient to depress
the mercury half an inch further, and sending through this compound
and highly attenuated atmosphere the beam of the electric light,
within the tube arises gradually a splendid azure, which strengthens
for a time, reaches a maximum of depth and purity, and then, as the
particles grow larger, passes into whitish blue. This experiment is
representative, and it illustrates a general principle. Various other
colourless substances of the most diverse properties, optical and
chemical, might be employed for this experiment. The _incipient
cloud_, in every case, would exhibit this superb blue; thus proving to
demonstration that particles of infinitesimal size, without any colour
of their own, and irrespective of those optical properties exhibited
by the substance in a massive state, are competent to produce the blue
colour of the sky.


§ 13. _Polarization of Skylight_.

But there is another subject connected with our firmament, of a more
subtle and recondite character than even its colour. I mean that
'mysterious and beautiful phenomenon,' as Sir John Herschel calls it,
the polarization of the light of the sky. Looking at various points of
the blue firmament through a Nicol prism, and turning the prism round
its axis, we soon notice variations of brightness. In certain
positions of the prism, and from certain points of the firmament, the
light appears to be wholly transmitted, while it is only necessary to
turn the prism round its axis through an angle of ninety degrees to
materially diminish the intensity of the light. Experiments of this
kind prove that the blue light sent to us by the firmament is
polarized, and on close scrutiny it is also found that the direction
of most perfect polarization is perpendicular to the solar rays. Were
the heavenly azure like the ordinary light of the sun, the turning of
the prism would have no effect upon it; it would be transmitted
equally during the entire rotation of the prism. The light of the sky
may be in great part quenched, because it is in great part polarized.

The same phenomenon is exhibited in perfection by our actinic clouds,
the only condition necessary to its production being the smallness of
the particles. In all cases, and with all substances, the cloud formed
at the commencement, when the precipitated particles are sufficiently
fine, is _blue_. In all cases, moreover, this fine blue cloud
polarizes _perfectly_ the beam which illuminates it, the direction of
polarization enclosing an angle of 90° with the axis of the
illuminating beam.

It is exceedingly interesting to observe both the growth and the decay
of this polarization. For ten or fifteen minutes after its first
appearance, the light from a vividly illuminated incipient cloud,
looked at horizontally, is absolutely quenched by a Nicol prism with
its longer diagonal vertical. But as the sky-blue is gradually
rendered impure by the introduction of particles of too large a size,
in other words, as real clouds begin to be formed, the polarization
begins to deteriorate, a portion of the light passing through the
prism in all its positions, as it does in the case of skylight. It is
worthy of note that for some time after the cessation of perfect
polarization the _residual_ light which passes, when the Nicol is in
its position of minimum transmission, is of a gorgeous blue, the
whiter light of the cloud being extinguished. When the cloud-texture
has become sufficiently coarse to approximate to that of ordinary
clouds, the rotation of the Nicol ceases to have any sensible effect
on the light discharged at right angles to the beam.

The perfection of the polarization in a direction perpendicular to the
illuminating beam may be also illustrated by the following experiment,
which has been executed with many vapours. A Nicol prism large enough
to embrace the entire beam of the electric lamp was placed between the
lamp and the experimental tube. Sending the beam polarized by the
Nicol through the tube, I placed myself in front of it, the eyes being
on a level with its axis, my assistant occupying a similar position
behind the tube. The short diagonal of the large Nicol was in the
first instance vertical, the plane of vibration of the emergent beam
being therefore also vertical. As the light continued to act, a superb
blue cloud visible to both my assistant and myself was slowly formed.
But this cloud, so deep and rich when looked at from the positions
mentioned, utterly disappeared when looked at vertically downwards,
or vertically upwards. Reflection from the cloud was not possible in
these directions. When the large Nicol was slowly turned round its
axis, the eye of the observer being on the level of the beam, and the
line of vision perpendicular to it, entire extinction of the light
emitted horizontally occurred when the longer diagonal of the large
Nicol was vertical. But a vivid blue cloud was seen when looked at
downwards or upwards. This truly fine experiment, which I should
certainly have made without suggestion, was, as a matter of fact,
first definitely suggested by a remark addressed to me in a letter by
Professor Stokes.

All the phenomena of colour and of polarization observable in the case
of skylight are manifested by those actinic clouds; and they exhibit
additional phenomena which it would be neither convenient to pursue,
nor perhaps possible to detect, in the actual firmament. They enable
us, for example, to follow the polarization from its first appearance
on the barely visible blue to its final extinction in the coarser
cloud. These changes, as far as it is now necessary to refer to them,
may be thus summed up:--

1. The actinic cloud, as long as it continues blue, discharges
polarized light in all directions, but the direction of maximum
polarization, like that of skylight, is at right angles to the
direction of the illuminating beam.

2. As long as the cloud remains distinctly blue, the light discharged
from it at right angles to the illuminating beam is _perfectly_
polarized. It may be utterly quenched by a Nicol prism, the cloud from
which it issues being caused to disappear. Any deviation from the
perpendicular enables a portion of the light to get through the prism.

3. The direction of vibration of the polarized light is at right
angles to the illuminating beam. Hence a plate of tourmaline, with its
axis parallel to the beam, stops the light, and with the axis
perpendicular to the beam transmits the light.

4. A plate of selenite placed between the Nicol and the actinic cloud
shows the colours of polarized light; in fact, the cloud itself plays
the part of a polarizing Nicol.

5. The particles of the blue cloud are immeasurably small, but they
increase gradually in size, and at a certain period of their growth
cease to discharge perfectly polarized light. For some time afterwards
the light that reaches the eye, through the Nicol in its position of
least transmission, is of a magnificent blue, far exceeding in depth
and purity that of the purest sky; thus the waves that first feel the
influence of size, at both limits of the polarization, are the
shortest waves of the spectrum. These are the first to accept
polarization, and they are the first to escape from it.



LECTURE V.

  RANGE OF VISION NOT COMMENSURATE WITH RANGE OF RADIATION
  THE ULTRA-VIOLET BAYS
  FLUORESCENCE
  THE RENDERING OF INVISIBLE RAYS VISIBLE
  VISION NOT THE ONLY SENSE APPEALED TO BY THE SOLAR AND ELECTRIC BEAM
  HEAT OF BEAM
  COMBUSTION BY TOTAL BEAM AT THE FOCI OF MIRRORS AND LENSES
  COMBUSTION THROUGH ICE-LENS
  IGNITION OF DIAMOND
  SEARCH FOR THE RAYS HERE EFFECTIVE
  SIR WILLIAM HERSCHEL'S DISCOVERY OF DARK SOLAR RAYS
  INVISIBLE RAYS THE BASIS OF THE VISIBLE
  DETACHMENT BY A RAY-FILTER OF THE INVISIBLE RAYS FROM THE VISIBLE
  COMBUSTION AT DARK FOCI
  CONVERSION OF HEAT-RAYS INTO LIGHT-RAYS
  CALORESCENCE
  PART PLAYED IN NATURE BY DARK RAYS
  IDENTITY OF LIGHT AND RADIANT HEAT
  INVISIBLE IMAGES
  REFLECTION, REFRACTION, PLANE POLARIZATION, DEPOLARIZATION,
    CIRCULAR POLARIZATION, DOUBLE REFRACTION, AND MAGNETIZATION
    OF RADIANT HEAT.


§ 1. _Range of Vision and of Radiation_.

The first question that we have to consider to-night is this: Is the
eye, as an organ of vision, commensurate with the whole range of solar
radiation--is it capable of receiving visual impressions from all the
rays emitted by the sun? The answer is negative. If we allowed
ourselves to accept for a moment that notion of gradual growth,
amelioration, and ascension, implied by the term _evolution_, we might
fairly conclude that there are stores of visual impressions awaiting
man, far greater than those now in his possession. Ritter discovered
in 1801 that beyond the extreme violet of the spectrum there is a vast
efflux of rays which are totally useless as regards our present powers
of vision. These ultra-violet waves, however, though incompetent to
awaken the optic nerve, can shake asunder the molecules of certain
compound substances on which they impinge, thus producing chemical
decomposition.

But though the blue, violet, and ultra-violet rays can act thus upon
certain substances, the fact is hardly sufficient to entitle them to
the name of 'chemical rays,' which is usually applied to distinguish
them from the other constituents of the spectrum. As regards their
action upon the salts of silver, and many other substances, they may
perhaps merit this title; but in the case of the grandest example of
the chemical action of light--the decomposition of carbonic acid in
the leaves of plants, with which my eminent friend Dr. Draper (now no
more) has so indissolubly associated his name--the yellow rays are
found to be the most active.

There are substances, however, on which the violet and ultra-violet
waves exert a special decomposing power; and, by permitting the
invisible spectrum to fall upon surfaces prepared with such
substances, we reveal both the existence and the extent of the
ultraviolet spectrum.


§ 2. _Ultra-violet Rays: Fluorescence_.

The method of exhibiting the action of the ultraviolet rays by their
chemical action has been long known; indeed, Thomas Young photographed
the ultra-violet rings of Newton. We have now to demonstrate their
presence in another way. As a general rule, bodies either transmit
light or absorb it; but there is a third case in which the light
falling upon the body is neither transmitted nor absorbed, but
converted into light of another kind. Professor Stokes, the occupant
of the chair of Newton in the University of Cambridge, has
demonstrated this change of one kind of light into another, and has
pushed his experiments so far as to render the invisible rays visible.

A large number of substances examined by Stokes, when excited by the
invisible ultra-violet waves, have been proved to emit light. You know
the rate of vibration corresponding to the extreme violet of the
spectrum; you are aware that to produce the impression of this colour,
the retina is struck 789 millions of millions of times in a second. At
this point, the retina ceases to be useful as an organ of vision; for,
though struck by waves of more rapid recurrence, they are incompetent
to awaken the sensation of light. But when such non-visual waves are
caused to impinge upon the molecules of certain substances--on those
of sulphate of quinine, for example--they compel those molecules, or
their constituent atoms, to vibrate; and the peculiarity is, that the
vibrations thus set up are _of slower period_ than those of the
exciting waves. By this lowering of the rate of vibration through the
intermediation of the sulphate of quinine, the invisible rays are
brought within the range of vision. We shall subsequently have
abundant opportunity for learning that transparency to the visible by
no means involves transparency to the invisible rays. Our bisulphide
of carbon, for example, which, employed in prisms, is so eminently
suitable for experiments on the visual rays, is by no means so
suitable for these ultra-violet rays. Flint glass is better, and rock
crystal is better than flint glass. A glass prism, however, will suit
our present purpose.

Casting by means of such a prism a spectrum, not upon the white
surface of our screen, but upon a sheet of paper which has been wetted
with a saturated solution of the sulphate of quinine and afterwards
dried, an obvious extension of the spectrum is revealed. We have, in
the first instance, a portion of the violet rendered whiter and more
brilliant; but, besides this, we have the gleaming of the colour
where, in the case of unprepared paper, nothing is seen. Other
substances produce a similar effect. A substance, for example,
recently discovered by President Morton, and named by him _Thallene_,
produces a very striking elongation of the spectrum, the new light
generated being of peculiar brilliancy.

Fluor spar, and some other substances, when raised to a temperature
still under redness, emit light. During the ages which have elapsed
since their formation, this capacity of shaking the ether into visual
tremors appears to have been enjoyed by these substances. Light has
been potential within them all this time; and, as well explained by
Draper, the heat, though not itself of visual intensity, can unlock
the molecules so as to enable them to exert their long-latent power of
vibration. This deportment of fluor spar determined Stokes in his
choice of a name for his great discovery: he called this rendering
visible of the ultra-violet rays _Fluorescence_.

By means of a deeply coloured violet glass, we cut off almost the
whole of the light of our electric beam; but this glass is peculiarly
transparent to the violet and ultra-violet rays. The violet beam now
crosses a large jar filled with water, into which I pour a solution of
sulphate of quinine. Clouds, to all appearance opaque, instantly
tumble downwards. Fragments of horse-chestnut bark thrown upon the
water also send down beautiful cloud-like strife. But these are not
clouds: there is nothing precipitated here: the observed action is an
action of _molecules_, not of _particles_. The medium before you is
not a turbid medium, for when you look through it at a luminous
surface it is perfectly clear.

If we paint upon a piece of paper a flower or a bouquet with the
sulphate of quinine, and expose it to the full beam, scarcely anything
is seen. But on interposing the violet glass, the design instantly
flashes forth in strong contrast with the deep surrounding violet.
President Morton has prepared for me a most beautiful example of such
a design which, when placed in the violet light, exhibits a peculiarly
brilliant fluorescence. From the experiments of Drs. Bence Jones and
Dupré, it would seem that there is some substance in the human body
resembling the sulphate of quinine, which causes all the tissues of
the body to be more or less fluorescent. All animal infusions show
this fluorescence. The crystalline lens of the eye exhibits the effect
in a very striking manner. When, for example, I plunge my eye into
this violet beam, I am conscious of a whitish-blue shimmer filling the
space before me. This is caused by fluorescent light generated in the
eye itself. Looked at from without, the crystalline lens at the same
time is seen to gleam vividly.

Long before its physical origin was understood this fluorescent light
attracted attention. Boyle describes it with great fulness and
exactness. 'We have sometimes,' he says, 'found in the shops of our
druggists certain wood which is there called _Lignum Nephriticum,_
because the inhabitants of the country where it grows are wont to use
the infusion of it, made in fair water, against the stone in the
kidneys. This wood may afford us an experiment which, besides the
singularity of it, may give no small assistance to an attentive
considerer towards the detection of the nature of colours. Take
_Lignum, Nephriticum_, and with a knife cut it into thin slices: put
about a handful of these slices into two or three or four pounds of
the purest spring water. Decant this impregnated water into a glass
phial; and if you hold it directly between the light and your eye, you
shall see it wholly tinted with an almost golden colour. But if you
hold this phial from the light, so that your eye be placed betwixt the
window and the phial, the liquid will appear of a deep and lovely
ceruleous colour.'

'These,' he continues, 'and other phenomena which I have observed in
this delightful experiment, divers of my friends have looked upon, not
without some wonder; and I remember an excellent oculist, finding by
accident in a friend's chamber a phial full of this liquor, which I
had given that friend, and having never heard anything of the
experiment, nor having anybody near him who could tell him what this
strange liquor might be, was a great while apprehensive, as he
presently afterwards told me, that some strange new distemper was
invading his eyes. And I confess that the unusualness of the
phenomenon made me very solicitous to find out the cause of this
experiment; and though I am far from pretending to have found it, yet
my enquiries have, I suppose, enabled me to give such hints as may
lead your greater sagacity to the discovery of the cause of this
wonder.'[21]

Goethe in his 'Farbenlehre' thus describes the fluorescence of
horse-chestnut bark:--'Let a strip of fresh horse-chestnut bark be
taken and clipped into a glass of water; the most perfect sky-blue
will be immediately produced.'[22] Sir John Herschel first noticed and
described the fluorescence of the sulphate of quinine, and showed that
the light proceeded from a thin stratum of the solution adjacent to
the surface where the light enters it. He showed, moreover, that the
incident beam, although not sensibly weakened in luminous intensity,
lost, in its transmission through the solution of sulphate of quinine,
the power of producing the blue fluorescent light. Sir David Brewster
also worked at the subject; but to Professor Stokes we are indebted
not only for its expansion, but for its full and final explanation.


§ 3. _The Heat of the Electric Beam. Ignition through a Lens of Ice.
Possible Cometary Temperature_.

But the waves from our incandescent carbon-points appeal to another
sense than that of vision. They not only produce light, but heat, as a
sensation. The magnified image of the carbon-points is now upon the
screen; and with a suitable instrument the heating power of the rays
which form that image might be readily demonstrated. In this case,
however, the heat is spread over too large an area to be very intense.
Drawing out the camera lens, and causing a movable screen to approach
the lamp, the image is seen to become smaller and smaller; the rays at
the same time becoming more and more concentrated, until finally they
are able to pierce black paper with a burning ring. Pushing back the
lens so as to render the rays parallel, and receiving them upon a
concave mirror, they are brought to a focus; paper placed at that
focus is caused to smoke and burn. Heat of this intensity may be
obtained with our ordinary camera and lens, and a concave mirror of
very moderate power.

[Illustration: Fig. 48.]

We will now adopt stronger measures with the radiation. In this larger
camera of blackened tin is placed a lamp, in all particulars similar
to those already employed. But instead of gathering up the rays from
the carbon-points by a condensing lens, we gather them up by a concave
mirror (_m_ _m'_, fig. 48), silvered in front and placed behind the
carbons (P). By this mirror we can cause the rays to issue through the
orifice in front of the camera, either parallel or convergent. They
are now parallel, and therefore to a certain extent diffused. We place
a convex lens (L) in the path of the beam; the light is converged to a
focus (C), and at that focus paper is not only pierced, but it is
instantly set ablaze.

Many metals may be burned up in the same way. In our first lecture
the combustibility of zinc was mentioned. Placing a strip of
sheet-zinc at this focus, it is instantly ignited, burning with its
characteristic purple flame. And now I will substitute for our glass
lens (L) one of a more novel character. In a smooth iron mould a lens
of pellucid ice has been formed. Placing it in the position occupied a
moment ago by the glass lens, I can see the beam brought to a sharp
focus. At the focus I place, a bit of black paper, with a little
gun-cotton folded up within it. The paper immediately ignites and the
cotton explodes. Strange, is it not, that the beam should possess such
heating power after having passed through so cold a substance? In his
arctic expeditions Dr. Scoresby succeeded in exploding gunpowder by
the sun's rays, converged by large lenses of ice; here we have
succeeded in producing the effect with a small lens, and with a
terrestrial source of heat.

In this experiment, you observe that, before the beam reaches the
ice-lens, it has passed through a glass cell containing water. The
beam is thus sifted of constituents, which, if permitted to fall upon
the lens, would injure its surface, and blur the focus. And this leads
me to say an anticipatory word regarding transparency. In our first
lecture we entered fully into the production of colours by absorption,
and we spoke repeatedly of the quenching of the rays of light. Did
this mean that the light was altogether annihilated? By no means. It
was simply so lowered in refrangibility as to escape the visual range.
It was converted into heat. Our red ribbon in the green of the
spectrum quenched the green, but if suitably examined its temperature
would have been found raised. Our green ribbon in the red of the
spectrum quenched the red, but its temperature at the same time was
augmented to a degree exactly equivalent to the light extinguished.
Our black ribbon, when passed through the spectrum, was found
competent to quench all its colours; but at every stage of its
progress an amount of heat was generated in the ribbon exactly
equivalent to the light lost. It is only when _absorption_ takes place
that heat is thus produced: and heat is always a result of absorption.

Examine the water, then, in front of the lamp after the beam has
passed through it: it is sensibly warm, and, if permitted to remain
there long enough, it might be made to boil. This is due to the
absorption, by the water, of a certain portion of the electric beam.
But a portion passes through unabsorbed, and does not at all
contribute to the heating of the water. Now, ice is also in great part
transparent to these latter rays, and therefore is but little melted
by them. Hence, by employing the portion of the beam transmitted by
water, we are able to keep our lens intact, and to produce by means of
it a sharply defined focus. Placed at that focus, white paper is not
ignited, because it fails to absorb the rays emergent from the
ice-lens. At the same place, however, black paper instantly burns,
because it absorbs the transmitted light.

And here it may be useful to refer to an estimate by Newton, based
upon doubtful data, but repeated by various astronomers of eminence
since his time. The comet of 1680, when nearest to the sun, was only a
sixth of the sun's diameter from his surface. Newton estimated its
temperature, in this position, to be more than two thousand times that
of molted iron. Now it is clear from the foregoing experiments that
the temperature of the comet could not be inferred from its nearness
to the sun. If its power of absorption were sufficiently low, the
comet might carry into the sun's neighbourhood the chill of stellar
space.


§ 4. _Combustion of a Diamond by Radiant Heat_.

The experiment of burning a diamond in oxygen by the concentrated rays
of the sun was repeated at Florence, in presence of Sir Humphry Davy,
on Tuesday, the 27th of March, 1814. It is thus described by
Faraday:--'To-day we made the grand experiment of burning the diamond,
and certainly the phenomena presented were extremely beautiful and
interesting. A glass globe containing about 22 cubical inches was
exhausted of air, and filled with pure oxygen. The diamond was
supported in the centre of this globe. The Duke's burning-glass was
the instrument used to apply heat to the diamond. It consists of two
double convex lenses, distant from each other about 3½ feet; the large
lens is about 14 or 15 inches in diameter, the smaller one about 3
inches in diameter. By means of the second lens the focus is very much
reduced, and the heat, when the sun shines brightly, rendered very
intense. The diamond was placed in the focus and anxiously watched. On
a sudden Sir H. Davy observed the diamond to burn visibly, and when
removed from the focus it was found to be in a state of active and
rapid combustion.'

The combustion of the diamond had never been effected by radiant heat
from a terrestrial source. I tried to accomplish this before crossing
the Atlantic, and succeeded in doing so. The small diamond now in my
hand is held by a loop of platinum wire. To protect it as far as
possible from air currents, and also to concentrate the heat upon it,
it is surrounded by a hood of sheet platinum. Bringing a jar of oxygen
underneath, I cause the focus of the electric beam to fall upon the
diamond. A small fraction of the time expended in the experiment
described by Faraday suffices to raise the diamond to a brilliant red.
Plunging it then into the oxygen, it glows like a little white star;
and it would continue to burn and glow until wholly consumed. The
focus can also be made to fall upon the diamond in oxygen, as in the
Florentine experiment: the result is the same. It was simply to secure
more complete mastery over the position of the focus, so as to cause
it to fall accurately upon the diamond, that the mode of experiment
here described was resorted to.


§ 5. _Ultra-red Rays: Calorescence_.

In the path of the beam issuing from our lamp I now place a cell with
glass sides containing a solution of alum. All the _light_ of the beam
passes through this solution. This light is received on a powerfully
converging mirror silvered in front, and brought to a focus by the
mirror. You can see the conical beam of reflected light tracking
itself through the dust of the room. A scrap of white paper placed at
the focus shines there with dazzling brightness, but it is not even
charred. On removing the alum cell, however, the paper instantly
inflames. There must, therefore, be something in this beam besides its
light. The _light_ is not absorbed by the white paper, and therefore
does not burn the paper; but there is something over and above the
light which _is_ absorbed, and which provokes combustion. What is this
something?

In the year 1800 Sir William Herschel passed a thermometer through
the various colours of the solar spectrum, and marked the rise of
temperature corresponding to each colour. He found the heating effect
to augment from the violet to the red; he did not, however, stop at
the red, but pushed his thermometer into the dark space beyond it.
Here he found the temperature actually higher than in any part of the
visible spectrum. By this important observation, he proved that the
sun emitted heat-rays which are entirely unfit for the purposes of
vision. The subject was subsequently taken up by Seebeck, Melloni,
Müller, and others, and within the last few years it has been found
capable of unexpected expansions and applications. I have devised a
method whereby the solar or electric beam can be so _filtered_ as to
detach from it, and preserve intact, this invisible ultra-red
emission, while the visible and ultra-violet emissions are wholly
intercepted. We are thus enabled to operate at will upon the purely
ultra-red waves.

In the heating of solid bodies to incandescence, this non-visual
emission is the necessary basis of the visual. A platinum wire is
stretched in front of the table, and through it an electric current
flows. It is warmed by the current, and may be felt to be warm by the
hand. It emits waves of heat, but no light. Augmenting the strength of
the current, the wire becomes hotter; it finally glows with a sober
red light. At this point Dr. Draper many years ago began an
interesting investigation. He employed a voltaic current to heat his
platinum, and he studied, by means of a prism, the successive
introduction of the colours of the spectrum. His first colour, as
here, was red; then came orange, then yellow, then green, and lastly
all the shades of blue. As the temperature of the platinum was
gradually augmented, the atoms were caused to vibrate more rapidly;
shorter waves were thus introduced, until finally waves were obtained
corresponding to the entire spectrum. As each successive colour was
introduced, the colours preceding it became more vivid. Now the
vividness or intensity of light, like that of sound, depends not upon
the length of the wave, but on the amplitude of the vibration. Hence,
as the less refrangible colours grew more intense when the more
refrangible ones were introduced, we are forced to conclude that side
by side with the introduction of the shorter waves we had an
augmentation of the amplitude of the longer ones.

These remarks apply not only to the visible emission examined by Dr.
Draper, but to the invisible emission which precedes the appearance of
any light. In the emission from the white-hot platinum wire now before
you, the lightless waves exist with which we started, only their
intensity has been increased a thousand-fold by the augmentation of
temperature necessary to the production of this white light. Both
effects are bound up together: in an incandescent solid, or in a
molten solid, you cannot have the shorter waves without this
intensification of the longer ones. A sun is possible only on these
conditions; hence Sir William Herschel's discovery of the invisible
ultra-red solar emission.

The invisible heat, emitted both by dark bodies and by luminous ones,
flies through space with the velosity of light, and is called _radiant
heat_. Now, radiant heat may be made a subtle and powerful explorer of
molecular condition, and, of late years, it has given a new
significance to the act of chemical combination. Take, for example,
the air we breathe. It is a mixture of oxygen and nitrogen; and it
behaves towards radiant heat like a vacuum, being incompetent to
absorb it in any sensible degree. But permit the same two gases to
unite chemically; then, without any augmentation of the quantity of
matter, without altering the gaseous condition, without interfering in
any way with the transparency of the gas, the act of chemical union is
accompanied by an enormous diminution of its _diathermancy_, or
perviousness to radiant heat.

The researches which established this result also proved the
elementary gases, generally, to be highly transparent to radiant heat.
This, again, led to the proof of the diathermancy of elementary
liquids, like bromine, and of solutions of the solid elements sulphur,
phosphorus, and iodine. A spectrum is now before you, and you notice
that the transparent bisulphide of carbon has no effect upon the
colours. Dropping into the liquid a few flakes of iodine, you see the
middle of the spectrum cut away. By augmenting the quantity of iodine,
we invade the entire spectrum, and finally cut it off altogether. Now,
the iodine, which proves itself thus hostile to the light, is
perfectly transparent to the ultra-red emission with which we have now
to deal. It, therefore, is to be our ray-filter.

Placing the alum-cell again in front of the electric lamp, we assure
ourselves, as before, of the utter inability of the concentrated light
to fire white paper-Introducing a cell containing the solution of
iodine, the light is entirely cut off; and then, on removing the
alum-cell, the white paper at the dark focus is instantly set on fire.
Black paper is more absorbent than white for these rays; and the
consequence is, that with it the suddenness and vigour of the
combustion are augmented. Zinc is burnt up at the same place,
magnesium bursts into vivid combustion, while a sheet of platinized
platinum, placed at the focus, is heated to whiteness.

Looked at through a prism, the white-hot platinum yields all the
colours of the spectrum. Before impinging upon the platinum, the waves
were of too slow recurrence to awaken vision; by the atoms of the
platinum, these long and sluggish waves are broken up into shorter
ones, being thus brought within the visual range. At the other end of
the spectrum, by the interposition of suitable substances, Professor
Stokes _lowered_ the refrangibility, so as to render the non-visual
rays visual, and to this change he gave the name of _Fluorescence_.
Here, by the intervention of the platinum, the refrangibility is
_raised_, so as to render the non-visual visual, and to this change I
have given the name of _Calorescence_.

At the perfectly invisible focus where these effects are produced, the
air may be as cold as ice. Air, as already stated, does not absorb
radiant heat, and is therefore not warmed by it. Nothing could more
forcibly illustrate the isolation, if I may use the term, of the
luminiferous ether from the air. The wave-motion of the one is heaped
up to an extraordinary degree of intensity, without producing any
sensible effect upon the other. I may add that, with suitable
precautions, the eye may be placed in a focus competent to heat
platinum to vivid redness, without experiencing any damage, or the
slightest sensation either of light or heat.

The important part played by these ultra-red rays in Nature may be
thus illustrated: I remove the iodine filter, and concentrate the
total beam upon a test tube containing water. It immediately begins to
splutter, and in a minute or two it _boils_. What boils it? Placing
the alum solution in front of the lamp, the boiling instantly ceases.
Now, the alum is pervious to all the luminous rays; hence it cannot be
these rays that caused the boiling. I now introduce the iodine, and
remove the alum: vigorous ebullition immediately recommences at the
invisible focus. So that we here fix upon the invisible ultra-red rays
the heating of the water.

We are thus enabled to understand the momentous part played by these
rays in Nature. It is to them that we owe the warming and the
consequent evaporation of the tropical ocean; it is to them,
therefore, that we owe our rains and snows. They are absorbed close to
the surface of the ocean, and warm the superficial water, while the
luminous rays plunge to great depths without producing any sensible
effect. But we can proceed further than this. Here is a large flask
containing a freezing mixture, which has so chilled the flask, that
the aqueous vapour of the air of this room has been condensed and
frozen upon it to a white fur. Introducing the alum-cell, and placing
the coating of hoar-frost at the intensely luminous focus of the
electric lamp, not a spicula of the dazzling frost is melted.
Introducing the iodine-cell, and removing the alum, a broad space of
the frozen coating is instantly melted away. Hence we infer that the
snow and ice, which feed the Rhone, the Rhine, and other rivers with
glaciers for their sources, are released from their imprisonment upon
the mountains by the invisible ultra-red rays of the sun.


§ 6. _Identity of Light and Radiant Heat. Reflection from Plane and
Curved Surfaces. Total Reflection of Heat_.

The growth of science is organic. That which today is an _end_ becomes
to-morrow a _means_ to a remoter end. Every new discovery in science
is immediately made the basis of other discoveries, or of new methods
of investigation. Thus about fifty years ago OErsted, of Copenhagen,
discovered the deflection of a magnetic needle by an electric current;
and about the same time Thomas Seebeck, of Berlin, discovered
thermoelectricity. These great discoveries were soon afterwards turned
to account, by Nobili and Melloni, in the construction of an
instrument which has vastly augmented our knowledge of radiant heat.
This instrument, which is called a _thermo-electric pile_, or more
briefly a thermo-pile, consists of thin bars of bismuth and antimony,
soldered alternately together at their ends, but separated from each
other elsewhere. From the ends of this 'thermo-pile' wires pass to a
galvanometer, which consists of a coil of covered wire, within and
above which are suspended two magnetic needles, joined to a rigid
system, and carefully defended from currents of air.

The action of the arrangement is this: the heat, falling on the pile,
produces an electric current; the current, passing through the coil,
deflects the needles, and the magnitude of the deflection may be made
a measure of the heat. The upper needle moves over a graduated dial
far too small to be directly seen. It is now, however, strongly
illuminated; and above it is a lens which, if permitted, would form an
image of the needle and dial upon the ceiling. There, however, it
could not be conveniently viewed. The beam is therefore received upon
a looking-glass, placed at the proper angle, which throws the image
upon a screen. In this way the motions of this small needle may be
made visible to you all.

The delicacy of this apparatus is such that in a room filled, as this
room now is, with an audience physically warm, it is exceedingly
difficult to work with it. My assistant stands several feet off. I
turn the pile towards him: the heat radiated from his face, even at
this distance, produces a deflection of 90°. I turn the instrument
towards a distant wall, a little below the average temperature of the
room. The needle descends and passes to the other side of zero,
declaring by this negative deflection that the pile has lost its
warmth by radiation against the cold wall. Possessed of this
instrument, of our ray-filter, and of our large Nicol prisms, we are
in a condition to investigate a subject of great philosophical
interest; one which long engaged the attention of some of our foremost
scientific workers--the substantial _identity of light and radiant
heat_.

That they are identical in _all_ respects cannot of course be the
case, for if they were they would act in the same manner upon all
instruments, the _eye_ included. The identity meant is such as
subsists between one colour and another, causing them to behave alike
as regards reflection, refraction, double refraction, and
polarization. Let us here run rapidly over the resemblances of light
and heat. As regards reflection from plane surfaces, we may employ a
looking-glass to reflect the light. Marking any point in the track of
the reflected beam, cutting off the light by the dissolved iodine,
and placing the pile at the marked point, the needle immediately
starts aside, showing that the heat is reflected in the same direction
as the light. This is true for every position of the mirror.
Recurring, for example, to the simple apparatus employed in our first
lecture (fig. 3, p. 11); moving the index attached to the mirror along
the divisions of our graduated arc (_m_ _n_), and determining by the
pile the positions of the invisible reflected beam, we prove that the
angular velocity of the heat-beam, like that of the light-beam, is
twice that of the mirror.

[Illustration: Fig. 49.]

As regards reflection from curved surfaces, the identity also holds
good. Receiving the beam from our electric lamp on a concave mirror
(_m_ _m_, fig. 49), it is gathered up into a cone of reflected light
rendered visible by the floating dust of the air; marking the apex of
the cone by a pointer, and cutting off the light by the iodine
solution (T), a moment's exposure of the pile (P) at the marked point
produces a violent deflection of the needle.

The common reflection and the total reflection of a beam of radiant
heat may be simultaneously demonstrated. From the nozzle of the lamp
(L, fig. 50) a beam impinges upon a plane mirror (M N), is reflected
upwards, and enters a right-angled prism, of which _a_ _b_ _c_ is the
section. It meets the hypothenuse at an obliquity greater than the
limiting angle,[23] and is therefore totally reflected. Quenching the
light by the ray-filter at F, and placing the pile at P, the totally
reflected heat-beam is immediately felt by the pile, and declared by
the galvanometric deflection.

[Illustration: Fig. 50.]


§ 7. _Invisible Images formed by Radiant Heat._

Perhaps no experiment proves more conclusively the substantial
identity of light and radiant heat, than the formation of invisible
heat-images. Employing the mirror already used to raise the beam to
its highest state of concentration, we obtain, as is well known, an
inverted image of the carbon points, formed by the light rays at the
focus. Cutting off the light by the ray-filter, and placing at the
focus a thin sheet of platinized platinum, the invisible rays declare
their presence and distribution, by stamping upon the platinum a
white-hot image of the carbons. (See fig. 51.)

[Illustration: Fig. 51.]


§ 8. _Polarization of Heat_.

Whether radiant heat be capable of polarization or not was for a long
time a subject of discussion. Bérard had announced affirmative
results, but Powell and Lloyd failed to verify them. The doubts thus
thrown upon the question were removed by the experiments of Forbes,
who first established the polarization and 'depolarization' of heat.
The subject was subsequently followed up by Melloni, an investigator
of consummate ability, who sagaciously turned to account his own
discovery, that the obscure rays of luminous sources are in part
transmitted by black glass. Intercepting by a plate of this glass the
light from an oil flame, and operating upon the transmitted invisible
heat, he obtained effects of polarization, far exceeding in magnitude
those which could be obtained with non-luminous sources. At present
the possession of our more perfect ray-filter, and more powerful
source of heat, enables us to pursue this identity question to its
utmost practical limits.

[Illustration: Fig. 52.]

Mounting our two Nicols (B and C, fig. 52) in front of the electric
lamp, with their principal sections crossed, no light reaches the
screen. Placing our thermo-electric pile (D) behind the prisms, with
its face turned towards the source, no deflection of the galvanometer
is observed. Interposing between the lamp (A) and the first prism (B)
our ray-filter, the light previously transmitted through the first
Nicol is quenched; and now the slightest turning of either Nicol opens
a way for the transmission of the heat, a very small rotation
sufficing to send the needle up to 90°. When the Nicol is turned back
to its first position, the needle again sinks to zero, thus
demonstrating, in the plainest manner, the polarization of the heat.

When the Nicols are crossed and the field is dark, you have seen, in
the case of light, the effect of introducing a plate of mica between
the polarizer and analyzer. In two positions the mica exerts no
sensible influence; in all others it does. A precisely analogous
deportment is observed as regards radiant heat. Introducing our
ray-filter, the thermo-pile, playing the part of an eye as regards the
invisible radiation, receives no heat when the eye receives no light;
but when the mica is so turned as to make its planes of vibration
oblique to those of the polarizer and analyzer, the heat immediately
passes through. So strong does the action become, that the momentary
plunging of the film of mica into the dark space between the Nicols
suffices to send the needle up to 90°. This is the effect to which the
term 'depolarization' has been applied; the experiment really proving
that with both light and heat we have the same resolution by the plate
of mica, and recompounding by the analyzer, of the ethereal
vibrations.

Removing the mica and restoring the needle once more to 0°, I
introduce between the Nicols a plate of quartz cut perpendicular to
the axis; the immediate deflection of the needle declares the
transmission of the heat, and when the transmitted beam is properly
examined, it is found to be circularly polarized, exactly as a beam of
light is polarized under the same conditions.


§ 9. _Double Refraction of Heat_.

I will now abandon the Nicols, and send through the piece of Iceland
spar (B, fig. 53), already employed (in Lecture III.) to illustrate
the double refraction of light, our sifted beam of invisible heat. To
determine the positions of the two images, let us first operate upon
the luminous beam. Marking the places of the light-images, we
introduce between N and L our ray-filter (not in the figure) and
quench the light. Causing the pile to approach one of the marked
places, the needle remains unmoved until the place has been attained;
here the pile at once detects the heat. Pushing the pile across the
interval separating the two marks, the needle first falls to 0°, and
then rises again to 90° in the second position. This proves the double
refraction of the heat.

[Illustration: Fig. 53.]

I now turn the Iceland spar: the needle remains fixed; there is no
alteration of the deflection. Passing the pile rapidly across to the
other mark, the deflection is maintained. Once more I turn the spar,
but now the needle falls to 0°, rising, however, again to 90° after a
rotation of 360°. We know that in the case of light the extraordinary
beam rotates round the ordinary one; and we have here been operating
on the extraordinary heat-beam, which, as regards double refraction,
behaves exactly like a beam of light.


§ 10. _Magnetization of Heat_.

To render our series of comparisons complete, we must demonstrate the
magnetization of heat. But here a slight modification of our
arrangement will be necessary. In repeating Faraday's experiment on
the magnetization of light, we had, in the first instance, our Nicols
crossed and the field rendered dark, a flash of light appearing upon
the screen when the magnet was excited. Now the quantity of light
transmitted in this case is really very small, its effect being
rendered striking through contrast with the preceding darkness. When
we so place the Nicols that their principal sections enclose an angle
of 45°, the excitement of the magnet causes a far greater positive
augmentation of the light, though the augmentation is not so well
_seen_ through lack of contrast, because here, at starting, the field
is illuminated.

In trying to magnetize our beam of heat, we will adopt this
arrangement. Here, however, at the outset, a considerable amount of
heat falls upon one face of the pile. This it is necessary to
neutralize, by permitting rays from another source to fall upon the
opposite face of the pile. The needle is thus brought to zero. Cutting
off the light by our ray-filter, and exciting the magnet, the needle
is instantly deflected, proving that the magnet has opened a door for
the heat, exactly as in Faraday's experiment it opened a door for the
light. Thus, in every case brought under our notice, the substantial
identity of light and radiant heat has been demonstrated.

By the refined experiments of Knoblauch, who worked long and
successfully at this question, the double refraction of heat, by
Iceland spar, was first demonstrated; but, though he employed the
luminous heat of the sun, the observed deflections were exceedingly
small. So, likewise, those eminent investigators De la Povostaye and
Desains succeeded in magnetizing a beam of heat; but though, in their
case also, the luminous solar heat was employed, the deflection
obtained did not amount to more than two or three degrees. With
_obscure_ radiant heat the effect, prior to the experiments now
brought before you, had not been obtained; but, with the arrangement
here described, we obtain deflections from purely invisible heat,
equal to 150 of the lower degrees of the galvanometer.


§ 11. _Distribution of Heat in the Electric Spectrum_.

We have finally to determine the position and magnitude of the
invisible radiation which produces these results. For this purpose we
employ a particular form of the thermo-pile. Its face is a rectangle,
which by movable side-pieces can be rendered as narrow as desirable.
Throwing a small and concentrated spectrum upon a screen, by means of
an endless screw we move the rectangular pile through the entire
spectrum, and determine in succession the thermal power of all its
colours.

[Illustration: SPECTRUM OF ELECTRIC LIGHT.]

When this instrument is brought to the violet end of the spectrum,
the heat is found to be almost insensible. As the pile gradually moves
from the violet towards the red, it encounters a gradually augmenting
heat. The red itself possesses the highest heating power of all the
colours of the spectrum. Pushing the pile into the dark space beyond
the red, the heat rises suddenly in intensity, and at some distance
beyond the red it attains a maximum. From this point the heat falls
somewhat more rapidly than it rose, and afterwards gradually fades
away.

Drawing a horizontal line to represent the length of the spectrum, and
erecting along it, at various points, perpendiculars proportional in
length to the heat existing at those points, we obtain a curve which
exhibits the distribution of heat in the prismatic spectrum. It is
represented in the adjacent figure. Beginning at the blue, the curve
rises, at first very gradually; towards the red it rises more rapidly,
the line C D (fig. 54, opposite page) representing the strength of the
extreme red radiation. Beyond the red it shoots upwards in a steep and
massive peak to B; whence it falls, rapidly for a time, and afterwards
gradually fades from the perception of the pile. This figure is the
result of more than twelve careful series of measurements, from each
of which the curve was constructed. On superposing all these curves, a
satisfactory agreement was found to exist between them. So that it may
safely be concluded that the areas of the dark and white spaces,
respectively, represent the relative energies of the visible and
invisible radiation. The one is 7.7 times the other.

But in verification, as already stated, consists the strength of
science. Determining in the first place the total emission from the
electric lamp, and then, by means of the iodine filter, determining
the ultra-red emission; the difference between both gives the luminous
emission. In this way, it is found that the energy of the invisible
emission is eight times that of the visible. No two methods could be
more opposed to each other, and hardly any two results could better
harmonize. I think, therefore, you may rely upon the accuracy of the
distribution of heat here assigned to the prismatic spectrum of the
electric light. There is nothing vague in the mode of investigation,
or doubtful in its conclusions. Spectra are, however, formed by
_diffraction_, wherein the distribution of both heat and light is
different from that produced by the prism. These diffractive spectra
have been examined with great skill by Draper and Langley. In the
prismatic spectrum the less refrangible rays are compressed into a
much smaller space than in the diffraction spectrum.



LECTURE VI.

PRINCIPLES OF SPECTRUM ANALYSIS
PRISMATIC ANALYSIS OF THE LIGHT OF INCANDESCENT VAPOURS
DISCONTINUOUS SPECTRA
SPECTRUM BANDS PROVED BY BUNSEN AND KIRCHHOFF TO BE CHARACTERISTIC
  OF THE VAPOUR
DISCOVERY OF RUBIDIUM, CÆSIUM, AND THALLIUM
RELATION OF EMISSION TO ABSORPTION
THE LINES OF FRAUNHOFER
THEIR EXPLANATION BY KIRCHHOFF
SOLAR CHEMISTRY INVOLVED IN THIS EXPLANATION
FOUCAULT'S EXPERIMENT
PRINCIPLES OF ABSORPTION
ANALOGY OF SOUND AND LIGHT
EXPERIMENTAL DEMONSTRATION OF THIS ANALOGY
RECENT APPLICATIONS OF THE SPECTROSCOPE
SUMMARY AND CONCLUSION.


We have employed as our source of light in these lectures the ends of
two rods of coke rendered incandescent by electricity. Coke is
particularly suitable for this purpose, because it can bear intense
heat without fusion or vaporization. It is also black, which helps the
light; for, other circumstances being equal, as shown experimentally
by Professor Balfour Stewart, the blacker the body the brighter will
be its light when incandescent. Still, refractory as carbon is, if we
closely examined our voltaic arc, or stream of light between the
carbon-points, we should find there incandescent carbon-vapour. And if
we could detach the light of this vapour from the more dazzling light
of the solid points, we should find its spectrum not only less
brilliant, but of a totally different character from the spectra that
we have already seen. Instead of being an unbroken succession of
colours from red to violet, the carbon-vapour would yield a few bands
of colour with spaces of darkness between them.

What is true of the carbon is true in a still more striking degree of
the metals, the most refractory of which can be fused, boiled, and
reduced to vapour by the electric current. From the incandescent
vapour the light, as a general rule, flashes in groups of rays of
definite degrees of refrangibility, spaces existing between group and
group, which are unfilled by rays of any kind. But the contemplation
of the facts will render this subject more intelligible than words can
make it. Within the camera is now placed a cylinder of carbon hollowed
out at the top; in the hollow is placed a fragment of the metal
thallium. Down upon this we bring the upper carbon-point, and then
separate the one from the other. A stream of incandescent
thallium-vapour passes between them, the magnified image of which is
now seen upon the screen. It is of a beautiful green colour. What is
the meaning of that green? We answer the question by subjecting the
light to prismatic analysis. Sent through the prism, its spectrum is
seen to consist of a single refracted band. Light of one degree of
refrangibility--that corresponding to this particular green--is
emitted by the thallium-vapour.

We will now remove the thallium and put a bit of silver in its place.
The are of silver is not to be distinguished from that of thallium; it
is not only green, but the same shade of green. Are they then alike?
Prismatic analysis enables us to answer the question. However
impossible it is to distinguish the one _colour_ from the other, it is
equally impossible to confound the _spectrum_ of incandescent
silver-vapour with that of thallium. In the case of silver, we have
two green bands instead of one.

If we add to the silver in our camera a bit of thallium, we shall
obtain the light of both metals. After waiting a little, we see that
the green of the thallium lies midway between the two greens of the
silver. Hence this similarity of colour.

But why have we to 'wait a little' before we see this effect? The
thallium band at first almost masks the silver bands by its superior
brightness. Indeed, the silver bands have wonderfully degenerated
since the bit of thallium was put in, and for a reason worth knowing.
It is the _resistance_ offered to the passage of the electric current
from carbon to carbon, that calls forth the power of the current to
produce heat. If the resistance were materially lessened, the heat
would be materially lessened; and if all resistance were abolished,
there would be no heat at all. Now, thallium is a much more fusible
and vaporizable metal than silver; and its vapour facilitates the
passage of the electricity to such a degree, as to render the current
almost incompetent to vaporize the more refractory silver. But the
thallium is gradually consumed; its vapour diminishes, the resistance
rises, until finally you see the two silver bands as brilliant as they
were at first.[24]

We have in these bands a perfectly unalterable characteristic of the
two metals. You never get other bands than these two green ones from
the silver, never other than the single green band from the thallium,
never other than the three green bands from the mixture of both
metals. Every known metal has its own particular bands, and in no
known case are the bands of two different metals alike in
refrangibility. It follows, therefore, that these spectra may be made
a sure test for the presence or absence of any particular metal. If we
pass from the metals to their alloys, we find no confusion. Copper
gives green bands; zinc gives blue and red bands; brass--an alloy of
copper and zinc--gives the bands of both metals, perfectly unaltered
in position or character.

But we are not confined to the metals themselves; the _salts_ of these
metals yield the bands of the metals. Chemical union is ruptured by a
sufficiently high heat; the vapour of the metal is set free, and it
yields its characteristic bands. The chlorides of the metals are
particularly suitable for experiments of this character. Common salt,
for example, is a compound of chlorine and sodium; in the electric
lamp it yields the spectrum of the metal sodium. The chlorides of
copper, lithium, and strontium yield, in like manner, the bands of
these metals.

When, therefore, Bunsen and Kirchhoff, the illustrious founders of
_spectrum analysis_, after having established by an exhaustive
examination the spectra of all known substances, discovered a spectrum
containing bands different from any known bands, they immediately
inferred the existence of a new metal. They were operating at the time
upon a residue, obtained by evaporating one of the mineral waters of
Germany. In that water they knew the unknown metal was concealed, but
vast quantities of it had to be evaporated before a residue could be
obtained sufficiently large to enable ordinary chemistry to grapple
with the metal. They, however, hunted it down, and it now stands
among chemical substances as the metal _Rubidium_. They subsequently
discovered a second metal, which they called _Cæsium_. Thus, having
first placed spectrum analysis on a sure foundation, they demonstrated
its capacity as an agent of discovery. Soon afterwards Mr. Crookes,
pursuing the same method, discovered the bright green band of
_Thallium_, and obtained the salts of the metal which yielded it. The
metal itself was first isolated in ingots by M. Lamy, a French
chemist.

All this relates to chemical discovery upon earth, where the materials
are in our own hands. But it was soon shown how spectrum analysis
might be applied to the investigation of the sun and stars; and this
result was reached through the solution of a problem which had been
long an enigma to natural philosophers. The scope and conquest of this
problem we must now endeavour to comprehend. A spectrum is _pure_ in
which the colours do not overlap each other. We purify the spectrum by
making our beam narrow, and by augmenting the number of our prisms.
When a pure spectrum of the sun has been obtained in this way, it is
found to be furrowed by innumerable dark lines. Four of them were
first seen by Dr. Wollaston, but they were afterwards multiplied and
measured by Fraunhofer with such masterly skill, that they are now
universally known as Fraunhofer's lines. To give an explanation of
these lines was, as I have said, a problem which long challenged the
attention of philosophers, and to Professor Kirchhoff belongs the
honour of having first conquered this problem.

(The positions of the principal lines, lettered according to
Fraunhofer, are shown in the annexed sketch (fig. 55) of the solar
spectrum. A is supposed to stand near the extreme red, and J near the
extreme violet.)

[Illustration: Fig. 55.]

The brief memoir of two pages, in which this immortal discovery is
recorded, was communicated to the Berlin Academy on October 27, 1859.
Fraunhofer had remarked in the spectrum of a candle flame two bright
lines, which coincide accurately, as to position, with the double dark
line D of the solar spectrum. These bright lines are produced with
particular intensity by the yellow flame derived from a mixture of
salt and alcohol. They are in fact the lines of sodium vapour.
Kirchhoff produced a spectrum by permitting the sunlight to enter his
telescope by a slit and prism, and in front of the slit he placed the
yellow sodium flame. As long as the spectrum remained feeble, there
always appeared two bright lines, derived from the flame, in the place
of the two dark lines D of the spectrum. In this case, such absorption
as the flame exerted upon the sunlight was more than atoned for by the
radiation from the flame. When, however, the solar spectrum was
rendered sufficiently intense, the bright bands vanished, and the two
dark Fraunhofer lines appeared with much greater sharpness and
distinctness than when the flame was not employed.

This result, be it noted, was not due to any real quenching of the
bright lines of the flame, but to the augmentation of the intensity of
the adjacent spectrum. The experiment proved to demonstration, that
when the white light sent through the flame was sufficiently intense,
the quantity which the flame absorbed was far in excess of that which
it radiated.

Here then is a result of the utmost significance. Kirchhoff
immediately inferred from it that the salt flame, which could
intensify so remarkably the dark lines of Fraunhofer, ought also to be
able to _produce_ them. The spectrum of the Drummond light is known to
exhibit the two bright lines of sodium, which, however, gradually
disappear as the modicum of sodium, contained as an impurity in the
incandescent lime, is exhausted. Kirchhoff formed a spectrum of the
limelight, and after the two bright lines had vanished, he placed his
salt flame in front of the slit. The two dark lines immediately
started forth. Thus, in the continuous spectrum of the lime-light, he
evoked, artificially, the lines D of Fraunhofer.

Kirchhoff knew that this was an action not peculiar to the sodium
flame, and he immediately extended his generalisation to all coloured
flames which yield sharply defined bright bands in their spectra.
White light, with all its constituents complete, sent through such
flames, would, he inferred, have those precise constituents absorbed,
whose refrangibilities are the same as those of the bright bands; so
that after passing through such flames, the white light, if
sufficiently intense, would have its spectrum furrowed by bands of
darkness. On the occasion here referred to Kirchhoff also succeeded in
reversing a bright band of lithium.

The long-standing difficulty of Fraunhofer's lines fell to pieces in
the presence of facts and reflections like these, which also carried
with them an immeasurable extension of the chemist's power. Kirchhoff
saw that from the agreement of the lines in the spectra of terrestrial
substances with Fraunhofer's lines, the presence of these substances
in the sun and fixed stars might be immediately inferred. Thus the
dark lines D in the solar spectrum proved the existence of sodium in
the solar atmosphere; while the bright lines discovered by Brewster in
a nitre flame, which had been proved to coincide exactly with certain
dark lines between A and B in the solar spectrum, proved the existence
of potassium in the sun.

All subsequent research verified the accuracy of these first daring
conclusions. In his second paper, communicated to the Berlin Academy
before the close of 1859, Kirchhoff proved the existence of iron in
the sun. The bright lines of the spectrum of iron vapour are
exceedingly numerous, and 65 of them were subsequently proved by
Kirchhoff to be absolutely identical in position with 65 dark
Fraunhofer's lines. Ångström and Thalén pushed the coincidences to 450
for iron, while, according to the same excellent investigators, the
following numbers express the coincidences, in the case of the
respective metals to which they are attached:--

Calcium     75
Barium      11
Magnesium    4
Manganese   57
Titanium   118
Chromium    18
Nickel      33
Cobalt      19
Hydrogen     4
Aluminium    2
Zinc         2
Copper       7

The probability is overwhelming that all these substances exist in the
atmosphere of the sun.

Kirchhoff's discovery profoundly modified the conceptions previously
entertained regarding the constitution of the sun, leading him to
views which, though they may be modified in detail, will, I believe,
remain substantially valid to the end of time. The sun, according to
Kirchhoff, consists of a molten nucleus which is surrounded by a
flaming atmosphere of lower temperature. The nucleus may, in part, be
_clouds_, mixed with, or underlying true vapour. The light of the
nucleus would give us a continuous spectrum, like that of the Drummond
light; but having to pass through the photosphere, as Kirchhoff's beam
passed through the sodium flame, those rays of the nucleus which the
photosphere emit are absorbed, and shaded lines, corresponding to the
rays absorbed, occur in the spectrum. Abolish the solar nucleus, and
we should have a spectrum showing a bright line in the place of every
dark line of Fraunhofer, just as, in the case of Kirchhoff's second
experiment, we should have the bright sodium lines of the flame if the
lime-light were withdrawn. These lines of Fraunhofer are therefore not
absolutely dark, but dark by an amount corresponding to the difference
between the light intercepted and the light emitted by the
photosphere.

Almost every great scientific discovery is approached
contemporaneously by many minds, the fact that one mind usually
confers upon it the distinctness of demonstration being an
illustration, not of genius isolated, but of genius in advance. Thus
Foucault, in 1849, came to the verge of Kirchhoff's discovery. By
converging an image of the sun upon a voltaic arc, and thus obtaining
the spectra of both sun and arc superposed, he found that the two
bright lines which, owing to the presence of a little sodium in the
carbons or in the air, are seen in the spectrum of the arc, coincide
with the dark lines D of the solar spectrum. The lines D he found to
he considerably strengthened by the passage of the solar light through
the voltaic arc.

Instead of the image of the sun, Foucault then projected upon the arc
the image of one of the solid incandescent carbon points, which of
itself would give a continuous spectrum; and he found that the lines D
were thus _generated_ in that spectrum. Foucault's conclusion from
this admirable experiment was 'that the arc is a medium which emits
the rays D on its own account, and at the same time absorbs them when
they come from another quarter.' Here he stopped. He did not extend
his observations beyond the voltaic arc; he did not offer any
explanation of the lines of Fraunhofer; he did not arrive at any
conception of solar chemistry, or of the constitution of the sun. His
beautiful experiment remained a germ without fruit, until the
discernment, ten years subsequently, of the whole class of phenomena
to which it belongs, enabled Kirchhoff to solve these great problems.

Soon after the publication of Kirchhoff's discovery, Professor Stokes,
who also, ten years prior to the discovery, had nearly anticipated it,
borrowed an illustration from sound, to explain the reciprocity of
radiation and absorption. A stretched string responds to aërial
vibrations which synchronize with its own. A great number of such
strings stretched in space would roughly represent a medium; and if
the note common to them all were sounded at a distance they would take
up or absorb its vibrations.

When a violin-bow is drawn across this tuning-fork, the room is
immediately filled with a musical sound, which may be regarded as the
_radiation_ or _emission_ of sound from the fork. A few days ago, on
sounding this fork, I noticed that when its vibrations were quenched,
the sound seemed to be continued, though more feebly. It appeared,
moreover, to come from under a distant table, where stood a number of
tuning-forks of different sizes and rates of vibration. One of these,
and one only, had been started by the sounding fork, and it was the
one whose rate of vibration was the same as that of the fork which
started it. This is an instance of the _absorption_ of the sound of
one fork by another. Placing two unisonant forks near each other,
sweeping the bow over one of them, and then quenching the agitated
fork, the other continues to sound; this other can re-excite the
former, and several transfers of sound between the two forks can be
thus effected. Placing a cent-piece on each prong of one of the forks,
we destroy its perfect synchronism with the other, and no such
communication of sound from the one to the other is then possible.

I have now to bring before you, on a suitable scale, the demonstration
that we can do with _light_ what has been here done with sound. For
several days in 1861 I endeavoured to accomplish this, with only
partial success. In iron dishes a mixture of dilute alcohol and salt
was placed, and warmed so as to promote vaporization. The vapour was
ignited, and through the yellow flame thus produced the beam from the
electric lamp was sent; but a faint darkening only of the yellow band
of a projected spectrum could be obtained. A trough was then made
which, when fed with the salt and alcohol, yielded a flame ten feet
thick; but the result of sending the light through this depth of flame
was still unsatisfactory. Remembering that the direct combustion of
sodium in a Bunsen's flame produces a yellow far more intense than
that of the salt flame, and inferring that the intensity of the colour
indicated the copiousness of the incandescent vapour, I sent through
the flame from metallic sodium the beam of the electric lamp. The
success was complete; and this experiment I wish now to repeat in your
presence.[25]

Firstly then you notice, when a fragment of sodium is placed in a
platinum spoon and introduced into a Bunsen's flame, an intensely
yellow light is produced. It corresponds in refrangibility with the
yellow band of the spectrum. Like our tuning-fork, it emits waves of a
special period. When the white light from the electric lamp is sent
through that flame, you will have ocular proof that the yellow flame
intercepts the yellow of the spectrum; in other words, that it absorbs
waves of the same period as its own, thus producing, to all intents
and purposes, a dark Fraunhofer's band in the place of the yellow.

In front of the slit (at L, fig. 56) through which the beam issues is
placed a Bunsen's burner (_b_) protected by a chimney (C). This beam,
after passing through a lens, traverses the prism (P) (in the real
experiment there was a pair of prisms), is there decomposed, and forms
a vivid continuous spectrum (S S) upon the screen. Introducing a
platinum spoon with its pellet of sodium into the Bunsen's flame, the
pellet first fuses, colours the flame intensely yellow, and at length
bursts into violent combustion. At the same moment the spectrum is
furrowed by an intensely dark band (D), two inches wide and two feet
long. Introducing and withdrawing the sodium flame in rapid
succession, the sudden appearance and disappearance of the band of
darkness is shown in a most striking manner. In contrast with the
adjacent brightness this band appears absolutely black, so vigorous is
the absorption. The blackness, however, is but relative, for upon the
dark space falls a portion of the light of the sodium flame.

[Illustration: Fig. 56.]

I have already referred to the experiment of Foucault; but other
workers also had been engaged on the borders of this subject before it
was taken up by Bunsen and Kirchhoff. With some modification I have on
a former occasion used the following words regarding the precursors of
the discovery of spectrum analysis, and solar chemistry:--'Mr. Talbot
had observed the bright lines in the spectra of coloured flames, and
both he and Sir John Herschel pointed out the possibility of making
prismatic analysis a chemical test of exceeding delicacy, though not
of entire certainty. More than a quarter of a century ago Dr. Miller
gave drawings and descriptions of the spectra of various coloured
flames. Wheatstone, with his accustomed acuteness, analyzed the light
of the electric spark, and proved that the metals between which the
spark passed determined the bright bands in its spectrum. In an
investigation described by Kirchhoff as "classical," Swan had shown
that 1/2,500,000 of a grain of sodium in a Bunsen's flame could be
detected by its spectrum. He also proved the constancy of the bright
lines in the spectra of hydrocarbon flames. Masson published a prize
essay on the bands of the induction spark; while Van der Willigen, and
more recently Plücker, have also given us beautiful drawings of
spectra obtained from the same source.

'But none of these distinguished men betrayed the least knowledge of
the connexion between the bright bands of the metals and the dark
lines of the solar spectrum; nor could spectrum analysis be said to be
placed upon anything like a safe foundation prior to the researches of
Bunsen and Kirchhoff. The man who, in a published paper, came nearest
to the philosophy of the subject was Ångström. In that paper,
translated by myself, and published in the "Philosophical Magazine"
for 1855, he indicates that the rays which a body absorbs are
precisely those which, when luminous, it can emit. In another place,
he speaks of one of his spectra giving the general impression of the
_reversal_ of the solar spectrum. But his memoir, philosophical as it
is, is distinctly marked by the uncertainty of his time. Foucault,
Thomson, and Balfour Stewart have all been near the discovery, while,
as already stated, it was almost hit by the acute but unpublished
conjecture of Stokes.'

Mentally, as well as physically, every year of the world's age is the
outgrowth and offspring of all preceding years. Science proves itself
to be a genuine product of Nature by growing according to this law. We
have no solution of continuity here. All great discoveries are duly
prepared for in two ways; first, by other discoveries which form their
prelude; and, secondly, by the sharpening of the inquiring intellect.
Thus Ptolemy grew out of Hipparchus, Copernicus out of both, Kepler
out of all three, and Newton out of all the four. Newton did not rise
suddenly from the sea-level of the intellect to his amazing elevation.
At the time that he appeared, the table-land of knowledge was already
high. He juts, it is true, above the table-land, as a massive peak;
still he is supported by the plateau, and a great part of his absolute
height is the height of humanity in his time. It is thus with the
discoveries of Kirchhoff. Much had been previously accomplished; this
he mastered, and then by the force of individual genius went beyond
it. He replaced uncertainty by certainty, vagueness by definiteness,
confusion by order; and I do not think that Newton has a surer claim
to the discoveries that have made his name immortal, than Kirchhoff
has to the credit of gathering up the fragmentary knowledge of his
time, of vastly extending it, and of infusing into it the life of
great principles.

With one additional point we will wind up our illustrations of the
principles of solar chemistry. Owing to the scattering of light by
matter floating mechanically in the earth's atmosphere, the sun is
seen not sharply defined, but surrounded by a luminous glare. Now, a
loud noise will drown a whisper, an intense light will overpower a
feeble one, and so this circumsolar glare prevents us from seeing many
striking appearances round the border of the sun. The glare is
abolished in total eclipses, when the moon comes between the earth and
the sun, and there are then seen a series of rose-coloured
protuberances, stretching sometimes tens of thousands of miles beyond
the dark edge of the moon. They are described by Vassenius in the
'Philosophical Transactions' for 1733; and were probably observed even
earlier than this. In 1842 they attracted great attention, and were
then compared to Alpine snow-peaks reddened by the evening sun. That
these prominences are flaming gas, and principally hydrogen gas, was
first proved by M. Janssen during an eclipse observed in India, on the
18th of August, 1868.

But the prominences may be rendered visible in sunshine; and for a
reason easily understood. You have seen in these lectures a single
prism employed to produce a spectrum, and you have seen a pair of
prisms employed. In the latter case, the dispersed white light, being
diffused over about twice the area, had all its colours
proportionately diluted. You have also seen one prism and a pair of
prisms employed to produce the bands of incandescent vapours; but here
the light of each band, being absolutely monochromatic, was incapable
of further dispersion by the second prism, and could not therefore be
weakened by such dispersion.

Apply these considerations to the circumsolar region. The glare of
white light round the sun can be dispersed and weakened to any extent,
by augmenting the number of prisms; while a monochromatic light,
mixed with this glare, and masked by it, would retain its intensity
unenfeebled by dispersion. Upon this consideration has been founded a
method of observation, applied independently by M. Janssen in India
and by Mr. Lockyer in England, by which the monochromatic bands of the
prominences are caused to obtain the mastery, and to appear in broad
daylight. By searching carefully and skilfully round the sun's rim,
Mr. Lockyer has proved these prominences to be mere local juttings
from a fiery envelope which entirely clasps the sun, and which he has
called the _Chromosphere_.

It would lead us far beyond the object of these lectures to dwell upon
the numerous interesting and important results obtained by Secchi,
Respighi, Young, and other distinguished men who have worked at the
chemistry of the sun and its appendages. Nor can I do more at present
than make a passing reference to the excellent labours of Dr. Huggins
in connexion with the fixed stars, nebulae, and comets. They, more
than any others, illustrate the literal truth of the statement, that
the establishment of spectrum analysis, and the explanation of
Fraunhofer's lines, carried with them an immeasurable extension of the
chemist's range. The truly powerful experiments of Professor Dewar are
daily adding to our knowledge, while the refined researches of Capt.
Abney and others are opening new fields of inquiry. But my object here
is to make principles plain, rather than to follow out the details of
their illustration.


SUMMARY AND CONCLUSION.

My desire in these lectures has been to show you, with as little
breach of continuity as possible, something of the past growth and
present aspect of a department of science, in which have laboured some
of the greatest intellects the world has ever seen. I have sought to
confer upon each experiment a distinct intellectual value, for
experiments ought to be the representatives and expositors of
thought--a language addressed to the eye as spoken words are to the
ear. In association with its context, nothing is more impressive or
instructive than a fit experiment; but, apart from its context, it
rather suits the conjurer's purpose of surprise, than the purpose of
education which ought to be the ruling motive of the scientific man.

And now a brief summary of our work will not be out of place. Our
present mastery over the laws and phenomena of light has its origin in
the desire of man to _know_. We have seen the ancients busy with this
problem, but, like a child who uses his arms aimlessly, for want of
the necessary muscular training, so these early men speculated vaguely
and confusedly regarding natural phenomena, not having had the
discipline needed to give clearness to their insight, and firmness to
their grasp of principles. They assured themselves of the rectilineal
propagation of light, and that the angle of incidence was equal to the
angle of reflection. For more than a thousand years--I might say,
indeed, for more than fifteen hundred years--the scientific intellect
appears as if smitten with paralysis, the fact being that, during this
time, the mental force, which might have run in the direction of
science, was diverted into other directions.

The course of investigation, as regards light, was resumed in 1100 by
an Arabian philosopher named Alhazen. Then it was taken up in
succession by Roger Bacon, Vitellio, and Kepler. These men, though
failing to detect the principles which ruled the facts, kept the fire
of investigation constantly burning. Then came the fundamental
discovery of Snell, that cornerstone of optics, as I have already
called it, and immediately afterwards we have the application, by
Descartes, of Snell's discovery to the explanation of the rainbow.
Following this we have the overthrow, by Roemer, of the notion of
Descartes, that light was transmitted instantaneously through space.
Then came Newton's crowning experiments on the analysis and synthesis
of white light, by which it was proved to be compounded of various
kinds of light of different degrees of refrangibility.

Up to his demonstration of the composition of white light, Newton had
been everywhere triumphant--triumphant in the heavens, triumphant on
the earth, and his subsequent experimental work is, for the most part,
of immortal value. But infallibility is not an attribute of man, and,
soon after his discovery of the nature of white light, Newton proved
himself human. He supposed that refraction and chromatic dispersion
went hand in hand, and that you could not abolish the one without at
the same time abolishing the other. Here Dollond corrected him.

But Newton committed a graver error than this. Science, as I sought to
make clear to you in our second lecture, is only in part a thing of
the senses. The roots of phenomena are embedded in a region beyond the
reach of the senses, and less than the root of the matter will never
satisfy the scientific mind. We find, accordingly, in this career of
optics the greatest minds constantly yearning to break the bounds of
the senses, and to trace phenomena to their subsensible foundation.
Thus impelled, they entered the region of theory, and here Newton,
though drawn from time to time towards truth, was drawn still more
strongly towards error; and he made error his substantial choice. His
experiments are imperishable, but his theory has passed away. For a
century it stood like a dam across the course of discovery; but, as
with all barriers that rest upon authority, and not upon truth, the
pressure from behind increased, and eventually swept the barrier away.

In 1808 Malus, looking through Iceland spar at the sun, reflected from
the window of the Luxembourg Palace in Paris, discovered the
polarization of light by reflection. As stated at the time, this
discovery ushered in the darkest hour in the fortunes of the wave
theory. But the darkness did not continue. In 1811 Arago discovered
the splendid chromatic phenomena which we have had illustrated by the
deportment of plates of gypsum in polarized light; he also discovered
the rotation of the plane of polarization by quartz-crystals. In 1813
Seebeck discovered the polarization of light by tourmaline. That same
year Brewster discovered those magnificent bands of colour that
surround the axes of biaxal crystals. In 1814 Wollaston discovered the
rings of Iceland spar. All these effects, which, without a theoretic
clue, would leave the human mind in a jungle of phenomena without
harmony or relation, were organically connected by the theory of
undulation.

The wave theory was applied and verified in all directions, Airy being
especially conspicuous for the severity and conclusiveness of his
proofs. A most remarkable verification fell to the lot of the late Sir
William Hamilton, of Dublin, who, taking up the theory where Fresnel
had left it, arrived at the conclusion that at four special points of
the 'wave-surface' in double-refracting crystals, the ray was divided,
not into two parts but into an infinite number of parts; forming at
these points a continuous conical envelope instead of two images. No
human eye had ever seen this envelope when Sir William Hamilton
inferred its existence. He asked Dr. Lloyd to test experimentally the
truth of his theoretic conclusion. Lloyd, taking a crystal of
arragonite, and following with the most scrupulous exactness the
indications of theory, cutting the crystal where theory said it ought
to be cut, observing it where theory said it ought to be observed,
discovered the luminous envelope which had previously been a mere idea
in the mind of the mathematician.

Nevertheless this great theory of undulation, like many another truth,
which in the long run has proved a blessing to humanity, had to
establish, by hot conflict, its right to existence. Illustrious names
were arrayed against it. It had been enunciated by Hooke, it had been
expounded and applied by Huyghens, it had been defended by Euler. But
they made no impression. And, indeed, the theory in their hands lacked
the strength of a demonstration. It first took the form of a
demonstrated verity in the hands of Thomas Young. He brought the waves
of light to bear upon each other, causing them to support each other,
and to extinguish each other at will. From their mutual actions he
determined their lengths, and applied his knowledge in all directions.
He finally showed that the difficulty of polarization yielded to the
grasp of theory.

After him came Fresnel, whose transcendent mathematical abilities
enabled him to give the theory a generality unattained by Young. He
seized it in its entirety; followed the ether into the hearts of
crystals of the most complicated structure, and into bodies subjected
to strain and pressure. He showed that the facts discovered by Malus,
Arago, Brewster, and Biot were so many ganglia, so to speak, of his
theoretic organism, deriving from it sustenance and explanation. With
a mind too strong for the body with which it was associated, that body
became a wreck long before it had become old, and Fresnel died,
leaving, however, behind him a name immortal in the annals of science.

One word more I should like to say regarding Fresnel. There are things
better even than science. Character is higher than Intellect, but it
is especially pleasant to those who wish to think well of human nature
when high intellect and upright character are found combined. They
were combined in this young Frenchman. In those hot conflicts of the
undulatory theory, he stood forth as a man of integrity, claiming no
more than his right, and ready to concede their rights to others. He
at once recognized and acknowledged the merits of Thomas Young.
Indeed, it was he, and his fellow-countryman Arago, who first startled
England into the consciousness of the injustice done to Young in the
'Edinburgh Review.'

I should like to read to you a brief extract from a letter written by
Fresnel to Young in 1824, as it throws a pleasant light upon the
character of the French philosopher. 'For a long time,' says Fresnel,
'that sensibility, or that vanity, which people call love of glory has
been much blunted in me. I labour much less to catch the suffrages of
the public, than to obtain that inward approval which has always been
the sweetest reward of my efforts. Without doubt, in moments of
disgust and discouragement, I have often needed the spur of vanity to
excite me to pursue my researches. But all the compliments I have
received from Arago, De la Place, and Biot never gave me so much
pleasure as the discovery of a theoretic truth or the confirmation of
a calculation by experiment.'

       *       *       *       *       *

This, then, is the core of the whole matter as regards science. It
must be cultivated for its own sake, for the pure love of truth,
rather than for the applause or profit that it brings. And now my
occupation in America is well-nigh gone. Still I will bespeak your
tolerance for a few concluding remarks, in reference to the men who
have bequeathed to us the vast body of knowledge of which I have
sought to give you some faint idea in these lectures. What was the
motive that spurred them on? What urged them to those battles and
those victories over reticent Nature, which have become the heritage
of the human race? It is never to be forgotten that not one of those
great investigators, from Aristotle down to Stokes and Kirchhoff, had
any practical end in view, according to the ordinary definition of the
word 'practical.' They did not propose to themselves money as an end,
and knowledge as a means of obtaining it. For the most part, they
nobly reversed this process, made knowledge their end, and such money
as they possessed the means of obtaining it.

We see to-day the issues of their work in a thousand practical forms,
and this may be thought sufficient to justify, if not ennoble, their
efforts. But they did not work for such issues; their reward was of a
totally different kind. In what way different? We love clothes, we
love luxuries, we love fine equipages, we love money, and any man who
can point to these as the result of his efforts in life, justifies
these results before all the world. In America and England, more
especially, he is a 'practical' man. But I would appeal confidently to
this assembly whether such things exhaust the demands of human nature?
The very presence here for six inclement nights of this great
audience, embodying so much of the mental force and refinement of this
vast city,[26] is an answer to my question. I need not tell such an
assembly that there are joys of the intellect as well as joys of the
body, or that these pleasures of the spirit constituted the reward of
our great investigators. Led on by the whisperings of natural truth,
through pain and self-denial, they often pursued their work. With the
ruling passion strong in death, some of them, when no longer able to
hold a pen, dictated to their friends the last results of their
labours, and then rested from them for ever.

Could we have seen these men at work, without any knowledge of the
consequences of their work, what should we have thought of them? To
the uninitiated, in their day, they might often appear as big children
playing with soap-bubbles and other trifles. It is so to this hour.
Could you watch the true investigator--your Henry or your Draper, for
example--in his laboratory, unless animated by his spirit, you could
hardly understand what keeps him there. Many of the objects which
rivet his attention might appear to you utterly trivial; and if you
were to ask him what is the _use_ of his work, the chances are that
you would confound him. He might not be able to express the use of it
in intelligible terms. He might not be able to assure you that it will
put a dollar into the pocket of any human being present or to come.
That scientific discovery _may_ put not only dollars into the pockets
of individuals, but millions into the exchequers of nations, the
history of science amply proves; but the hope of its doing so never
was, and it never can be, the motive power of the investigator.

I know that some risk is run in speaking thus before practical men. I
know what De Tocqueville says of you. 'The man of the North,' he says,
'has not only experience, but knowledge. He, however, does not care
for science as a pleasure, and only embraces it with avidity when it
leads to useful applications.' But what, I would ask, are the hopes of
useful applications which have caused you so many times to fill this
place, in spite of snow-drifts and biting cold? What, I may ask, is
the origin of that kindness which drew me from my work in London to
address you here, and which, if I permitted it, would send me home a
millionaire? Not because I had taught you to make a single cent by
science am I here to-night, but because I tried to the best of my
ability to present science to the world as an intellectual good.
Surely no two terms were ever so distorted and misapplied with
reference to man, in his higher relations, as these terms useful and
practical. Let us expand our definitions until they embrace all the
needs of man, his highest intellectual needs inclusive. It is
specially on this ground of its administering to the higher needs of
the intellect; it is mainly because I believe it to be wholesome, not
only as a source of knowledge but as a means of discipline, that I
urge the claims of science upon your attention.

But with reference to material needs and joys, surely pure science has
also a word to say. People sometimes speak as if steam had not been
studied before James Watt, or electricity before Wheatstone and Morse;
whereas, in point of fact, Watt and Wheatstone and Morse, with all
their practicality, were the mere outcome of antecedent forces, which
acted without reference to practical ends. This also, I think, merits
a moment's attention. You are delighted, and with good reason, with
your electric telegraphs, proud of your steam-engines and your
factories, and charmed with the productions of photography. You see
daily, with just elation, the creation of new forms of industry--new
powers of adding to the wealth and comfort of society. Industrial
England is heaving with forces tending to this end; and the pulse of
industry beats still stronger in the United States. And yet, when
analyzed, what are industrial America and industrial England?

If you can tolerate freedom of speech on my part, I will answer this
question by an illustration. Strip a strong arm, and regard the
knotted muscles when the hand is clenched and the arm bent. Is this
exhibition of energy the work of the muscle alone? By no means. The
muscle is the channel of an influence, without which it would be as
powerless as a lump of plastic dough. It is the delicate unseen nerve
that unlocks the power of the muscle. And without those filaments of
genius, which have been shot like nerves through the body of society
by the original discoverer, industrial America, and industrial
England, would be very much in the condition of that plastic dough.

At the present time there is a cry in England for technical education,
and it is a cry in which the most commonplace intellect can join, its
necessity is so obvious. But there is no such cry for original
investigation. Still, without this, as surely as the stream dwindles
when the spring dies, so surely will 'technical education' lose all
force of growth, all power of reproduction. Our great investigators
have given us sufficient work for a time; but if their spirit die out,
we shall find ourselves eventually in the condition of those Chinese
mentioned by De Tocqueville, who, having forgotten the scientific
origin of what they did, were at length compelled to copy without
variation the inventions of an ancestry wiser than themselves, who had
drawn their inspiration direct from Nature.

Both England and America have reason to bear those things in mind, for
the largeness and nearness of material results are only too likely to
cause both countries to forget the small spiritual beginnings of such
results, in the mind of the scientific discoverer. You multiply, but
he creates. And if you starve him, or otherwise kill him--nay, if you
fail to secure for him free scope and encouragement--you not only lose
the motive power of intellectual progress, but infallibly sever
yourselves from the springs of industrial life.

What has been said of technical operations holds equally good for
education, for here also the original investigator constitutes the
fountain-head of knowledge. It belongs to the teacher to give this
knowledge the requisite form; an honourable and often a difficult
task. But it is a task which receives its final sanctification, when
the teacher himself honestly tries to add a rill to the great stream
of scientific discovery. Indeed, it may be doubted whether the real
life of science can be fully felt and communicated by the man who has
not himself been taught by direct communion with Nature. We may, it is
true, have good and instructive lectures from men of ability, the
whole of whose knowledge is second-hand, just as we may have good and
instructive sermons from intellectually able and unregenerate men. But
for that power of science, which corresponds to what the Puritan
fathers would call experimental religion in the heart, you must ascend
to the original investigator.

To keep society as regards science in healthy play, three classes of
workers are necessary: Firstly, the investigator of natural truth,
whose vocation it is to pursue that truth, and extend the field of
discovery for the truth's own sake and without reference to practical
ends. Secondly, the teacher of natural truth, whose vocation it is to
give public diffusion to the knowledge already won by the discoverer.
Thirdly, the applier of natural truth, whose vocation it is to make
scientific knowledge available for the needs, comforts, and luxuries
of civilized life. These three classes ought to co-exist and interact.
Now, the popular notion of science, both in this country and in
England, often relates not to science strictly so called, but to the
applications of science. Such applications, especially on this
continent, are so astounding--they spread themselves so largely and
umbrageously before the public eye--that they often shut out from view
those workers who are engaged in the quieter and profounder business
of original investigation.

Take the electric telegraph as an example, which has been repeatedly
forced upon my attention of late. I am not here to attenuate in the
slightest degree the services of those who, in England and America,
have given the telegraph a form so wonderfully fitted for public use.
They earned a great reward, and they have received it. But I should be
untrue to you and to myself if I failed to tell you that, however high
in particular respects their claims and qualities may be, your
practical men did not discover the electric telegraph. The discovery
of the electric telegraph implies the discovery of electricity itself,
and the development of its laws and phenomena. Such discoveries are
not made by practical men, and they never will be made by them,
because their minds are beset by ideas which, though of the highest
value from one point of view, are not those which stimulate the
original discoverer.

The ancients discovered the electricity of amber; and Gilbert, in the
year 1600, extended the discovery to other bodies. Then followed
Boyle, Von Guericke, Gray, Canton, Du Fay, Kleist, Cunæus, and your
own Franklin. But their form of electricity, though tried, did not
come into use for telegraphic purposes. Then appeared the great
Italian Volta, who discovered the source of electricity which bears
his name, and applied the most profound insight, and the most delicate
experimental skill to its development. Then arose the man who added to
the powers of his intellect all the graces of the human heart, Michael
Faraday, the discoverer of the great domain of magneto-electricity.
OErsted discovered the deflection of the magnetic needle, and Arago and
Sturgeon the magnetization of iron by the electric current. The
voltaic circuit finally found its theoretic Newton in Ohm; while
Henry, of Princeton, who had the sagacity to recognize the merits of
Ohm while they were still decried in his own country, was at this time
in the van of experimental inquiry.

In the works of these men you have all the materials employed at this
hour, in all the forms of the electric telegraph. Nay, more; Gauss,
the illustrious astronomer, and Weber, the illustrious natural
philosopher, both professors in the University of Göttingen, wishing
to establish a rapid mode of communication between the observatory and
the physical cabinet of the university, did this by means of an
electric telegraph. Thus, before your practical men appeared upon the
scene, the force had been discovered, its laws investigated and made
sure, the most complete mastery of its phenomena had been
attained--nay, its applicability to telegraphic purposes
demonstrated--by men whose sole reward for their labours was the noble
excitement of research, and the joy attendant on the discovery of
natural truth.

Are we to ignore all this? We do so at our peril. For I say again
that, behind all our practical applications, there is a region of
intellectual action to which practical men have rarely contributed,
but from which they draw all their supplies. Cut them off from this
region, and they become eventually helpless. In no case is the adage
truer, 'Other men laboured, but ye are entered into their labours,'
than in the case of the discoverer and applier of natural truth. But
now a word on the other side. While practical men are not the men to
make the necessary antecedent discoveries, the cases are rare, though,
in our day, not absent, in which the discoverer knows how to turn his
labours to practical account. Different qualities of mind and habits
of thought are usually needed in the two cases; and while I wish to
give emphatic utterance to the claims of those whose position, owing
to the simple fact of their intellectual elevation, is often
misunderstood, I am not here to exalt the one class of workers at the
expense of the other. They are the necessary complements of each
other. But remember that one class is sure to be taken care of. All
the material rewards of society are already within their reach, while
that same society habitually ascribes to them intellectual
achievements which were never theirs. This cannot but act to the
detriment of those studies out of which, not only our knowledge of
nature, but our present industrial arts themselves, have sprung, and
from which the rising genius of the country is incessantly tempted
away.

Pasteur, one of the most illustrious members of the Institute of
France, in accounting for the disastrous overthrow of his country,
and the predominance of Germany in the late war, expresses himself
thus: 'Few persons comprehend the real origin of the marvels of
industry and the wealth of nations. I need no further proof of this
than the employment, more and more frequent, in official language, and
in writings of all sorts, of the erroneous expression _applied
science_. The abandonment of scientific careers by men capable of
pursuing them with distinction, was recently deplored in the presence
of a minister of the greatest talent. The statesman endeavoured to
show that we ought not to be surprised at this result, because _in our
day the reign of theoretic science yielded place to that of applied
science_. Nothing could be more erroneous than this opinion, nothing,
I venture to say, more dangerous, even to practical life, than the
consequences which might flow from these words. They have rested in my
mind as a proof of the imperious necessity of reform in our superior
education. There exists no category of the sciences, to which the name
of applied science could be rightly given. _We have science, and the
applications of science_, which are united together as the tree and
its fruit.'

And Cuvier, the great comparative anatomist, writes thus upon the same
theme: 'These grand practical innovations are the mere applications of
truths of a higher order, not sought with a practical intent, but
pursued for their own sake, and solely through an ardour for
knowledge. Those who applied them could not have discovered them; but
those who discovered them had no inclination to pursue them to a
practical end. Engaged in the high regions whither their thoughts had
carried them, they hardly perceived these practical issues though
born of their own deeds. These rising workshops, these peopled
colonies, those ships which furrow the seas--this abundance, this
luxury, this tumult--all this comes from discoveries in science, and
it all remains strange to the discoverers. At the point where science
merges into practice they abandon it; it concerns them no more.'

When the Pilgrim Fathers landed at Plymouth Rock, and when Penn made
his treaty with the Indians, the new-comers had to build their houses,
to cultivate the earth, and to take care of their souls. In such a
community science, in its more abstract forms, was not to be thought
of. And at the present hour, when your hardy Western pioneers stand
face to face with stubborn Nature, piercing the mountains and subduing
the forest and the prairie, the pursuit of science, for its own sake,
is not to be expected. The first need of man is food and shelter; but
a vast portion of this continent is already raised far beyond this
need. The gentlemen of New York, Brooklyn, Boston, Philadelphia,
Baltimore, and Washington have already built their houses, and very
beautiful they are; they have also secured their dinners, to the
excellence of which I can also bear testimony. They have, in fact,
reached that precise condition of well-being and independence when a
culture, as high as humanity has yet reached, may be justly demanded
at their hands. They have reached that maturity, as possessors of
wealth and leisure, when the investigator of natural truth, for the
truth's own sake, ought to find among them promoters and protectors.

Among the many problems before them they have this to solve, whether
a republic is able to foster the highest forms of genius. You are
familiar with the writings of De Tocqueville, and must be aware of the
intense sympathy which he felt for your institutions; and this
sympathy is all the more valuable from the philosophic candour with
which he points out not only your merits, but your defects and
dangers. Now if I come here to speak of science in America in a
critical and captious spirit, an invisible radiation from my words and
manner will enable you to find me out, and will guide your treatment
of me to-night. But if I in no unfriendly spirit--in a spirit, indeed,
the reverse of unfriendly--venture to repeat before you what this
great historian and analyst of democratic institutions said of
America, I am persuaded that you will hear me out. He wrote some three
and twenty years ago, and, perhaps, would not write the same to-day;
but it will do nobody any harm to have his words repeated, and, if
necessary, laid to heart.

In a work published in 1850, De Tocqueville says: 'It must be
confessed that, among the civilized peoples of our age, there are few
in which the highest sciences have made so little progress as in the
United States.'[27] He declares his conviction that, had you been
alone in the universe, you would soon have discovered that you cannot
long make progress in practical science without cultivating theoretic
science at the same time. But, according to De Tocqueville, you are
not thus alone. He refuses to separate America from its ancestral
home; and it is there, he contends, that you collect the treasures of
the intellect, without taking the trouble to create them.

De Tocqueville evidently doubts the capacity of a democracy to foster
genius as it was fostered in the ancient aristocracies. 'The future,'
he says, 'will prove whether the passion for profound knowledge, so
rare and so fruitful, can be born and developed as readily in
democratic societies as in aristocracies. For my part,' he continues,
'I can hardly believe it.' He speaks of the unquiet feverishness of
democratic communities, not in times of great excitement, for such
times may give an extraordinary impetus to ideas, but in times of
peace. There is then, he says, 'a small and uncomfortable agitation, a
sort of incessant attrition of man against man, which troubles and
distracts the mind without imparting to it either loftiness or
animation.' It rests with you to prove whether these things are
necessarily so--whether scientific genius cannot find, in the midst of
you, a tranquil home.

I should be loth to gainsay so keen an observer and so profound a
political writer, but, since my arrival in this country, I have been
unable to see anything in the constitution of society, to prevent a
student, with the root of the matter in him, from bestowing the most
steadfast devotion on pure science. If great scientific results are
not achieved in America, it is not to the small agitations of society
that I should be disposed to ascribe the defect, but to the fact that
the men among you who possess the endowments necessary for profound
scientific inquiry, are laden with duties of administration, or
tuition, so heavy as to be utterly incompatible with the continuous
and tranquil meditation which original investigation demands. It may
well be asked whether Henry would have been transformed into an
administrator, or whether Draper would have forsaken science to write
history, if the original investigator had been honoured as he ought to
be in this land. I hardly think they would. Still I do not imagine
this state of things likely to last. In America there is a willingness
on the part of individuals to devote their fortunes, in the matter of
education, to the service of the commonwealth, which is probably
without a parallel elsewhere; and this willingness requires but wise
direction to enable you effectually to wipe away the reproach of De
Tocqueville.

Your most difficult problem will be, not to build institutions, but to
discover men. You may erect laboratories and endow them; you may
furnish them with all the appliances needed for inquiry; in so doing
you are but creating opportunity for the exercise of powers which come
from sources entirely beyond your reach. You cannot create genius by
bidding for it. In biblical language, it is the gift of God; and the
most you could do, were your wealth, and your willingness to apply it,
a million-fold what they are, would be to make sure that this glorious
plant shall have the freedom, light, and warmth necessary for its
development. We see from time to time a noble tree dragged down by
parasitic runners. These the gardener can remove, though the vital
force of the tree itself may lie beyond him: and so, in many a case
you men of wealth can liberate genius from the hampering toils which
the struggle for existence often casts around it.

Drawn by your kindness, I have come here to give these lectures, and
now that my visit to America has become almost a thing of the past, I
look back upon it as a memory without a single stain. No lecturer was
ever rewarded as I have been. From this vantage-ground, however, let
me remind you that the work of the lecturer is not the highest work;
that in science, the lecturer is usually the distributor of
intellectual wealth amassed by better men. And though lecturing and
teaching, in moderation, will in general promote their moral health,
it is not solely or even chiefly, as lecturers, but as investigators,
that your highest men ought to be employed. You have scientific genius
amongst you--not sown broadcast, believe me, it is sown thus
nowhere--but still scattered here and there. Take all unnecessary
impediments out of its way. Keep your sympathetic eye upon the
originator of knowledge. Give him the freedom necessary for his
researches, not overloading him, either with the duties of tuition or
of administration, nor demanding from him so-called practical
results--above all things, avoiding that question which ignorance so
often addresses to genius: 'What is the use of your work?' Let him
make truth his object, however unpractical for the time being it may
appear. If you cast your bread thus upon the waters, be assured it
will return to you, though it be after many days.



APPENDIX.

ON THE SPECTRA OF POLARIZED LIGHT.


Mr. William Spottiswoode introduced some years ago to the members of
the Royal Institution, in a very striking form, a series of
experiments on the spectra of polarized light. With his large Nicol
prisms he in the first place repeated and explained the experiments of
Foucault and Fizeau, and subsequently enriched the subject by very
beautiful additions of his own. I here append a portion of the
abstract of his discourse:--

    'It is well known that if a plate of selenite sufficiently thin be
    placed between two Nicol's prisms, or, more technically speaking,
    between a polarizer and analyzer, colour will be produced. And the
    question proposed is, What is the nature of that colour? is it
    simply a pure colour of the spectrum, or is it a compound, and if
    so, what are its component parts? The answer given by the wave
    theory is in brief this: In its passage through the selenite plate
    the rays have been so separated in the direction of their vibrations
    and in the velocity of their transmission, that, when re-compounded
    by means of the analyzer, they have in some instances neutralized
    one another. If this be the case, the fact ought to be visible when
    the beam emerging from the analyzer is dispersed by the prism; for
    then we have the rays of all the different colours ranged side by
    side, and, if any be wanting, their absence will be shown by the
    appearance of a dark band in their place in the spectrum. But not
    only so; the spectrum ought also to give an account of the other
    phenomena exhibited by the selenite when the analyzer is turned
    round, viz. that when the angle of turning amounts to 45°, all trace
    of colour disappears; and also that when the angle amounts to 90°,
    colour reappears, not, however, the original colour, but one
    complementary to it.

    'You see in the spectrum of the reddish light produced by the
    selenite a broad but dark band in the blue; when the analyzer is
    turned round the band becomes less and less dark, until when the
    angle of turning amounts to 45° it has entirely disappeared. At this
    stage each part of the spectrum has its own proportional intensity,
    and the whole produces the colourless image seen without the
    spectroscope. Lastly, as the turning of the analyzer is continued, a
    dark band appears in the red, the part of the spectrum complementary
    to that occupied by the first band; and the darkness is most
    complete when the turning amounts to 90°. Thus we have from the
    spectroscope a complete account of what has taken place to produce
    the original colour and its changes.

    'It is further well known that the colour produced by a selenite, or
    other crystal plate, is dependent upon the thickness of the plate.
    And, in fact, if a series of plates be taken, giving different
    colours, their spectra are found to show bands arranged in different
    positions. The thinner plates show bands in the parts of the
    spectrum nearest to the violet, where the waves are shorter, and
    consequently give rise to redder colours; while the thicker show
    bands nearer to the red, where the waves are longer and consequently
    supply bluer tints.

    'When the thickness of the plate is continually increased, so that
    the colour produced has gone through the complete cycle of the
    spectrum, a further increase of thickness causes a reproduction of
    the colours in the same order; but it will be noticed that at each
    recurrence of the cycle the tints become paler, until when a number
    of cycles have been performed, and the thickness of the plate is
    considerable, all trace of colour is lost. Let us now take a series
    of plates, the first two of which, as you see, give colours; with
    the others which are successively of greater thickness the tints are
    so feeble that they can scarcely be distinguished. The spectrum of
    the first shows a single band; that of the second, two; showing that
    the second series of tints is not identical with the first, but that
    it is produced by the extinction of two colours from the components
    of white light. The spectra of the others show series of bands more
    and more numerous in proportion to the thickness of the plate, an
    array which may be increased indefinitely. The total light, then, of
    which the spectrum is deprived by the thicker plates is taken from a
    greater number of its parts; or, in other words, the light which
    still remains is distributed more and more evenly over the spectrum;
    and in the same proportion the sum total of it approaches more and
    more nearly to white light.

    'These experiments were made more than thirty years ago by the
    French philosophers, MM. Foucault and Fizeau.

    'If instead of selenite, Iceland spar, or other ordinary crystals,
    we use plates of quartz cut perpendicularly to the axis, and turn
    the analyzer round as before, the light, instead of exhibiting only
    one colour and its complementary with an intermediate stage in which
    colour is absent, changes continuously in tint; and the order of the
    colour depends partly upon the direction in which the analyzer is
    turned, and partly upon the character of the crystal, _i.e._ whether
    it is right-handed or left-handed. If we examine the spectrum in
    this case we find that the dark band never disappears, but marches
    from one end of the spectrum to another, or _vice versâ_, precisely
    in such a direction as to give rise to the tints seen by direct
    projection.

    'The kind of polarization effected by the quartz plates is called
    circular, while that effected by the other class of crystals is
    called plane, on account of the form of the vibrations executed by
    the molecules of æther; and this leads us to examine a little more
    closely the nature of the polarization of different parts of these
    spectra of polarized light.

    'Now, two things are clear: first, that if the light be
    plane-polarized--that is, if all the vibrations throughout the
    entire ray are rectilinear and in one plane--they must in all their
    bearings have reference to a particular direction in space, so that
    they will be differently affected by different positions of the
    analyzer. Secondly, that if the vibrations be circular, they will be
    affected in precisely the same way (whatever that may be) in all
    positions of the analyzer. This statement merely recapitulates a
    fundamental point in polarization. In fact, plane-polarized light is
    alternately transmitted and extinguished by the analyzer as it is
    turned through 90°; while circularly polarized light [if we could
    get a single ray] remains to all appearance unchanged. And if we
    examine carefully the spectrum of light which has passed through a
    selenite, or other ordinary crystal, we shall find that, commencing
    with two consecutive bands in position, the parts occupied by the
    bands and those midway between them are plane-polarized, for they
    become alternately dark and bright; while the intermediate parts,
    _i.e._ the parts at one-fourth of the distance from one band to the
    next, remain permanently bright. These are, in fact, circularly
    polarized. But it would be incorrect to conclude from this
    experiment alone that such is really the case, because the same
    appearance would be seen if those parts were unpolarized, _i.e._ in
    the condition of ordinary lights. And on such a supposition we
    should conclude with equal justice that the parts on either side of
    the parts last mentioned (e.g. the parts separated by eighth parts
    of the interval between two bands) were partially polarized. But
    there is an instrument of very simple construction, called a
    "quarter-undulation plate," a plate usually of mica, whose thickness
    is an odd multiple of a quarter of a wave-length, which enables us
    to discriminate between light unpolarized and circularly polarized.
    The exact mechanical effect produced upon the ray could hardly be
    explained in detail within our present limits of time; but suffice
    it for the present to say that, when placed in a proper position,
    the plate transforms plane into circular and circular into plane
    polarization. That being so, the parts which were originally banded
    ought to remain bright, and those which originally remained bright
    ought to become banded during the rotation of the analyzer. The
    general effect to the eye will consequently be a general shifting of
    the bands through one-fourth of the space which separates each pair.

    'Circular polarization, like circular motion generally, may of
    course be of two kinds, which differ only in the direction of the
    motion. And, in fact, to convert the circular polarization produced
    by this plate from one of these kinds to the other (say from
    right-handed to left-handed, or _vice versâ_), we have only to turn
    the plate round through 90°. Conversely, right-handed circular
    polarization will be changed by the plate into plane-polarization in
    one direction, while left-handed will be changed into plane at right
    angles to the first. Hence if the plate be turned round through 90°
    we shall see that the bands are shifted in a direction opposite to
    that in which they were moved at first. In this therefore we have
    evidence not only that the polarization immediately on either side
    of a band is circular; but also that that immediately on the one
    side is right-handed, while that immediately on the other is
    left-handed[28].

    'If time permitted, I might enter still further into detail, and
    show that the polarization between the plane and the circular is
    elliptical, and even the positions of the longer and shorter axes
    and the direction of motion in each case. But sufficient has,
    perhaps, been said for our present purpose.

    'Before proceeding to the more varied forms of spectral bands,
    which I hope presently to bring under your notice, I should like to
    ask your attention for a few minutes to the peculiar phenomena
    exhibited when two plates of selenite giving complementary colours
    are used. The appearance of the spectrum varies with the relative
    position of the plates. If they are similarly placed--that is, as if
    they were one plate of crystal--they will behave as a single plate,
    whose thickness is the sum of the thicknesses of each, and will
    produce double the number of bands which one alone would give; and
    when the analyzer is turned, the bands will disappear and re-appear
    in their complementary positions, as usual in the case of
    plane-polarization. If one of them be turned round through 45°, a
    single band will be seen at a particular position in the spectrum.
    This breaks into two, which recede from one another towards the red
    and violet ends respectively, or advance towards one another
    according to the direction in which the analyzer is turned. If the
    plate be turned through 45° in the opposite direction, the effects
    will be reversed. The darkness of the bands is, however, not equally
    complete during their whole passage. Lastly, if one of the plates be
    turned through 90°, no bands will be seen, and the spectrum will be
    alternately bright and dark, as if no plates were used, except only
    that the polarization is itself turned through 90°.

    'If a wedge-shaped crystal be used, the bands, instead of being
    straight, will cross the spectrum diagonally, the direction of the
    diagonal (dexter or sinister) being determined by the position of
    the thicker end of the wedge. If two similar wedges be used with
    their thickest ends together, they will act as a wedge whose angle
    and whose thickness is double of the first. If they be placed in the
    reverse position they will act as a flat plate, and the bands will
    again cross the spectrum in straight lines at right angles to its
    length.

    'If a concave plate be used the bands will dispose themselves in a
    fanlike arrangement, their divergence depending upon the distance of
    the slit from the centre of concavity.

    'If two quartz wedges, one of which has the optic axis parallel to
    the edge of the refractory angle, and the other perpendicular to it,
    but in one of the planes containing the angle (Babinet's
    Compensator), the appearances of the bands are very various.

    'The diagonal bands, besides sometimes doubling themselves as with
    ordinary wedges, sometimes combine so as to form longitudinal
    (instead of transverse) bands; and sometimes cross one another so as
    to form a diaper pattern with bright compartments in a dark
    framework, and _vice versâ_, according to the position of the
    plates.

    'The effects of different dispositions of the interposed crystals
    might be varied indefinitely; but enough has perhaps been said to
    show the delicacy of the method of spectrum analysis as applied to
    the examination of polarized light.'

       *       *       *       *       *

The singular and beautiful effect obtained with a circular plate of
selenite, thin at the centre, and gradually thickening towards the
circumference, is easily connected with a similar effect obtained with
Newton's rings. Let a thin slice of light fall upon the glasses which
show the rings, so as to cover a narrow central vertical zone passing
through them all. The image of this zone upon the screen is crossed by
portions of the iris-rings. Subjecting the reflected beam to prismatic
analysis, the resultant spectrum may be regarded as an indefinite
number of images of the zone placed side by side. In the image before
dispersion we have _iris-rings_, the extinction of the light being
nowhere complete; but when the different colours are separated by
dispersion, each colour is crossed transversely by its own system of
dark interference bands, which become gradually closer with the
increasing refrangibility of the light. The complete spectrum,
therefore, appears furrowed by a system of continuous dark bands,
crossing the colours transversely, and approaching each other as they
pass from red to blue.

In the case of the plate of selenite, a slit is placed in front of the
polarizer, and the film of selenite is held close to the slit, so that
the light passes through the central zone of the film. As in the case
of Newton's rings, the image of the zone is crossed by iris-coloured
bands; but when subjected to prismatic dispersion, the light of the
zone yields a spectrum furrowed by bands of complete darkness exactly
as in the case of Newton's rings and for a similar reason. This is the
beautiful effect described by Mr. Spottiswoode as the fanlike
arrangement of the bands--the fan opening out at the red end of the
spectrum.

       *       *       *       *       *

_MEASUREMENT OF THE WAVES OF LIGHT._

The diffraction fringes described in Lecture II., instead of being
formed on the retina, may be formed on a screen, or upon ground glass,
when they can be looked at through a magnifying lens from behind, or
they can be observed in the air when the ground glass is removed.
Instead of permitting them to form on the retina, we will suppose them
formed on a screen. This places us in a condition to understand, even
without trigonometry, the solution of the important problem of
measuring _the length_ of a wave of light.

We will suppose the screen so distant that the rays falling upon it
from the two margins of the slit are sensibly parallel. We have
learned in Lecture II. that the first of the dark bands corresponds to
a difference of marginal path of one undulation; the second dark band
to a difference of path of two undulations; the third dark band to a
difference of three undulations, and so on. Now the angular distance
of the bands from the centre is capable of exact measurement; this
distance depending, as already stated, on the width of the slit. With
a slit 1.35 millimeter wide,[29] Schwerd found the angular distance of
the first dark band from the centre of the field to be 1'38"; the
angular distances of the second, third, fourth dark bands being twice,
three times, four times this quantity.

[Illustration: Fig. 57.]

Let A B, fig. 57, be the plate in which the slit is cut, and C D the
grossly exaggerated width of the slit, with the beam of red light
proceeding from it at the obliquity corresponding to the first dark
band. Let fall a perpendicular from one edge, D, of the slit on the
marginal ray of the other edge at _d_. The distance, C _d_, between
the foot of this perpendicular and the other edge is the length of a
wave of the light. The angle C D _d_, moreover, being equal to R C R',
is, in the case now under consideration, 1'38". From the centre D,
with the width D C as radius, describe a semicircle; its radius D C
being 1.35 millimeter, the length of this semicircle is found by an
easy calculation to be 4.248 millimeters. The length C _d_ is so small
that it sensibly coincides with the arc of the circle. Hence the
length of the semicircle is to the length C _d_ of the wave as 180° to
1'38", or, reducing all to seconds, as 648,000" to 98". Thus, we have
the proportion--

    648,000 : 98 :: 4.248 to the wave-length C _d_.

Making the calculation, we find the wave-length for this particular
kind of light to be 0.000643 of a millimeter, or 0.000026 of an inch.

FOOTNOTES:

[Footnote 1: Among whom may be especially mentioned the late Sir
Edmund Head, Bart., with whom I had many conversations on this
subject.]

[Footnote 2: At whose hands it gives me pleasure to state I have
always experienced honourable and liberal treatment.]

[Footnote 3: One of the earliest of these came from Mr. John Amory
Lowell of Boston.]

[Footnote 4: It will be subsequently shown how this simple apparatus
may be employed to determine the 'polarizing angle' of a liquid.]

[Footnote 5: From this principle Sir John Herschel deduces in a simple
and elegant manner the fundamental law of reflection.--See _Familiar
Lectures_, p. 236.]

[Footnote 6: The low dispersive power of water masks, as Helmholtz has
remarked, the imperfect achromatism of the eye. With the naked eye I
can see a distant blue disk sharply defined, but not a red one. I can
also see the lines which mark the upper and lower boundaries of a
horizontally refracted spectrum sharp at the blue end, but ill-defined
at the red end. Projecting a luminous disk upon a screen, and covering
one semicircle of the aperture with a red and the other with a blue or
green glass, the difference between the apparent sizes of the two
semicircles is in my case, and in numerous other cases, extraordinary.
Many persons, however, see the apparent sizes of the two semicircles
reversed. If with a spectacle glass I correct the dispersion of the
red light over the retina, then the blue ceases to give a sharply
defined image. Thus examined, the departure of the eye from
achromatism appears very gross indeed.]

[Footnote 7: Both in foliage and in flowers there are striking
differences of absorption. The copper beech and the green beech, for
example, take in different rays. But the very growth of the tree is
due to some of the rays thus taken in. Are the chemical rays, then,
the same in the copper and the green beech? In two such flowers as the
primrose and the violet, where the absorptions, to judge by the
colours, are almost complementary, are the chemically active rays the
same? The general relation of colour to chemical action is worthy of
the application of the method by which Dr. Draper proved so
conclusively the chemical potency of the yellow rays of the sun.]

[Footnote 8: Young, Helmholtz, and Maxwell reduce all differences of
hue to combinations in different proportions of three primary colours.
It is demonstrable by experiment that from the red, green, and violet
_all_ the other colours of the spectrum may be obtained.

Some years ago Sir Charles Wheatstone drew my attention to a work by
Christian Ernst Wünsch, Leipzig 1792, in which the author announces
the proposition that there are neither five nor seven, but only three
simple colours in white light. Wünsch produced five spectra, with five
prisms and five small apertures, and he mixed the colours first in
pairs, and afterwards in other ways and proportions. His result is
that red is a _simple_ colour incapable of being decomposed; that
orange is compounded of intense red and weak green; that yellow is a
mixture of intense red and intense green; that green is a _simple_
colour; that blue is compounded of saturated green and saturated
violet; that indigo is a mixture of saturated violet and weak green;
while violet is a pure _simple_ colour. He also finds that yellow and
indigo blue produce _white_ by their mixture. Yellow mixed with bright
blue (Hochblau) also produces white, which seems, however, to have a
tinge of green, while the pigments of these two colours when mixed
always give a more or less beautiful green, Wünsch very emphatically
distinguishes the mixture of pigments from that of lights. Speaking of
the generation of yellow, he says, 'I say expressly _red and green
light_, because I am speaking about light-colours (Lichtfarben), and
not about pigments.' However faulty his theories may be, Wünsch's
experiments appear in the main to be precise and conclusive. Nearly
ten years subsequently, Young adopted red, green, and violet as the
three primary colours, each of them capable of producing three
sensations, one of which, however, predominates over the two others.
Helmholtz adopts, elucidates, and enriches this notion. (_Popular
Lectures_, p. 249. The paper of Helmholtz on the mixture of colours,
translated by myself, is published in the _Philosophical Magazine_ for
1852. Maxwell's memoir on the Theory of Compound Colours is published
in the _Philosophical Transactions_, vol. 150, p. 67.)]

[Footnote 9: The following charming extract, bearing upon this point,
was discovered and written out for me by my deeply lamented friend Dr.
Bence Jones, when Hon. Secretary to the Royal Institution:--

    'In every kind of magnitude there is a degree or sort to which our
    sense is proportioned, the perception and knowledge of which is of
    the greatest use to mankind. The same is the groundwork of
    philosophy; for, though all sorts and degrees are equally the object
    of philosophical speculation, yet it is from those which are
    proportioned to sense that a philosopher must set out in his
    inquiries, ascending or descending afterwards as his pursuits may
    require. He does well indeed to take his views from many points of
    sight, and supply the defects of sense by a well-regulated
    imagination; nor is he to be confined by any limit in space or time;
    but, as his knowledge of Nature is founded on the observation of
    sensible things, he must begin with these, and must often return to
    them to examine his progress by them. Here is his secure hold: and
    as he sets out from thence, so if he likewise trace not often his
    steps backwards with caution, he will be in hazard of losing his way
    in the labyrinths of Nature.'--(_Maclaurin: An Account of Sir I.
    Newton's Philosophical Discoveries. Written 1728; second edition_,
    1750; pp. 18, 19.)
]

[Footnote 10: I do not wish to encumber the conception here with the
details of the motion, but I may draw attention to the beautiful model
of Prof. Lyman, wherein waves are shown to be produced by the
_circular_ motion of the particles. This, as proved by the brothers
Weber, is the real motion in the case of water-waves.]

[Footnote 11: Copied from Weber's _Wellenlehre_.]

[Footnote 12: See _Lectures on Sound_, 1st and 2nd ed., Lecture VII.;
and 3rd ed., Chap. VIII. Longmans.]

[Footnote 13: _Boyle's Works_, Birch's edition, p. 675.]

[Footnote 14: Page 743.]

[Footnote 15: The beautiful plumes produced by water-crystallization
have been successfully photographed by Professor Lockett.]

[Footnote 16: In a little volume entitled 'Forms of Water,' I have
mentioned that cold iron floats upon molten iron. In company with my
friend Sir William Armstrong, I had repeated opportunities of
witnessing this fact in his works at Elswick, 1863. Faraday, I
remember, spoke to me subsequently of the perfection of iron castings
as probably due to the swelling of the metal on solidification. Beyond
this, I have given the subject no special attention; and I know that
many intelligent iron-founders doubt the fact of expansion. It is
quite possible that the solid floats because it is not _wetted_ by the
molten iron, its volume being virtually augmented by capillary
repulsion. Certain flies walk freely upon water in virtue of an action
of this kind. With bismuth, however, it is easy to burst iron bottles
by the force of solidification.]

[Footnote 17: This beautiful law is usually thus expressed: _The index
of refraction of any substance is the tangent of its polarizing
angle_. With the aid of this law and an apparatus similar to that
figured at page 15, we can readily determine the index of refraction
of any liquid. The refracted and reflected beams being visible, they
can readily be caused to inclose a right angle. The polarizing angle
of the liquid may be thus found with the sharpest precision. It is
then only necessary to seek out its natural tangent to obtain the
index of refraction.]

[Footnote 18: Whewell.]

[Footnote 19: Removed from us since these words were written.]

[Footnote 20: The only essay known to me on the Undulatory Theory,
from the pen of an American writer, is an excellent one by President
Barnard, published in the Smithsonian Report for 1862.]

[Footnote 21: _Boyle's Works_, Birch's edition, vol. i. pp, 729 and
730.]

[Footnote 22: _Werke_, B. xxix. p. 24.]

[Footnote 23: Defined in Lecture I.]

[Footnote 24: This circumstance ought not to be lost sight of in the
examination of compound spectra. Other similar instances might be
cited.]

[Footnote 25: The dark band produced when the sodium is placed within
the lamp was observed on the same occasion. Then was also observed for
the first time the magnificent blue band of lithium which the Bunsen's
flame fails to bring out.]

[Footnote 26: New York: for more than a decade no such weather had
been experienced. The snow was so deep that the ordinary means of
locomotion were for a time suspended.]

[Footnote 27: 'Il faut reconnaître que parmi les peuples civilisés de
nos jours il en est pen chez qui les hautes sciences aient fait moins
de progrès qu'aux États-Unis, ou qui aient fourni moins de grands
artistes, de poëtes illustres et de célèbres écrivains.' (_De la
Démocratie en Amérique_, etc. tome ii. p. 36.)]

[Footnote 28: At these points the two rectangular vibrations into
which the original polarized ray is resolved by the plates of gypsum,
act upon each other like the two rectangular impulses imparted to our
pendulum in Lecture IV., one being given when the pendulum is at the
limit of its swing. Vibration is thus converted into rotation.]

[Footnote 29: The millimeter is about 1/25th of an inch.]



INDEX.


Absorption, principles of, 199

Airy, Sir George, severity and conclusiveness of his proofs, 209

Alhazen, his inquiry respecting light, 14, 207

Analyzer, polarizer and, 127
----recompounding of the two systems of waves by the analyzer, 129

Ångström, his paper on spectrum analysis, 202

Arago, François, and Dr. Young, 50
----his discoveries respecting light, 208

Atomic polarity, 93-96

Bacon, Roger, his inquiry respecting light, 14, 207

Bartholinus, Erasmus, on Iceland spar, 112

Bérard on polarization of heat, 180

Blackness, meaning of, 32

Boyle, Robert, his observations on colours, 65, 66
----his remarks on fluorescence, 163, 164

Bradley, James, discovers the aberration of light, 21, 22

Brewster, Sir David, his chief objection to the undulatory theory of
light, 47

Brewster, Sir David, his discovery in biaxal crystals, 209

Brougham, Mr. (afterwards Lord), ridicules Dr. T. Young's
speculations, 50, 51

Cæsium, discovery of, 193

Calorescence, 174

Clouds, actinic, 152-154
----polarization of, 155

Colours of thin plates, 64
----Boyle's observations on, 65, 66
----Hooke on the colours of thin plates, 67
----of striated surfaces, 89, 90

Comet of 1680, Newton's estimate of the temperature of, 168

Crookes, Mr., his discovery of thallium, 193

Crystals, action of, upon light, 98
----built by polar force, 98
----illustrations of crystallization, 99
----architecture of, considered as an introduction to their action upon
    light, 98
----bearings of crystallization upon optical phenomena, 106

Crystals, rings surrounding the axes of, uniaxal and biaxal, 145

Cuvier on ardour for knowledge, 220

De Tocqueville, writings of, 215, 222, 223

Descartes, his explanation of the rainbow, 24, 25
----his ideas respecting the transmission of light, 43
----his notion of light, 207

Diamond, ignition of a, in oxygen, 169

Diathermancy, 173

Diffraction of light, phenomena of, 78
----bands, 78, 79
----explanation of, 80
----colours produced by, 89

Dollond, his experiments on achromatism, 28

Draper, Dr., his investigation on heat, 172

Drummond light, spectrum of, 195


Earth, daily orbit of, 74

Electric beam, heat of the, 168

Electricity, discoveries in, 217, 218

Emission theory of light, bases of the, 45
----Newton espouses the theory, and the results of this espousal, 77

Ether, Huyghens and Euler advocate and defend the conception of an, 48, 58
----objected to by Newton, 58

Euler espouses and defends the conception of an ether, 48, 58

Eusebius on the natural philosophers of his time, 13

Expansion by cold, 104

Experiment, uses of, 3

Eye, the, its imperfections, grown for ages towards perfection, 8
----imperfect achromatism of the, 29, _note_


Faraday, Michael, his discovery of magneto-electricity, 218

'Fits,' theory of, 73
----its explanation of Newton's rings, 74
----overthrow of the theory, 77

Fizeau determines the velocity of light, 22

Fluorescence, Stokes's discovery of, 161
----the name, 174

Forbes, Professor, polarizes and depolarizes heat, 180

Foucault, determines the velocity of light, 22
----his experiments on absorption, 197, 198

Fraunhofer, his theoretical calculations respecting diffraction, 87
----his lines, 193
------their explanation by Kirchhoff, 193

Fresnel, and Dr. Young, 50
----his theoretical calculations respecting diffraction, 87
----his mathematical abilities and immortal name, 210


Goethe on fluorescence, 165

Gravitation, origin of the notion of the attraction of, 92
----strength of the theory of, 148

Grimaldi, his discovery with respect to light, 56
----Young's generalizations of, 56


Hamilton, Sir William, of Dublin, his discovery of conical refraction, 209

Heat, generation of, 6
----Dr. Draper's investigation respecting, 171

Helmholtz, his estimate of the genius of Young, 50
----on the imperfect achromatism of the eye, 29 _note_, 31
----reveals the cause of green in the case of pigments, 37

Henry, Professor Joseph, his invitation, 2

Herschel, Sir John, his theoretical calculations respecting
diffraction, 87
----first notices and describes the fluorescence of sulphate of quinine,
    165
----his experiments on spectra, 201

Herschel, Sir William, his experiments on the heat of the various
colours of the solar spectrum, 171

Hooke, Robert, on the colours of thin plates, 67
----his remarks on the idea that light and heat are modes of motion, 68

Horse-chestnut bark, fluorescence of, 165

Huggins, Dr., his labours, 205

Huyghens advocates the conception of ether, 48, 58
----his celebrated principle, 83

Huyghens on the double refraction of Iceland spar, 112


Iceland spar, 109
----double refraction caused by, 110
----this double refraction first treated by Erasmus Bartholinus, 112
----character of the beams emergent from, 114
----tested by tourmaline, 116
----Knoblauch's demonstration of the double refraction of, 185

Ice-lens, combustion through, 167

Imagination, scope of the, 42
----note by Maclaurin on this point, 43 _note_


Janssen, M., on the rose-coloured solar prominences, 204

Jupiter, Roemer's observations of the moons of, 20

Jupiter's distance from the sun, 20


Kepler, his investigations on the refraction of light, 14, 207

Kirchhoff, Professor, his explanation of Fraunhofer's lines, 193
----his precursors, 201
----his claims, 203

Knoblauch, his demonstration of the double refraction of heat of
Iceland spar, 185


Lactantius, on the natural philosophers of his time, 13

Lamy, M., isolates thallium in ingots, 193

Lesley, Professor, his invitation, 2

Light familiar to the ancients, 5
----generation of, 6, 7
----spherical aberration of, 8
----the rectilineal propagation of, and mode of producing it, 9
----illustration showing that the angle of incidence is equal to the
    angle of reflection, 10, 11
----sterility of the Middle Ages, 13
----history of refraction, 14
----demonstration of the fact of refraction, 14
----partial and total reflection of, 16-20
----velocity of, 20
----Bradley's discovery of the aberration of light, 21, 22
----principle of least time, 23
----Descartes and the rainbow, 24
----Newton's analysis of, 26, 27
----synthesis of white light, 30
----complementary colours, 31
----yellow and blue lights produce white by their mixture, 31
----what is the meaning of blackness? 32
----analysis of the action of pigments upon, 33
----absorption, 34
----mixture of pigments contrasted with mixture of lights, 37
----Wünsch on three simple colours in white light, 39 _note_
----Newton arrives at the emission theory, 45
----Young's discovery of the undulatory theory, 49
----illustrations of wave-motion, 58
----interference of sound-waves, 58
----velocity of, 60
----principle of interference of waves of, 61
----phenomena which first suggested the undulatory theory 62-69
----soap-bubbles and their colours, 62-65
----Newton's rings, 69-77
----his espousal of the emission theory, and the results of this
    espousal, 77
----transmitted light, 77
----diffraction, 77, 89
----origin of the notion of the attraction of gravitation, 92
----polarity, how generated, 93
----action of crystals upon, 98
----refraction of, 106
----elasticity and density, 108
----double refraction, 109
----chromatic phenomena produced by crystals in polarized, 121
----the Nicol prism, 122
----mechanism of, 125
----vibrations, 125
----composition and resolution of vibrations, 128
----polarizer and analyzer, 127
----recompounding the two systems of waves by the analyzer, 129
----interference thus rendered possible, 131
----chromatic phenomena produced by quartz, 139
----magnetization, of, 141
----rings surrounding the axes of crystals, 143
----colour and polarization of sky, 149, 154
----range of vision incommensurate with range of radiation, 159
----effect of thallene on the spectrum, 162
----fluorescence, 162
----transparency, 167
----the ultra-red rays, 170
----part played in Nature by these rays, 175
----conversion of heat-rays into light-rays, 176
----identity of radiant heat and, 177
----polarization of heat, 180
----principles of spectrum analysis, 189
----spectra of incandescent vapours, 190
----Fraunhofer's lines, and Kirchhoff's explanation of them, 193
----solar chemistry, 195-197
----demonstration of analogy between sound and, 198, 199
----Kirchhoff and his precursors, 201
----rose-coloured solar prominences, 204
----results obtained by various workers, 205
----summary and conclusion, 206
----polarized, the spectra of, 227
----measurement of the waves of, 234

Lignum Nephriticum, fluorescence of, 164

Lloyd, Dr., on polarization of heat, 180, 209

Lockyer, Mr., on the rose-coloured solar prominences, 205

Lycopodium, diffraction effects caused by the spores of, 88


Magnetization of light, 141

Malus, his discovery respecting reflected light through Iceland spar, 115
----discovers the polarization of light by reflection, 208

Masson, his essay on the bands of the induction spark, 202

Melloni, on the polarization of heat, 180

Metals, combustion of, 5, 6
----spectrum analysis of, 190
----spectrum bands proved by Bunsen and Kirchhoff to be characteristic
of the vapour of, 192

Mill, John Stuart, his scepticism regarding the undulatory theory, 149

Miller, Dr., his drawings and descriptions of the spectra of various
coloured flames, 201

Morton, Professor, his discovery of thallene, 162

Mother-of-pearl, colours of, 90


Nature, a savage's interpretation of, 4

Newton, Sir Isaac, his experiments on the composition of solar light, 26
----his spectrum, 27
----dispersion, 27
----arrives at the emission theory of light, 45
----his objection to the conception of an ether espoused and defended by
    Huyghens and Euler, 58
----his optical career, 70
----his rings, 69-77
----his rings explained by the theory of 'fits,' 73
----espouses the emission theory, 77
----effects of this espousal, 77
----his idea of gravitation, 92
----his errors, 208

Nicol prism, the, 122


Ocean, colour of the, 35

OErsted, discovers the deflection of a magnetic needle by an electric
current, 176

Optics, science of, 4


Pasteur referred to, 219

Physical theories, origin of, 41-44

Pigments, analysis of the action of, upon light, 33
----mixture of, contrasted with mixture of lights, 37
----Helmholtz reveals the cause of the green in the case of mixed blue
    and yellow pigments, 37
----impurity of natural colours, 37

Pitch of sound, 59

Plücker, his drawings of spectra, 202

Polariscope, stained glass in the, 130,131
----unannealed glass in the, 136

Polarity, notion of, how generated, 93
----atomic, 93-96
----structural arrangements due to, 96
----polarization of light, 112
----tested by tourmaline, 116
----and by reflection and refraction, 119
----depolarization, 120

Polarization of light, 112
----circular, 140
----sky-light, 149, 157
----of artificial sky, 156
----of radiant heat, 180

Polarizer and analyzer, 127

Poles of a magnet, 93

Powell, Professor, on polarization of heat, 180

Prism, the Nicol, 122


Quartz, chromatic phenomena produced by, 139


Radiant heat, 172
----diathermancy, or perviousness to radiant heat, 173
----conversion of heat-rays into light rays, 174
----formation of invisible heat-images, 179
----polarization of, 180
----double refraction, 182
----magnetization of, 184

Rainbow, Descartes' explanation of the, 24

Refraction, demonstration of, 14

Refraction of light, 106
----double, 109

Reflection, partial and total, 16-20

Respighi, results obtained by, 205

Ritter, his discovery of the ultraviolet rays of the sun, 159

Roemer, Olav, his observations of Jupiter's moons, 20
----his determination of the velocity of light, 21

Rubidium, discovery of, 193

Rusting of iron, what it is, 5


Schwerd, his observations respecting diffraction, 87

Science, growth of, 176, 203

Scoresby, Dr., succeeds in exploding gunpowder by the sun's rays
conveyed by large lenses of ice, 167

Secchi, results obtained by, 205

Seebeck, Thomas, discovers thermo-electricity, 176
----discovers the polarization of light by tourmaline, 208

Selenite, experiments with thick and thin plates of, 124

Silver spectrum, analysis of, 190, 191

Sky-light, colour and polarization of, 149, 154
----generation of artificial skies, 152

Snell, Willebrord, his discovery, 14
----his law, 15, 24

Soap-bubbles and their colours, 63, 65

Sound, early notions of the ancients respecting, 51
----interference of waves of, 58
----pitch of, 59
----analogies of light and, 56
----demonstration of analogy between, and light, 198, 199

Sonorous vibrations, action of, 134

Spectrum analysis, principles of, 189

Spectra of incandescent vapours, 190
----discontinuous, 191, 192
----of polarized light, 227

Spectrum bands proved by Bunsen and Kirchhoff to be characteristic of
the vapour, 192
----its capacity as an agent of discovery, 193
----analysis of the sun and stars, 193

Spottiswoode, Mr. William, 123, 227

Stewart, Professor Balfour, 202

Stokes, Professor, results of his examination of substances excited by
the ultra-violet waves, 161
----his discovery of fluorescence, 162
----on fluorescence, 165
----nearly anticipates Kirchhoff's discovery, 198, 202

Striated surfaces, colours of, 89

Sulphate of quinine first noticed and described by Sir John Herschel, 165

Sun, chemistry of the, 195

Sun, rose-coloured solar prominences, 204


Talbot, Mr., his experiments, 201

Tartaric acid, irregular crystallization of, and its effects, 131

Thallene, its effect on the spectrum, 162

Thallium, spectrum analysis of, 190, 191
----discovery of, 193
----isolated in ingots by M. Lamy, 193

Theory, relation of, to experience, 91

Thermo-electric pile, 176

Thermo-electricity, discovery of, 176

Tombeline, Mont, inverted image of, 19

Tourmaline, polarization of light by means of, 112

Transmitted light, reason for, 77

Transparency, remarks on, 167


Ultra-violet sun-rays, discovered by Ritter, 159
----effects of, 160

Ultra-red rays of the solar spectrum, 171
----part played by the, 173

Undulatory theory of light, bases of the, 47
----Sir David Brewster's chief objection to the, 47

Undulatory theory of light, Young's foundation of the, 49
----phenomena which first suggested the, 62, 69
----Mr. Mill's scepticism regarding the, 143
----a demonstrated verity in the hands of Young, 210


Vassenius describes the rose-coloured solar prominences in 1733, 204

Vitellio, his skill and conscientiousness, 14
----his investigations respecting light, 207

Voltaic battery, use of, and its production of heat, 6, 7


Water, deportment of, considered and explained, 105, 106

Waves of water, 51
----length of a wave, 52
----interference of waves, 53-55

Wertheim, M., his instrument for the determination of strains and
pressures by the colours of polarized light, 134

Wheatstone, Sir Charles, his analysis of the light of the electric
spark, 202

Whirlpool Rapids, illustration of the principle of the interference of
waves at the, 55

Willigen, Van der, his drawings of spectra, 202

Wollaston, Dr., first observes lines in solar spectrum, 193
----discovers the rings of Iceland spar, 209

Woodbury, Mr., on the impurity of natural colours, 37

Wünsch, Christian Ernst, on the three simple colours in white
lights, 39 _note_
----his experiments, 39 _note_


Young, Dr. Thomas, his discovery of Egyptian hieroglyphics, 49;
----and the undulatory theory of light, 49
----Helmholtz's estimate of him, 50
----ridiculed by Brougham in the 'Edinburgh Review,' 50
----generalizes Grimaldi's observation on light, 56, 57
----photographs the ultra-violet rings of Newton, 160





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