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+*** START OF THE PROJECT GUTENBERG EBOOK 14000 ***
+
+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
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
+
+*** END OF THE PROJECT GUTENBERG EBOOK 14000 ***
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+<div>*** START OF THE PROJECT GUTENBERG EBOOK 14000 ***</div>
+
+<h1>SIX LECTURES ON LIGHT</h1>
+<h4>DELIVERED IN THE UNITED STATES</h4>
+<h5>IN</h5>
+<h4>1872-1873</h4>
+<h3>BY</h3>
+<h2>JOHN TYNDALL, D.C.L., LL,D., F.R.S.</h2>
+<p class="center">LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE ROYAL
+INSTITUTION OF GREAT BRITAIN<br />
+<br />
+<br /></p>
+<div class="figcenter" style="width: 505px;"><img src=
+"images/frontispiece.jpg" width="505" height="659" alt=
+"Sir Thomas Laurence PRA Pinx Henry Adlarc. Sc." title=
+"Sir Thomas Laurence PRA Pinx Henry Adlarc. Sc." /></div>
+<div class="figcenter" style="width: 420px;"><img src=
+"images/sig.png" width="420" height="105" alt=
+"(Signature) Thomas Young" title="" /></div>
+<p class="center">London: Longmans &amp; Co.</p>
+<p class="center"><i>SIXTH IMPRESSION</i></p>
+<p class="center">LONGMANS, GREEN, AND CO.</p>
+<p class="center">39 PATERNOSTER ROW, LONDON</p>
+<p class="center">NEW YORK AND BOMBAY</p>
+<p class="center">1906</p>
+<h3>PREFACE TO THE FOURTH EDITION.</h3>
+<p>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.</p>
+<p>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.</p>
+<p>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.</p>
+<p>J.T.</p>
+<p style="text-align: right;">ALP LUSGEN: <i>October</i> 1885.</p>
+<hr style="width: 65%;" />
+<h2><a name="CONTENTS" id="CONTENTS"></a>CONTENTS.</h2>
+<div style="margin-left: 20%; margin-right: 20%">
+<p><a href="#LECTURE_I"><b>LECTURE I.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Introductory</li>
+<li>Uses of Experiment</li>
+<li>Early Scientific Notions</li>
+<li>Sciences of Observation</li>
+<li>Knowledge of the Ancients regarding Light</li>
+<li>Defects of the Eye</li>
+<li>Our Instruments</li>
+<li>Rectilineal Propagation of Light</li>
+<li>Law of Incidence and Reflection</li>
+<li>Sterility of the Middle Ages</li>
+<li>Refraction</li>
+<li>Discovery of Snell</li>
+<li>Partial and Total Reflection</li>
+<li>Velocity of Light</li>
+<li>Roemer, Bradley, Foucault, and Fizeau</li>
+<li>Principle of Least Action</li>
+<li>Descartes and the Rainbow</li>
+<li>Newton's Experiments on the Composition of Solar Light</li>
+<li>His Mistake regarding Achromatism</li>
+<li>Synthesis of White Light</li>
+<li>Yellow and Blue Lights produce White by their Mixture</li>
+<li>Colours of Natural Bodies</li>
+<li>Absorption</li>
+<li>Mixture of Pigments contrasted with Mixture of Lights</li>
+</ul>
+</div>
+<p><a href="#LECTURE_II"><b>LECTURE II.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Origin of Physical Theories</li>
+<li>Scope of the Imagination</li>
+<li>Newton and the Emission Theory</li>
+<li>Verification of Physical Theories</li>
+<li>The Luminiferous Ether</li>
+<li>Wave-theory of Light</li>
+<li>Thomas Young</li>
+<li>Fresnel and Arago</li>
+<li>Conception of Wave-motion</li>
+<li>Interference of Waves</li>
+<li>Constitution of Sound-waves</li>
+<li>Analogies of Sound and Light</li>
+<li>Illustrations of Wave-motion</li>
+<li>Interference of Sound Waves</li>
+<li>Optical Illustrations</li>
+<li>Pitch and Colour</li>
+<li>Lengths of the Waves of Light and Rates of Vibration of
+the</li>
+<li>Ether-particles</li>
+<li>Interference of Light</li>
+<li>Phenomena which first suggested the Undulatory Theory</li>
+<li>Boyle and Hooke</li>
+<li>The Colours of thin Plates</li>
+<li>The Soap-bubble</li>
+<li>Newton's Rings</li>
+<li>Theory of 'Fits'</li>
+<li>Its Explanation of the Rings</li>
+<li>Overthrow of the Theory</li>
+<li>Diffraction of Light</li>
+<li>Colours produced by Diffraction</li>
+<li>Colours of Mother-of-Pearl.</li>
+</ul>
+</div>
+<p><a href="#LECTURE_III"><b>LECTURE III.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Relation of Theories to Experience</li>
+<li>Origin of the Notion of the Attraction of Gravitation</li>
+<li>Notion of Polarity, how generated</li>
+<li>Atomic Polarity</li>
+<li>Structural Arrangements due to Polarity</li>
+<li>Architecture of Crystals considered as an Introduction to
+their</li>
+<li>Action upon Light</li>
+<li>Notion of Atomic Polarity applied to Crystalline Structure</li>
+<li>Experimental Illustrations</li>
+<li>Crystallization of Water</li>
+<li>Expansion by Heat and by Cold</li>
+<li>Deportment of Water considered and explained</li>
+<li>Bearings of Crystallization on Optical Phenomena</li>
+<li>Refraction</li>
+<li>Double Refraction</li>
+<li>Polarization</li>
+<li>Action of Tourmaline</li>
+<li>Character of the Beams emergent from Iceland Spar</li>
+<li>Polarization by ordinary Refraction and Reflection</li>
+<li>Depolarization.</li>
+</ul>
+</div>
+<p><a href="#LECTURE_IV"><b>LECTURE IV.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Chromatic Phenomena produced by Crystals in Polarized
+Light</li>
+<li>The Nicol Prism</li>
+<li>Polarizer and Analyzer</li>
+<li>Action of Thick and Thin Plates of Selenite</li>
+<li>Colours dependent on Thickness</li>
+<li>Resolution of Polarized Beam into two others by the
+Selenite</li>
+<li>One of them more retarded than the other</li>
+<li>Recompounding of the two Systems of Waves by the Analyzer</li>
+<li>Interference thus rendered possible</li>
+<li>Consequent Production of Colours</li>
+<li>Action of Bodies mechanically strained or pressed</li>
+<li>Action of Sonorous Vibrations</li>
+<li>Action of Glass strained or pressed by Heat</li>
+<li>Circular Polarization</li>
+<li>Chromatic Phenomena produced by Quartz</li>
+<li>The Magnetization of Light</li>
+<li>Rings surrounding the Axes of Crystals</li>
+<li>Biaxal and Uniaxal Crystals</li>
+<li>Grasp of the Undulatory Theory</li>
+<li>The Colour and Polarization of Sky-light</li>
+<li>Generation of Artificial Skies.</li>
+</ul>
+</div>
+<p><a href="#LECTURE_V"><b>LECTURE V.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Range of Vision not commensurate with Range of Radiation</li>
+<li>The Ultra-violet Rays</li>
+<li>Fluorescence</li>
+<li>The rendering of invisible Rays visible</li>
+<li>Vision not the only Sense appealed to by the Solar and Electric
+Beam</li>
+<li>Heat of Beam</li>
+<li>Combustion by Total Beam at the Foci of Mirrors and Lenses</li>
+<li>Combustion through Ice-lens</li>
+<li>Ignition of Diamond</li>
+<li>Search for the Rays here effective</li>
+<li>Sir William Herschel's Discovery of dark Solar Rays</li>
+<li>Invisible Rays the Basis of the Visible</li>
+<li>Detachment by a Ray-filter of the Invisible Rays from the
+Visible</li>
+<li>Combustion at Dark Foci</li>
+<li>Conversion of Heat-rays into Light-rays</li>
+<li>Calorescence</li>
+<li>Part played in Nature by Dark Rays</li>
+<li>Identity of Light and Radiant Heat</li>
+<li>Invisible Images</li>
+<li>Reflection, Refraction, Plane Polarization, Depolarization,
+Circular Polarization, Double Refraction, and Magnetization of
+Radiant Heat</li>
+</ul>
+</div>
+<p><a href="#LECTURE_VI"><b>LECTURE VI.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Principles of Spectrum Analysis</li>
+<li>Prismatic Analysis of the Light of Incandescent Vapours</li>
+<li>Discontinuous Spectra</li>
+<li>Spectrum Bands proved by Bunsen and Kirchhoff to be
+characteristic of the Vapour</li>
+<li>Discovery of Rubidium, C&aelig;sium, and Thallium</li>
+<li>Relation of Emission to Absorption</li>
+<li>The Lines of Fraunhofer</li>
+<li>Their Explanation by Kirchhoff</li>
+<li>Solar Chemistry involved in this Explanation</li>
+<li>Foucault's Experiment</li>
+<li>Principles of Absorption</li>
+<li>Analogy of Sound and Light</li>
+<li>Experimental Demonstration of this Analogy</li>
+<li>Recent Applications of the Spectroscope</li>
+<li>Summary and Conclusion</li>
+</ul>
+</div>
+<p><a href="#APPENDIX"><b>APPENDIX.</b></a></p>
+<div style="margin-left: 2em;">
+<p><a href="#ON_THE_SPECTRA_OF_POLARIZED_LIGHT">On the Spectra of
+Polarized Light</a></p>
+<p><a href="#MEASUREMENT_OF_THE_WAVES_OF_LIGHT">Measurement of the
+Waves of Light</a></p>
+</div>
+<p><a href="#INDEX"><b>INDEX.</b></a></p>
+</div>
+<div><a name="Page_1" id="Page_1"></a><span class="pagenum">[Pg
+1]</span></div>
+<hr style="width: 65%;" />
+<h1>ON LIGHT</h1>
+<h2><a name="LECTURE_I" id="LECTURE_I"></a>LECTURE I.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>INTRODUCTORY</li>
+<li>USES OF EXPERIMENT</li>
+<li>EARLY SCIENTIFIC NOTIONS</li>
+<li>SCIENCES OF OBSERVATION</li>
+<li>KNOWLEDGE OF THE ANCIENTS REGARDING LIGHT</li>
+<li>DEFECTS OF THE EYE</li>
+<li>OUR INSTRUMENTS</li>
+<li>RECTILINEAL PROPAGATION OF LIGHT</li>
+<li>LAW OF INCIDENCE AND REFLECTION</li>
+<li>STERILITY OF THE MIDDLE AGES</li>
+<li>REFRACTION</li>
+<li>DISCOVERY OF SNELL</li>
+<li>PARTIAL AND TOTAL REFLECTION</li>
+<li>VELOCITY OF LIGHT</li>
+<li>ROEMER, BRADLEY, FOUCAULT, AND FIZEAU</li>
+<li>PRINCIPLE OF LEAST ACTION</li>
+<li>DESCARTES AND THE RAINBOW</li>
+<li>NEWTON'S EXPERIMENTS ON THE COMPOSITION OF SOLAR LIGHT</li>
+<li>HIS MISTAKE AS REGARDS ACHROMATISM</li>
+<li>SYNTHESIS OF WHITE LIGHT</li>
+<li>YELLOW AND BLUE LIGHTS PRODUCE WHITE BY THEIR MIXTURE</li>
+<li>COLOURS OF NATURAL BODIES</li>
+<li>ABSORPTION</li>
+<li>MIXTURE OF PIGMENTS CONTRASTED WITH MIXTURE OF LIGHTS.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Introduction</i>.</h3>
+<p>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<a name="FNanchor_1_1" id=
+"FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a>
+who deemed it good for neither world to be isolated from the other,
+<a name="Page_2" id="Page_2"></a><span class="pagenum">[Pg
+2]</span>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.</p>
+<p>The works here referred to were, for the most part, republished
+by the Messrs. Appleton of New York,<a name="FNanchor_2_2" id=
+"FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a>
+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<a name=
+"FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class=
+"fnanchor">[3]</a> 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.</p>
+<p>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 <a name="Page_3" id="Page_3"></a><span class=
+"pagenum">[Pg 3]</span>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.</p>
+<h3>&sect; 2. <i>Subject of the Course. Source of Light
+employed.</i></h3>
+<p>Experiments have two great uses&mdash;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.</p>
+<p>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 <a name=
+"Page_4" id="Page_4"></a><span class="pagenum">[Pg 4]</span>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.</p>
+<p>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 <i>causality</i>&mdash;the assumption that
+natural things did not come of themselves, but had unseen
+antecedents&mdash;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.</p>
+<p>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&mdash;and that historically a
+long one&mdash;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 <a name="Page_5" id="Page_5"></a><span class=
+"pagenum">[Pg 5]</span>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.</p>
+<p>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
+<i>experiment</i>, 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.</p>
+<p>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 <a name="Page_6" id=
+"Page_6"></a><span class="pagenum">[Pg 6]</span>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.</p>
+<p>The generation of this light and of this heat merits a moment's
+attention. Before you is an instrument&mdash;a small voltaic
+battery&mdash;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.</p>
+<p>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 <a name="Page_7"
+id="Page_7"></a><span class="pagenum">[Pg 7]</span>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.</p>
+<div class="figcenter" style="width: 444px;"><img src=
+"images/fig01.jpg" width="444" height="307" alt="Fig. 1." title=
+"" /> <b>Fig. 1.</b></div>
+<p>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 <a name="Page_8" id=
+"Page_8"></a><span class="pagenum">[Pg 8]</span>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.</p>
+<p>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 <i>towards</i> 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 <i>whole</i> 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 <i>spherical aberration</i>, 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&mdash;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 <a name="Page_9" id="Page_9"></a><span class=
+"pagenum">[Pg 9]</span>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.</p>
+<h3>&sect; 3. <i>Rectilineal Propagation of Light. Elementary
+Experiments. Law of Reflection.</i></h3>
+<p>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 <i>air</i> 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.</p>
+<div class="figleft" style="width: 445px;"><img src=
+"images/fig02.jpg" width="445" height="250" alt="Fig. 2." title=
+"" /> <b>Fig. 2.</b></div>
+<p>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 <a name="Page_10"
+id="Page_10"></a><span class="pagenum">[Pg 10]</span>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.</p>
+<div class="figright" style="width: 475px;"><img src=
+"images/fig03.jpg" width="475" height="311" alt="Fig. 3." title=
+"" /> <b>Fig. 3.</b></div>
+<p>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 <a name="Page_11" id="Page_11"></a><span class=
+"pagenum">[Pg 11]</span>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 <i>o</i>,
+<i>o</i> 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 <i>m</i> is found accurately equal
+to the arc from 5 to <i>n</i>. 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.</p>
+<p>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 <a name="Page_12" id=
+"Page_12"></a><span class="pagenum">[Pg 12]</span>reflected from it
+is twice that of the reflecting mirror. A simple experiment will
+make this plain. The arc (<i>m n</i>, 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.</p>
+<p>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
+demon<a name="Page_13" id="Page_13"></a><span class="pagenum">[Pg
+13]</span>strated. 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.</p>
+<h3>&sect; 4. <i>The Refraction of Light. Total
+Reflection.</i></h3>
+<p>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
+<i>&agrave; priori</i> 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&mdash;'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;&mdash;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.'</p>
+<p>As regards the refraction of light, the course of <a name=
+"Page_14" id="Page_14"></a><span class="pagenum">[Pg 14]</span>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.</p>
+<p>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 <a name="Page_15" id=
+"Page_15"></a><span class="pagenum">[Pg 15]</span>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 <i>reflection</i> (along O R) accompanies refraction, the beam
+dividing itself at the point of incidence into a refracted and a
+reflected portion.<a name="FNanchor_4_4" id=
+"FNanchor_4_4"></a><a href="#Footnote_4_4" class=
+"fnanchor">[4]</a></p>
+<div class="figright" style="width: 450px;"><img src=
+"images/fig04.jpg" width="450" height="254" alt="Fig. 4." title=
+"" /> <b>Fig. 4.</b></div>
+<p>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 <i>m</i> E, there
+is refraction: it is bent at E and strikes the <a name="Page_16"
+id="Page_16"></a><span class="pagenum">[Pg 16]</span>circle at
+<i>n</i>. When it is incident along <i>m'</i> E there is also
+refraction at E, the beam striking the point <i>n'</i>. From the
+ends of the two incident beams, let the perpendiculars <i>m</i>
+<i>o</i>, <i>m'</i> <i>o'</i> be drawn upon B D, and from the ends
+of the refracted beams let the perpendiculars <i>p</i> <i>n</i>,
+<i>p'</i> <i>n'</i> be also drawn. Measure the lengths of <i>o
+m</i> and of <i>p</i> <i>n</i>, and divide the one by the other.
+You obtain a certain quotient. In like manner divide <i>m'</i>
+<i>o'</i> by the corresponding perpendicular <i>p'</i> <i>n'</i>;
+you obtain precisely the same quotient. Snell, in fact, found this
+quotient to be <i>a constant quantity</i> for each particular
+substance, though it varied in amount from one substance to
+another. He called the quotient the <i>index of refraction</i>.</p>
+<div class="figleft" style="width: 253px;"><img src=
+"images/fig05.jpg" width="253" height="253" alt="Fig. 5" title=
+"" /> <b>Fig. 5</b></div>
+<p>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 <i>partial</i>. In this case
+the most powerfully reflecting substances either transmit or absorb
+a portion of the incident light. At a perpendicular incidence
+<a name="Page_17" id="Page_17"></a><span class="pagenum">[Pg
+17]</span>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&deg;, for example, water reflects 22 rays, at
+60&deg; it reflects 65 rays, at 80&deg; 333 rays; while at an
+incidence of 89&frac12;&deg;, 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,
+<i>total</i>.</p>
+<p>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&mdash;the principle of reversibility.<a name=
+"FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class=
+"fnanchor">[5]</a> In the case of refraction, for instance, when
+the ray passes obliquely from air into water, it is bent
+<i>towards</i> the perpendicular; when it passes from water to air,
+it is bent <i>from</i> the perpendicular, and accurately reverses
+its course. Thus in fig. 5, if <i>m</i> E <i>n</i> be the track of
+a ray in passing from air into water, <i>n</i> E <i>m</i> 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 <i>m</i> E or <i>m&prime;</i> 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 <a name="Page_18" id="Page_18"></a><span class=
+"pagenum">[Pg 18]</span>pursue say the course E <i>n</i>&Prime;.
+Conversely, if the light start from <i>n</i>&Prime;, 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
+<i>n</i>&#8244; E, which lies beyond <i>n</i>&Prime; E? The answer
+is, it will not quit the water at all, but will be <i>totally</i>
+reflected (along E <i>x</i>). 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 <i>n</i>&#8244;) being equal to the angle
+of reflection (D E <i>x</i>).</p>
+<div class="figright" style="width: 252px;"><img src=
+"images/fig06.jpg" width="252" height="243" alt="Fig. 6" title=
+"" /> <b>Fig. 6</b></div>
+<p>Total reflection may be thus simply illustrated:&mdash;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
+<a name="Page_19" id="Page_19"></a><span class="pagenum">[Pg
+19]</span>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.</p>
+<p>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.</p>
+<p>The angle which marks the limit beyond which total reflection
+takes place is called the <i>limiting angle</i> (it is marked in
+fig. 6 by the strong line E <i>n</i>&Prime;). It must evidently
+diminish as the refractive index increases. For water it is
+48&frac12;&deg;, for flint glass 38&deg;41', and for diamond
+23&deg;42'. Thus all the light incident from two complete
+quadrants, or 180&deg;, in the case of diamond, is condensed into
+an angular space of 47&deg;22' (twice 23&deg;42') by refraction.
+Coupled with its great refraction, are <a name="Page_20" id=
+"Page_20"></a><span class="pagenum">[Pg 20]</span>the great
+dispersive and great reflective powers of diamond; hence the
+extraordinary radiance of the gem, both as regards white light and
+prismatic light.</p>
+<h3>&sect; 5. <i>Velocity of Light. Aberration. Principle of least
+Action.</i></h3>
+<p>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.</p>
+<p>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.</p>
+<p>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
+<a name="Page_21" id="Page_21"></a><span class="pagenum">[Pg
+21]</span>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.'</p>
+<p>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.</p>
+<p>The velocity of light, as determined by Roemer, is 192,500 miles
+in a second.</p>
+<p>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 <a name="Page_22" id=
+"Page_22"></a><span class="pagenum">[Pg 22]</span>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.'</p>
+<p>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&mdash;a man of the
+rarest mechanical genius&mdash;solved the problem without quitting
+<a name="Page_23" id="Page_23"></a><span class="pagenum">[Pg
+23]</span>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.</p>
+<p>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 <i>least time</i>. 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.</p>
+<div><a name="Page_24" id="Page_24"></a><span class="pagenum">[Pg
+24]</span></div>
+<h3>&sect; 6. <i>Descartes' Explanation of the Rainbow</i>.</h3>
+<p>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.</p>
+<p>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 42&frac12;&deg; 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 42&frac12;&deg; 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.</p>
+<p>From the eye of the observer conceive another line to be drawn,
+enclosing an angle, not of 42&frac12;&deg;, but of 40&frac12;&deg;,
+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. <a name=
+"Page_25" id="Page_25"></a><span class="pagenum">[Pg
+25]</span>These two bands constitute the limiting colours of the
+rainbow, and between them the bands corresponding to the other
+colours lie.</p>
+<p>Thus the line drawn from the eye to the <i>middle</i> of the
+bow, and the line drawn through the eye to the sun, always enclose
+an angle of about 41&deg;. To account for this was the great
+difficulty, which remained unsolved up to the time of
+Descartes.</p>
+<p>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 <i>almost parallel to each other</i>. They were thus
+enabled to preserve their intensity through long atmospheric
+distances. At all other angles the rays quitted the drop
+<i>divergent</i>, 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.</p>
+<p>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&mdash;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
+<a name="Page_26" id="Page_26"></a><span class="pagenum">[Pg
+26]</span>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&mdash;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 <i>image</i> of the bow seen in the
+sky.</p>
+<h3>&sect; 7. <i>Analysis and Synthesis of Light. Doctrine of
+Colours</i>.</h3>
+<p>In the rainbow a new phenomenon was introduced&mdash;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 <i>composite</i>, not simple.
+His elongated image <a name="Page_27" id="Page_27"></a><span class=
+"pagenum">[Pg 27]</span>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.</p>
+<p>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 <i>spectrum</i>. Newton divided the spectrum into seven
+parts&mdash;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 <i>dispersion</i>.</p>
+<div class="figcenter" style="width: 443px;"><img src=
+"images/fig07.jpg" width="443" height="303" alt="Fig. 7." title=
+"" /> <b>Fig. 7.</b></div>
+<p>This was the first <i>analysis</i> of solar light by Newton;
+<a name="Page_28" id="Page_28"></a><span class="pagenum">[Pg
+28]</span>but the scientific mind is fond of verification, and
+never neglects it where it is possible. Newton completed his proof
+by <i>synthesis</i> 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.</p>
+<div class="figcenter" style="width: 430px;"><img src=
+"images/fig08.jpg" width="430" height="321" alt="Fig. 8." title=
+"" /> <b>Fig. 8.</b></div>
+<p>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&mdash;lenses yielding no colour&mdash;which Newton thought
+an impossi<a name="Page_29" id="Page_29"></a><span class=
+"pagenum">[Pg 29]</span>bility. By setting a
+water-prism&mdash;water contained in a wedge-shaped vessel with
+glass sides (B, fig. 8)&mdash;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 <i>white</i>; but though the dispersion is abolished, there
+remains a very sensible amount of refraction.</p>
+<p>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.<a name="FNanchor_6_6"
+id="FNanchor_6_6"></a><a href="#Footnote_6_6" class=
+"fnanchor">[6]</a></p>
+<div class="figcenter" style="width: 445px;"><img src=
+"images/fig09.jpg" width="445" height="305" alt="Fig. 9." title=
+"" /> <b>Fig. 9.</b></div>
+<p><a name="Page_30" id="Page_30"></a><span class="pagenum">[Pg
+30]</span>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 <a name="Page_31" id=
+"Page_31"></a><span class="pagenum">[Pg 31]</span>leave the
+residual portion. On the screen are now two coloured rectangles
+produced in this way. These are <i>complementary</i>
+colours&mdash;colours which, by their union, produce white. Note,
+that by judicious management, one of these colours is rendered
+<i>yellow</i>, and the other <i>blue</i>. I withdraw the thin
+prism; yellow and blue immediately commingle, and we have
+<i>white</i> as the result of their union. On our way, then, we
+remove the fallacy, first exposed by W&uuml;nsch, and afterwards
+independently by Helmholtz, that the mixture of blue and yellow
+lights produces green.</p>
+<p>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.</p>
+<p>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.</p>
+<p>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
+<i>selective</i>, not <i>creative</i>. There is no colour
+<i>generated</i> 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&mdash;<a name="Page_32" id="Page_32"></a><span class=
+"pagenum">[Pg 32]</span>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.</p>
+<p>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&mdash;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.</p>
+<p>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 <i>negative</i>
+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 <a name=
+"Page_33" id="Page_33"></a><span class="pagenum">[Pg 33]</span>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.</p>
+<p>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</p>
+<div class="blockquot">
+<p>'Clothed in white samite, mystic, wonderful;'</p>
+</div>
+<p>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.</p>
+<h3>&sect; 8. <i>Colours of Pigments as distinguished from Colours
+of Light</i>.</h3>
+<p>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 <a name="Page_34" id="Page_34"></a><span class="pagenum">[Pg
+34]</span>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.</p>
+<p>In the case of pigments, then, the light is <i>reflected</i> at
+the limiting surfaces of the particles, but it is in part
+<i>absorbed</i> 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
+<i>through</i> 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.</p>
+<p>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 <a name="Page_35" id="Page_35"></a><span class="pagenum">[Pg
+35]</span>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.</p>
+<p>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 <i>black</i>, 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.</p>
+<p>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 <a name="Page_36" id=
+"Page_36"></a><span class="pagenum">[Pg 36]</span>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 <i>reflecting surface</i>,
+the water between the eye and it the <i>absorbing medium</i>.</p>
+<p>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.</p>
+<p>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, pro<a name="Page_37" id=
+"Page_37"></a><span class="pagenum">[Pg 37]</span>ducing white by
+their mixture. The mixture of blue and yellow <i>pigments</i>
+undoubtedly produces green, but the mixture of pigments is a
+totally different thing from the mixture of lights.</p>
+<p>Helmholtz has revealed the cause of the green produced by a
+mixture of blue and yellow pigments. No natural colour is
+<i>pure</i>. 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.</p>
+<p>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 <a name="Page_38" id=
+"Page_38"></a><span class="pagenum">[Pg 38]</span>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.</p>
+<p>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.<a name="FNanchor_7_7"
+id="FNanchor_7_7"></a><a href="#Footnote_7_7" class=
+"fnanchor">[7]</a></p>
+<p><a name="Page_39" id="Page_39"></a><span class="pagenum">[Pg
+39]</span>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,<a name="FNanchor_8_8" id=
+"FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a>
+must be highly complex.</p>
+<p><a name="Page_40" id="Page_40"></a><span class="pagenum">[Pg
+40]</span>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&mdash;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&mdash;and
+it would be mere presumption to dogmatize as to what she
+meant&mdash;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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_41" id="Page_41"></a><span class="pagenum">[Pg
+41]</span></div>
+<h2><a name="LECTURE_II" id="LECTURE_II"></a>LECTURE II.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>ORIGIN OF PHYSICAL THEORIES</li>
+<li>SCOPE OF THE IMAGINATION</li>
+<li>NEWTON AND THE EMISSION THEORY</li>
+<li>VERIFICATION OF PHYSICAL THEORIES</li>
+<li>THE LUMINIFEROUS ETHER</li>
+<li>WAVE THEORY OF LIGHT</li>
+<li>THOMAS YOUNG</li>
+<li>FRESNEL AND ARAGO</li>
+<li>CONCEPTION OF WAVE-MOTION</li>
+<li>INTERFERENCE OF WAVES</li>
+<li>CONSTITUTION OF SOUND-WAVES</li>
+<li>ANALOGIES OF SOUND AND LIGHT</li>
+<li>ILLUSTRATIONS OF WAVE-MOTION</li>
+<li>INTERFERENCE OF SOUND-WAVES</li>
+<li>OPTICAL ILLUSTRATIONS</li>
+<li>PITCH AND COLOUR</li>
+<li>LENGTHS OF THE WAVES OF LIGHT AND RATES OF VIBRATION OF</li>
+<li>THE ETHER-PARTICLES</li>
+<li>INTERFERENCE OF LIGHT</li>
+<li>PHENOMENA WHICH FIRST SUGGESTED THE UNDULATORY THEORY</li>
+<li>BOYLE AND HOOKE</li>
+<li>THE COLOURS OF THIN PLATES</li>
+<li>THE SOAP-BUBBLE</li>
+<li>NEWTON'S RINGS</li>
+<li>THEORY OF 'FITS'</li>
+<li>ITS EXPLANATION OF THE RINGS</li>
+<li>OVER-THROW OF THE THEORY</li>
+<li>DIFFRACTION OF LIGHT</li>
+<li>COLOURS PRODUCED BY DIFFRACTION</li>
+<li>COLOURS OF MOTHER-OF-PEARL.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Origin and Scope of Physical Theories</i>.</h3>
+<p>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.</p>
+<p>Let us, then, inquire what this thing is that we have been
+generating, reflecting, refracting and analyzing.</p>
+<p><a name="Page_42" id="Page_42"></a><span class="pagenum">[Pg
+42]</span>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.</p>
+<p>This conception of physical theory implies, as you perceive, the
+exercise of the imagination&mdash;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, <a name="Page_43" id=
+"Page_43"></a><span class="pagenum">[Pg 43]</span>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.<a name="FNanchor_9_9" id=
+"FNanchor_9_9"></a><a href="#Footnote_9_9" class=
+"fnanchor">[9]</a></p>
+<p>Descartes imagined space to be filled with something that
+transmitted light <i>instantaneously</i>. 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 <a name="Page_44" id=
+"Page_44"></a><span class="pagenum">[Pg 44]</span>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.</p>
+<h3>&sect; 2. <i>The Emission Theory of Light</i>.</h3>
+<p>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 <a name="Page_45" id=
+"Page_45"></a><span class="pagenum">[Pg 45]</span>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 <i>as if</i>
+light consisted of such particles, and this was Newton's
+justification for introducing them.</p>
+<p>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&mdash;say from air on to glass or water&mdash;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 <a name=
+"Page_46" id="Page_46"></a><span class="pagenum">[Pg 46]</span>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.</p>
+<p>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.</p>
+<p>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 <a name="Page_47"
+id="Page_47"></a><span class="pagenum">[Pg 47]</span>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.</p>
+<p>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.</p>
+<h3>&sect; 3. <i>The Undulatory Theory of Light</i>.</h3>
+<p>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 <i>luminiferous ether</i> 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 <a name=
+"Page_48" id="Page_48"></a><span class="pagenum">[Pg 48]</span>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.</p>
+<p>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
+<i>prove</i> 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.</p>
+<p>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 <a name="Page_49" id="Page_49"></a><span class=
+"pagenum">[Pg 49]</span>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.</p>
+<p>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 <a name="Page_50" id=
+"Page_50"></a><span class="pagenum">[Pg 50]</span>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."</p>
+<p>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&mdash;hidden from the appreciative intellect of
+his country-men&mdash;deemed in fact a dreamer, through the
+vigorous sarcasm of a writer who had then possession of the public
+ear, and who in the <i>Edinburgh Review</i> 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, especi<a name="Page_51" id="Page_51"></a><span class=
+"pagenum">[Pg 51]</span>ally 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&mdash;if it be a fact that public disbelief weakens a man's
+force&mdash;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.</p>
+<h3>&sect; 4. <i>Wave-Motion, Interference of Waves, 'Whirlpool
+Rapids' of Niagara</i>.</h3>
+<p>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.</p>
+<p>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 <a name="Page_52" id=
+"Page_52"></a><span class="pagenum">[Pg 52]</span>of the wave
+itself, and the motion of the particles which at any moment
+constitute the wave.</p>
+<p>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 <i>sinus</i> 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 <i>form</i>, and not the
+transference of the substance which constitutes the wave.</p>
+<p>The <i>length</i> of the wave is the distance from crest to
+crest, while the distance through which the individual particles
+oscillate is called the <i>amplitude</i> of the oscillation. You
+will notice that in this description the particles of water are
+made to vibrate <i>across</i> the line of propagation.<a name=
+"FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10"
+class="fnanchor">[10]</a></p>
+<p><a name="Page_53" id="Page_53"></a><span class="pagenum">[Pg
+53]</span>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 <i>still</i>
+water. This action of wave upon wave is technically called
+<i>interference</i>, a term, to be remembered.</p>
+<div class="figcenter" style="width: 438px;"><img src=
+"images/fig10.jpg" width="438" height="443" alt="Fig. 10." title=
+"" /> <b>Fig. 10.</b></div>
+<p>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 <a name="Page_54" id=
+"Page_54"></a><span class="pagenum">[Pg 54]</span>figure.<a name=
+"FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11"
+class="fnanchor">[11]</a> 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:&mdash;</p>
+<div class="poem">
+<div class="stanza"><span>'Thou can'st not wave thy staff in the
+air,<br /></span> <span class="i2">Or dip thy paddle in the
+lake,<br /></span> <span>But it carves the brow of beauty
+there.<br /></span> <span class="i2">And the ripples in rhymes the
+oars forsake.'<br /></span></div>
+</div>
+<p><a name="Page_55" id="Page_55"></a><span class="pagenum">[Pg
+55]</span>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.</p>
+<p>Two kinds of motion are here obviously active, a motion of
+translation and a motion of undulation&mdash;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.</p>
+<p>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 <i>sides</i> of
+the river. Against these the water rises and sinks rhythmically but
+violently, large waves being <a name="Page_56" id=
+"Page_56"></a><span class="pagenum">[Pg 56]</span>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.</p>
+<h3>&sect; 5. <i>Analogies of Sound and Light.</i></h3>
+<p>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
+<a name="Page_57" id="Page_57"></a><span class="pagenum">[Pg
+57]</span>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 <i>waves</i> 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.</p>
+<p>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; <a name="Page_58" id="Page_58"></a><span class="pagenum">[Pg
+58]</span>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, <i>in the direction of propagation</i>. 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
+<i>across</i> the line of propagation. The vibrations of the air
+are <i>longitudinal</i>, those of the ether <i>transversal</i>.</p>
+<p>The most familiar illustration of the interference of
+sound-waves is furnished by the <i>beats</i> 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 <a name="Page_59" id="Page_59"></a><span class=
+"pagenum">[Pg 59]</span>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 <i>half a wavelength</i> 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 <i>three half-waves</i> in advance of the other. In general
+terms, the waves conspire when the one series is an <i>even</i>
+number of half-wave lengths, and they destroy each other when the
+one series is an <i>odd</i> 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.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href=
+"#Footnote_12_12" class="fnanchor">[12]</a></p>
+<p>The <i>pitch</i> of sound is wholly determined by the rapidity
+of the vibration, as the <i>intensity</i> is by the amplitude. What
+pitch is to the ear in acoustics, colour is to the eye in the
+undulatory theory of light. <a name="Page_60" id=
+"Page_60"></a><span class="pagenum">[Pg 60]</span>Though never
+seen, the lengths of the waves of light have been determined. Their
+existence is proved <i>by their effects</i>, 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.</p>
+<p>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. <i>All these waves enter the eye, and strike the retina
+at the back of the eye in one second</i>. 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.</p>
+<p>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 <a name="Page_61" id=
+"Page_61"></a><span class="pagenum">[Pg 61]</span>other point.
+Every star declares by its light its undamaged individuality, as if
+it alone had sent its thrills through space.</p>
+<h3>&sect; 6. <i>Interference of Light</i>.</h3>
+<div class="figleft" style="width: 465px;"><img src=
+"images/fig11.jpg" width="465" height="150" alt="Fig. 11." title=
+"" /> <b>Fig. 11.</b></div>
+<p>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 <i>m</i> <i>n</i>) 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 <i>even</i> number of
+semi-undulations in advance of the other. But if the one system be
+half a wave-length (as at A' <i>a</i>', fig. 12), or any <i>odd</i>
+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 <i>lift</i> the particles of ether at the precise places where
+the other tends to <i>depress</i> them; hence, through the <a name=
+"Page_62" id="Page_62"></a><span class="pagenum">[Pg
+62]</span>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.</p>
+<div class="figright" style="width: 480px;"><img src=
+"images/fig12.jpg" width="480" height="88" alt="Fig. 12." title=
+"" /> <b>Fig. 12.</b></div>
+<p>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.</p>
+<h3>&sect; 7. <i>Colours of thin Films. Observations of Boyle and
+Hooke</i>.</h3>
+<p>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
+<i>colours of thin plates</i>. 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 <a name=
+"Page_63" id="Page_63"></a><span class="pagenum">[Pg
+63]</span>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.</p>
+<p>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.</p>
+<p>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. <a name="Page_64" id="Page_64"></a><span class=
+"pagenum">[Pg 64]</span>Different colours, therefore, must appear
+at different thicknesses of the film.</p>
+<p>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.</p>
+<p>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&mdash;black, because it is pure and of great
+depth&mdash;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 <a name="Page_65" id=
+"Page_65"></a><span class="pagenum">[Pg 65]</span>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.</p>
+<p>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:&mdash;</p>
+<p>'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 <a name="Page_66" id="Page_66"></a><span class=
+"pagenum">[Pg 66]</span>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.'<a name=
+"FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13"
+class="fnanchor">[13]</a></p>
+<p>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.'<a name=
+"FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14"
+class="fnanchor">[14]</a></p>
+<p><a name="Page_67" id="Page_67"></a><span class="pagenum">[Pg
+67]</span>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
+lamin&aelig;, 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:&mdash;</p>
+<p>'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
+<a name="Page_68" id="Page_68"></a><span class="pagenum">[Pg
+68]</span>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&mdash;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, &amp;c.</p>
+<p>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 <i>of fiery burning
+bodies</i> 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 <i>a vibrative motion.'</i> 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.</p>
+<p><a name="Page_69" id="Page_69"></a><span class="pagenum">[Pg
+69]</span>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, <i>that the
+reflection from the further or under side of the body is the
+principal cause of the production of these colours.</i>'</p>
+<p>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.</p>
+<h3>&sect; 8. <i>Newton's Rings. Relation of Colour to Thickness of
+Film</i>.</h3>
+<div class="figright" style="width: 371px;"><img src=
+"images/fig13.jpg" width="371" height="81" alt="Fig. 13" title=
+"" /> <b>Fig. 13</b></div>
+<p>In this way, then, by the active operation of different minds,
+facts are observed, examined, and the precise <a name="Page_70" id=
+"Page_70"></a><span class="pagenum">[Pg 70]</span>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 <a name=
+"Page_71" id="Page_71"></a><span class="pagenum">[Pg
+71]</span>superposed, a series <i>of iris-coloured</i> circles was
+obtained. A magnified image of <i>Newton's rings</i> 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.</p>
+<div class="figleft" style="width: 278px;"><img src=
+"images/fig14.jpg" width="278" height="275" alt="Fig. 14" title=
+"" /> <b>Fig. 14</b></div>
+<p>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 <a name="Page_72" id=
+"Page_72"></a><span class="pagenum">[Pg 72]</span>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.</p>
+<p>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&mdash;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
+<a name="Page_73" id="Page_73"></a><span class="pagenum">[Pg
+73]</span>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 <i>some
+change in the condition of the particle itself</i>. The self-same
+particle, he affirmed, was affected by 'fits' of easy transmission
+and reflection.</p>
+<h3>&sect; 9. <i>Theory of 'Fits' applied to Newton's
+Rings</i>.</h3>
+<p>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.</p>
+<p><a name="Page_74" id="Page_74"></a><span class="pagenum">[Pg
+74]</span>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 <i>d</i>; then Newton found the distance corresponding to
+the second dark ring 2 <i>d</i>; the thickness corresponding to the
+third dark ring 3 <i>d</i>; the thickness corresponding to the
+tenth dark ring 10 <i>d</i>, and so on. Surely there must be some
+hidden meaning in this little distance, <i>d</i>, 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 <i>periodic recurrence</i>. 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&mdash;that is, in twenty-four hours&mdash;our planet performs
+a complete rotation; and in the time required to pass over the
+distance <i>d</i>, Newton's light-particle might be supposed to
+perform a complete rotation. True, the light-particle is smaller
+than the planet, and the distance <i>d</i>, instead of being a
+million <a name="Page_75" id="Page_75"></a><span class=
+"pagenum">[Pg 75]</span>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.</p>
+<p>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
+<i>once</i> 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 <i>and be lost to the
+eye</i>. All round the place of contact, wherever the film
+possesses this precise thickness, the light will equally
+disappear&mdash;we shall therefore have a ring of darkness.</p>
+<p>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 <i>d</i>, the particle has time to perform, <i>two</i>
+complete rotations within the film; when the thickness is 3 <i>d,
+three</i> complete rotations; when 10 <i>d, ten</i> 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.</p>
+<p>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 &frac12;<i>d</i>; 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 <a name="Page_76" id=
+"Page_76"></a><span class="pagenum">[Pg 76]</span>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 1&frac12;<i>d</i>, 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.</p>
+<p>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.</p>
+<p>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 <i>single surface</i>; 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 <a name="Page_77" id=
+"Page_77"></a><span class="pagenum">[Pg 77]</span>the surfaces of
+the film, and when this is done the rings vanish altogether.</p>
+<p>Rings of feeble intensity are also formed by <i>transmitted</i>
+light. These are referred by the undulatory theory to the
+interference of waves which have passed <i>directly</i> through the
+film, with others which have suffered <i>two</i> reflections within
+the film, and are thus completely accounted for.</p>
+<h3>&sect; 10. <i>The Diffraction of Light</i>.</h3>
+<p>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.</p>
+<p>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 <a name="Page_78" id=
+"Page_78"></a><span class="pagenum">[Pg 78]</span>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 <i>Diffraction</i>.</p>
+<p>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 <i>point</i> 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 <i>line</i> 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.</p>
+<p>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.</p>
+<p>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 <a name="Page_79" id="Page_79"></a><span class=
+"pagenum">[Pg 79]</span>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.</p>
+<p>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.</p>
+<div class="figcenter" style="width: 450px;"><img src=
+"images/fig15.jpg" width="450" height="197" alt="Fig. 15." title=
+"" /> <b>Fig. 15.</b></div>
+<p>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 <i>narrower</i>, and they are <i>closer
+together</i> than the red ones.</p>
+<p>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
+<a name="Page_80" id="Page_80"></a><span class="pagenum">[Pg
+80]</span>represented in fig. 16. When <i>white light</i>,
+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.</p>
+<div class="figcenter" style="width: 496px;"><img src=
+"images/fig16.jpg" width="496" height="208" alt="Fig. 16." title=
+"" /> <b>Fig. 16.</b></div>
+<h3>&sect; 11. <i>Application of the Wave-theory to the Phenomena
+of Diffraction</i>.</h3>
+<p>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.</p>
+<p>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&mdash;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
+<a name="Page_81" id="Page_81"></a><span class="pagenum">[Pg
+81]</span>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.</p>
+<p>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 <i>phase</i> 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 <i>opposite</i>
+phases of vibration.</p>
+<div class="figleft" style="width: 238px;"><img src=
+"images/fig17.jpg" width="238" height="238" alt="Fig 17." title=
+"" /> <b>Fig. 17.</b></div>
+<p>There is still another point to be cleared up&mdash;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 <i>m</i> <i>n</i> be the position of the ridge of one of the
+waves at any moment, and <i>m'</i> <i>n'</i> 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 <a name="Page_82" id="Page_82"></a><span class=
+"pagenum">[Pg 82]</span>wave <i>m</i> <i>n</i> 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 <i>m</i>
+<i>n</i> <i>does</i> 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 <i>m</i> <i>n</i> and <i>m'</i> <i>n'</i>,
+the coalescence of all these little waves would build up the large
+ridge <i>m'</i> <i>n'</i> 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.</p>
+<div class="figright" style="width: 343px;"><img src=
+"images/fig18.jpg" width="343" height="253" alt="Fig. 18." title=
+"" /> <b>Fig. 18.</b></div>
+<p>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, <i>every point of <a name="Page_83" id=
+"Page_83"></a><span class="pagenum">[Pg 83]</span>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</i>. This is the celebrated principle of Huyghens: we have now
+to examine how these secondary waves act upon each other.</p>
+<p>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
+<a name="Page_84" id="Page_84"></a><span class="pagenum">[Pg
+84]</span>undiminished light produces the brilliant central band of
+the series.</p>
+<p>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.</p>
+<div class="figleft" style="width: 368px;"><img src=
+"images/fig19.jpg" width="368" height="251" alt="Fig. 19." title=
+"" /> <b>Fig. 19.</b></div>
+<p>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?</p>
+<p>Let us fix our attention upon the particular oblique line that
+passes through the <i>centre</i> 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 <i>e</i> R' equal to P R', join P and <i>e</i>,
+and draw O <i>d</i> parallel to P e. A e is then the length of a
+<a name="Page_85" id="Page_85"></a><span class="pagenum">[Pg
+85]</span>wave of light, while A <i>d</i> 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 <i>x</i> R', on the one side of O R', finds a
+line <i>x</i>' R' upon the other side of O R', from which its path
+differs by half an undulation&mdash;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 <i>a whole
+wave-length</i> different from each other.</p>
+<p>When the difference between the paths of the marginal waves is
+<i>half a wave-length,</i> a partial destruction of the light is
+effected. The luminous intensity corresponding to this obliquity is
+a little less than one-half&mdash;accurately 0.4&mdash;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.</p>
+<p>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 <a name="Page_86" id=
+"Page_86"></a><span class="pagenum">[Pg 86]</span>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 <i>even</i> number
+of semi-undulations, we have complete extinction; while, when the
+marginal difference is an <i>odd</i> number of semi-undulations, we
+have only partial extinction, a portion of the beam remaining as a
+luminous band.</p>
+<p>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.</p>
+<p>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 <a name="Page_87" id=
+"Page_87"></a><span class="pagenum">[Pg 87]</span>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.</p>
+<div class="figcenter" style="width: 381px;"><img src=
+"images/fig20.jpg" width="381" height="416" alt="Fig. 20." title=
+"" /> <b>Fig. 20.</b></div>
+<p><a name="Page_88" id="Page_88"></a><span class="pagenum">[Pg
+88]</span>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 <a name=
+"Page_89" id="Page_89"></a><span class="pagenum">[Pg
+89]</span>vapours of various liquids in an intensely illuminated
+tube are, as I have elsewhere shewn, exceedingly fine.</p>
+<div class="figcenter" style="width: 382px;"><img src=
+"images/fig21.jpg" width="382" height="442" alt="Fig. 21." title=
+"" /> <b>Fig. 21.</b></div>
+<p>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 <i>smaller</i>, 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.</p>
+<p>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 <a name=
+"Page_90" id="Page_90"></a><span class="pagenum">[Pg
+90]</span>waves does not extinguish the longer ones, hence the
+phenomena of colours. These are called the colours of <i>striated
+surfaces</i>. 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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_91" id="Page_91"></a><span class="pagenum">[Pg
+91]</span></div>
+<h2><a name="LECTURE_III" id="LECTURE_III"></a>LECTURE III.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>RELATION OF THEORIES TO EXPERIENCE</li>
+<li>ORIGIN OF THE NOTION OF THE ATTRACTION OF GRAVITATION</li>
+<li>NOTION OF POLARITY, HOW GENERATED</li>
+<li>ATOMIC POLARITY</li>
+<li>STRUCTURAL ARRANGEMENTS DUE TO POLARITY</li>
+<li>ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION</li>
+<li>TO THEIR ACTION UPON LIGHT</li>
+<li>NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE</li>
+<li>EXPERIMENTAL ILLUSTRATIONS</li>
+<li>CRYSTALLIZATION OF WATER</li>
+<li>EXPANSION BY HEAT AND BY COLD</li>
+<li>DEPORTMENT OF WATER CONSIDERED AND EXPLAINED</li>
+<li>BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA</li>
+<li>REFRACTION</li>
+<li>DOUBLE REFRACTION</li>
+<li>POLARIZATION</li>
+<li>ACTION OF TOURMALINE</li>
+<li>CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR</li>
+<li>POLARIZATION BY ORDINARY REFRACTION AND REFLECTION</li>
+<li>DEPOLARIZATION</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Derivation of Theoretic Conceptions from
+Experience.</i></h3>
+<p>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 C&aelig;sar 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 <a name=
+"Page_92" id="Page_92"></a><span class="pagenum">[Pg
+92]</span>framing theories, does the imagination <i>create</i> its
+materials. It expands, diminishes, moulds, and refines, as the case
+may be, materials derived from the world of fact and
+observation.</p>
+<p>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.</p>
+<p>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 oscil<a name=
+"Page_93" id="Page_93"></a><span class="pagenum">[Pg
+93]</span>lations 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 <i>doubleness</i> of the
+magnetic force is called <i>polarity</i>, and the points near the
+ends of the magnet in which the forces seem concentrated are called
+its <i>poles</i>.</p>
+<div class="figright" style="width: 160px;"><img src=
+"images/fig22.jpg" width="160" height="306" alt="Fig. 22." title=
+"" /> <b>Fig. 22.</b></div>
+<p>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&mdash;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 <a name="Page_94" id=
+"Page_94"></a><span class="pagenum">[Pg 94]</span>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&mdash;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.</p>
+<p>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.</p>
+<div class="figleft" style="width: 430px;"><img src=
+"images/fig23.jpg" width="430" height="413" alt=
+"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."
+title="" /> <b>Fig. 23.<br />
+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.</b></div>
+<p>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&mdash;to iron filings, for
+example&mdash;we find that they act substantially as the needles,
+arranging themselves in definite forms, in obedience to the
+magnetic action.</p>
+<p>Placing a sheet of paper or glass over a bar magnet and
+showering iron filings upon the paper, I notice a <a name="Page_95"
+id="Page_95"></a><span class="pagenum">[Pg 95]</span>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 <a name="Page_96" id="Page_96"></a><span class=
+"pagenum">[Pg 96]</span>curves which have been so long familiar to
+scientific men (fig. 23).</p>
+<p>(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.)</p>
+<p>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.</p>
+<p>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 <i>structural arrangement</i>. 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.</p>
+<h3>&sect; 2. <i>Theory of Crystallization.</i></h3>
+<p>Now this idea of structure, as produced by polar force, opens a
+way for the intellect into an entirely new <a name="Page_97" id=
+"Page_97"></a><span class="pagenum">[Pg 97]</span><a name="Page_98"
+id="Page_98"></a>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&mdash;possibly a full-formed
+diamond, as it quitted the hand of Nature, not yet having got into
+the hands of the lapidary.</p>
+<div class="figright" style="width: 428px;"><img src=
+"images/fig24.jpg" width="428" height="912" alt="Fig. 24." title=
+"" /> <b>Fig. 24.</b></div>
+<p>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. <a name="Page_99" id="Page_99"></a><span class=
+"pagenum">[Pg 99]</span>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.</p>
+<p>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 <i>nursed</i> with proper care,
+crystals of these substances may be caused to grow to a great
+size.</p>
+<p>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, <a name="Page_100"
+id="Page_100"></a><span class="pagenum">[Pg 100]</span>more solid
+matter is contained in it than corresponds to its temperature.
+Still the molecules show no sign of building themselves
+together.</p>
+<p>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.</p>
+<p>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 <a name="Page_101" id=
+"Page_101"></a><span class="pagenum">[Pg 101]</span>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.</p>
+<p>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
+spicul&aelig; branch from the trunk, and from these branches others
+shoot; but the angles enclosed by the spicul&aelig; 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 <a name="Page_102" id=
+"Page_102"></a><span class="pagenum">[Pg 102]</span>the accidents
+of crystallization; but in one particular they assert their
+superiority over all such accidents&mdash;<i>angular magnitude</i>
+is always rigidly preserved.</p>
+<p>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.</p>
+<p>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 <a name="Page_103"
+id="Page_103"></a><span class="pagenum">[Pg 103]</span>matter,'
+will be very different from those of the generations past.</p>
+<p>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.<a name="FNanchor_15_15" id=
+"FNanchor_15_15"></a><a href="#Footnote_15_15" class=
+"fnanchor">[15]</a> 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 spicul&aelig; to the angle of 60 degrees.</p>
+<p>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&deg; 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 <a name="Page_104" id="Page_104"></a><span class=
+"pagenum">[Pg 104]</span>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.</p>
+<p>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:&mdash;</p>
+<p>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.</p>
+<p>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
+<i>expansion by cold</i> 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&deg; Fahr. Crystallization has <a name="Page_105" id=
+"Page_105"></a><span class="pagenum">[Pg 105]</span>virtually here
+commenced, the molecules preparing themselves for the subsequent
+act of solidification, which occurs at 32&deg;, 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.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href=
+"#Footnote_16_16" class="fnanchor">[16]</a></p>
+<p>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:&mdash;</p>
+<p>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.</p>
+<p>But besides the unpolar force of gravity, which <a name=
+"Page_106" id="Page_106"></a><span class="pagenum">[Pg
+106]</span>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&deg;. 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 <i>as wholes</i>. Previous to
+reaching the temperature 39&deg; 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.</p>
+<h3>&sect; 3. <i>Ordinary Refraction of Light explained by the Wave
+Theory</i>.</h3>
+<p>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 por<a name="Page_107" id=
+"Page_107"></a><span class="pagenum">[Pg 107]</span>tion 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.</p>
+<div class="figleft" style="width: 446px;"><img src=
+"images/fig25.jpg" width="446" height="256" alt="Fig. 25." title=
+"" /> <b>Fig. 25.</b></div>
+<p>But suppose the wave, before reaching the glass, to be
+<i>oblique</i> 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 <i>refracted</i>.</p>
+<p>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 <a name="Page_108" id=
+"Page_108"></a><span class="pagenum">[Pg 108]</span>glass as 3: 2.
+Let A B C (fig. 25) be the section of our prism, and <i>a</i>
+<i>b</i> the section of a plane wave approaching it in the
+direction of the arrow. When it reaches <i>c</i> <i>d</i>, 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 <i>c</i> <i>e</i>, the
+wave in the glass will have passed over only two-thirds of this
+distance, or <i>d</i> <i>f</i>. The line <i>e</i> <i>f</i> now
+marks the front of the wave. Immersed wholly in the glass it
+pursues its way to <i>g</i> <i>h</i>, where the end <i>g</i> of the
+wave is on the point of escaping into the air. During the time
+required by the end <i>h</i> of the wave to pass over the distance
+<i>h</i> <i>k</i> to the surface of the prism, the other end
+<i>g</i>, moving more rapidly, will have reached the point
+<i>i</i>. The wave, therefore, has again changed its front, so that
+after its emergence from the prism it will pass on to <i>l</i>
+<i>m</i>, 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.</p>
+<h3>&sect; 4. <i>Double Refraction of Light explained by the Wave
+Theory</i>.</h3>
+<p>The two elements of rapidity of propagation, both of sound and
+light, in any substance whatever, are <i>elasticity</i> and
+<i>density</i>, the speed increasing with the former and
+diminishing with the latter. The enormous velocity of light in
+stellar space is attainable because <a name="Page_109" id=
+"Page_109"></a><span class="pagenum">[Pg 109]</span>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 <i>double refraction</i>.</p>
+<p>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.</p>
+<p>I am unwilling to quit this subject before raising it to
+unmistakable clearness in your minds. The <a name="Page_110" id=
+"Page_110"></a><span class="pagenum">[Pg 110]</span>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.
+<i>They do both</i>, and hence immediately divide themselves into
+two systems propagated with different velocities. Double refraction
+is the necessary consequence.</p>
+<h3>&sect; 4. <i>Double Refraction of Light explained by the Wave
+Theory</i>.</h3>
+<div class="figright" style="width: 453px;"><img src=
+"images/fig26.jpg" width="453" height="290" alt="Fig. 26." title=
+"" /> <b>Fig. 26.</b></div>
+<p>By means of Iceland spar cut in the proper direction, double
+refraction is capable of easy illustration. Causing <a name=
+"Page_111" id="Page_111"></a><span class="pagenum">[Pg
+111]</span>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.</p>
+<p>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
+<i>ordinary ray</i>: 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
+<i>extraordinary ray</i>. 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.<a name="Page_112" id=
+"Page_112"></a><span class="pagenum">[Pg 112]</span></p>
+<h3>&sect; 5. <i>Polarization of Light explained by the Wave
+Theory</i>.</h3>
+<p>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 <i>two-sidedness</i>
+with the <i>two-endedness</i> of a magnet, wherein consists its
+polarity, the two beams came subsequently to be described as
+<i>polarized</i>.</p>
+<p>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 <i>across</i> 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.</p>
+<p>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
+<a name="Page_113" id="Page_113"></a><span class="pagenum">[Pg
+113]</span>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 <i>plane polarized light</i>.</p>
+<div class="figleft" style="width: 196px;"><img src=
+"images/fig27.jpg" width="196" height="69" alt="Fig. 27." title=
+"" /> <b>Fig. 27.</b></div>
+<div class="figright" style="width: 150px;"><img src=
+"images/fig28.jpg" width="150" height="200" alt="Fig. 28." title=
+"" /> <b>Fig. 28.</b></div>
+<p>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 (<i>t</i> <i>t</i>, fig. 27) is
+now before you. I place parallel to it another plate (<i>t'</i>
+<i>t'</i>): the green of the <a name="Page_114" id=
+"Page_114"></a><span class="pagenum">[Pg 114]</span>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.</p>
+<p>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 <i>edges</i> of the
+waves, the green light being then quenched. In the other case the
+<i>sides</i> of the waves strike the mirror, and the green light is
+reflected. To <a name="Page_115" id="Page_115"></a><span class=
+"pagenum">[Pg 115]</span>render the extinction complete, the light
+must be received upon the mirror at a special angle. What this
+angle is we shall learn presently.</p>
+<p>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&deg; with the perpendicular to the glass,
+the <i>whole</i> 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 <i>the polarizing
+angle</i>.</p>
+<p>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.<a name="FNanchor_17_17" id=
+"FNanchor_17_17"></a><a href="#Footnote_17_17" class=
+"fnanchor">[17]</a> The polarizing angle augments with the index of
+refraction. For water it is 52&frac12;&deg;; for glass, as already
+stated, 58&deg;; while for diamond it is 68&deg;.</p>
+<p>And now let us try to make substantially the <a name="Page_116"
+id="Page_116"></a><span class="pagenum">[Pg 116]</span>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.</p>
+<p>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 <a name="Page_117" id=
+"Page_117"></a><span class="pagenum">[Pg 117]</span>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).</p>
+<div class="figcenter" style="width: 337px;"><img src=
+"images/fig29.jpg" width="337" height="151" alt="Fig. 29." title=
+"" /> <b>Fig. 29.</b></div>
+<div class="figcenter" style="width: 333px;"><img src=
+"images/fig30.jpg" width="333" height="151" alt="Fig. 30." title=
+"" /> <b>Fig. 30.</b></div>
+<p>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).<a name="Page_118" id=
+"Page_118"></a><span class="pagenum">[Pg 118]</span></p>
+<div class="figcenter" style="width: 357px;"><img src=
+"images/fig31.jpg" width="357" height="150" alt="Fig. 31." title=
+"" /> <b>Fig. 31.</b></div>
+<div class="figcenter" style="width: 395px;"><img src=
+"images/fig32.jpg" width="395" height="273" alt="Fig. 32." title=
+"" /> <b>Fig. 32.</b></div>
+<p>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, <a name="Page_119" id=
+"Page_119"></a><span class="pagenum">[Pg 119]</span>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.</p>
+<div class="figcenter" style="width: 331px;"><img src=
+"images/fig33.jpg" width="331" height="270" alt="Fig. 33." title=
+"" /> <b>Fig. 33.</b></div>
+<p>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 <i>transmitted</i> 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 <i>a bundle</i>
+of plates, we so increase the quantity as to render the transmitted
+beam, for all practical purposes, <i>perfectly</i> 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.</p>
+<p>One word more. When the tourmalines are crossed, <a name=
+"Page_120" id="Page_120"></a><span class="pagenum">[Pg
+120]</span>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, <i>its plane of vibration is
+changed</i>: 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, <i>depolarization</i>. Its proper meaning will be
+disclosed in our next lecture.</p>
+<p>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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_121" id="Page_121"></a><span class="pagenum">[Pg
+121]</span></div>
+<h2><a name="LECTURE_IV" id="LECTURE_IV"></a>LECTURE IV.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>CHROMATIC PHENOMENA PRODUCED BY CRYSTALS IN POLARIZED
+LIGHT</li>
+<li>THE NICOL PRISM</li>
+<li>POLARIZER AND ANALYZER</li>
+<li>ACTION OF THICK AND THIN PLATES OF SELENITE</li>
+<li>COLOURS DEPENDENT ON THICKNESS</li>
+<li>RESOLUTION OF POLARIZED BEAM INTO TWO OTHERS BY THE
+SELENITE</li>
+<li>ONE OF THEM MORE RETARDED THAN THE OTHER</li>
+<li>RECOMPOUNDING OF THE TWO SYSTEMS OF WAVES BY THE ANALYZER</li>
+<li>INTERFERENCE THUS RENDERED POSSIBLE</li>
+<li>CONSEQUENT PRODUCTION OF COLOURS</li>
+<li>ACTION OF BODIES MECHANICALLY STRAINED OR PRESSED</li>
+<li>ACTION OF SONOROUS VIBRATIONS</li>
+<li>ACTION OF GLASS STRAINED OR PRESSED BY HEAT</li>
+<li>CIRCULAR POLARIZATION</li>
+<li>CHROMATIC PHENOMENA PRODUCED BY QUARTZ</li>
+<li>THE MAGNETIZATION OF LIGHT</li>
+<li>RINGS SURROUNDING THE AXES OF CRYSTALS</li>
+<li>BIAXAL AND UNIAXAL CRYSTALS</li>
+<li>GRASP OF THE UNDULATORY THEORY</li>
+<li>THE COLOUR AND POLARIZATION OF SKY-LIGHT</li>
+<li>GENERATION OF ARTIFICIAL SKIES.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Action of Crystals on Polarized Light: the Nicol
+Prism.</i></h3>
+<p>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
+<a name="Page_122" id="Page_122"></a><span class="pagenum">[Pg
+122]</span>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.</p>
+<div class="figright" style="width: 170px;"><img src=
+"images/fig34.jpg" width="170" height="368" alt="Fig. 34." title=
+"" /> <b>Fig. 34.</b></div>
+<p>The beams, as you know, are refracted differently, and from
+this, as made plain in &sect;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.</p>
+<p>Let <i>b x, c y</i> (fig. 34) represent the section of an
+elongated rhomb of Iceland spar cloven from the crystal. Let this
+rhomb be cut along the plane <i>b c</i>; 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 <a name=
+"Page_123" id="Page_123"></a><span class="pagenum">[Pg
+123]</span>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 <i>b c</i> is
+the section shall be perpendicular, or nearly so, to the two end
+surfaces of the rhomb <i>b x, c y</i>.</p>
+<p>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.</p>
+<p>(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.)<a name="Page_124" id="Page_124"></a><span class=
+"pagenum">[Pg 124]</span></p>
+<h3>&sect; 2. <i>Colours of Films of Selenite in Polarized
+Light</i>.</h3>
+<p>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 <i>thin</i> you have sometimes
+not only light, but <i>coloured</i> 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&mdash;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.</p>
+<p>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 <a name="Page_125"
+id="Page_125"></a><span class="pagenum">[Pg 125]</span>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&mdash;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.</p>
+<h3>&sect; 3. <i>Colours of Crystals in Polarized Light explained
+by the Undulatory Theory</i>.</h3>
+<p>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 <i>vibrations</i>. We treat the
+luminiferous ether on mechanical principles, and, from <a name=
+"Page_126" id="Page_126"></a><span class="pagenum">[Pg
+126]</span>the composition and resolution of its vibrations we
+deduce all the phenomena displayed by crystals in polarized
+light.</p>
+<div class="figleft" style="width: 261px;"><img src=
+"images/fig35.jpg" width="261" height="120" alt="Fig. 35." title=
+"" /> <b>Fig. 35.</b></div>
+<p>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 <i>a</i> <i>b</i> represent the amplitude of an oblique
+ethereal vibration before it reaches A B. From <i>a</i> and
+<i>b</i> let the two perpendiculars <i>a</i> <i>c</i> and <i>b</i>
+<i>d</i> be drawn upon the axis: then <i>c</i> <i>d</i> will be the
+amplitude of the transmitted vibration.</p>
+<p>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 direc<a name="Page_127"
+id="Page_127"></a><span class="pagenum">[Pg 127]</span>tions, 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 <i>oblique</i> to
+the two tourmaline axes; then, you see it exercises the power,
+demonstrated in the last lecture, of partially restoring the
+light.</p>
+<div class="figright" style="width: 380px;"><img src=
+"images/fig36.jpg" width="380" height="270" alt="Fig. 36." title=
+"" /> <b>Fig. 36.</b></div>
+<p>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.</p>
+<p>First, then, we have a prism which receives the light from the
+electric lamp, and which is called the <i>polarizer</i>. Then we
+have the plate of gypsum (supposed to be placed at S, fig. 36), and
+then the <a name="Page_128" id="Page_128"></a><span class=
+"pagenum">[Pg 128]</span>prism in front, which is called the
+<i>analyzer</i>. 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
+(<i>a</i> <i>b</i>) 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 (<i>a</i>
+<i>c</i>, <i>a</i> <i>f</i>, <i>b</i> <i>d</i>, <i>b</i> <i>e</i>)
+on the two arms of the cross; then the distances (<i>c</i>
+<i>d</i>, <i>e</i> <i>f</i>) between the feet of these
+perpendiculars represent the amplitudes of two rectangular
+vibrations, which are the <i>components</i> 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.</p>
+<div class="figleft" style="width: 216px;"><img src=
+"images/fig37.jpg" width="216" height="211" alt="Fig. 37." title=
+"" /> <b>Fig. 37.</b></div>
+<p>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
+<a name="Page_129" id="Page_129"></a><span class="pagenum">[Pg
+129]</span>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.</p>
+<p>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.</p>
+<p>(The best way of obtaining a knowledge of these phenomena is to
+construct a model of thin wood or <a name="Page_130" id=
+"Page_130"></a><span class="pagenum">[Pg 130]</span>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 <i>complementary</i> phenomena, when the planes of
+vibration are perpendicular to each other.)</p>
+<p>In considering the next point, we will operate, for the sake of
+simplicity, with monochromatic light&mdash;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
+<i>odd</i> number of half wave-lengths, produces extinction; at all
+thicknesses, on the other hand, which correspond to a retardation
+of an <i>even</i> number of half <a name="Page_131" id=
+"Page_131"></a><span class="pagenum">[Pg 131]</span>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.</p>
+<p>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
+<i>iris-coloured</i> rings produced by the white light.</p>
+<p>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
+<a name="Page_132" id="Page_132"></a><span class="pagenum">[Pg
+132]</span>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.</p>
+<h3>&sect; 4. <i>Colours produced by Strain and Pressure.</i></h3>
+<p>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 <i>strained</i> longitudinally; its
+concave surface, that next my knee, is longitudinally
+<i>pressed</i>. 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.</p>
+<p><a name="Page_133" id="Page_133"></a><span class="pagenum">[Pg
+133]</span>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.</p>
+<p>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.</p>
+<div class="figright" style="width: 165px;"><img src=
+"images/fig38.jpg" width="165" height="358" alt="Fig. 38" title=
+"" /> <b>Fig. 38</b></div>
+<p>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 <a name="Page_134" id="Page_134"></a><span class=
+"pagenum">[Pg 134]</span>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.</p>
+<p>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 <a name="Page_135" id="Page_135"></a><span class=
+"pagenum">[Pg 135]</span>with its centre rarefied. The ends of the
+strip suffer neither condensation nor rarefaction.</p>
+<p>If we introduce the strip of glass (<i>s</i> <i>s'</i>, 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 (<i>h</i>, 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, <a name="Page_136" id=
+"Page_136"></a><span class="pagenum">[Pg 136]</span>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.</p>
+<div class="figcenter" style="width: 558px;"><img src=
+"images/fig39.jpg" width="558" height="363" alt="Fig. 39." title=
+"" /> <b>Fig. 39.</b></div>
+<h3>&sect; 5. <i>Colours of Unannealed Glass</i>.</h3>
+<p>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 <a name="Page_137" id=
+"Page_137"></a><span class="pagenum">[Pg 137]</span>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.</p>
+<div class="figleft" style="width: 197px;"><img src=
+"images/fig40.jpg" width="197" height="198" alt="Fig. 40." title=
+"" /> <b>Fig. 40.</b></div>
+<div class="figright" style="width: 195px;"><img src=
+"images/fig41.jpg" width="195" height="197" alt="Fig. 41." title=
+"" /> <b>Fig. 41.</b></div>
+<p>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 <a name="Page_138"
+id="Page_138"></a><span class="pagenum">[Pg 138]</span>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.</p>
+<div class="figcenter" style="width: 444px;"><img src=
+"images/fig42.jpg" width="444" height="442" alt="Fig. 42." title=
+"" /> <b>Fig. 42.</b></div>
+<h3>&sect; 6. <i>Circular Polarization.</i></h3>
+<p>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 <a name="Page_139" id=
+"Page_139"></a><span class="pagenum">[Pg 139]</span>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 <i>a plane</i>.
+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.</p>
+<p>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.</p>
+<p>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 <a name="Page_140" id="Page_140"></a><span class=
+"pagenum">[Pg 140]</span>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 <i>circularly
+polarized</i>. 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.</p>
+<h3>&sect; 7. <i>Complementary Colours of Bi-refracting Spar in
+Circularly Polarized Light. Proof that Yellow and Blue are
+Complementary.</i></h3>
+<div class="figright" style="width: 403px;"><img src=
+"images/fig43.jpg" width="403" height="228" alt="Fig. 43." title=
+"" /> <b>Fig. 43.</b></div>
+<p>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 <a name="Page_141" id=
+"Page_141"></a><span class="pagenum">[Pg 141]</span>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.)</p>
+<h3>&sect; 8. <i>The Magnetization of Light.</i></h3>
+<p>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
+<a name="Page_142" id="Page_142"></a><span class="pagenum">[Pg
+142]</span>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.</p>
+<div class="figright" style="width: 430px;"><img src=
+"images/fig44.jpg" width="430" height="283" alt="Fig. 44" title=
+"" /> <b>Fig. 44</b></div>
+<p>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.</p>
+<p>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 <a name="Page_143" id=
+"Page_143"></a><span class="pagenum">[Pg 143]</span>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.</p>
+<h3>&sect; 9. <i>Iris-rings surrounding the Axes of
+Crystals.</i></h3>
+<p>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, <a name=
+"Page_144" id="Page_144"></a><span class="pagenum">[Pg
+144]</span>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 <i>optic axis</i> of the
+crystal.</p>
+<p>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
+<i>conical</i> 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.</p>
+<p>Placing the plate of Iceland spar between the crossed <a name=
+"Page_145" id="Page_145"></a><span class="pagenum">[Pg
+145]</span>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
+<i>either</i> prism, cannot get through <i>both</i>. This complete
+interception produces the arms of the cross.</p>
+<div class="figcenter" style="width: 268px;"><img src=
+"images/fig45.jpg" width="268" height="265" alt="Fig. 45." title=
+"" /> <b>Fig. 45.</b></div>
+<p>With monochromatic light the rings would be simply bright and
+black&mdash;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&deg; 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-<a name="Page_146" id=
+"Page_146"></a><span class="pagenum">[Pg 146]</span>waves give rise
+to iris-colours when white light is employed.</p>
+<div class="figleft" style="width: 206px;"><img src=
+"images/fig46.jpg" width="206" height="202" alt="Fig. 46." title=
+"" /> <b>Fig. 46.</b></div>
+<div class="figright" style="width: 278px;"><img src=
+"images/fig47.jpg" width="278" height="210" alt="Fig. 47." title=
+"" /> <b>Fig. 47.</b></div>
+<p>Besides the <i>regular</i> crystals which produce double
+refraction in no direction, and the <i>uniaxal</i> crystals which
+produce it in all directions but one, Brewster discovered that in a
+large class of crystals there are <i>two</i> directions in which
+double refraction does not take place. These are called
+<i>biaxal</i> 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, <a name="Page_147"
+id="Page_147"></a><span class="pagenum">[Pg 147]</span>forms a
+<i>lemniscata</i>; 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.</p>
+<h3>&sect; 10. <i>Power of the Wave Theory</i>.</h3>
+<p>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.</p>
+<p>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 <a name="Page_148" id="Page_148"></a><span class=
+"pagenum">[Pg 148]</span>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.'<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href=
+"#Footnote_18_18" class="fnanchor">[18]</a></p>
+<p>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 <a name="Page_149" id=
+"Page_149"></a><span class="pagenum">[Pg 149]</span>than those of
+the solar system. Accept if you will the scepticism of Mr.
+Mill<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href=
+"#Footnote_19_19" class="fnanchor">[19]</a> regarding the
+undulatory theory; but if your scepticism be philosophical, it will
+wrap the theory of gravitation in the same or in greater
+doubt.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href=
+"#Footnote_20_20" class="fnanchor">[20]</a></p>
+<h3>&sect; 11. <i>The Blue of the Sky</i>.</h3>
+<p>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 <a name=
+"Page_150" id="Page_150"></a><span class="pagenum">[Pg
+150]</span>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.</p>
+<p>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.</p>
+<p>A small pebble, placed in the way of the ring-ripples <a name=
+"Page_151" id="Page_151"></a><span class="pagenum">[Pg
+151]</span>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 <i>are</i> 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.</p>
+<p>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.</p>
+<p>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 <a name="Page_152"
+id="Page_152"></a><span class="pagenum">[Pg 152]</span>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.</p>
+<p>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 Br&uuml;cke 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.</p>
+<h3>&sect; 12. <i>Artificial Sky</i>.</h3>
+<p>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 <a name="Page_153" id=
+"Page_153"></a><span class="pagenum">[Pg 153]</span>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 2&frac12; 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 <i>precipitated</i> 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.</p>
+<p>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 <i>blue
+cloud</i>. 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, <i>it only</i> 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 <a name="Page_154" id=
+"Page_154"></a><span class="pagenum">[Pg 154]</span>intermediate
+position between these clouds and true cloudless vapour.</p>
+<p>It is possible to make the particles of this <i>actinic
+cloud</i> 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
+<i>incipient cloud</i>, 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.</p>
+<h3>&sect; 13. <i>Polarization of Skylight</i>.</h3>
+<p>But there is another subject connected with our firmament, of a
+more subtle and recondite character <a name="Page_155" id=
+"Page_155"></a><span class="pagenum">[Pg 155]</span>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.</p>
+<p>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 <i>blue</i>. In all cases,
+moreover, this fine blue cloud polarizes <i>perfectly</i> the beam
+which illuminates it, the direction of polarization enclosing an
+angle of 90&deg; with the axis of the illuminating beam.</p>
+<p>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 name="Page_156" id=
+"Page_156"></a><span class="pagenum">[Pg 156]</span>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
+<i>residual</i> 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.</p>
+<p>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 <a name="Page_157" id="Page_157"></a><span class=
+"pagenum">[Pg 157]</span>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.</p>
+<p>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:&mdash;</p>
+<p>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.</p>
+<p>2. As long as the cloud remains distinctly blue, the light
+discharged from it at right angles to the illuminating beam is
+<i>perfectly</i> polarized. It may be utterly quenched by a Nicol
+prism, the cloud from which it issues being caused to disappear.
+Any deviation from <a name="Page_158" id=
+"Page_158"></a><span class="pagenum">[Pg 158]</span>the
+perpendicular enables a portion of the light to get through the
+prism.</p>
+<p>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.</p>
+<p>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.</p>
+<p>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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_159" id="Page_159"></a><span class="pagenum">[Pg
+159]</span></div>
+<h2><a name="LECTURE_V" id="LECTURE_V"></a>LECTURE V.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>RANGE OF VISION NOT COMMENSURATE WITH RANGE OF RADIATION</li>
+<li>THE ULTRA-VIOLET BAYS</li>
+<li>FLUORESCENCE</li>
+<li>THE RENDERING OF INVISIBLE RAYS VISIBLE</li>
+<li>VISION NOT THE ONLY SENSE APPEALED TO BY THE SOLAR AND ELECTRIC
+BEAM</li>
+<li>HEAT OF BEAM</li>
+<li>COMBUSTION BY TOTAL BEAM AT THE FOCI OF MIRRORS AND LENSES</li>
+<li>COMBUSTION THROUGH ICE-LENS</li>
+<li>IGNITION OF DIAMOND</li>
+<li>SEARCH FOR THE RAYS HERE EFFECTIVE</li>
+<li>SIR WILLIAM HERSCHEL'S DISCOVERY OF DARK SOLAR RAYS</li>
+<li>INVISIBLE RAYS THE BASIS OF THE VISIBLE</li>
+<li>DETACHMENT BY A RAY-FILTER OF THE INVISIBLE RAYS FROM THE
+VISIBLE</li>
+<li>COMBUSTION AT DARK FOCI</li>
+<li>CONVERSION OF HEAT-RAYS INTO LIGHT-RAYS</li>
+<li>CALORESCENCE</li>
+<li>PART PLAYED IN NATURE BY DARK RAYS</li>
+<li>IDENTITY OF LIGHT AND RADIANT HEAT</li>
+<li>INVISIBLE IMAGES</li>
+<li>REFLECTION, REFRACTION, PLANE POLARIZATION, DEPOLARIZATION,
+CIRCULAR<br />
+&nbsp;&nbsp;&nbsp;&nbsp;POLARIZATION, DOUBLE REFRACTION, AND
+MAGNETIZATION OF RADIANT HEAT.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Range of Vision and of Radiation</i>.</h3>
+<p>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&mdash;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 <i>evolution</i>, 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
+<a name="Page_160" id="Page_160"></a><span class="pagenum">[Pg
+160]</span>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.</p>
+<p>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&mdash;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&mdash;the yellow rays are found to be the most
+active.</p>
+<p>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.</p>
+<h3>&sect; 2. <i>Ultra-violet Rays: Fluorescence</i>.</h3>
+<p>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 con<a name="Page_161" id=
+"Page_161"></a><span class="pagenum">[Pg 161]</span>verted 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.</p>
+<p>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&mdash;on those of sulphate of
+quinine, for example&mdash;they compel those molecules, or their
+constituent atoms, to vibrate; and the peculiarity is, that the
+vibrations thus set up are <i>of slower period</i> 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.</p>
+<p><a name="Page_162" id="Page_162"></a><span class="pagenum">[Pg
+162]</span>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 <i>Thallene</i>, produces a very striking
+elongation of the spectrum, the new light generated being of
+peculiar brilliancy.</p>
+<p>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 <i>Fluorescence</i>.</p>
+<p>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-<a name=
+"Page_163" id="Page_163"></a><span class="pagenum">[Pg
+163]</span>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
+<i>molecules</i>, not of <i>particles</i>. The medium before you is
+not a turbid medium, for when you look through it at a luminous
+surface it is perfectly clear.</p>
+<p>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 Dupr&eacute;, 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.</p>
+<p>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 <i>Lignum
+Nephriticum,</i> because the inhabitants of the country where it
+grows <a name="Page_164" id="Page_164"></a><span class=
+"pagenum">[Pg 164]</span>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 <i>Lignum,
+Nephriticum</i>, 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.'</p>
+<p>'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.'<a name="FNanchor_21_21" id=
+"FNanchor_21_21"></a><a href="#Footnote_21_21" class=
+"fnanchor">[21]</a></p>
+<p><a name="Page_165" id="Page_165"></a><span class="pagenum">[Pg
+165]</span>Goethe in his 'Farbenlehre' thus describes the
+fluorescence of horse-chestnut bark:&mdash;'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.'<a name=
+"FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22"
+class="fnanchor">[22]</a> 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.</p>
+<h3>&sect; 3. <i>The Heat of the Electric Beam. Ignition through a
+Lens of Ice. Possible Cometary Temperature</i>.</h3>
+<p>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 <a name="Page_166" id=
+"Page_166"></a><span class="pagenum">[Pg 166]</span>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.</p>
+<div class="figcenter" style="width: 365px;"><img src=
+"images/fig48.jpg" width="365" height="268" alt="Fig. 48." title=
+"" /> <b>Fig. 48.</b></div>
+<p>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 (<i>m</i> <i>m'</i>, 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.</p>
+<p><a name="Page_167" id="Page_167"></a><span class="pagenum">[Pg
+167]</span>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.</p>
+<p>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 <a name="Page_168" id=
+"Page_168"></a><span class="pagenum">[Pg 168]</span>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 <i>absorption</i>
+takes place that heat is thus produced: and heat is always a result
+of absorption.</p>
+<p>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.</p>
+<p>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 <a name="Page_169"
+id="Page_169"></a><span class="pagenum">[Pg 169]</span>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.</p>
+<h3>&sect; 4. <i>Combustion of a Diamond by Radiant Heat</i>.</h3>
+<p>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:&mdash;'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 3&frac12; 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.'</p>
+<p>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 <a name=
+"Page_170" id="Page_170"></a><span class="pagenum">[Pg
+170]</span>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.</p>
+<h3>&sect; 5. <i>Ultra-red Rays: Calorescence</i>.</h3>
+<p>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
+<i>light</i> 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 <i>light</i> is not
+absorbed by the white paper, and therefore does not burn the paper;
+but there is something over and above the light which <i>is</i>
+absorbed, and which provokes combustion. What is this
+something?</p>
+<p><a name="Page_171" id="Page_171"></a><span class="pagenum">[Pg
+171]</span>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, M&uuml;ller, 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 <i>filtered</i> 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.</p>
+<p>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, <a name="Page_172" id=
+"Page_172"></a><span class="pagenum">[Pg 172]</span>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.</p>
+<p>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.</p>
+<p>The invisible heat, emitted both by dark bodies and by luminous
+ones, flies through space with the velosity of light, and is called
+<i>radiant heat</i>. Now, radiant heat may be made a subtle and
+powerful explorer of molecular condition, and, of late years, it
+has given a new <a name="Page_173" id="Page_173"></a><span class=
+"pagenum">[Pg 173]</span>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 <i>diathermancy</i>, or
+perviousness to radiant heat.</p>
+<p>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.</p>
+<p>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 <a name="Page_174" id="Page_174"></a><span class=
+"pagenum">[Pg 174]</span>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.</p>
+<p>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 <i>lowered</i> the refrangibility, so
+as to render the non-visual rays visual, and to this change he gave
+the name of <i>Fluorescence</i>. Here, by the intervention of the
+platinum, the refrangibility is <i>raised</i>, so as to render the
+non-visual visual, and to this change I have given the name of
+<i>Calorescence</i>.</p>
+<p>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.</p>
+<p>The important part played by these ultra-red rays <a name=
+"Page_175" id="Page_175"></a><span class="pagenum">[Pg
+175]</span>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
+<i>boils</i>. 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.</p>
+<p>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.<a name="Page_176" id=
+"Page_176"></a><span class="pagenum">[Pg 176]</span></p>
+<h3>&sect; 6. <i>Identity of Light and Radiant Heat. Reflection
+from Plane and Curved Surfaces. Total Reflection of Heat</i>.</h3>
+<p>The growth of science is organic. That which today is an
+<i>end</i> becomes to-morrow a <i>means</i> 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 &OElig;rsted, 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 <i>thermo-electric pile</i>, 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.</p>
+<p>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 <a name="Page_177" id=
+"Page_177"></a><span class="pagenum">[Pg 177]</span>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.</p>
+<p>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&deg;. 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&mdash;the substantial
+<i>identity of light and radiant heat</i>.</p>
+<p>That they are identical in <i>all</i> respects cannot of course
+be the case, for if they were they would act in the same manner
+upon all instruments, the <i>eye</i> 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 <a name="Page_178" id="Page_178"></a><span class=
+"pagenum">[Pg 178]</span>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 (<i>m</i> <i>n</i>), 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.</p>
+<div class="figcenter" style="width: 425px;"><img src=
+"images/fig49.jpg" width="425" height="288" alt="FIG 49." title=
+"" /> <b>FIG 49.</b></div>
+<p>As regards reflection from curved surfaces, the identity also
+holds good. Receiving the beam from our electric lamp on a concave
+mirror (<i>m</i> <i>m</i>, 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.</p>
+<p><a name="Page_179" id="Page_179"></a><span class="pagenum">[Pg
+179]</span>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
+<i>a</i> <i>b</i> <i>c</i> is the section. It meets the hypothenuse
+at an obliquity greater than the limiting angle,<a name=
+"FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23"
+class="fnanchor">[23]</a> 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.</p>
+<div class="figcenter" style="width: 500px;"><img src=
+"images/fig50.jpg" width="500" height="310" alt="Fig. 50." title=
+"" /> <b>Fig. 50.</b></div>
+<h3>&sect; 7. <i>Invisible Images formed by Radiant Heat.</i></h3>
+<p>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 <a name="Page_180" id="Page_180"></a><span class=
+"pagenum">[Pg 180]</span>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.)</p>
+<div class="figcenter" style="width: 219px;"><img src=
+"images/fig51.jpg" width="219" height="215" alt="Fig. 51." title=
+"" /> <b>Fig. 51.</b></div>
+<h3>&sect; 8. <i>Polarization of Heat</i>.</h3>
+<p>Whether radiant heat be capable of polarization or not was for a
+long time a subject of discussion. B&eacute;rard 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 <a name=
+"Page_181" id="Page_181"></a><span class="pagenum">[Pg
+181]</span>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.</p>
+<div class="figcenter" style="width: 421px;"><img src=
+"images/fig52.jpg" width="421" height="296" alt="Fig. 52." title=
+"" /> <b>Fig. 52.</b></div>
+<p>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&deg;. 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.</p>
+<p><a name="Page_182" id="Page_182"></a><span class="pagenum">[Pg
+182]</span>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&deg;. 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.</p>
+<p>Removing the mica and restoring the needle once more to 0&deg;,
+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.</p>
+<h3>&sect; 9. <i>Double Refraction of Heat</i>.</h3>
+<p>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 <a name="Page_183" id=
+"Page_183"></a><span class="pagenum">[Pg 183]</span>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&deg;, and then rises
+again to 90&deg; in the second position. This proves the double
+refraction of the heat.</p>
+<div class="figcenter" style="width: 408px;"><img src=
+"images/fig53.jpg" width="408" height="383" alt="Fig. 53." title=
+"" /> <b>Fig. 53.</b></div>
+<p>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&deg;, rising, however, again
+<a name="Page_184" id="Page_184"></a><span class="pagenum">[Pg
+184]</span>to 90&deg; after a rotation of 360&deg;. 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.</p>
+<h3>&sect; 10. <i>Magnetization of Heat</i>.</h3>
+<p>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&deg;, the
+excitement of the magnet causes a far greater positive augmentation
+of the light, though the augmentation is not so well <i>seen</i>
+through lack of contrast, because here, at starting, the field is
+illuminated.</p>
+<p>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 <a name="Page_185" id=
+"Page_185"></a><span class="pagenum">[Pg 185]</span>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.</p>
+<p>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 <i>obscure</i> 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.</p>
+<h3>&sect; 11. <i>Distribution of Heat in the Electric
+Spectrum</i>.</h3>
+<p>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.</p>
+<div class="figcenter" style="width: 600px;"><img src=
+"images/fig54.jpg" width="600" height="287" alt=
+"SPECTRUM OF ELECTRIC LIGHT." title="" /> <b>SPECTRUM OF ELECTRIC
+LIGHT.</b></div>
+<p>When this instrument is brought to the violet end <a name=
+"Page_186" id="Page_186"></a><span class="pagenum">[Pg
+186]</span><a name="Page_187" id="Page_187"></a>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.</p>
+<p>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.</p>
+<p>But in verification, as already stated, consists the strength of
+science. Determining in the first place <a name="Page_188" id=
+"Page_188"></a><span class="pagenum">[Pg 188]</span>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 <i>diffraction</i>,
+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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_189" id="Page_189"></a><span class="pagenum">[Pg
+189]</span></div>
+<h2><a name="LECTURE_VI" id="LECTURE_VI"></a>LECTURE VI.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>PRINCIPLES OF SPECTRUM ANALYSIS</li>
+<li>PRISMATIC ANALYSIS OF THE LIGHT OF INCANDESCENT VAPOURS</li>
+<li>DISCONTINUOUS SPECTRA</li>
+<li>SPECTRUM BANDS PROVED BY BUNSEN AND KIRCHHOFF TO BE
+CHARACTERISTIC</li>
+<li>OF THE VAPOUR</li>
+<li>DISCOVERY OF RUBIDIUM, CAESIUM, AND THALLIUM</li>
+<li>RELATION OF EMISSION TO ABSORPTION</li>
+<li>THE LINES OF FRAUNHOFER</li>
+<li>THEIR EXPLANATION BY KIRCHHOFF</li>
+<li>SOLAR CHEMISTRY INVOLVED IN THIS EXPLANATION</li>
+<li>FOUCAULT'S EXPERIMENT</li>
+<li>PRINCIPLES OF ABSORPTION</li>
+<li>ANALOGY OF SOUND AND LIGHT</li>
+<li>EXPERIMENTAL DEMONSTRATION OF THIS ANALOGY</li>
+<li>RECENT APPLICATIONS OF THE SPECTROSCOPE</li>
+<li>SUMMARY AND CONCLUSION.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<p>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, <a name="Page_190" id="Page_190"></a><span class=
+"pagenum">[Pg 190]</span>the carbon-vapour would yield a few bands
+of colour with spaces of darkness between them.</p>
+<p>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&mdash;that
+corresponding to this particular green&mdash;is emitted by the
+thallium-vapour.</p>
+<p>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
+<i>colour</i> from the other, it is equally impossible to confound
+the <i>spectrum</i> of incandescent silver-vapour with that of
+<a name="Page_191" id="Page_191"></a><span class="pagenum">[Pg
+191]</span>thallium. In the case of silver, we have two green bands
+instead of one.</p>
+<p>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.</p>
+<p>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 <i>resistance</i> 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.<a name=
+"FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24"
+class="fnanchor">[24]</a></p>
+<p>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 <a name="Page_192" id=
+"Page_192"></a><span class="pagenum">[Pg 192]</span>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&mdash;an alloy of copper and zinc&mdash;gives the
+bands of both metals, perfectly unaltered in position or
+character.</p>
+<p>But we are not confined to the metals themselves; the
+<i>salts</i> 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.</p>
+<p>When, therefore, Bunsen and Kirchhoff, the illustrious founders
+of <i>spectrum analysis</i>, 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 <a name="Page_193" id=
+"Page_193"></a><span class="pagenum">[Pg 193]</span>it now stands
+among chemical substances as the metal <i>Rubidium</i>. They
+subsequently discovered a second metal, which they called
+<i>C&aelig;sium</i>. 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 <i>Thallium</i>, and obtained
+the salts of the metal which yielded it. The metal itself was first
+isolated in ingots by M. Lamy, a French chemist.</p>
+<p>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 <i>pure</i> 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.</p>
+<p>(The positions of the principal lines, lettered according to
+Fraunhofer, are shown in the annexed sketch <a name="Page_194" id=
+"Page_194"></a><span class="pagenum">[Pg 194]</span>(fig. 55) of
+the solar spectrum. A is supposed to stand near the extreme red,
+and J near the extreme violet.)</p>
+<div class="figleft" style="width: 82px;"><img src=
+"images/fig55.jpg" width="82" height="600" alt="Fig. 55." title=
+"" /> <b>Fig. 55.</b></div>
+<p>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.</p>
+<p>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 <a name="Page_195" id=
+"Page_195"></a><span class="pagenum">[Pg 195]</span>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.</p>
+<p>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 <i>produce</i> 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.</p>
+<p>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.</p>
+<p>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 <a name="Page_196" id=
+"Page_196"></a><span class="pagenum">[Pg 196]</span>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.</p>
+<p>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. &Aring;ngstr&ouml;m and Thal&eacute;n 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:&mdash;</p>
+<table border="0" cellpadding="2" cellspacing="0" summary="">
+<tr>
+<td align='left'>Calcium</td>
+<td align='right'>75</td>
+</tr>
+<tr>
+<td align='left'>Barium</td>
+<td align='right'>11</td>
+</tr>
+<tr>
+<td align='left'>Magnesium</td>
+<td align='right'>4</td>
+</tr>
+<tr>
+<td align='left'>Manganese</td>
+<td align='right'>57</td>
+</tr>
+<tr>
+<td align='left'>Titanium</td>
+<td align='right'>118</td>
+</tr>
+<tr>
+<td align='left'>Chromium</td>
+<td align='right'>18</td>
+</tr>
+<tr>
+<td align='left'>Nickel</td>
+<td align='right'>33</td>
+</tr>
+<tr>
+<td align='left'>Cobalt</td>
+<td align='right'>19</td>
+</tr>
+<tr>
+<td align='left'>Hydrogen</td>
+<td align='right'>4</td>
+</tr>
+<tr>
+<td align='left'>Aluminium</td>
+<td align='right'>2</td>
+</tr>
+<tr>
+<td align='left'>Zinc</td>
+<td align='right'>2</td>
+</tr>
+<tr>
+<td align='left'>Copper</td>
+<td align='right'>7</td>
+</tr>
+</table>
+<p>The probability is overwhelming that all these substances exist
+in the atmosphere of the sun.</p>
+<p>Kirchhoff's discovery profoundly modified the conceptions
+previously entertained regarding the constitution of the sun,
+leading him to views which, though <a name="Page_197" id=
+"Page_197"></a><span class="pagenum">[Pg 197]</span>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 <i>clouds</i>, 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.</p>
+<p>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 <a name="Page_198" id="Page_198"></a><span class=
+"pagenum">[Pg 198]</span>he found to he considerably strengthened
+by the passage of the solar light through the voltaic arc.</p>
+<p>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 <i>generated</i> 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.</p>
+<p>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 a&euml;rial 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.</p>
+<p>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 <i>radiation</i> or <i>emission</i> of sound from the fork. A
+few days ago, on sound<a name="Page_199" id=
+"Page_199"></a><span class="pagenum">[Pg 199]</span>ing 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 <i>absorption</i> 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.</p>
+<p>I have now to bring before you, on a suitable scale, the
+demonstration that we can do with <i>light</i> 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 <a name="Page_200" id="Page_200"></a><span class=
+"pagenum">[Pg 200]</span>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.<a name="FNanchor_25_25" id=
+"FNanchor_25_25"></a><a href="#Footnote_25_25" class=
+"fnanchor">[25]</a></p>
+<p>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.</p>
+<p>In front of the slit (at L, fig. 56) through which the beam
+issues is placed a Bunsen's burner (<i>b</i>) 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 <a name="Page_201" id="Page_201"></a><span class=
+"pagenum">[Pg 201]</span>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.</p>
+<div class="figright" style="width: 441px;"><img src=
+"images/fig56.jpg" width="441" height="252" alt="Fig. 56." title=
+"" /> <b>Fig. 56.</b></div>
+<p>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:&mdash;'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
+<a name="Page_202" id="Page_202"></a><span class="pagenum">[Pg
+202]</span>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 Pl&uuml;cker, have also given us
+beautiful drawings of spectra obtained from the same source.</p>
+<p>'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
+&Aring;ngstr&ouml;m. 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 <i>reversal</i> 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.'</p>
+<p><a name="Page_203" id="Page_203"></a><span class="pagenum">[Pg
+203]</span>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.</p>
+<p>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 <a name=
+"Page_204" id="Page_204"></a><span class="pagenum">[Pg
+204]</span>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.</p>
+<p>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.</p>
+<p>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
+<a name="Page_205" id="Page_205"></a><span class="pagenum">[Pg
+205]</span>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
+<i>Chromosphere</i>.</p>
+<p>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.<a name="Page_206" id="Page_206"></a><span class=
+"pagenum">[Pg 206]</span></p>
+<h3>SUMMARY AND CONCLUSION.</h3>
+<p>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&mdash;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.</p>
+<p>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 <i>know</i>. 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 <a name="Page_207" id=
+"Page_207"></a><span class="pagenum">[Pg 207]</span>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&mdash;I might say, indeed, for more than fifteen hundred
+years&mdash;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.</p>
+<p>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.</p>
+<p>Up to his demonstration of the composition of white light,
+Newton had been everywhere triumphant&mdash;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 <a name="Page_208" id=
+"Page_208"></a><span class="pagenum">[Pg 208]</span>went hand in
+hand, and that you could not abolish the one without at the same
+time abolishing the other. Here Dollond corrected him.</p>
+<p>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.</p>
+<p>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
+<a name="Page_209" id="Page_209"></a><span class="pagenum">[Pg
+209]</span>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.</p>
+<p>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.</p>
+<p>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 <a name="Page_210" id="Page_210"></a><span class="pagenum">[Pg
+210]</span>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.</p>
+<p>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.</p>
+<p>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 <a name="Page_211" id="Page_211"></a><span class=
+"pagenum">[Pg 211]</span>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.'</p>
+<p>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.'</p>
+<hr style='width: 45%;' />
+<p>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 <a name="Page_212"
+id="Page_212"></a><span class="pagenum">[Pg 212]</span>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.</p>
+<p>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,<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href=
+"#Footnote_26_26" class="fnanchor">[26]</a> 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 <a name="Page_213" id=
+"Page_213"></a><span class="pagenum">[Pg 213]</span>the last
+results of their labours, and then rested from them for ever.</p>
+<p>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&mdash;your
+Henry or your Draper, for example&mdash;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
+<i>use</i> 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 <i>may</i> 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.</p>
+<p>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 <a name="Page_214" id="Page_214"></a><span class=
+"pagenum">[Pg 214]</span>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.</p>
+<p>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&mdash;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 <a name="Page_215" id="Page_215"></a><span class="pagenum">[Pg
+215]</span>analyzed, what are industrial America and industrial
+England?</p>
+<p>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.</p>
+<p>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.</p>
+<p>Both England and America have reason to bear those things in
+mind, for the largeness and nearness of <a name="Page_216" id=
+"Page_216"></a><span class="pagenum">[Pg 216]</span>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&mdash;nay, if you fail to secure
+for him free scope and encouragement&mdash;you not only lose the
+motive power of intellectual progress, but infallibly sever
+yourselves from the springs of industrial life.</p>
+<p>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.</p>
+<p>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 <a name="Page_217" id="Page_217"></a><span class=
+"pagenum">[Pg 217]</span>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&mdash;they spread themselves so
+largely and umbrageously before the public eye&mdash;that they
+often shut out from view those workers who are engaged in the
+quieter and profounder business of original investigation.</p>
+<p>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.</p>
+<p>The ancients discovered the electricity of amber; and Gilbert,
+in the year 1600, extended the discovery <a name="Page_218" id=
+"Page_218"></a><span class="pagenum">[Pg 218]</span>to other
+bodies. Then followed Boyle, Von Guericke, Gray, Canton, Du Fay,
+Kleist, Cun&aelig;us, 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. &OElig;rsted
+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.</p>
+<p>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
+G&ouml;ttingen, 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&mdash;nay, its
+applicability to telegraphic purposes demonstrated&mdash;by men
+whose sole reward for their labours was the noble <a name=
+"Page_219" id="Page_219"></a><span class="pagenum">[Pg
+219]</span>excitement of research, and the joy attendant on the
+discovery of natural truth.</p>
+<p>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.</p>
+<p>Pasteur, one of the most illustrious members of the Institute of
+France, in accounting for the disastrous <a name="Page_220" id=
+"Page_220"></a><span class="pagenum">[Pg 220]</span>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 <i>applied science</i>. 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 <i>in our day the
+reign of theoretic science yielded place to that of applied
+science</i>. 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. <i>We have science, and the applications of science</i>,
+which are united together as the tree and its fruit.'</p>
+<p>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 <a name="Page_221" id=
+"Page_221"></a><span class="pagenum">[Pg 221]</span>issues though
+born of their own deeds. These rising workshops, these peopled
+colonies, those ships which furrow the seas&mdash;this abundance,
+this luxury, this tumult&mdash;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.'</p>
+<p>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.</p>
+<p>Among the many problems before them they have <a name="Page_222"
+id="Page_222"></a><span class="pagenum">[Pg 222]</span>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&mdash;in a spirit, indeed, the reverse of
+unfriendly&mdash;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.</p>
+<p>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.'<a name="FNanchor_27_27" id=
+"FNanchor_27_27"></a><a href="#Footnote_27_27" class=
+"fnanchor">[27]</a> 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; <a name="Page_223" id=
+"Page_223"></a><span class="pagenum">[Pg 223]</span>and it is
+there, he contends, that you collect the treasures of the
+intellect, without taking the trouble to create them.</p>
+<p>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&mdash;whether
+scientific genius cannot find, in the midst of you, a tranquil
+home.</p>
+<p>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 <a name="Page_224" id="Page_224"></a><span class=
+"pagenum">[Pg 224]</span>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.</p>
+<p>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.</p>
+<p>Drawn by your kindness, I have come here to give these lectures,
+and now that my visit to America has <a name="Page_225" id=
+"Page_225"></a><span class="pagenum">[Pg 225]</span>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&mdash;not sown broadcast, believe me, it is sown thus
+nowhere&mdash;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&mdash;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.</p>
+<div><a name="Page_226" id="Page_226"></a><span class="pagenum">[Pg
+226]</span></div>
+<hr style="width: 65%;" />
+<div><a name="Page_227" id="Page_227"></a><span class="pagenum">[Pg
+227]</span></div>
+<h2><a name="APPENDIX" id="APPENDIX"></a>APPENDIX.</h2>
+<h3><a name="ON_THE_SPECTRA_OF_POLARIZED_LIGHT" id=
+"ON_THE_SPECTRA_OF_POLARIZED_LIGHT"></a>ON THE SPECTRA OF POLARIZED
+LIGHT.</h3>
+<p>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:&mdash;</p>
+<div class="blockquot">
+<p>'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 <a name="Page_228" id="Page_228"></a><span class=
+"pagenum">[Pg 228]</span>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&deg;, all trace of
+colour disappears; and also that when the angle amounts to 90&deg;,
+colour reappears, not, however, the original colour, but one
+complementary to it.</p>
+<p>'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&deg; 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&deg;. Thus we have
+from the spectroscope a complete account of what has taken place to
+produce the original colour and its changes.</p>
+<p>'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.</p>
+<p>'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 <a name="Page_229" id=
+"Page_229"></a><span class="pagenum">[Pg 229]</span>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.</p>
+<p>'These experiments were made more than thirty years ago by the
+French philosophers, MM. Foucault and Fizeau.</p>
+<p>'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>i.e.</i> 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 <i>vice vers&acirc;</i>, precisely in such
+a direction as to give rise to the tints seen by direct
+projection.</p>
+<p>'The kind of polarization effected by the quartz plates is
+called circular, while that effected by the other class of <a name=
+"Page_230" id="Page_230"></a><span class="pagenum">[Pg
+230]</span>crystals is called plane, on account of the form of the
+vibrations executed by the molecules of &aelig;ther; and this leads
+us to examine a little more closely the nature of the polarization
+of different parts of these spectra of polarized light.</p>
+<p>'Now, two things are clear: first, that if the light be
+plane-polarized&mdash;that is, if all the vibrations throughout the
+entire ray are rectilinear and in one plane&mdash;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&deg;; 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>i.e.</i> 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>i.e.</i> 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 <a name=
+"Page_231" id="Page_231"></a><span class="pagenum">[Pg
+231]</span>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.</p>
+<p>'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 <i>vice vers&acirc;</i>), we have
+only to turn the plate round through 90&deg;. 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&deg; 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<a name=
+"FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28"
+class="fnanchor">[28]</a>.</p>
+<p>'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.</p>
+<p><a name="Page_232" id="Page_232"></a><span class="pagenum">[Pg
+232]</span>'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&mdash;that is, as if they were one plate of
+crystal&mdash;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&deg;,
+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&deg; 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&deg;, 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&deg;.</p>
+<p>'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.</p>
+<p>'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.</p>
+<p><a name="Page_233" id="Page_233"></a><span class="pagenum">[Pg
+233]</span>'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.</p>
+<p>'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 <i>vice vers&acirc;</i>, according to the position
+of the plates.</p>
+<p>'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.'</p>
+</div>
+<hr style='width: 45%;' />
+<p>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 <i>iris-rings</i>,
+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, <a name="Page_234" id=
+"Page_234"></a><span class="pagenum">[Pg 234]</span>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.</p>
+<p>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&mdash;the
+fan opening out at the red end of the spectrum.</p>
+<hr style='width: 45%;' />
+<h3><a name="MEASUREMENT_OF_THE_WAVES_OF_LIGHT" id=
+"MEASUREMENT_OF_THE_WAVES_OF_LIGHT"></a><i>MEASUREMENT OF THE WAVES
+OF LIGHT.</i></h3>
+<p>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 <i>the length</i> of a wave of
+light.</p>
+<div class="figright" style="width: 313px;"><img src=
+"images/fig57.jpg" width="313" height="196" alt="Fig. 57." title=
+"" /> <b>Fig. 57.</b></div>
+<p>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 differ<a name="Page_235" id="Page_235"></a><span class=
+"pagenum">[Pg 235]</span>ence 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,<a name=
+"FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29"
+class="fnanchor">[29]</a> 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.</p>
+<p>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 <i>d</i>. The
+distance, C <i>d</i>, between the foot of this perpendicular and
+the other edge is the length of a wave of the light. The angle C D
+<i>d</i>, 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 <i>d</i> is so
+small that it sensibly coincides with the arc of the circle. Hence
+the length of the semicircle is to the length C <i>d</i> of the
+wave as 180&deg; to <a name="Page_236" id=
+"Page_236"></a><span class="pagenum">[Pg 236]</span>1'38", or,
+reducing all to seconds, as 648,000" to 98". Thus, we have the
+proportion&mdash;</p>
+<div class="blockquot">
+<p>648,000 : 98 :: 4.248 to the wave-length C <i>d</i>.</p>
+</div>
+<p>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.</p>
+<div class="footnotes">
+<p class="center">FOOTNOTES:</p>
+<div class="footnote">
+<p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href=
+"#FNanchor_1_1"><span class="label">[1]</span></a> Among whom may
+be especially mentioned the late Sir Edmund Head, Bart., with whom
+I had many conversations on this subject.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href=
+"#FNanchor_2_2"><span class="label">[2]</span></a> At whose hands
+it gives me pleasure to state I have always experienced honourable
+and liberal treatment.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href=
+"#FNanchor_3_3"><span class="label">[3]</span></a> One of the
+earliest of these came from Mr. John Amory Lowell of Boston.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href=
+"#FNanchor_4_4"><span class="label">[4]</span></a> It will be
+subsequently shown how this simple apparatus may be employed to
+determine the 'polarizing angle' of a liquid.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href=
+"#FNanchor_5_5"><span class="label">[5]</span></a> From this
+principle Sir John Herschel deduces in a simple and elegant manner
+the fundamental law of reflection.&mdash;See <i>Familiar
+Lectures</i>, p. 236.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href=
+"#FNanchor_6_6"><span class="label">[6]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href=
+"#FNanchor_7_7"><span class="label">[7]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href=
+"#FNanchor_8_8"><span class="label">[8]</span></a> 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
+<i>all</i> the other colours of the spectrum may be obtained.</p>
+<p>Some years ago Sir Charles Wheatstone drew my attention to a
+work by Christian Ernst W&uuml;nsch, Leipzig 1792, in which the
+author announces the proposition that there are neither five nor
+seven, but only three simple colours in white light. W&uuml;nsch
+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 <i>simple</i>
+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 <i>simple</i> 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 <i>simple</i> colour. He also finds that yellow and indigo
+blue produce <i>white</i> 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, W&uuml;nsch
+very emphatically distinguishes the mixture of pigments from that
+of lights. Speaking of the generation of yellow, he says, 'I say
+expressly <i>red and green light</i>, because I am speaking about
+light-colours (Lichtfarben), and not about pigments.' However
+faulty his theories may be, W&uuml;nsch'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. (<i>Popular Lectures</i>, p.
+249. The paper of Helmholtz on the mixture of colours, translated
+by myself, is published in the <i>Philosophical Magazine</i> for
+1852. Maxwell's memoir on the Theory of Compound Colours is
+published in the <i>Philosophical Transactions</i>, vol. 150, p.
+67.)</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href=
+"#FNanchor_9_9"><span class="label">[9]</span></a> 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:&mdash;</p>
+<div class="blockquot">
+<p>'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.'&mdash;(<i>Maclaurin: An
+Account of Sir I. Newton's Philosophical Discoveries. Written 1728;
+second edition</i>, 1750; pp. 18, 19.)</p>
+</div>
+</div>
+<div class="footnote">
+<p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href=
+"#FNanchor_10_10"><span class="label">[10]</span></a> 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 <i>circular</i> motion of the
+particles. This, as proved by the brothers Weber, is the real
+motion in the case of water-waves.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href=
+"#FNanchor_11_11"><span class="label">[11]</span></a> Copied from
+Weber's <i>Wellenlehre</i>.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href=
+"#FNanchor_12_12"><span class="label">[12]</span></a> See
+<i>Lectures on Sound</i>, 1st and 2nd ed., Lecture VII.; and 3rd
+ed., Chap. VIII. Longmans.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href=
+"#FNanchor_13_13"><span class="label">[13]</span></a> <i>Boyle's
+Works</i>, Birch's edition, p. 675.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href=
+"#FNanchor_14_14"><span class="label">[14]</span></a> Page 743.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href=
+"#FNanchor_15_15"><span class="label">[15]</span></a> The beautiful
+plumes produced by water-crystallization have been successfully
+photographed by Professor Lockett.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href=
+"#FNanchor_16_16"><span class="label">[16]</span></a> 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 <i>wetted</i> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href=
+"#FNanchor_17_17"><span class="label">[17]</span></a> This
+beautiful law is usually thus expressed: <i>The index of refraction
+of any substance is the tangent of its polarizing angle</i>. 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href=
+"#FNanchor_18_18"><span class="label">[18]</span></a> Whewell.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href=
+"#FNanchor_19_19"><span class="label">[19]</span></a> Removed from
+us since these words were written.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href=
+"#FNanchor_20_20"><span class="label">[20]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href=
+"#FNanchor_21_21"><span class="label">[21]</span></a> <i>Boyle's
+Works</i>, Birch's edition, vol. i. pp, 729 and 730.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href=
+"#FNanchor_22_22"><span class="label">[22]</span></a> <i>Werke</i>,
+B. xxix. p. 24.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href=
+"#FNanchor_23_23"><span class="label">[23]</span></a> Defined in
+Lecture I.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href=
+"#FNanchor_24_24"><span class="label">[24]</span></a> This
+circumstance ought not to be lost sight of in the examination of
+compound spectra. Other similar instances might be cited.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href=
+"#FNanchor_25_25"><span class="label">[25]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href=
+"#FNanchor_26_26"><span class="label">[26]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href=
+"#FNanchor_27_27"><span class="label">[27]</span></a> 'Il faut
+reconna&icirc;tre que parmi les peuples civilis&eacute;s de nos
+jours il en est pen chez qui les hautes sciences aient fait moins
+de progr&egrave;s qu'aux &Eacute;tats-Unis, ou qui aient fourni
+moins de grands artistes, de po&euml;tes illustres et de
+c&eacute;l&egrave;bres &eacute;crivains.' (<i>De la
+D&eacute;mocratie en Am&eacute;rique</i>, etc. tome ii. p. 36.)</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href=
+"#FNanchor_28_28"><span class="label">[28]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href=
+"#FNanchor_29_29"><span class="label">[29]</span></a> The
+millimeter is about 1/25th of an inch.</p>
+</div>
+</div>
+<hr style="width: 65%;" />
+<div><a name="Page_237" id="Page_237"></a><span class="pagenum">[Pg
+237]</span></div>
+<h2><a name="INDEX" id="INDEX"></a>INDEX.</h2>
+<div>Absorption, principles of, <a href="#Page_199">199</a><br />
+<br />
+Airy, Sir George, severity and conclusiveness of his proofs,
+<a href="#Page_209">209</a><br />
+<br />
+Alhazen, his inquiry respecting light, <a href="#Page_14">14</a>,
+<a href="#Page_207">207</a><br />
+<br />
+Analyzer, polarizer and, <a href="#Page_127">127</a><br />
+&mdash;&mdash;recompounding of the two systems of waves by the
+analyzer, <a href="#Page_129">129</a><br />
+<br />
+&Aring;ngstr&ouml;m, his paper on spectrum analysis, <a href=
+"#Page_202">202</a><br />
+<br />
+Arago, Fran&ccedil;ois, and Dr. Young, <a href=
+"#Page_50">50</a><br />
+&mdash;&mdash;his discoveries respecting light, <a href=
+"#Page_208">208</a><br />
+<br />
+Atomic polarity, <a href="#Page_93">93-96</a><br />
+<br />
+Bacon, Roger, his inquiry respecting light, <a href=
+"#Page_14">14</a>, <a href="#Page_207">207</a><br />
+<br />
+Bartholinus, Erasmus, on Iceland spar, <a href=
+"#Page_112">112</a><br />
+<br />
+B&eacute;rard on polarization of heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Blackness, meaning of, <a href="#Page_32">32</a><br />
+<br />
+Boyle, Robert, his observations on colours, <a href=
+"#Page_65">65</a>, <a href="#Page_66">66</a><br />
+&mdash;&mdash;his remarks on fluorescence, <a href=
+"#Page_163">163</a>, <a href="#Page_164">164</a><br />
+<br />
+Bradley, James, discovers the aberration of light, <a href=
+"#Page_21">21</a>, <a href="#Page_22">22</a><br />
+<br />
+Brewster, Sir David, his chief objection to the undulatory theory
+of light, <a href="#Page_47">47</a><br />
+<br />
+Brewster, Sir David, his discovery in biaxal crystals, <a href=
+"#Page_209">209</a><br />
+<br />
+Brougham, Mr. (afterwards Lord), ridicules Dr. T. Young's
+speculations, <a href="#Page_50">50</a>, <a href=
+"#Page_51">51</a><br />
+<br />
+C&aelig;sium, discovery of, <a href="#Page_193">193</a><br />
+<br />
+Calorescence, <a href="#Page_174">174</a><br />
+<br />
+Clouds, actinic, <a href="#Page_152">152-154</a><br />
+&mdash;&mdash;polarization of, <a href="#Page_155">155</a><br />
+<br />
+Colours of thin plates, <a href="#Page_64">64</a><br />
+&mdash;&mdash;Boyle's observations on, <a href="#Page_65">65</a>,
+<a href="#Page_66">66</a><br />
+&mdash;&mdash;Hooke on the colours of thin plates, <a href=
+"#Page_67">67</a><br />
+&mdash;&mdash;of striated surfaces, <a href="#Page_89">89</a>,
+<a href="#Page_90">90</a><br />
+<br />
+Comet of 1680, Newton's estimate of the temperature of, <a href=
+"#Page_168">168</a><br />
+<br />
+Crookes, Mr., his discovery of thallium, <a href=
+"#Page_193">193</a><br />
+<br />
+Crystals, action of, upon light, <a href="#Page_98">98</a><br />
+&mdash;&mdash;built by polar force, <a href="#Page_98">98</a><br />
+&mdash;&mdash;illustrations of crystallization, <a href=
+"#Page_99">99</a><br />
+&mdash;&mdash;architecture of, considered as an introduction to
+their action upon light, <a href="#Page_98">98</a><br />
+&mdash;&mdash;bearings of crystallization upon optical phenomena,
+<a href="#Page_106">106</a><br />
+<br />
+Crystals, rings surrounding the axes of, uniaxal and biaxal,
+<a href="#Page_145">145</a><br />
+<br />
+Cuvier on ardour for knowledge, <a href="#Page_220">220</a><br />
+<br />
+De Tocqueville, writings of, <a href="#Page_215">215</a>, <a href=
+"#Page_222">222</a>, <a href="#Page_223">223</a><br />
+<a name="Page_238" id="Page_238"></a><span class="pagenum">[Pg
+238]</span><br />
+Descartes, his explanation of the rainbow, <a href=
+"#Page_24">24</a>, <a href="#Page_25">25</a><br />
+&mdash;&mdash;his ideas respecting the transmission of light,
+<a href="#Page_43">43</a><br />
+&mdash;&mdash;his notion of light, <a href=
+"#Page_207">207</a><br />
+<br />
+Diamond, ignition of a, in oxygen, <a href=
+"#Page_169">169</a><br />
+<br />
+Diathermancy, <a href="#Page_173">173</a><br />
+<br />
+Diffraction of light, phenomena of, <a href="#Page_78">78</a><br />
+&mdash;&mdash;bands, <a href="#Page_78">78</a>, <a href=
+"#Page_79">79</a><br />
+&mdash;&mdash;explanation of, <a href="#Page_80">80</a><br />
+&mdash;&mdash;colours produced by, <a href="#Page_89">89</a><br />
+<br />
+Dollond, his experiments on achromatism, <a href=
+"#Page_28">28</a><br />
+<br />
+Draper, Dr., his investigation on heat, <a href=
+"#Page_172">172</a><br />
+<br />
+Drummond light, spectrum of, <a href="#Page_195">195</a><br />
+<br />
+<br />
+Earth, daily orbit of, <a href="#Page_74">74</a><br />
+<br />
+Electric beam, heat of the, <a href="#Page_168">168</a><br />
+<br />
+Electricity, discoveries in, <a href="#Page_217">217</a>, <a href=
+"#Page_218">218</a><br />
+<br />
+Emission theory of light, bases of the, <a href=
+"#Page_45">45</a><br />
+&mdash;&mdash;Newton espouses the theory, and the results of this
+espousal, <a href="#Page_77">77</a><br />
+<br />
+Ether, Huyghens and Euler advocate and defend the conception of an,
+<a href="#Page_48">48</a>, <a href="#Page_58">58</a><br />
+&mdash;&mdash;objected to by Newton, <a href=
+"#Page_58">58</a><br />
+<br />
+Euler espouses and defends the conception of an ether, <a href=
+"#Page_48">48</a>, <a href="#Page_58">58</a><br />
+<br />
+Eusebius on the natural philosophers of his time, <a href=
+"#Page_13">13</a><br />
+<br />
+Expansion by cold, <a href="#Page_104">104</a><br />
+<br />
+Experiment, uses of, <a href="#Page_3">3</a><br />
+<br />
+Eye, the, its imperfections, grown for ages towards perfection,
+<a href="#Page_8">8</a><br />
+&mdash;&mdash;imperfect achromatism of the, <a href=
+"#Page_29">29</a>, <a href="#Footnote_6_6"><i>note</i></a><br />
+<br />
+<br />
+Faraday, Michael, his discovery of magneto-electricity, <a href=
+"#Page_218">218</a><br />
+<br />
+'Fits,' theory of, <a href="#Page_73">73</a><br />
+&mdash;&mdash;its explanation of Newton's rings, <a href=
+"#Page_74">74</a><br />
+&mdash;&mdash;overthrow of the theory, <a href=
+"#Page_77">77</a><br />
+<br />
+Fizeau determines the velocity of light, <a href=
+"#Page_22">22</a><br />
+<br />
+Fluorescence, Stokes's discovery of, <a href=
+"#Page_161">161</a><br />
+&mdash;&mdash;the name, <a href="#Page_174">174</a><br />
+<br />
+Forbes, Professor, polarizes and depolarizes heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Foucault, determines the velocity of light, <a href=
+"#Page_22">22</a><br />
+&mdash;&mdash;his experiments on absorption, <a href=
+"#Page_197">197</a>, <a href="#Page_198">198</a><br />
+<br />
+Fraunhofer, his theoretical calculations respecting diffraction,
+<a href="#Page_87">87</a><br />
+&mdash;&mdash;his lines, <a href="#Page_193">193</a><br />
+&mdash;&mdash;&mdash;their explanation by Kirchhoff, <a href=
+"#Page_193">193</a><br />
+<br />
+Fresnel, and Dr. Young, <a href="#Page_50">50</a><br />
+&mdash;&mdash;his theoretical calculations respecting diffraction,
+<a href="#Page_87">87</a><br />
+&mdash;&mdash;his mathematical abilities and immortal name,
+<a href="#Page_210">210</a><br />
+<br />
+<br />
+Goethe on fluorescence, <a href="#Page_165">165</a><br />
+<br />
+Gravitation, origin of the notion of the attraction of, <a href=
+"#Page_92">92</a><br />
+&mdash;&mdash;strength of the theory of, <a href=
+"#Page_148">148</a><br />
+<br />
+Grimaldi, his discovery with respect to light, <a href=
+"#Page_56">56</a><br />
+<a name="Page_239" id="Page_239"></a><span class="pagenum">[Pg
+239]</span> &mdash;&mdash;Young's generalizations of, <a href=
+"#Page_56">56</a><br />
+<br />
+<br />
+Hamilton, Sir William, of Dublin, his discovery of conical
+refraction, <a href="#Page_209">209</a><br />
+<br />
+Heat, generation of, <a href="#Page_6">6</a><br />
+&mdash;&mdash;Dr. Draper's investigation respecting, <a href=
+"#Page_171">171</a><br />
+<br />
+Helmholtz, his estimate of the genius of Young, <a href=
+"#Page_50">50</a><br />
+&mdash;&mdash;on the imperfect achromatism of the eye, <a href=
+"#Page_29">29</a>, <a href="#Footnote_6_6"><i>note</i></a>,
+<a href="#Page_31">31</a><br />
+&mdash;&mdash;reveals the cause of green in the case of pigments,
+<a href="#Page_37">37</a><br />
+<br />
+Henry, Professor Joseph, his invitation, <a href=
+"#Page_2">2</a><br />
+<br />
+Herschel, Sir John, his theoretical calculations respecting
+diffraction, <a href="#Page_87">87</a><br />
+&mdash;&mdash;first notices and describes the fluorescence of
+sulphate of quinine, <a href="#Page_165">165</a><br />
+&mdash;&mdash;his experiments on spectra, <a href=
+"#Page_201">201</a><br />
+<br />
+Herschel, Sir William, his experiments on the heat of the various
+colours of the solar spectrum, <a href="#Page_171">171</a><br />
+<br />
+Hooke, Robert, on the colours of thin plates, <a href=
+"#Page_67">67</a><br />
+&mdash;&mdash;his remarks on the idea that light and heat are modes
+of motion, <a href="#Page_68">68</a><br />
+<br />
+Horse-chestnut bark, fluorescence of, <a href=
+"#Page_165">165</a><br />
+<br />
+Huggins, Dr., his labours, <a href="#Page_205">205</a><br />
+<br />
+Huyghens advocates the conception of ether, <a href=
+"#Page_48">48</a>, <a href="#Page_58">58</a><br />
+&mdash;&mdash;his celebrated principle, <a href=
+"#Page_83">83</a><br />
+<br />
+Huyghens on the double refraction of Iceland spar, <a href=
+"#Page_112">112</a><br />
+<br />
+<br />
+Iceland spar, <a href="#Page_109">109</a><br />
+&mdash;&mdash;double refraction caused by, <a href=
+"#Page_110">110</a><br />
+&mdash;&mdash;this double refraction first treated by Erasmus
+Bartholinus, <a href="#Page_112">112</a><br />
+&mdash;&mdash;character of the beams emergent from, <a href=
+"#Page_114">114</a><br />
+&mdash;&mdash;tested by tourmaline, <a href=
+"#Page_116">116</a><br />
+&mdash;&mdash;Knoblauch's demonstration of the double refraction
+of, <a href="#Page_185">185</a><br />
+<br />
+Ice-lens, combustion through, <a href="#Page_167">167</a><br />
+<br />
+Imagination, scope of the, <a href="#Page_42">42</a><br />
+&mdash;&mdash;note by Maclaurin on this point, 43 <i>note</i><br />
+<br />
+<br />
+Janssen, M., on the rose-coloured solar prominences, <a href=
+"#Page_204">204</a><br />
+<br />
+Jupiter, Roemer's observations of the moons of, <a href=
+"#Page_20">20</a><br />
+<br />
+Jupiter's distance from the sun, <a href="#Page_20">20</a><br />
+<br />
+<br />
+Kepler, his investigations on the refraction of light, <a href=
+"#Page_14">14</a>, <a href="#Page_207">207</a><br />
+<br />
+Kirchhoff, Professor, his explanation of Fraunhofer's lines,
+<a href="#Page_193">193</a><br />
+&mdash;&mdash;his precursors, <a href="#Page_201">201</a><br />
+&mdash;&mdash;his claims, <a href="#Page_203">203</a><br />
+<br />
+Knoblauch, his demonstration of the double refraction of heat of
+Iceland spar, <a href="#Page_185">185</a><br />
+<br />
+<br />
+Lactantius, on the natural philosophers of his time, <a href=
+"#Page_13">13</a><br />
+<br />
+Lamy, M., isolates thallium in ingots, <a href=
+"#Page_193">193</a><br />
+<a name="Page_240" id="Page_240"></a><span class="pagenum">[Pg
+240]</span><br />
+Lesley, Professor, his invitation, <a href="#Page_2">2</a><br />
+<br />
+Light familiar to the ancients, <a href="#Page_5">5</a><br />
+&mdash;&mdash;generation of, <a href="#Page_6">6</a>, <a href=
+"#Page_7">7</a><br />
+&mdash;&mdash;spherical aberration of, <a href=
+"#Page_8">8</a><br />
+&mdash;&mdash;the rectilineal propagation of, and mode of producing
+it, <a href="#Page_9">9</a><br />
+&mdash;&mdash;illustration showing that the angle of incidence is
+equal to the angle of reflection, <a href="#Page_10">10</a>,
+<a href="#Page_11">11</a><br />
+&mdash;&mdash;sterility of the Middle Ages, <a href=
+"#Page_13">13</a><br />
+&mdash;&mdash;history of refraction, <a href=
+"#Page_14">14</a><br />
+&mdash;&mdash;demonstration of the fact of refraction, <a href=
+"#Page_14">14</a><br />
+&mdash;&mdash;partial and total reflection of, <a href=
+"#Page_16">16-20</a><br />
+&mdash;&mdash;velocity of, <a href="#Page_20">20</a><br />
+&mdash;&mdash;Bradley's discovery of the aberration of light,
+<a href="#Page_21">21</a>, <a href="#Page_22">22</a><br />
+&mdash;&mdash;principle of least time, <a href=
+"#Page_23">23</a><br />
+&mdash;&mdash;Descartes and the rainbow, <a href=
+"#Page_24">24</a><br />
+&mdash;&mdash;Newton's analysis of, <a href="#Page_26">26</a>,
+<a href="#Page_27">27</a><br />
+&mdash;&mdash;synthesis of white light, <a href=
+"#Page_30">30</a><br />
+&mdash;&mdash;complementary colours, <a href=
+"#Page_31">31</a><br />
+&mdash;&mdash;yellow and blue lights produce white by their
+mixture, <a href="#Page_31">31</a><br />
+&mdash;&mdash;what is the meaning of blackness? <a href=
+"#Page_32">32</a><br />
+&mdash;&mdash;analysis of the action of pigments upon, <a href=
+"#Page_33">33</a><br />
+&mdash;&mdash;absorption, <a href="#Page_34">34</a><br />
+&mdash;&mdash;mixture of pigments contrasted with mixture of
+lights, <a href="#Page_37">37</a><br />
+&mdash;&mdash;W&uuml;nsch on three simple colours in white light,
+<a href="#Page_39">39</a> <a href=
+"#Footnote_8_8"><i>note</i></a><br />
+&mdash;&mdash;Newton arrives at the emission theory, <a href=
+"#Page_45">45</a><br />
+&mdash;&mdash;Young's discovery of the undulatory theory, <a href=
+"#Page_49">49</a><br />
+&mdash;&mdash;illustrations of wave-motion, <a href=
+"#Page_58">58</a><br />
+&mdash;&mdash;interference of sound-waves, <a href=
+"#Page_58">58</a><br />
+&mdash;&mdash;velocity of, <a href="#Page_60">60</a><br />
+&mdash;&mdash;principle of interference of waves of, <a href=
+"#Page_61">61</a><br />
+&mdash;&mdash;phenomena which first suggested the undulatory theory
+<a href="#Page_62">62-69</a><br />
+&mdash;&mdash;soap-bubbles and their colours, <a href=
+"#Page_62">62-65</a><br />
+&mdash;&mdash;Newton's rings, <a href="#Page_77">69-77</a><br />
+&mdash;&mdash;his espousal of the emission theory, and the results
+of this espousal, <a href="#Page_77">77</a><br />
+&mdash;&mdash;transmitted light, <a href="#Page_77">77</a><br />
+&mdash;&mdash;diffraction, <a href="#Page_77">77</a>, <a href=
+"#Page_89">89</a><br />
+&mdash;&mdash;origin of the notion of the attraction of
+gravitation, <a href="#Page_92">92</a><br />
+&mdash;&mdash;polarity, how generated, <a href=
+"#Page_93">93</a><br />
+&mdash;&mdash;action of crystals upon, <a href=
+"#Page_98">98</a><br />
+&mdash;&mdash;refraction of, <a href="#Page_106">106</a><br />
+&mdash;&mdash;elasticity and density, <a href=
+"#Page_108">108</a><br />
+&mdash;&mdash;double refraction, <a href="#Page_109">109</a><br />
+&mdash;&mdash;chromatic phenomena produced by crystals in
+polarized, <a href="#Page_121">121</a><br />
+&mdash;&mdash;the Nicol prism, <a href="#Page_122">122</a><br />
+&mdash;&mdash;mechanism of, <a href="#Page_125">125</a><br />
+&mdash;&mdash;vibrations, <a href="#Page_125">125</a><br />
+&mdash;&mdash;composition and resolution of vibrations, <a href=
+"#Page_128">128</a><br />
+&mdash;&mdash;polarizer and analyzer, <a href=
+"#Page_127">127</a><br />
+&mdash;&mdash;recompounding the two systems of waves by the
+analyzer, <a href="#Page_129">129</a><br />
+&mdash;&mdash;interference thus rendered possible, <a href=
+"#Page_131">131</a><br />
+&mdash;&mdash;chromatic phenomena produced by quartz, <a href=
+"#Page_139">139</a><br />
+&mdash;&mdash;magnetization, of, <a href="#Page_141">141</a><br />
+&mdash;&mdash;rings surrounding the axes of crystals, <a href=
+"#Page_143">143</a><br />
+&mdash;&mdash;colour and polarization of sky, <a href=
+"#Page_149">149</a>, <a href="#Page_154">154</a><br />
+&mdash;&mdash;range of vision incommensurate with range of
+radiation, <a href="#Page_159">159</a><br />
+&mdash;&mdash;effect of thallene on the spectrum, 162<br />
+<a name="Page_241" id="Page_241"></a><span class="pagenum">[Pg
+241]</span> &mdash;&mdash;fluorescence, <a href=
+"#Page_162">162</a><br />
+&mdash;&mdash;transparency, <a href="#Page_167">167</a><br />
+&mdash;&mdash;the ultra-red rays, <a href="#Page_170">170</a><br />
+&mdash;&mdash;part played in Nature by these rays, <a href=
+"#Page_175">175</a><br />
+&mdash;&mdash;conversion of heat-rays into light-rays, <a href=
+"#Page_176">176</a><br />
+&mdash;&mdash;identity of radiant heat and, <a href=
+"#Page_177">177</a><br />
+&mdash;&mdash;polarization of heat, <a href=
+"#Page_180">180</a><br />
+&mdash;&mdash;principles of spectrum analysis, <a href=
+"#Page_189">189</a><br />
+&mdash;&mdash;spectra of incandescent vapours, <a href=
+"#Page_190">190</a><br />
+&mdash;&mdash;Fraunhofer's lines, and Kirchhoff's explanation of
+them, <a href="#Page_193">193</a><br />
+&mdash;&mdash;solar chemistry, <a href=
+"#Page_195">195-197</a><br />
+&mdash;&mdash;demonstration of analogy between sound and, <a href=
+"#Page_198">198</a>, <a href="#Page_199">199</a><br />
+&mdash;&mdash;Kirchhoff and his precursors, <a href=
+"#Page_201">201</a><br />
+&mdash;&mdash;rose-coloured solar prominences, <a href=
+"#Page_204">204</a><br />
+&mdash;&mdash;results obtained by various workers, <a href=
+"#Page_205">205</a><br />
+&mdash;&mdash;summary and conclusion, <a href=
+"#Page_206">206</a><br />
+&mdash;&mdash;polarized, the spectra of, <a href=
+"#Page_227">227</a><br />
+&mdash;&mdash;measurement of the waves of, <a href=
+"#Page_234">234</a><br />
+<br />
+Lignum Nephriticum, fluorescence of, <a href=
+"#Page_164">164</a><br />
+<br />
+Lloyd, Dr., on polarization of heat, <a href="#Page_180">180</a>,
+<a href="#Page_209">209</a><br />
+<br />
+Lockyer, Mr., on the rose-coloured solar prominences, <a href=
+"#Page_205">205</a><br />
+<br />
+Lycopodium, diffraction effects caused by the spores of, <a href=
+"#Page_88">88</a><br />
+<br />
+<br />
+Magnetization of light, <a href="#Page_141">141</a><br />
+<br />
+Malus, his discovery respecting reflected light through Iceland
+spar, <a href="#Page_115">115</a><br />
+&mdash;&mdash;discovers the polarization of light by reflection,
+<a href="#Page_208">208</a><br />
+<br />
+Masson, his essay on the bands of the induction spark, <a href=
+"#Page_202">202</a><br />
+<br />
+Melloni, on the polarization of heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Metals, combustion of, <a href="#Page_5">5</a>, <a href=
+"#Page_6">6</a><br />
+&mdash;&mdash;spectrum analysis of, <a href=
+"#Page_190">190</a><br />
+&mdash;&mdash;spectrum bands proved by Bunsen and Kirchhoff to be
+characteristic of the vapour of, <a href="#Page_192">192</a><br />
+<br />
+Mill, John Stuart, his scepticism regarding the undulatory theory,
+<a href="#Page_149">149</a><br />
+<br />
+Miller, Dr., his drawings and descriptions of the spectra of
+various coloured flames, <a href="#Page_201">201</a><br />
+<br />
+Morton, Professor, his discovery of thallene, <a href=
+"#Page_162">162</a><br />
+<br />
+Mother-of-pearl, colours of, <a href="#Page_90">90</a><br />
+<br />
+<br />
+Nature, a savage's interpretation of, <a href="#Page_4">4</a><br />
+<br />
+Newton, Sir Isaac, his experiments on the composition of solar
+light, <a href="#Page_26">26</a><br />
+&mdash;&mdash;his spectrum, <a href="#Page_27">27</a><br />
+&mdash;&mdash;dispersion, <a href="#Page_27">27</a><br />
+&mdash;&mdash;arrives at the emission theory of light, <a href=
+"#Page_45">45</a><br />
+&mdash;&mdash;his objection to the conception of an ether espoused
+and defended by Huyghens and Euler, <a href="#Page_58">58</a><br />
+&mdash;&mdash;his optical career, <a href="#Page_70">70</a><br />
+&mdash;&mdash;his rings, <a href="#Page_69">69-77</a><br />
+&mdash;&mdash;his rings explained by the theory of 'fits,' <a href=
+"#Page_73">73</a><br />
+&mdash;&mdash;espouses the emission theory, <a href=
+"#Page_77">77</a><br />
+&mdash;&mdash;effects of this espousal, <a href=
+"#Page_77">77</a><br />
+&mdash;&mdash;his idea of gravitation, <a href=
+"#Page_92">92</a><br />
+&mdash;&mdash;his errors, <a href="#Page_208">208</a><br />
+<br />
+Nicol prism, the, <a href="#Page_122">122</a><br />
+<br />
+<br />
+Ocean, colour of the, <a href="#Page_35">35</a><br />
+<a name="Page_242" id="Page_242"></a><span class="pagenum">[Pg
+242]</span><br />
+&OElig;rsted, discovers the deflection of a magnetic needle by an
+electric current, <a href="#Page_176">176</a><br />
+<br />
+Optics, science of, <a href="#Page_4">4</a><br />
+<br />
+<br />
+Pasteur referred to, <a href="#Page_219">219</a><br />
+<br />
+Physical theories, origin of, <a href="#Page_41">41-44</a><br />
+<br />
+Pigments, analysis of the action of, upon light, <a href=
+"#Page_33">33</a><br />
+&mdash;&mdash;mixture of, contrasted with mixture of lights,
+<a href="#Page_37">37</a><br />
+&mdash;&mdash;Helmholtz reveals the cause of the green in the case
+of mixed blue and yellow pigments, <a href="#Page_37">37</a><br />
+&mdash;&mdash;impurity of natural colours, <a href=
+"#Page_37">37</a><br />
+<br />
+Pitch of sound, <a href="#Page_59">59</a><br />
+<br />
+Pl&uuml;cker, his drawings of spectra, <a href=
+"#Page_202">202</a><br />
+<br />
+Polariscope, stained glass in the, 130,<a href=
+"#Page_131">131</a><br />
+&mdash;&mdash;unannealed glass in the, <a href=
+"#Page_136">136</a><br />
+<br />
+Polarity, notion of, how generated, <a href="#Page_93">93</a><br />
+&mdash;&mdash;atomic, <a href="#Page_93">93-96</a><br />
+&mdash;&mdash;structural arrangements due to, <a href=
+"#Page_96">96</a><br />
+&mdash;&mdash;polarization of light, <a href=
+"#Page_112">112</a><br />
+&mdash;&mdash;tested by tourmaline, <a href=
+"#Page_116">116</a><br />
+&mdash;&mdash;and by reflection and refraction, <a href=
+"#Page_119">119</a><br />
+&mdash;&mdash;depolarization, <a href="#Page_120">120</a><br />
+<br />
+Polarization of light, <a href="#Page_112">112</a><br />
+&mdash;&mdash;circular, <a href="#Page_140">140</a><br />
+&mdash;&mdash;sky-light, <a href="#Page_149">149</a>, <a href=
+"#Page_157">157</a><br />
+&mdash;&mdash;of artificial sky, <a href="#Page_156">156</a><br />
+&mdash;&mdash;of radiant heat, <a href="#Page_180">180</a><br />
+<br />
+Polarizer and analyzer, <a href="#Page_127">127</a><br />
+<br />
+Poles of a magnet, <a href="#Page_93">93</a><br />
+<br />
+Powell, Professor, on polarization of heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Prism, the Nicol, <a href="#Page_122">122</a><br />
+<br />
+<br />
+Quartz, chromatic phenomena produced by, <a href=
+"#Page_139">139</a><br />
+<br />
+<br />
+Radiant heat, <a href="#Page_172">172</a><br />
+&mdash;&mdash;diathermancy, or perviousness to radiant heat,
+<a href="#Page_173">173</a><br />
+&mdash;&mdash;conversion of heat-rays into light rays, <a href=
+"#Page_174">174</a><br />
+&mdash;&mdash;formation of invisible heat-images, <a href=
+"#Page_179">179</a><br />
+&mdash;&mdash;polarization of, <a href="#Page_180">180</a><br />
+&mdash;&mdash;double refraction, <a href="#Page_182">182</a><br />
+&mdash;&mdash;magnetization of, <a href="#Page_184">184</a><br />
+<br />
+Rainbow, Descartes' explanation of the, <a href=
+"#Page_24">24</a><br />
+<br />
+Refraction, demonstration of, <a href="#Page_14">14</a><br />
+<br />
+Refraction of light, <a href="#Page_106">106</a><br />
+&mdash;&mdash;double, <a href="#Page_109">109</a><br />
+<br />
+Reflection, partial and total, <a href="#Page_20">16-20</a><br />
+<br />
+Respighi, results obtained by, <a href="#Page_205">205</a><br />
+<br />
+Ritter, his discovery of the ultraviolet rays of the sun, <a href=
+"#Page_159">159</a><br />
+<br />
+Roemer, Olav, his observations of Jupiter's moons, <a href=
+"#Page_20">20</a><br />
+&mdash;&mdash;his determination of the velocity of light, <a href=
+"#Page_21">21</a><br />
+<br />
+Rubidium, discovery of, <a href="#Page_193">193</a><br />
+<br />
+Rusting of iron, what it is, <a href="#Page_5">5</a><br />
+<br />
+<br />
+Schwerd, his observations respecting diffraction, <a href=
+"#Page_87">87</a><br />
+<br />
+Science, growth of, <a href="#Page_176">176</a>, <a href=
+"#Page_203">203</a><br />
+<br />
+Scoresby, Dr., succeeds in exploding gunpowder by the sun's rays
+conveyed by large lenses of ice, <a href="#Page_167">167</a><br />
+<br />
+Secchi, results obtained by, <a href="#Page_205">205</a><br />
+<br />
+Seebeck, Thomas, discovers thermo-electricity, <a href=
+"#Page_176">176</a><br />
+&mdash;&mdash;discovers the polarization of light by tourmaline,
+<a href="#Page_208">208</a><br />
+<br />
+Selenite, experiments with thick and thin plates of, <a href=
+"#Page_124">124</a><br />
+<a name="Page_243" id="Page_243"></a><span class="pagenum">[Pg
+243]</span><br />
+Silver spectrum, analysis of, <a href="#Page_190">190</a>, <a href=
+"#Page_191">191</a><br />
+<br />
+Sky-light, colour and polarization of, <a href="#Page_149">149</a>,
+<a href="#Page_154">154</a><br />
+&mdash;&mdash;generation of artificial skies, <a href=
+"#Page_152">152</a><br />
+<br />
+Snell, Willebrord, his discovery, <a href="#Page_14">14</a><br />
+&mdash;&mdash;his law, <a href="#Page_15">15</a>, <a href=
+"#Page_24">24</a><br />
+<br />
+Soap-bubbles and their colours, <a href="#Page_63">63</a>, <a href=
+"#Page_65">65</a><br />
+<br />
+Sound, early notions of the ancients respecting, <a href=
+"#Page_51">51</a><br />
+&mdash;&mdash;interference of waves of, <a href=
+"#Page_58">58</a><br />
+&mdash;&mdash;pitch of, <a href="#Page_59">59</a><br />
+&mdash;&mdash;analogies of light and, <a href=
+"#Page_56">56</a><br />
+&mdash;&mdash;demonstration of analogy between, and light, <a href=
+"#Page_198">198</a>, <a href="#Page_199">199</a><br />
+<br />
+Sonorous vibrations, action of, <a href="#Page_134">134</a><br />
+<br />
+Spectrum analysis, principles of, <a href="#Page_189">189</a><br />
+<br />
+Spectra of incandescent vapours, <a href="#Page_190">190</a><br />
+&mdash;&mdash;discontinuous, <a href="#Page_191">191</a>, <a href=
+"#Page_192">192</a><br />
+&mdash;&mdash;of polarized light, <a href="#Page_227">227</a><br />
+<br />
+Spectrum bands proved by Bunsen and Kirchhoff to be characteristic
+of the vapour, <a href="#Page_192">192</a><br />
+&mdash;&mdash;its capacity as an agent of discovery, <a href=
+"#Page_193">193</a><br />
+&mdash;&mdash;analysis of the sun and stars, <a href=
+"#Page_193">193</a><br />
+<br />
+Spottiswoode, Mr. William, <a href="#Page_123">123</a>, <a href=
+"#Page_227">227</a><br />
+<br />
+Stewart, Professor Balfour, <a href="#Page_202">202</a><br />
+<br />
+Stokes, Professor, results of his examination of substances excited
+by the ultra-violet waves, <a href="#Page_161">161</a><br />
+&mdash;&mdash;his discovery of fluorescence, <a href=
+"#Page_162">162</a><br />
+&mdash;&mdash;on fluorescence, <a href="#Page_165">165</a><br />
+&mdash;&mdash;nearly anticipates Kirchhoff's discovery, <a href=
+"#Page_198">198</a>, <a href="#Page_202">202</a><br />
+<br />
+Striated surfaces, colours of, <a href="#Page_89">89</a><br />
+<br />
+Sulphate of quinine first noticed and described by Sir John
+Herschel, <a href="#Page_165">165</a><br />
+<br />
+Sun, chemistry of the, <a href="#Page_195">195</a><br />
+<br />
+Sun, rose-coloured solar prominences, <a href=
+"#Page_204">204</a><br />
+<br />
+<br />
+Talbot, Mr., his experiments, <a href="#Page_201">201</a><br />
+<br />
+Tartaric acid, irregular crystallization of, and its effects,
+<a href="#Page_131">131</a><br />
+<br />
+Thallene, its effect on the spectrum, <a href=
+"#Page_162">162</a><br />
+<br />
+Thallium, spectrum analysis of, <a href="#Page_190">190</a>,
+<a href="#Page_191">191</a><br />
+&mdash;&mdash;discovery of, <a href="#Page_193">193</a><br />
+&mdash;&mdash;isolated in ingots by M. Lamy, <a href=
+"#Page_193">193</a><br />
+<br />
+Theory, relation of, to experience, <a href="#Page_91">91</a><br />
+<br />
+Thermo-electric pile, <a href="#Page_176">176</a><br />
+<br />
+Thermo-electricity, discovery of, <a href="#Page_176">176</a><br />
+<br />
+Tombeline, Mont, inverted image of, <a href="#Page_19">19</a><br />
+<br />
+Tourmaline, polarization of light by means of, <a href=
+"#Page_112">112</a><br />
+<br />
+Transmitted light, reason for, <a href="#Page_77">77</a><br />
+<br />
+Transparency, remarks on, <a href="#Page_167">167</a><br />
+<br />
+<br />
+Ultra-violet sun-rays, discovered by Ritter, <a href=
+"#Page_159">159</a><br />
+&mdash;&mdash;effects of, <a href="#Page_160">160</a><br />
+<br />
+Ultra-red rays of the solar spectrum, <a href=
+"#Page_171">171</a><br />
+&mdash;&mdash;part played by the, <a href="#Page_173">173</a><br />
+<br />
+Undulatory theory of light, bases of the, <a href=
+"#Page_47">47</a><br />
+&mdash;&mdash;Sir David Brewster's chief objection to the, <a href=
+"#Page_47">47</a><br />
+<br />
+Undulatory theory of light, Young's foundation of the, <a href=
+"#Page_49">49</a><br />
+<a name="Page_244" id="Page_244"></a><span class="pagenum">[Pg
+244]</span> &mdash;&mdash;phenomena which first suggested the,
+<a href="#Page_62">62</a>, <a href="#Page_69">69</a><br />
+&mdash;&mdash;Mr. Mill's scepticism regarding the, <a href=
+"#Page_143">143</a><br />
+&mdash;&mdash;a demonstrated verity in the hands of Young, <a href=
+"#Page_210">210</a><br />
+<br />
+<br />
+Vassenius describes the rose-coloured solar prominences in 1733,
+<a href="#Page_204">204</a><br />
+<br />
+Vitellio, his skill and conscientiousness, <a href=
+"#Page_14">14</a><br />
+&mdash;&mdash;his investigations respecting light, <a href=
+"#Page_207">207</a><br />
+<br />
+Voltaic battery, use of, and its production of heat, <a href=
+"#Page_6">6</a>, <a href="#Page_7">7</a><br />
+<br />
+<br />
+Water, deportment of, considered and explained, <a href=
+"#Page_105">105</a>, <a href="#Page_106">106</a><br />
+<br />
+Waves of water, <a href="#Page_51">51</a><br />
+&mdash;&mdash;length of a wave, <a href="#Page_52">52</a><br />
+&mdash;&mdash;interference of waves, <a href=
+"#Page_53">53-55</a><br />
+<br />
+Wertheim, M., his instrument for the determination of strains and
+pressures by the colours of polarized light, <a href=
+"#Page_134">134</a><br />
+<br />
+Wheatstone, Sir Charles, his analysis of the light of the electric
+spark, <a href="#Page_202">202</a><br />
+<br />
+Whirlpool Rapids, illustration of the principle of the interference
+of waves at the, <a href="#Page_55">55</a><br />
+<br />
+Willigen, Van der, his drawings of spectra, <a href=
+"#Page_202">202</a><br />
+<br />
+Wollaston, Dr., first observes lines in solar spectrum, <a href=
+"#Page_193">193</a><br />
+&mdash;&mdash;discovers the rings of Iceland spar, <a href=
+"#Page_209">209</a><br />
+<br />
+Woodbury, Mr., on the impurity of natural colours, <a href=
+"#Page_37">37</a><br />
+<br />
+W&uuml;nsch, Christian Ernst, on the three simple colours in white
+lights, <a href="#Page_39">39</a> <a href=
+"#Footnote_8_8"><i>note</i></a><br />
+&mdash;&mdash;his experiments, <a href="#Page_39">39</a> <a href=
+"#Footnote_8_8"><i>note</i></a><br />
+<br />
+<br />
+Young, Dr. Thomas, his discovery of Egyptian hieroglyphics,
+<a href="#Page_49">49</a><br />
+&mdash;&mdash;and the undulatory theory of light, <a href=
+"#Page_49">49</a><br />
+&mdash;&mdash;Helmholtz's estimate of him, <a href=
+"#Page_50">50</a><br />
+&mdash;&mdash;ridiculed by Brougham in the 'Edinburgh Review,'
+<a href="#Page_50">50</a><br />
+&mdash;&mdash;generalizes Grimaldi's observation on light, <a href=
+"#Page_56">56</a>, <a href="#Page_57">57</a><br />
+&mdash;&mdash;photographs the ultra-violet rings of Newton,
+<a href="#Page_160">160</a><br /></div>
+
+<div>*** END OF THE PROJECT GUTENBERG EBOOK 14000 ***</div>
+</body>
+</html>
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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #14000 (https://www.gutenberg.org/ebooks/14000)
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+The Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Six Lectures on Light
+       Delivered In The United States In 1872-1873
+
+Author: John Tyndall
+
+Release Date: November 10, 2004 [EBook #14000]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK SIX LECTURES ON LIGHT ***
+
+
+
+
+Produced by Clare Boothby, Stephen Schulze and the PG Online
+Distributed Proofreading Team.
+
+
+
+
+
+
+
+
+
+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
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
+
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+
+The Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Six Lectures on Light
+       Delivered In The United States In 1872-1873
+
+Author: John Tyndall
+
+Release Date: November 10, 2004 [EBook #14000]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK SIX LECTURES ON LIGHT ***
+
+
+
+
+Produced by Clare Boothby, Stephen Schulze and the PG Online
+Distributed Proofreading Team.
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+</pre>
+
+<h1>SIX LECTURES ON LIGHT</h1>
+<h4>DELIVERED IN THE UNITED STATES</h4>
+<h5>IN</h5>
+<h4>1872-1873</h4>
+<h3>BY</h3>
+<h2>JOHN TYNDALL, D.C.L., LL,D., F.R.S.</h2>
+<p class="center">LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE ROYAL
+INSTITUTION OF GREAT BRITAIN<br />
+<br />
+<br /></p>
+<div class="figcenter" style="width: 505px;"><img src=
+"images/frontispiece.jpg" width="505" height="659" alt=
+"Sir Thomas Laurence PRA Pinx Henry Adlarc. Sc." title=
+"Sir Thomas Laurence PRA Pinx Henry Adlarc. Sc." /></div>
+<div class="figcenter" style="width: 420px;"><img src=
+"images/sig.png" width="420" height="105" alt=
+"(Signature) Thomas Young" title="" /></div>
+<p class="center">London: Longmans &amp; Co.</p>
+<p class="center"><i>SIXTH IMPRESSION</i></p>
+<p class="center">LONGMANS, GREEN, AND CO.</p>
+<p class="center">39 PATERNOSTER ROW, LONDON</p>
+<p class="center">NEW YORK AND BOMBAY</p>
+<p class="center">1906</p>
+<h3>PREFACE TO THE FOURTH EDITION.</h3>
+<p>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.</p>
+<p>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.</p>
+<p>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.</p>
+<p>J.T.</p>
+<p style="text-align: right;">ALP LUSGEN: <i>October</i> 1885.</p>
+<hr style="width: 65%;" />
+<h2><a name="CONTENTS" id="CONTENTS"></a>CONTENTS.</h2>
+<div style="margin-left: 20%; margin-right: 20%">
+<p><a href="#LECTURE_I"><b>LECTURE I.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Introductory</li>
+<li>Uses of Experiment</li>
+<li>Early Scientific Notions</li>
+<li>Sciences of Observation</li>
+<li>Knowledge of the Ancients regarding Light</li>
+<li>Defects of the Eye</li>
+<li>Our Instruments</li>
+<li>Rectilineal Propagation of Light</li>
+<li>Law of Incidence and Reflection</li>
+<li>Sterility of the Middle Ages</li>
+<li>Refraction</li>
+<li>Discovery of Snell</li>
+<li>Partial and Total Reflection</li>
+<li>Velocity of Light</li>
+<li>Roemer, Bradley, Foucault, and Fizeau</li>
+<li>Principle of Least Action</li>
+<li>Descartes and the Rainbow</li>
+<li>Newton's Experiments on the Composition of Solar Light</li>
+<li>His Mistake regarding Achromatism</li>
+<li>Synthesis of White Light</li>
+<li>Yellow and Blue Lights produce White by their Mixture</li>
+<li>Colours of Natural Bodies</li>
+<li>Absorption</li>
+<li>Mixture of Pigments contrasted with Mixture of Lights</li>
+</ul>
+</div>
+<p><a href="#LECTURE_II"><b>LECTURE II.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Origin of Physical Theories</li>
+<li>Scope of the Imagination</li>
+<li>Newton and the Emission Theory</li>
+<li>Verification of Physical Theories</li>
+<li>The Luminiferous Ether</li>
+<li>Wave-theory of Light</li>
+<li>Thomas Young</li>
+<li>Fresnel and Arago</li>
+<li>Conception of Wave-motion</li>
+<li>Interference of Waves</li>
+<li>Constitution of Sound-waves</li>
+<li>Analogies of Sound and Light</li>
+<li>Illustrations of Wave-motion</li>
+<li>Interference of Sound Waves</li>
+<li>Optical Illustrations</li>
+<li>Pitch and Colour</li>
+<li>Lengths of the Waves of Light and Rates of Vibration of
+the</li>
+<li>Ether-particles</li>
+<li>Interference of Light</li>
+<li>Phenomena which first suggested the Undulatory Theory</li>
+<li>Boyle and Hooke</li>
+<li>The Colours of thin Plates</li>
+<li>The Soap-bubble</li>
+<li>Newton's Rings</li>
+<li>Theory of 'Fits'</li>
+<li>Its Explanation of the Rings</li>
+<li>Overthrow of the Theory</li>
+<li>Diffraction of Light</li>
+<li>Colours produced by Diffraction</li>
+<li>Colours of Mother-of-Pearl.</li>
+</ul>
+</div>
+<p><a href="#LECTURE_III"><b>LECTURE III.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Relation of Theories to Experience</li>
+<li>Origin of the Notion of the Attraction of Gravitation</li>
+<li>Notion of Polarity, how generated</li>
+<li>Atomic Polarity</li>
+<li>Structural Arrangements due to Polarity</li>
+<li>Architecture of Crystals considered as an Introduction to
+their</li>
+<li>Action upon Light</li>
+<li>Notion of Atomic Polarity applied to Crystalline Structure</li>
+<li>Experimental Illustrations</li>
+<li>Crystallization of Water</li>
+<li>Expansion by Heat and by Cold</li>
+<li>Deportment of Water considered and explained</li>
+<li>Bearings of Crystallization on Optical Phenomena</li>
+<li>Refraction</li>
+<li>Double Refraction</li>
+<li>Polarization</li>
+<li>Action of Tourmaline</li>
+<li>Character of the Beams emergent from Iceland Spar</li>
+<li>Polarization by ordinary Refraction and Reflection</li>
+<li>Depolarization.</li>
+</ul>
+</div>
+<p><a href="#LECTURE_IV"><b>LECTURE IV.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Chromatic Phenomena produced by Crystals in Polarized
+Light</li>
+<li>The Nicol Prism</li>
+<li>Polarizer and Analyzer</li>
+<li>Action of Thick and Thin Plates of Selenite</li>
+<li>Colours dependent on Thickness</li>
+<li>Resolution of Polarized Beam into two others by the
+Selenite</li>
+<li>One of them more retarded than the other</li>
+<li>Recompounding of the two Systems of Waves by the Analyzer</li>
+<li>Interference thus rendered possible</li>
+<li>Consequent Production of Colours</li>
+<li>Action of Bodies mechanically strained or pressed</li>
+<li>Action of Sonorous Vibrations</li>
+<li>Action of Glass strained or pressed by Heat</li>
+<li>Circular Polarization</li>
+<li>Chromatic Phenomena produced by Quartz</li>
+<li>The Magnetization of Light</li>
+<li>Rings surrounding the Axes of Crystals</li>
+<li>Biaxal and Uniaxal Crystals</li>
+<li>Grasp of the Undulatory Theory</li>
+<li>The Colour and Polarization of Sky-light</li>
+<li>Generation of Artificial Skies.</li>
+</ul>
+</div>
+<p><a href="#LECTURE_V"><b>LECTURE V.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Range of Vision not commensurate with Range of Radiation</li>
+<li>The Ultra-violet Rays</li>
+<li>Fluorescence</li>
+<li>The rendering of invisible Rays visible</li>
+<li>Vision not the only Sense appealed to by the Solar and Electric
+Beam</li>
+<li>Heat of Beam</li>
+<li>Combustion by Total Beam at the Foci of Mirrors and Lenses</li>
+<li>Combustion through Ice-lens</li>
+<li>Ignition of Diamond</li>
+<li>Search for the Rays here effective</li>
+<li>Sir William Herschel's Discovery of dark Solar Rays</li>
+<li>Invisible Rays the Basis of the Visible</li>
+<li>Detachment by a Ray-filter of the Invisible Rays from the
+Visible</li>
+<li>Combustion at Dark Foci</li>
+<li>Conversion of Heat-rays into Light-rays</li>
+<li>Calorescence</li>
+<li>Part played in Nature by Dark Rays</li>
+<li>Identity of Light and Radiant Heat</li>
+<li>Invisible Images</li>
+<li>Reflection, Refraction, Plane Polarization, Depolarization,
+Circular Polarization, Double Refraction, and Magnetization of
+Radiant Heat</li>
+</ul>
+</div>
+<p><a href="#LECTURE_VI"><b>LECTURE VI.</b></a></p>
+<div style="font-size: smaller;">
+<ul>
+<li>Principles of Spectrum Analysis</li>
+<li>Prismatic Analysis of the Light of Incandescent Vapours</li>
+<li>Discontinuous Spectra</li>
+<li>Spectrum Bands proved by Bunsen and Kirchhoff to be
+characteristic of the Vapour</li>
+<li>Discovery of Rubidium, C&aelig;sium, and Thallium</li>
+<li>Relation of Emission to Absorption</li>
+<li>The Lines of Fraunhofer</li>
+<li>Their Explanation by Kirchhoff</li>
+<li>Solar Chemistry involved in this Explanation</li>
+<li>Foucault's Experiment</li>
+<li>Principles of Absorption</li>
+<li>Analogy of Sound and Light</li>
+<li>Experimental Demonstration of this Analogy</li>
+<li>Recent Applications of the Spectroscope</li>
+<li>Summary and Conclusion</li>
+</ul>
+</div>
+<p><a href="#APPENDIX"><b>APPENDIX.</b></a></p>
+<div style="margin-left: 2em;">
+<p><a href="#ON_THE_SPECTRA_OF_POLARIZED_LIGHT">On the Spectra of
+Polarized Light</a></p>
+<p><a href="#MEASUREMENT_OF_THE_WAVES_OF_LIGHT">Measurement of the
+Waves of Light</a></p>
+</div>
+<p><a href="#INDEX"><b>INDEX.</b></a></p>
+</div>
+<div><a name="Page_1" id="Page_1"></a><span class="pagenum">[Pg
+1]</span></div>
+<hr style="width: 65%;" />
+<h1>ON LIGHT</h1>
+<h2><a name="LECTURE_I" id="LECTURE_I"></a>LECTURE I.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>INTRODUCTORY</li>
+<li>USES OF EXPERIMENT</li>
+<li>EARLY SCIENTIFIC NOTIONS</li>
+<li>SCIENCES OF OBSERVATION</li>
+<li>KNOWLEDGE OF THE ANCIENTS REGARDING LIGHT</li>
+<li>DEFECTS OF THE EYE</li>
+<li>OUR INSTRUMENTS</li>
+<li>RECTILINEAL PROPAGATION OF LIGHT</li>
+<li>LAW OF INCIDENCE AND REFLECTION</li>
+<li>STERILITY OF THE MIDDLE AGES</li>
+<li>REFRACTION</li>
+<li>DISCOVERY OF SNELL</li>
+<li>PARTIAL AND TOTAL REFLECTION</li>
+<li>VELOCITY OF LIGHT</li>
+<li>ROEMER, BRADLEY, FOUCAULT, AND FIZEAU</li>
+<li>PRINCIPLE OF LEAST ACTION</li>
+<li>DESCARTES AND THE RAINBOW</li>
+<li>NEWTON'S EXPERIMENTS ON THE COMPOSITION OF SOLAR LIGHT</li>
+<li>HIS MISTAKE AS REGARDS ACHROMATISM</li>
+<li>SYNTHESIS OF WHITE LIGHT</li>
+<li>YELLOW AND BLUE LIGHTS PRODUCE WHITE BY THEIR MIXTURE</li>
+<li>COLOURS OF NATURAL BODIES</li>
+<li>ABSORPTION</li>
+<li>MIXTURE OF PIGMENTS CONTRASTED WITH MIXTURE OF LIGHTS.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Introduction</i>.</h3>
+<p>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<a name="FNanchor_1_1" id=
+"FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a>
+who deemed it good for neither world to be isolated from the other,
+<a name="Page_2" id="Page_2"></a><span class="pagenum">[Pg
+2]</span>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.</p>
+<p>The works here referred to were, for the most part, republished
+by the Messrs. Appleton of New York,<a name="FNanchor_2_2" id=
+"FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a>
+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<a name=
+"FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class=
+"fnanchor">[3]</a> 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.</p>
+<p>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 <a name="Page_3" id="Page_3"></a><span class=
+"pagenum">[Pg 3]</span>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.</p>
+<h3>&sect; 2. <i>Subject of the Course. Source of Light
+employed.</i></h3>
+<p>Experiments have two great uses&mdash;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.</p>
+<p>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 <a name=
+"Page_4" id="Page_4"></a><span class="pagenum">[Pg 4]</span>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.</p>
+<p>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 <i>causality</i>&mdash;the assumption that
+natural things did not come of themselves, but had unseen
+antecedents&mdash;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.</p>
+<p>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&mdash;and that historically a
+long one&mdash;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 <a name="Page_5" id="Page_5"></a><span class=
+"pagenum">[Pg 5]</span>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.</p>
+<p>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
+<i>experiment</i>, 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.</p>
+<p>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 <a name="Page_6" id=
+"Page_6"></a><span class="pagenum">[Pg 6]</span>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.</p>
+<p>The generation of this light and of this heat merits a moment's
+attention. Before you is an instrument&mdash;a small voltaic
+battery&mdash;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.</p>
+<p>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 <a name="Page_7"
+id="Page_7"></a><span class="pagenum">[Pg 7]</span>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.</p>
+<div class="figcenter" style="width: 444px;"><img src=
+"images/fig01.jpg" width="444" height="307" alt="Fig. 1." title=
+"" /> <b>Fig. 1.</b></div>
+<p>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 <a name="Page_8" id=
+"Page_8"></a><span class="pagenum">[Pg 8]</span>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.</p>
+<p>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 <i>towards</i> 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 <i>whole</i> 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 <i>spherical aberration</i>, 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&mdash;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 <a name="Page_9" id="Page_9"></a><span class=
+"pagenum">[Pg 9]</span>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.</p>
+<h3>&sect; 3. <i>Rectilineal Propagation of Light. Elementary
+Experiments. Law of Reflection.</i></h3>
+<p>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 <i>air</i> 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.</p>
+<div class="figleft" style="width: 445px;"><img src=
+"images/fig02.jpg" width="445" height="250" alt="Fig. 2." title=
+"" /> <b>Fig. 2.</b></div>
+<p>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 <a name="Page_10"
+id="Page_10"></a><span class="pagenum">[Pg 10]</span>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.</p>
+<div class="figright" style="width: 475px;"><img src=
+"images/fig03.jpg" width="475" height="311" alt="Fig. 3." title=
+"" /> <b>Fig. 3.</b></div>
+<p>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 <a name="Page_11" id="Page_11"></a><span class=
+"pagenum">[Pg 11]</span>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 <i>o</i>,
+<i>o</i> 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 <i>m</i> is found accurately equal
+to the arc from 5 to <i>n</i>. 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.</p>
+<p>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 <a name="Page_12" id=
+"Page_12"></a><span class="pagenum">[Pg 12]</span>reflected from it
+is twice that of the reflecting mirror. A simple experiment will
+make this plain. The arc (<i>m n</i>, 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.</p>
+<p>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
+demon<a name="Page_13" id="Page_13"></a><span class="pagenum">[Pg
+13]</span>strated. 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.</p>
+<h3>&sect; 4. <i>The Refraction of Light. Total
+Reflection.</i></h3>
+<p>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
+<i>&agrave; priori</i> 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&mdash;'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;&mdash;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.'</p>
+<p>As regards the refraction of light, the course of <a name=
+"Page_14" id="Page_14"></a><span class="pagenum">[Pg 14]</span>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.</p>
+<p>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 <a name="Page_15" id=
+"Page_15"></a><span class="pagenum">[Pg 15]</span>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 <i>reflection</i> (along O R) accompanies refraction, the beam
+dividing itself at the point of incidence into a refracted and a
+reflected portion.<a name="FNanchor_4_4" id=
+"FNanchor_4_4"></a><a href="#Footnote_4_4" class=
+"fnanchor">[4]</a></p>
+<div class="figright" style="width: 450px;"><img src=
+"images/fig04.jpg" width="450" height="254" alt="Fig. 4." title=
+"" /> <b>Fig. 4.</b></div>
+<p>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 <i>m</i> E, there
+is refraction: it is bent at E and strikes the <a name="Page_16"
+id="Page_16"></a><span class="pagenum">[Pg 16]</span>circle at
+<i>n</i>. When it is incident along <i>m'</i> E there is also
+refraction at E, the beam striking the point <i>n'</i>. From the
+ends of the two incident beams, let the perpendiculars <i>m</i>
+<i>o</i>, <i>m'</i> <i>o'</i> be drawn upon B D, and from the ends
+of the refracted beams let the perpendiculars <i>p</i> <i>n</i>,
+<i>p'</i> <i>n'</i> be also drawn. Measure the lengths of <i>o
+m</i> and of <i>p</i> <i>n</i>, and divide the one by the other.
+You obtain a certain quotient. In like manner divide <i>m'</i>
+<i>o'</i> by the corresponding perpendicular <i>p'</i> <i>n'</i>;
+you obtain precisely the same quotient. Snell, in fact, found this
+quotient to be <i>a constant quantity</i> for each particular
+substance, though it varied in amount from one substance to
+another. He called the quotient the <i>index of refraction</i>.</p>
+<div class="figleft" style="width: 253px;"><img src=
+"images/fig05.jpg" width="253" height="253" alt="Fig. 5" title=
+"" /> <b>Fig. 5</b></div>
+<p>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 <i>partial</i>. In this case
+the most powerfully reflecting substances either transmit or absorb
+a portion of the incident light. At a perpendicular incidence
+<a name="Page_17" id="Page_17"></a><span class="pagenum">[Pg
+17]</span>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&deg;, for example, water reflects 22 rays, at
+60&deg; it reflects 65 rays, at 80&deg; 333 rays; while at an
+incidence of 89&frac12;&deg;, 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,
+<i>total</i>.</p>
+<p>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&mdash;the principle of reversibility.<a name=
+"FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class=
+"fnanchor">[5]</a> In the case of refraction, for instance, when
+the ray passes obliquely from air into water, it is bent
+<i>towards</i> the perpendicular; when it passes from water to air,
+it is bent <i>from</i> the perpendicular, and accurately reverses
+its course. Thus in fig. 5, if <i>m</i> E <i>n</i> be the track of
+a ray in passing from air into water, <i>n</i> E <i>m</i> 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 <i>m</i> E or <i>m&prime;</i> 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 <a name="Page_18" id="Page_18"></a><span class=
+"pagenum">[Pg 18]</span>pursue say the course E <i>n</i>&Prime;.
+Conversely, if the light start from <i>n</i>&Prime;, 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
+<i>n</i>&#8244; E, which lies beyond <i>n</i>&Prime; E? The answer
+is, it will not quit the water at all, but will be <i>totally</i>
+reflected (along E <i>x</i>). 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 <i>n</i>&#8244;) being equal to the angle
+of reflection (D E <i>x</i>).</p>
+<div class="figright" style="width: 252px;"><img src=
+"images/fig06.jpg" width="252" height="243" alt="Fig. 6" title=
+"" /> <b>Fig. 6</b></div>
+<p>Total reflection may be thus simply illustrated:&mdash;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
+<a name="Page_19" id="Page_19"></a><span class="pagenum">[Pg
+19]</span>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.</p>
+<p>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.</p>
+<p>The angle which marks the limit beyond which total reflection
+takes place is called the <i>limiting angle</i> (it is marked in
+fig. 6 by the strong line E <i>n</i>&Prime;). It must evidently
+diminish as the refractive index increases. For water it is
+48&frac12;&deg;, for flint glass 38&deg;41', and for diamond
+23&deg;42'. Thus all the light incident from two complete
+quadrants, or 180&deg;, in the case of diamond, is condensed into
+an angular space of 47&deg;22' (twice 23&deg;42') by refraction.
+Coupled with its great refraction, are <a name="Page_20" id=
+"Page_20"></a><span class="pagenum">[Pg 20]</span>the great
+dispersive and great reflective powers of diamond; hence the
+extraordinary radiance of the gem, both as regards white light and
+prismatic light.</p>
+<h3>&sect; 5. <i>Velocity of Light. Aberration. Principle of least
+Action.</i></h3>
+<p>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.</p>
+<p>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.</p>
+<p>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
+<a name="Page_21" id="Page_21"></a><span class="pagenum">[Pg
+21]</span>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.'</p>
+<p>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.</p>
+<p>The velocity of light, as determined by Roemer, is 192,500 miles
+in a second.</p>
+<p>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 <a name="Page_22" id=
+"Page_22"></a><span class="pagenum">[Pg 22]</span>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.'</p>
+<p>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&mdash;a man of the
+rarest mechanical genius&mdash;solved the problem without quitting
+<a name="Page_23" id="Page_23"></a><span class="pagenum">[Pg
+23]</span>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.</p>
+<p>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 <i>least time</i>. 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.</p>
+<div><a name="Page_24" id="Page_24"></a><span class="pagenum">[Pg
+24]</span></div>
+<h3>&sect; 6. <i>Descartes' Explanation of the Rainbow</i>.</h3>
+<p>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.</p>
+<p>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 42&frac12;&deg; 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 42&frac12;&deg; 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.</p>
+<p>From the eye of the observer conceive another line to be drawn,
+enclosing an angle, not of 42&frac12;&deg;, but of 40&frac12;&deg;,
+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. <a name=
+"Page_25" id="Page_25"></a><span class="pagenum">[Pg
+25]</span>These two bands constitute the limiting colours of the
+rainbow, and between them the bands corresponding to the other
+colours lie.</p>
+<p>Thus the line drawn from the eye to the <i>middle</i> of the
+bow, and the line drawn through the eye to the sun, always enclose
+an angle of about 41&deg;. To account for this was the great
+difficulty, which remained unsolved up to the time of
+Descartes.</p>
+<p>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 <i>almost parallel to each other</i>. They were thus
+enabled to preserve their intensity through long atmospheric
+distances. At all other angles the rays quitted the drop
+<i>divergent</i>, 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.</p>
+<p>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&mdash;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
+<a name="Page_26" id="Page_26"></a><span class="pagenum">[Pg
+26]</span>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&mdash;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 <i>image</i> of the bow seen in the
+sky.</p>
+<h3>&sect; 7. <i>Analysis and Synthesis of Light. Doctrine of
+Colours</i>.</h3>
+<p>In the rainbow a new phenomenon was introduced&mdash;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 <i>composite</i>, not simple.
+His elongated image <a name="Page_27" id="Page_27"></a><span class=
+"pagenum">[Pg 27]</span>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.</p>
+<p>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 <i>spectrum</i>. Newton divided the spectrum into seven
+parts&mdash;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 <i>dispersion</i>.</p>
+<div class="figcenter" style="width: 443px;"><img src=
+"images/fig07.jpg" width="443" height="303" alt="Fig. 7." title=
+"" /> <b>Fig. 7.</b></div>
+<p>This was the first <i>analysis</i> of solar light by Newton;
+<a name="Page_28" id="Page_28"></a><span class="pagenum">[Pg
+28]</span>but the scientific mind is fond of verification, and
+never neglects it where it is possible. Newton completed his proof
+by <i>synthesis</i> 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.</p>
+<div class="figcenter" style="width: 430px;"><img src=
+"images/fig08.jpg" width="430" height="321" alt="Fig. 8." title=
+"" /> <b>Fig. 8.</b></div>
+<p>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&mdash;lenses yielding no colour&mdash;which Newton thought
+an impossi<a name="Page_29" id="Page_29"></a><span class=
+"pagenum">[Pg 29]</span>bility. By setting a
+water-prism&mdash;water contained in a wedge-shaped vessel with
+glass sides (B, fig. 8)&mdash;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 <i>white</i>; but though the dispersion is abolished, there
+remains a very sensible amount of refraction.</p>
+<p>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.<a name="FNanchor_6_6"
+id="FNanchor_6_6"></a><a href="#Footnote_6_6" class=
+"fnanchor">[6]</a></p>
+<div class="figcenter" style="width: 445px;"><img src=
+"images/fig09.jpg" width="445" height="305" alt="Fig. 9." title=
+"" /> <b>Fig. 9.</b></div>
+<p><a name="Page_30" id="Page_30"></a><span class="pagenum">[Pg
+30]</span>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 <a name="Page_31" id=
+"Page_31"></a><span class="pagenum">[Pg 31]</span>leave the
+residual portion. On the screen are now two coloured rectangles
+produced in this way. These are <i>complementary</i>
+colours&mdash;colours which, by their union, produce white. Note,
+that by judicious management, one of these colours is rendered
+<i>yellow</i>, and the other <i>blue</i>. I withdraw the thin
+prism; yellow and blue immediately commingle, and we have
+<i>white</i> as the result of their union. On our way, then, we
+remove the fallacy, first exposed by W&uuml;nsch, and afterwards
+independently by Helmholtz, that the mixture of blue and yellow
+lights produces green.</p>
+<p>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.</p>
+<p>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.</p>
+<p>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
+<i>selective</i>, not <i>creative</i>. There is no colour
+<i>generated</i> 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&mdash;<a name="Page_32" id="Page_32"></a><span class=
+"pagenum">[Pg 32]</span>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.</p>
+<p>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&mdash;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.</p>
+<p>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 <i>negative</i>
+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 <a name=
+"Page_33" id="Page_33"></a><span class="pagenum">[Pg 33]</span>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.</p>
+<p>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</p>
+<div class="blockquot">
+<p>'Clothed in white samite, mystic, wonderful;'</p>
+</div>
+<p>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.</p>
+<h3>&sect; 8. <i>Colours of Pigments as distinguished from Colours
+of Light</i>.</h3>
+<p>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 <a name="Page_34" id="Page_34"></a><span class="pagenum">[Pg
+34]</span>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.</p>
+<p>In the case of pigments, then, the light is <i>reflected</i> at
+the limiting surfaces of the particles, but it is in part
+<i>absorbed</i> 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
+<i>through</i> 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.</p>
+<p>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 <a name="Page_35" id="Page_35"></a><span class="pagenum">[Pg
+35]</span>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.</p>
+<p>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 <i>black</i>, 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.</p>
+<p>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 <a name="Page_36" id=
+"Page_36"></a><span class="pagenum">[Pg 36]</span>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 <i>reflecting surface</i>,
+the water between the eye and it the <i>absorbing medium</i>.</p>
+<p>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.</p>
+<p>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, pro<a name="Page_37" id=
+"Page_37"></a><span class="pagenum">[Pg 37]</span>ducing white by
+their mixture. The mixture of blue and yellow <i>pigments</i>
+undoubtedly produces green, but the mixture of pigments is a
+totally different thing from the mixture of lights.</p>
+<p>Helmholtz has revealed the cause of the green produced by a
+mixture of blue and yellow pigments. No natural colour is
+<i>pure</i>. 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.</p>
+<p>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 <a name="Page_38" id=
+"Page_38"></a><span class="pagenum">[Pg 38]</span>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.</p>
+<p>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.<a name="FNanchor_7_7"
+id="FNanchor_7_7"></a><a href="#Footnote_7_7" class=
+"fnanchor">[7]</a></p>
+<p><a name="Page_39" id="Page_39"></a><span class="pagenum">[Pg
+39]</span>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,<a name="FNanchor_8_8" id=
+"FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a>
+must be highly complex.</p>
+<p><a name="Page_40" id="Page_40"></a><span class="pagenum">[Pg
+40]</span>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&mdash;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&mdash;and
+it would be mere presumption to dogmatize as to what she
+meant&mdash;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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_41" id="Page_41"></a><span class="pagenum">[Pg
+41]</span></div>
+<h2><a name="LECTURE_II" id="LECTURE_II"></a>LECTURE II.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>ORIGIN OF PHYSICAL THEORIES</li>
+<li>SCOPE OF THE IMAGINATION</li>
+<li>NEWTON AND THE EMISSION THEORY</li>
+<li>VERIFICATION OF PHYSICAL THEORIES</li>
+<li>THE LUMINIFEROUS ETHER</li>
+<li>WAVE THEORY OF LIGHT</li>
+<li>THOMAS YOUNG</li>
+<li>FRESNEL AND ARAGO</li>
+<li>CONCEPTION OF WAVE-MOTION</li>
+<li>INTERFERENCE OF WAVES</li>
+<li>CONSTITUTION OF SOUND-WAVES</li>
+<li>ANALOGIES OF SOUND AND LIGHT</li>
+<li>ILLUSTRATIONS OF WAVE-MOTION</li>
+<li>INTERFERENCE OF SOUND-WAVES</li>
+<li>OPTICAL ILLUSTRATIONS</li>
+<li>PITCH AND COLOUR</li>
+<li>LENGTHS OF THE WAVES OF LIGHT AND RATES OF VIBRATION OF</li>
+<li>THE ETHER-PARTICLES</li>
+<li>INTERFERENCE OF LIGHT</li>
+<li>PHENOMENA WHICH FIRST SUGGESTED THE UNDULATORY THEORY</li>
+<li>BOYLE AND HOOKE</li>
+<li>THE COLOURS OF THIN PLATES</li>
+<li>THE SOAP-BUBBLE</li>
+<li>NEWTON'S RINGS</li>
+<li>THEORY OF 'FITS'</li>
+<li>ITS EXPLANATION OF THE RINGS</li>
+<li>OVER-THROW OF THE THEORY</li>
+<li>DIFFRACTION OF LIGHT</li>
+<li>COLOURS PRODUCED BY DIFFRACTION</li>
+<li>COLOURS OF MOTHER-OF-PEARL.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Origin and Scope of Physical Theories</i>.</h3>
+<p>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.</p>
+<p>Let us, then, inquire what this thing is that we have been
+generating, reflecting, refracting and analyzing.</p>
+<p><a name="Page_42" id="Page_42"></a><span class="pagenum">[Pg
+42]</span>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.</p>
+<p>This conception of physical theory implies, as you perceive, the
+exercise of the imagination&mdash;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, <a name="Page_43" id=
+"Page_43"></a><span class="pagenum">[Pg 43]</span>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.<a name="FNanchor_9_9" id=
+"FNanchor_9_9"></a><a href="#Footnote_9_9" class=
+"fnanchor">[9]</a></p>
+<p>Descartes imagined space to be filled with something that
+transmitted light <i>instantaneously</i>. 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 <a name="Page_44" id=
+"Page_44"></a><span class="pagenum">[Pg 44]</span>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.</p>
+<h3>&sect; 2. <i>The Emission Theory of Light</i>.</h3>
+<p>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 <a name="Page_45" id=
+"Page_45"></a><span class="pagenum">[Pg 45]</span>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 <i>as if</i>
+light consisted of such particles, and this was Newton's
+justification for introducing them.</p>
+<p>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&mdash;say from air on to glass or water&mdash;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 <a name=
+"Page_46" id="Page_46"></a><span class="pagenum">[Pg 46]</span>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.</p>
+<p>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.</p>
+<p>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 <a name="Page_47"
+id="Page_47"></a><span class="pagenum">[Pg 47]</span>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.</p>
+<p>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.</p>
+<h3>&sect; 3. <i>The Undulatory Theory of Light</i>.</h3>
+<p>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 <i>luminiferous ether</i> 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 <a name=
+"Page_48" id="Page_48"></a><span class="pagenum">[Pg 48]</span>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.</p>
+<p>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
+<i>prove</i> 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.</p>
+<p>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 <a name="Page_49" id="Page_49"></a><span class=
+"pagenum">[Pg 49]</span>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.</p>
+<p>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 <a name="Page_50" id=
+"Page_50"></a><span class="pagenum">[Pg 50]</span>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."</p>
+<p>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&mdash;hidden from the appreciative intellect of
+his country-men&mdash;deemed in fact a dreamer, through the
+vigorous sarcasm of a writer who had then possession of the public
+ear, and who in the <i>Edinburgh Review</i> 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, especi<a name="Page_51" id="Page_51"></a><span class=
+"pagenum">[Pg 51]</span>ally 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&mdash;if it be a fact that public disbelief weakens a man's
+force&mdash;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.</p>
+<h3>&sect; 4. <i>Wave-Motion, Interference of Waves, 'Whirlpool
+Rapids' of Niagara</i>.</h3>
+<p>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.</p>
+<p>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 <a name="Page_52" id=
+"Page_52"></a><span class="pagenum">[Pg 52]</span>of the wave
+itself, and the motion of the particles which at any moment
+constitute the wave.</p>
+<p>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 <i>sinus</i> 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 <i>form</i>, and not the
+transference of the substance which constitutes the wave.</p>
+<p>The <i>length</i> of the wave is the distance from crest to
+crest, while the distance through which the individual particles
+oscillate is called the <i>amplitude</i> of the oscillation. You
+will notice that in this description the particles of water are
+made to vibrate <i>across</i> the line of propagation.<a name=
+"FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10"
+class="fnanchor">[10]</a></p>
+<p><a name="Page_53" id="Page_53"></a><span class="pagenum">[Pg
+53]</span>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 <i>still</i>
+water. This action of wave upon wave is technically called
+<i>interference</i>, a term, to be remembered.</p>
+<div class="figcenter" style="width: 438px;"><img src=
+"images/fig10.jpg" width="438" height="443" alt="Fig. 10." title=
+"" /> <b>Fig. 10.</b></div>
+<p>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 <a name="Page_54" id=
+"Page_54"></a><span class="pagenum">[Pg 54]</span>figure.<a name=
+"FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11"
+class="fnanchor">[11]</a> 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:&mdash;</p>
+<div class="poem">
+<div class="stanza"><span>'Thou can'st not wave thy staff in the
+air,<br /></span> <span class="i2">Or dip thy paddle in the
+lake,<br /></span> <span>But it carves the brow of beauty
+there.<br /></span> <span class="i2">And the ripples in rhymes the
+oars forsake.'<br /></span></div>
+</div>
+<p><a name="Page_55" id="Page_55"></a><span class="pagenum">[Pg
+55]</span>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.</p>
+<p>Two kinds of motion are here obviously active, a motion of
+translation and a motion of undulation&mdash;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.</p>
+<p>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 <i>sides</i> of
+the river. Against these the water rises and sinks rhythmically but
+violently, large waves being <a name="Page_56" id=
+"Page_56"></a><span class="pagenum">[Pg 56]</span>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.</p>
+<h3>&sect; 5. <i>Analogies of Sound and Light.</i></h3>
+<p>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
+<a name="Page_57" id="Page_57"></a><span class="pagenum">[Pg
+57]</span>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 <i>waves</i> 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.</p>
+<p>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; <a name="Page_58" id="Page_58"></a><span class="pagenum">[Pg
+58]</span>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, <i>in the direction of propagation</i>. 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
+<i>across</i> the line of propagation. The vibrations of the air
+are <i>longitudinal</i>, those of the ether <i>transversal</i>.</p>
+<p>The most familiar illustration of the interference of
+sound-waves is furnished by the <i>beats</i> 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 <a name="Page_59" id="Page_59"></a><span class=
+"pagenum">[Pg 59]</span>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 <i>half a wavelength</i> 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 <i>three half-waves</i> in advance of the other. In general
+terms, the waves conspire when the one series is an <i>even</i>
+number of half-wave lengths, and they destroy each other when the
+one series is an <i>odd</i> 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.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href=
+"#Footnote_12_12" class="fnanchor">[12]</a></p>
+<p>The <i>pitch</i> of sound is wholly determined by the rapidity
+of the vibration, as the <i>intensity</i> is by the amplitude. What
+pitch is to the ear in acoustics, colour is to the eye in the
+undulatory theory of light. <a name="Page_60" id=
+"Page_60"></a><span class="pagenum">[Pg 60]</span>Though never
+seen, the lengths of the waves of light have been determined. Their
+existence is proved <i>by their effects</i>, 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.</p>
+<p>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. <i>All these waves enter the eye, and strike the retina
+at the back of the eye in one second</i>. 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.</p>
+<p>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 <a name="Page_61" id=
+"Page_61"></a><span class="pagenum">[Pg 61]</span>other point.
+Every star declares by its light its undamaged individuality, as if
+it alone had sent its thrills through space.</p>
+<h3>&sect; 6. <i>Interference of Light</i>.</h3>
+<div class="figleft" style="width: 465px;"><img src=
+"images/fig11.jpg" width="465" height="150" alt="Fig. 11." title=
+"" /> <b>Fig. 11.</b></div>
+<p>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 <i>m</i> <i>n</i>) 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 <i>even</i> number of
+semi-undulations in advance of the other. But if the one system be
+half a wave-length (as at A' <i>a</i>', fig. 12), or any <i>odd</i>
+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 <i>lift</i> the particles of ether at the precise places where
+the other tends to <i>depress</i> them; hence, through the <a name=
+"Page_62" id="Page_62"></a><span class="pagenum">[Pg
+62]</span>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.</p>
+<div class="figright" style="width: 480px;"><img src=
+"images/fig12.jpg" width="480" height="88" alt="Fig. 12." title=
+"" /> <b>Fig. 12.</b></div>
+<p>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.</p>
+<h3>&sect; 7. <i>Colours of thin Films. Observations of Boyle and
+Hooke</i>.</h3>
+<p>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
+<i>colours of thin plates</i>. 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 <a name=
+"Page_63" id="Page_63"></a><span class="pagenum">[Pg
+63]</span>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.</p>
+<p>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.</p>
+<p>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. <a name="Page_64" id="Page_64"></a><span class=
+"pagenum">[Pg 64]</span>Different colours, therefore, must appear
+at different thicknesses of the film.</p>
+<p>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.</p>
+<p>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&mdash;black, because it is pure and of great
+depth&mdash;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 <a name="Page_65" id=
+"Page_65"></a><span class="pagenum">[Pg 65]</span>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.</p>
+<p>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:&mdash;</p>
+<p>'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 <a name="Page_66" id="Page_66"></a><span class=
+"pagenum">[Pg 66]</span>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.'<a name=
+"FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13"
+class="fnanchor">[13]</a></p>
+<p>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.'<a name=
+"FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14"
+class="fnanchor">[14]</a></p>
+<p><a name="Page_67" id="Page_67"></a><span class="pagenum">[Pg
+67]</span>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
+lamin&aelig;, 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:&mdash;</p>
+<p>'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
+<a name="Page_68" id="Page_68"></a><span class="pagenum">[Pg
+68]</span>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&mdash;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, &amp;c.</p>
+<p>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 <i>of fiery burning
+bodies</i> 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 <i>a vibrative motion.'</i> 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.</p>
+<p><a name="Page_69" id="Page_69"></a><span class="pagenum">[Pg
+69]</span>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, <i>that the
+reflection from the further or under side of the body is the
+principal cause of the production of these colours.</i>'</p>
+<p>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.</p>
+<h3>&sect; 8. <i>Newton's Rings. Relation of Colour to Thickness of
+Film</i>.</h3>
+<div class="figright" style="width: 371px;"><img src=
+"images/fig13.jpg" width="371" height="81" alt="Fig. 13" title=
+"" /> <b>Fig. 13</b></div>
+<p>In this way, then, by the active operation of different minds,
+facts are observed, examined, and the precise <a name="Page_70" id=
+"Page_70"></a><span class="pagenum">[Pg 70]</span>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 <a name=
+"Page_71" id="Page_71"></a><span class="pagenum">[Pg
+71]</span>superposed, a series <i>of iris-coloured</i> circles was
+obtained. A magnified image of <i>Newton's rings</i> 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.</p>
+<div class="figleft" style="width: 278px;"><img src=
+"images/fig14.jpg" width="278" height="275" alt="Fig. 14" title=
+"" /> <b>Fig. 14</b></div>
+<p>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 <a name="Page_72" id=
+"Page_72"></a><span class="pagenum">[Pg 72]</span>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.</p>
+<p>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&mdash;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
+<a name="Page_73" id="Page_73"></a><span class="pagenum">[Pg
+73]</span>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 <i>some
+change in the condition of the particle itself</i>. The self-same
+particle, he affirmed, was affected by 'fits' of easy transmission
+and reflection.</p>
+<h3>&sect; 9. <i>Theory of 'Fits' applied to Newton's
+Rings</i>.</h3>
+<p>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.</p>
+<p><a name="Page_74" id="Page_74"></a><span class="pagenum">[Pg
+74]</span>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 <i>d</i>; then Newton found the distance corresponding to
+the second dark ring 2 <i>d</i>; the thickness corresponding to the
+third dark ring 3 <i>d</i>; the thickness corresponding to the
+tenth dark ring 10 <i>d</i>, and so on. Surely there must be some
+hidden meaning in this little distance, <i>d</i>, 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 <i>periodic recurrence</i>. 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&mdash;that is, in twenty-four hours&mdash;our planet performs
+a complete rotation; and in the time required to pass over the
+distance <i>d</i>, Newton's light-particle might be supposed to
+perform a complete rotation. True, the light-particle is smaller
+than the planet, and the distance <i>d</i>, instead of being a
+million <a name="Page_75" id="Page_75"></a><span class=
+"pagenum">[Pg 75]</span>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.</p>
+<p>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
+<i>once</i> 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 <i>and be lost to the
+eye</i>. All round the place of contact, wherever the film
+possesses this precise thickness, the light will equally
+disappear&mdash;we shall therefore have a ring of darkness.</p>
+<p>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 <i>d</i>, the particle has time to perform, <i>two</i>
+complete rotations within the film; when the thickness is 3 <i>d,
+three</i> complete rotations; when 10 <i>d, ten</i> 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.</p>
+<p>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 &frac12;<i>d</i>; 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 <a name="Page_76" id=
+"Page_76"></a><span class="pagenum">[Pg 76]</span>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 1&frac12;<i>d</i>, 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.</p>
+<p>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.</p>
+<p>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 <i>single surface</i>; 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 <a name="Page_77" id=
+"Page_77"></a><span class="pagenum">[Pg 77]</span>the surfaces of
+the film, and when this is done the rings vanish altogether.</p>
+<p>Rings of feeble intensity are also formed by <i>transmitted</i>
+light. These are referred by the undulatory theory to the
+interference of waves which have passed <i>directly</i> through the
+film, with others which have suffered <i>two</i> reflections within
+the film, and are thus completely accounted for.</p>
+<h3>&sect; 10. <i>The Diffraction of Light</i>.</h3>
+<p>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.</p>
+<p>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 <a name="Page_78" id=
+"Page_78"></a><span class="pagenum">[Pg 78]</span>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 <i>Diffraction</i>.</p>
+<p>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 <i>point</i> 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 <i>line</i> 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.</p>
+<p>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.</p>
+<p>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 <a name="Page_79" id="Page_79"></a><span class=
+"pagenum">[Pg 79]</span>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.</p>
+<p>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.</p>
+<div class="figcenter" style="width: 450px;"><img src=
+"images/fig15.jpg" width="450" height="197" alt="Fig. 15." title=
+"" /> <b>Fig. 15.</b></div>
+<p>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 <i>narrower</i>, and they are <i>closer
+together</i> than the red ones.</p>
+<p>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
+<a name="Page_80" id="Page_80"></a><span class="pagenum">[Pg
+80]</span>represented in fig. 16. When <i>white light</i>,
+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.</p>
+<div class="figcenter" style="width: 496px;"><img src=
+"images/fig16.jpg" width="496" height="208" alt="Fig. 16." title=
+"" /> <b>Fig. 16.</b></div>
+<h3>&sect; 11. <i>Application of the Wave-theory to the Phenomena
+of Diffraction</i>.</h3>
+<p>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.</p>
+<p>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&mdash;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
+<a name="Page_81" id="Page_81"></a><span class="pagenum">[Pg
+81]</span>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.</p>
+<p>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 <i>phase</i> 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 <i>opposite</i>
+phases of vibration.</p>
+<div class="figleft" style="width: 238px;"><img src=
+"images/fig17.jpg" width="238" height="238" alt="Fig 17." title=
+"" /> <b>Fig. 17.</b></div>
+<p>There is still another point to be cleared up&mdash;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 <i>m</i> <i>n</i> be the position of the ridge of one of the
+waves at any moment, and <i>m'</i> <i>n'</i> 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 <a name="Page_82" id="Page_82"></a><span class=
+"pagenum">[Pg 82]</span>wave <i>m</i> <i>n</i> 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 <i>m</i>
+<i>n</i> <i>does</i> 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 <i>m</i> <i>n</i> and <i>m'</i> <i>n'</i>,
+the coalescence of all these little waves would build up the large
+ridge <i>m'</i> <i>n'</i> 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.</p>
+<div class="figright" style="width: 343px;"><img src=
+"images/fig18.jpg" width="343" height="253" alt="Fig. 18." title=
+"" /> <b>Fig. 18.</b></div>
+<p>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, <i>every point of <a name="Page_83" id=
+"Page_83"></a><span class="pagenum">[Pg 83]</span>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</i>. This is the celebrated principle of Huyghens: we have now
+to examine how these secondary waves act upon each other.</p>
+<p>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
+<a name="Page_84" id="Page_84"></a><span class="pagenum">[Pg
+84]</span>undiminished light produces the brilliant central band of
+the series.</p>
+<p>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.</p>
+<div class="figleft" style="width: 368px;"><img src=
+"images/fig19.jpg" width="368" height="251" alt="Fig. 19." title=
+"" /> <b>Fig. 19.</b></div>
+<p>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?</p>
+<p>Let us fix our attention upon the particular oblique line that
+passes through the <i>centre</i> 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 <i>e</i> R' equal to P R', join P and <i>e</i>,
+and draw O <i>d</i> parallel to P e. A e is then the length of a
+<a name="Page_85" id="Page_85"></a><span class="pagenum">[Pg
+85]</span>wave of light, while A <i>d</i> 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 <i>x</i> R', on the one side of O R', finds a
+line <i>x</i>' R' upon the other side of O R', from which its path
+differs by half an undulation&mdash;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 <i>a whole
+wave-length</i> different from each other.</p>
+<p>When the difference between the paths of the marginal waves is
+<i>half a wave-length,</i> a partial destruction of the light is
+effected. The luminous intensity corresponding to this obliquity is
+a little less than one-half&mdash;accurately 0.4&mdash;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.</p>
+<p>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 <a name="Page_86" id=
+"Page_86"></a><span class="pagenum">[Pg 86]</span>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 <i>even</i> number
+of semi-undulations, we have complete extinction; while, when the
+marginal difference is an <i>odd</i> number of semi-undulations, we
+have only partial extinction, a portion of the beam remaining as a
+luminous band.</p>
+<p>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.</p>
+<p>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 <a name="Page_87" id=
+"Page_87"></a><span class="pagenum">[Pg 87]</span>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.</p>
+<div class="figcenter" style="width: 381px;"><img src=
+"images/fig20.jpg" width="381" height="416" alt="Fig. 20." title=
+"" /> <b>Fig. 20.</b></div>
+<p><a name="Page_88" id="Page_88"></a><span class="pagenum">[Pg
+88]</span>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 <a name=
+"Page_89" id="Page_89"></a><span class="pagenum">[Pg
+89]</span>vapours of various liquids in an intensely illuminated
+tube are, as I have elsewhere shewn, exceedingly fine.</p>
+<div class="figcenter" style="width: 382px;"><img src=
+"images/fig21.jpg" width="382" height="442" alt="Fig. 21." title=
+"" /> <b>Fig. 21.</b></div>
+<p>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 <i>smaller</i>, 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.</p>
+<p>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 <a name=
+"Page_90" id="Page_90"></a><span class="pagenum">[Pg
+90]</span>waves does not extinguish the longer ones, hence the
+phenomena of colours. These are called the colours of <i>striated
+surfaces</i>. 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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_91" id="Page_91"></a><span class="pagenum">[Pg
+91]</span></div>
+<h2><a name="LECTURE_III" id="LECTURE_III"></a>LECTURE III.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>RELATION OF THEORIES TO EXPERIENCE</li>
+<li>ORIGIN OF THE NOTION OF THE ATTRACTION OF GRAVITATION</li>
+<li>NOTION OF POLARITY, HOW GENERATED</li>
+<li>ATOMIC POLARITY</li>
+<li>STRUCTURAL ARRANGEMENTS DUE TO POLARITY</li>
+<li>ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION</li>
+<li>TO THEIR ACTION UPON LIGHT</li>
+<li>NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE</li>
+<li>EXPERIMENTAL ILLUSTRATIONS</li>
+<li>CRYSTALLIZATION OF WATER</li>
+<li>EXPANSION BY HEAT AND BY COLD</li>
+<li>DEPORTMENT OF WATER CONSIDERED AND EXPLAINED</li>
+<li>BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA</li>
+<li>REFRACTION</li>
+<li>DOUBLE REFRACTION</li>
+<li>POLARIZATION</li>
+<li>ACTION OF TOURMALINE</li>
+<li>CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR</li>
+<li>POLARIZATION BY ORDINARY REFRACTION AND REFLECTION</li>
+<li>DEPOLARIZATION</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Derivation of Theoretic Conceptions from
+Experience.</i></h3>
+<p>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 C&aelig;sar 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 <a name=
+"Page_92" id="Page_92"></a><span class="pagenum">[Pg
+92]</span>framing theories, does the imagination <i>create</i> its
+materials. It expands, diminishes, moulds, and refines, as the case
+may be, materials derived from the world of fact and
+observation.</p>
+<p>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.</p>
+<p>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 oscil<a name=
+"Page_93" id="Page_93"></a><span class="pagenum">[Pg
+93]</span>lations 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 <i>doubleness</i> of the
+magnetic force is called <i>polarity</i>, and the points near the
+ends of the magnet in which the forces seem concentrated are called
+its <i>poles</i>.</p>
+<div class="figright" style="width: 160px;"><img src=
+"images/fig22.jpg" width="160" height="306" alt="Fig. 22." title=
+"" /> <b>Fig. 22.</b></div>
+<p>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&mdash;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 <a name="Page_94" id=
+"Page_94"></a><span class="pagenum">[Pg 94]</span>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&mdash;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.</p>
+<p>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.</p>
+<div class="figleft" style="width: 430px;"><img src=
+"images/fig23.jpg" width="430" height="413" alt=
+"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."
+title="" /> <b>Fig. 23.<br />
+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.</b></div>
+<p>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&mdash;to iron filings, for
+example&mdash;we find that they act substantially as the needles,
+arranging themselves in definite forms, in obedience to the
+magnetic action.</p>
+<p>Placing a sheet of paper or glass over a bar magnet and
+showering iron filings upon the paper, I notice a <a name="Page_95"
+id="Page_95"></a><span class="pagenum">[Pg 95]</span>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 <a name="Page_96" id="Page_96"></a><span class=
+"pagenum">[Pg 96]</span>curves which have been so long familiar to
+scientific men (fig. 23).</p>
+<p>(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.)</p>
+<p>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.</p>
+<p>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 <i>structural arrangement</i>. 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.</p>
+<h3>&sect; 2. <i>Theory of Crystallization.</i></h3>
+<p>Now this idea of structure, as produced by polar force, opens a
+way for the intellect into an entirely new <a name="Page_97" id=
+"Page_97"></a><span class="pagenum">[Pg 97]</span><a name="Page_98"
+id="Page_98"></a>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&mdash;possibly a full-formed
+diamond, as it quitted the hand of Nature, not yet having got into
+the hands of the lapidary.</p>
+<div class="figright" style="width: 428px;"><img src=
+"images/fig24.jpg" width="428" height="912" alt="Fig. 24." title=
+"" /> <b>Fig. 24.</b></div>
+<p>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. <a name="Page_99" id="Page_99"></a><span class=
+"pagenum">[Pg 99]</span>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.</p>
+<p>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 <i>nursed</i> with proper care,
+crystals of these substances may be caused to grow to a great
+size.</p>
+<p>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, <a name="Page_100"
+id="Page_100"></a><span class="pagenum">[Pg 100]</span>more solid
+matter is contained in it than corresponds to its temperature.
+Still the molecules show no sign of building themselves
+together.</p>
+<p>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.</p>
+<p>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 <a name="Page_101" id=
+"Page_101"></a><span class="pagenum">[Pg 101]</span>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.</p>
+<p>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
+spicul&aelig; branch from the trunk, and from these branches others
+shoot; but the angles enclosed by the spicul&aelig; 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 <a name="Page_102" id=
+"Page_102"></a><span class="pagenum">[Pg 102]</span>the accidents
+of crystallization; but in one particular they assert their
+superiority over all such accidents&mdash;<i>angular magnitude</i>
+is always rigidly preserved.</p>
+<p>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.</p>
+<p>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 <a name="Page_103"
+id="Page_103"></a><span class="pagenum">[Pg 103]</span>matter,'
+will be very different from those of the generations past.</p>
+<p>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.<a name="FNanchor_15_15" id=
+"FNanchor_15_15"></a><a href="#Footnote_15_15" class=
+"fnanchor">[15]</a> 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 spicul&aelig; to the angle of 60 degrees.</p>
+<p>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&deg; 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 <a name="Page_104" id="Page_104"></a><span class=
+"pagenum">[Pg 104]</span>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.</p>
+<p>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:&mdash;</p>
+<p>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.</p>
+<p>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
+<i>expansion by cold</i> 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&deg; Fahr. Crystallization has <a name="Page_105" id=
+"Page_105"></a><span class="pagenum">[Pg 105]</span>virtually here
+commenced, the molecules preparing themselves for the subsequent
+act of solidification, which occurs at 32&deg;, 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.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href=
+"#Footnote_16_16" class="fnanchor">[16]</a></p>
+<p>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:&mdash;</p>
+<p>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.</p>
+<p>But besides the unpolar force of gravity, which <a name=
+"Page_106" id="Page_106"></a><span class="pagenum">[Pg
+106]</span>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&deg;. 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 <i>as wholes</i>. Previous to
+reaching the temperature 39&deg; 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.</p>
+<h3>&sect; 3. <i>Ordinary Refraction of Light explained by the Wave
+Theory</i>.</h3>
+<p>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 por<a name="Page_107" id=
+"Page_107"></a><span class="pagenum">[Pg 107]</span>tion 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.</p>
+<div class="figleft" style="width: 446px;"><img src=
+"images/fig25.jpg" width="446" height="256" alt="Fig. 25." title=
+"" /> <b>Fig. 25.</b></div>
+<p>But suppose the wave, before reaching the glass, to be
+<i>oblique</i> 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 <i>refracted</i>.</p>
+<p>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 <a name="Page_108" id=
+"Page_108"></a><span class="pagenum">[Pg 108]</span>glass as 3: 2.
+Let A B C (fig. 25) be the section of our prism, and <i>a</i>
+<i>b</i> the section of a plane wave approaching it in the
+direction of the arrow. When it reaches <i>c</i> <i>d</i>, 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 <i>c</i> <i>e</i>, the
+wave in the glass will have passed over only two-thirds of this
+distance, or <i>d</i> <i>f</i>. The line <i>e</i> <i>f</i> now
+marks the front of the wave. Immersed wholly in the glass it
+pursues its way to <i>g</i> <i>h</i>, where the end <i>g</i> of the
+wave is on the point of escaping into the air. During the time
+required by the end <i>h</i> of the wave to pass over the distance
+<i>h</i> <i>k</i> to the surface of the prism, the other end
+<i>g</i>, moving more rapidly, will have reached the point
+<i>i</i>. The wave, therefore, has again changed its front, so that
+after its emergence from the prism it will pass on to <i>l</i>
+<i>m</i>, 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.</p>
+<h3>&sect; 4. <i>Double Refraction of Light explained by the Wave
+Theory</i>.</h3>
+<p>The two elements of rapidity of propagation, both of sound and
+light, in any substance whatever, are <i>elasticity</i> and
+<i>density</i>, the speed increasing with the former and
+diminishing with the latter. The enormous velocity of light in
+stellar space is attainable because <a name="Page_109" id=
+"Page_109"></a><span class="pagenum">[Pg 109]</span>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 <i>double refraction</i>.</p>
+<p>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.</p>
+<p>I am unwilling to quit this subject before raising it to
+unmistakable clearness in your minds. The <a name="Page_110" id=
+"Page_110"></a><span class="pagenum">[Pg 110]</span>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.
+<i>They do both</i>, and hence immediately divide themselves into
+two systems propagated with different velocities. Double refraction
+is the necessary consequence.</p>
+<h3>&sect; 4. <i>Double Refraction of Light explained by the Wave
+Theory</i>.</h3>
+<div class="figright" style="width: 453px;"><img src=
+"images/fig26.jpg" width="453" height="290" alt="Fig. 26." title=
+"" /> <b>Fig. 26.</b></div>
+<p>By means of Iceland spar cut in the proper direction, double
+refraction is capable of easy illustration. Causing <a name=
+"Page_111" id="Page_111"></a><span class="pagenum">[Pg
+111]</span>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.</p>
+<p>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
+<i>ordinary ray</i>: 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
+<i>extraordinary ray</i>. 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.<a name="Page_112" id=
+"Page_112"></a><span class="pagenum">[Pg 112]</span></p>
+<h3>&sect; 5. <i>Polarization of Light explained by the Wave
+Theory</i>.</h3>
+<p>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 <i>two-sidedness</i>
+with the <i>two-endedness</i> of a magnet, wherein consists its
+polarity, the two beams came subsequently to be described as
+<i>polarized</i>.</p>
+<p>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 <i>across</i> 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.</p>
+<p>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
+<a name="Page_113" id="Page_113"></a><span class="pagenum">[Pg
+113]</span>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 <i>plane polarized light</i>.</p>
+<div class="figleft" style="width: 196px;"><img src=
+"images/fig27.jpg" width="196" height="69" alt="Fig. 27." title=
+"" /> <b>Fig. 27.</b></div>
+<div class="figright" style="width: 150px;"><img src=
+"images/fig28.jpg" width="150" height="200" alt="Fig. 28." title=
+"" /> <b>Fig. 28.</b></div>
+<p>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 (<i>t</i> <i>t</i>, fig. 27) is
+now before you. I place parallel to it another plate (<i>t'</i>
+<i>t'</i>): the green of the <a name="Page_114" id=
+"Page_114"></a><span class="pagenum">[Pg 114]</span>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.</p>
+<p>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 <i>edges</i> of the
+waves, the green light being then quenched. In the other case the
+<i>sides</i> of the waves strike the mirror, and the green light is
+reflected. To <a name="Page_115" id="Page_115"></a><span class=
+"pagenum">[Pg 115]</span>render the extinction complete, the light
+must be received upon the mirror at a special angle. What this
+angle is we shall learn presently.</p>
+<p>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&deg; with the perpendicular to the glass,
+the <i>whole</i> 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 <i>the polarizing
+angle</i>.</p>
+<p>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.<a name="FNanchor_17_17" id=
+"FNanchor_17_17"></a><a href="#Footnote_17_17" class=
+"fnanchor">[17]</a> The polarizing angle augments with the index of
+refraction. For water it is 52&frac12;&deg;; for glass, as already
+stated, 58&deg;; while for diamond it is 68&deg;.</p>
+<p>And now let us try to make substantially the <a name="Page_116"
+id="Page_116"></a><span class="pagenum">[Pg 116]</span>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.</p>
+<p>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 <a name="Page_117" id=
+"Page_117"></a><span class="pagenum">[Pg 117]</span>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).</p>
+<div class="figcenter" style="width: 337px;"><img src=
+"images/fig29.jpg" width="337" height="151" alt="Fig. 29." title=
+"" /> <b>Fig. 29.</b></div>
+<div class="figcenter" style="width: 333px;"><img src=
+"images/fig30.jpg" width="333" height="151" alt="Fig. 30." title=
+"" /> <b>Fig. 30.</b></div>
+<p>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).<a name="Page_118" id=
+"Page_118"></a><span class="pagenum">[Pg 118]</span></p>
+<div class="figcenter" style="width: 357px;"><img src=
+"images/fig31.jpg" width="357" height="150" alt="Fig. 31." title=
+"" /> <b>Fig. 31.</b></div>
+<div class="figcenter" style="width: 395px;"><img src=
+"images/fig32.jpg" width="395" height="273" alt="Fig. 32." title=
+"" /> <b>Fig. 32.</b></div>
+<p>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, <a name="Page_119" id=
+"Page_119"></a><span class="pagenum">[Pg 119]</span>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.</p>
+<div class="figcenter" style="width: 331px;"><img src=
+"images/fig33.jpg" width="331" height="270" alt="Fig. 33." title=
+"" /> <b>Fig. 33.</b></div>
+<p>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 <i>transmitted</i> 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 <i>a bundle</i>
+of plates, we so increase the quantity as to render the transmitted
+beam, for all practical purposes, <i>perfectly</i> 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.</p>
+<p>One word more. When the tourmalines are crossed, <a name=
+"Page_120" id="Page_120"></a><span class="pagenum">[Pg
+120]</span>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, <i>its plane of vibration is
+changed</i>: 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, <i>depolarization</i>. Its proper meaning will be
+disclosed in our next lecture.</p>
+<p>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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_121" id="Page_121"></a><span class="pagenum">[Pg
+121]</span></div>
+<h2><a name="LECTURE_IV" id="LECTURE_IV"></a>LECTURE IV.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>CHROMATIC PHENOMENA PRODUCED BY CRYSTALS IN POLARIZED
+LIGHT</li>
+<li>THE NICOL PRISM</li>
+<li>POLARIZER AND ANALYZER</li>
+<li>ACTION OF THICK AND THIN PLATES OF SELENITE</li>
+<li>COLOURS DEPENDENT ON THICKNESS</li>
+<li>RESOLUTION OF POLARIZED BEAM INTO TWO OTHERS BY THE
+SELENITE</li>
+<li>ONE OF THEM MORE RETARDED THAN THE OTHER</li>
+<li>RECOMPOUNDING OF THE TWO SYSTEMS OF WAVES BY THE ANALYZER</li>
+<li>INTERFERENCE THUS RENDERED POSSIBLE</li>
+<li>CONSEQUENT PRODUCTION OF COLOURS</li>
+<li>ACTION OF BODIES MECHANICALLY STRAINED OR PRESSED</li>
+<li>ACTION OF SONOROUS VIBRATIONS</li>
+<li>ACTION OF GLASS STRAINED OR PRESSED BY HEAT</li>
+<li>CIRCULAR POLARIZATION</li>
+<li>CHROMATIC PHENOMENA PRODUCED BY QUARTZ</li>
+<li>THE MAGNETIZATION OF LIGHT</li>
+<li>RINGS SURROUNDING THE AXES OF CRYSTALS</li>
+<li>BIAXAL AND UNIAXAL CRYSTALS</li>
+<li>GRASP OF THE UNDULATORY THEORY</li>
+<li>THE COLOUR AND POLARIZATION OF SKY-LIGHT</li>
+<li>GENERATION OF ARTIFICIAL SKIES.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Action of Crystals on Polarized Light: the Nicol
+Prism.</i></h3>
+<p>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
+<a name="Page_122" id="Page_122"></a><span class="pagenum">[Pg
+122]</span>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.</p>
+<div class="figright" style="width: 170px;"><img src=
+"images/fig34.jpg" width="170" height="368" alt="Fig. 34." title=
+"" /> <b>Fig. 34.</b></div>
+<p>The beams, as you know, are refracted differently, and from
+this, as made plain in &sect;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.</p>
+<p>Let <i>b x, c y</i> (fig. 34) represent the section of an
+elongated rhomb of Iceland spar cloven from the crystal. Let this
+rhomb be cut along the plane <i>b c</i>; 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 <a name=
+"Page_123" id="Page_123"></a><span class="pagenum">[Pg
+123]</span>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 <i>b c</i> is
+the section shall be perpendicular, or nearly so, to the two end
+surfaces of the rhomb <i>b x, c y</i>.</p>
+<p>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.</p>
+<p>(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.)<a name="Page_124" id="Page_124"></a><span class=
+"pagenum">[Pg 124]</span></p>
+<h3>&sect; 2. <i>Colours of Films of Selenite in Polarized
+Light</i>.</h3>
+<p>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 <i>thin</i> you have sometimes
+not only light, but <i>coloured</i> 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&mdash;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.</p>
+<p>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 <a name="Page_125"
+id="Page_125"></a><span class="pagenum">[Pg 125]</span>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&mdash;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.</p>
+<h3>&sect; 3. <i>Colours of Crystals in Polarized Light explained
+by the Undulatory Theory</i>.</h3>
+<p>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 <i>vibrations</i>. We treat the
+luminiferous ether on mechanical principles, and, from <a name=
+"Page_126" id="Page_126"></a><span class="pagenum">[Pg
+126]</span>the composition and resolution of its vibrations we
+deduce all the phenomena displayed by crystals in polarized
+light.</p>
+<div class="figleft" style="width: 261px;"><img src=
+"images/fig35.jpg" width="261" height="120" alt="Fig. 35." title=
+"" /> <b>Fig. 35.</b></div>
+<p>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 <i>a</i> <i>b</i> represent the amplitude of an oblique
+ethereal vibration before it reaches A B. From <i>a</i> and
+<i>b</i> let the two perpendiculars <i>a</i> <i>c</i> and <i>b</i>
+<i>d</i> be drawn upon the axis: then <i>c</i> <i>d</i> will be the
+amplitude of the transmitted vibration.</p>
+<p>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 direc<a name="Page_127"
+id="Page_127"></a><span class="pagenum">[Pg 127]</span>tions, 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 <i>oblique</i> to
+the two tourmaline axes; then, you see it exercises the power,
+demonstrated in the last lecture, of partially restoring the
+light.</p>
+<div class="figright" style="width: 380px;"><img src=
+"images/fig36.jpg" width="380" height="270" alt="Fig. 36." title=
+"" /> <b>Fig. 36.</b></div>
+<p>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.</p>
+<p>First, then, we have a prism which receives the light from the
+electric lamp, and which is called the <i>polarizer</i>. Then we
+have the plate of gypsum (supposed to be placed at S, fig. 36), and
+then the <a name="Page_128" id="Page_128"></a><span class=
+"pagenum">[Pg 128]</span>prism in front, which is called the
+<i>analyzer</i>. 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
+(<i>a</i> <i>b</i>) 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 (<i>a</i>
+<i>c</i>, <i>a</i> <i>f</i>, <i>b</i> <i>d</i>, <i>b</i> <i>e</i>)
+on the two arms of the cross; then the distances (<i>c</i>
+<i>d</i>, <i>e</i> <i>f</i>) between the feet of these
+perpendiculars represent the amplitudes of two rectangular
+vibrations, which are the <i>components</i> 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.</p>
+<div class="figleft" style="width: 216px;"><img src=
+"images/fig37.jpg" width="216" height="211" alt="Fig. 37." title=
+"" /> <b>Fig. 37.</b></div>
+<p>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
+<a name="Page_129" id="Page_129"></a><span class="pagenum">[Pg
+129]</span>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.</p>
+<p>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.</p>
+<p>(The best way of obtaining a knowledge of these phenomena is to
+construct a model of thin wood or <a name="Page_130" id=
+"Page_130"></a><span class="pagenum">[Pg 130]</span>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 <i>complementary</i> phenomena, when the planes of
+vibration are perpendicular to each other.)</p>
+<p>In considering the next point, we will operate, for the sake of
+simplicity, with monochromatic light&mdash;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
+<i>odd</i> number of half wave-lengths, produces extinction; at all
+thicknesses, on the other hand, which correspond to a retardation
+of an <i>even</i> number of half <a name="Page_131" id=
+"Page_131"></a><span class="pagenum">[Pg 131]</span>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.</p>
+<p>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
+<i>iris-coloured</i> rings produced by the white light.</p>
+<p>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
+<a name="Page_132" id="Page_132"></a><span class="pagenum">[Pg
+132]</span>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.</p>
+<h3>&sect; 4. <i>Colours produced by Strain and Pressure.</i></h3>
+<p>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 <i>strained</i> longitudinally; its
+concave surface, that next my knee, is longitudinally
+<i>pressed</i>. 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.</p>
+<p><a name="Page_133" id="Page_133"></a><span class="pagenum">[Pg
+133]</span>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.</p>
+<p>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.</p>
+<div class="figright" style="width: 165px;"><img src=
+"images/fig38.jpg" width="165" height="358" alt="Fig. 38" title=
+"" /> <b>Fig. 38</b></div>
+<p>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 <a name="Page_134" id="Page_134"></a><span class=
+"pagenum">[Pg 134]</span>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.</p>
+<p>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 <a name="Page_135" id="Page_135"></a><span class=
+"pagenum">[Pg 135]</span>with its centre rarefied. The ends of the
+strip suffer neither condensation nor rarefaction.</p>
+<p>If we introduce the strip of glass (<i>s</i> <i>s'</i>, 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 (<i>h</i>, 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, <a name="Page_136" id=
+"Page_136"></a><span class="pagenum">[Pg 136]</span>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.</p>
+<div class="figcenter" style="width: 558px;"><img src=
+"images/fig39.jpg" width="558" height="363" alt="Fig. 39." title=
+"" /> <b>Fig. 39.</b></div>
+<h3>&sect; 5. <i>Colours of Unannealed Glass</i>.</h3>
+<p>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 <a name="Page_137" id=
+"Page_137"></a><span class="pagenum">[Pg 137]</span>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.</p>
+<div class="figleft" style="width: 197px;"><img src=
+"images/fig40.jpg" width="197" height="198" alt="Fig. 40." title=
+"" /> <b>Fig. 40.</b></div>
+<div class="figright" style="width: 195px;"><img src=
+"images/fig41.jpg" width="195" height="197" alt="Fig. 41." title=
+"" /> <b>Fig. 41.</b></div>
+<p>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 <a name="Page_138"
+id="Page_138"></a><span class="pagenum">[Pg 138]</span>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.</p>
+<div class="figcenter" style="width: 444px;"><img src=
+"images/fig42.jpg" width="444" height="442" alt="Fig. 42." title=
+"" /> <b>Fig. 42.</b></div>
+<h3>&sect; 6. <i>Circular Polarization.</i></h3>
+<p>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 <a name="Page_139" id=
+"Page_139"></a><span class="pagenum">[Pg 139]</span>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 <i>a plane</i>.
+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.</p>
+<p>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.</p>
+<p>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 <a name="Page_140" id="Page_140"></a><span class=
+"pagenum">[Pg 140]</span>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 <i>circularly
+polarized</i>. 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.</p>
+<h3>&sect; 7. <i>Complementary Colours of Bi-refracting Spar in
+Circularly Polarized Light. Proof that Yellow and Blue are
+Complementary.</i></h3>
+<div class="figright" style="width: 403px;"><img src=
+"images/fig43.jpg" width="403" height="228" alt="Fig. 43." title=
+"" /> <b>Fig. 43.</b></div>
+<p>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 <a name="Page_141" id=
+"Page_141"></a><span class="pagenum">[Pg 141]</span>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.)</p>
+<h3>&sect; 8. <i>The Magnetization of Light.</i></h3>
+<p>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
+<a name="Page_142" id="Page_142"></a><span class="pagenum">[Pg
+142]</span>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.</p>
+<div class="figright" style="width: 430px;"><img src=
+"images/fig44.jpg" width="430" height="283" alt="Fig. 44" title=
+"" /> <b>Fig. 44</b></div>
+<p>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.</p>
+<p>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 <a name="Page_143" id=
+"Page_143"></a><span class="pagenum">[Pg 143]</span>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.</p>
+<h3>&sect; 9. <i>Iris-rings surrounding the Axes of
+Crystals.</i></h3>
+<p>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, <a name=
+"Page_144" id="Page_144"></a><span class="pagenum">[Pg
+144]</span>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 <i>optic axis</i> of the
+crystal.</p>
+<p>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
+<i>conical</i> 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.</p>
+<p>Placing the plate of Iceland spar between the crossed <a name=
+"Page_145" id="Page_145"></a><span class="pagenum">[Pg
+145]</span>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
+<i>either</i> prism, cannot get through <i>both</i>. This complete
+interception produces the arms of the cross.</p>
+<div class="figcenter" style="width: 268px;"><img src=
+"images/fig45.jpg" width="268" height="265" alt="Fig. 45." title=
+"" /> <b>Fig. 45.</b></div>
+<p>With monochromatic light the rings would be simply bright and
+black&mdash;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&deg; 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-<a name="Page_146" id=
+"Page_146"></a><span class="pagenum">[Pg 146]</span>waves give rise
+to iris-colours when white light is employed.</p>
+<div class="figleft" style="width: 206px;"><img src=
+"images/fig46.jpg" width="206" height="202" alt="Fig. 46." title=
+"" /> <b>Fig. 46.</b></div>
+<div class="figright" style="width: 278px;"><img src=
+"images/fig47.jpg" width="278" height="210" alt="Fig. 47." title=
+"" /> <b>Fig. 47.</b></div>
+<p>Besides the <i>regular</i> crystals which produce double
+refraction in no direction, and the <i>uniaxal</i> crystals which
+produce it in all directions but one, Brewster discovered that in a
+large class of crystals there are <i>two</i> directions in which
+double refraction does not take place. These are called
+<i>biaxal</i> 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, <a name="Page_147"
+id="Page_147"></a><span class="pagenum">[Pg 147]</span>forms a
+<i>lemniscata</i>; 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.</p>
+<h3>&sect; 10. <i>Power of the Wave Theory</i>.</h3>
+<p>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.</p>
+<p>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 <a name="Page_148" id="Page_148"></a><span class=
+"pagenum">[Pg 148]</span>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.'<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href=
+"#Footnote_18_18" class="fnanchor">[18]</a></p>
+<p>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 <a name="Page_149" id=
+"Page_149"></a><span class="pagenum">[Pg 149]</span>than those of
+the solar system. Accept if you will the scepticism of Mr.
+Mill<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href=
+"#Footnote_19_19" class="fnanchor">[19]</a> regarding the
+undulatory theory; but if your scepticism be philosophical, it will
+wrap the theory of gravitation in the same or in greater
+doubt.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href=
+"#Footnote_20_20" class="fnanchor">[20]</a></p>
+<h3>&sect; 11. <i>The Blue of the Sky</i>.</h3>
+<p>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 <a name=
+"Page_150" id="Page_150"></a><span class="pagenum">[Pg
+150]</span>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.</p>
+<p>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.</p>
+<p>A small pebble, placed in the way of the ring-ripples <a name=
+"Page_151" id="Page_151"></a><span class="pagenum">[Pg
+151]</span>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 <i>are</i> 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.</p>
+<p>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.</p>
+<p>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 <a name="Page_152"
+id="Page_152"></a><span class="pagenum">[Pg 152]</span>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.</p>
+<p>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 Br&uuml;cke 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.</p>
+<h3>&sect; 12. <i>Artificial Sky</i>.</h3>
+<p>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 <a name="Page_153" id=
+"Page_153"></a><span class="pagenum">[Pg 153]</span>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 2&frac12; 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 <i>precipitated</i> 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.</p>
+<p>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 <i>blue
+cloud</i>. 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, <i>it only</i> 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 <a name="Page_154" id=
+"Page_154"></a><span class="pagenum">[Pg 154]</span>intermediate
+position between these clouds and true cloudless vapour.</p>
+<p>It is possible to make the particles of this <i>actinic
+cloud</i> 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
+<i>incipient cloud</i>, 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.</p>
+<h3>&sect; 13. <i>Polarization of Skylight</i>.</h3>
+<p>But there is another subject connected with our firmament, of a
+more subtle and recondite character <a name="Page_155" id=
+"Page_155"></a><span class="pagenum">[Pg 155]</span>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.</p>
+<p>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 <i>blue</i>. In all cases,
+moreover, this fine blue cloud polarizes <i>perfectly</i> the beam
+which illuminates it, the direction of polarization enclosing an
+angle of 90&deg; with the axis of the illuminating beam.</p>
+<p>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 name="Page_156" id=
+"Page_156"></a><span class="pagenum">[Pg 156]</span>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
+<i>residual</i> 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.</p>
+<p>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 <a name="Page_157" id="Page_157"></a><span class=
+"pagenum">[Pg 157]</span>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.</p>
+<p>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:&mdash;</p>
+<p>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.</p>
+<p>2. As long as the cloud remains distinctly blue, the light
+discharged from it at right angles to the illuminating beam is
+<i>perfectly</i> polarized. It may be utterly quenched by a Nicol
+prism, the cloud from which it issues being caused to disappear.
+Any deviation from <a name="Page_158" id=
+"Page_158"></a><span class="pagenum">[Pg 158]</span>the
+perpendicular enables a portion of the light to get through the
+prism.</p>
+<p>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.</p>
+<p>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.</p>
+<p>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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_159" id="Page_159"></a><span class="pagenum">[Pg
+159]</span></div>
+<h2><a name="LECTURE_V" id="LECTURE_V"></a>LECTURE V.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>RANGE OF VISION NOT COMMENSURATE WITH RANGE OF RADIATION</li>
+<li>THE ULTRA-VIOLET BAYS</li>
+<li>FLUORESCENCE</li>
+<li>THE RENDERING OF INVISIBLE RAYS VISIBLE</li>
+<li>VISION NOT THE ONLY SENSE APPEALED TO BY THE SOLAR AND ELECTRIC
+BEAM</li>
+<li>HEAT OF BEAM</li>
+<li>COMBUSTION BY TOTAL BEAM AT THE FOCI OF MIRRORS AND LENSES</li>
+<li>COMBUSTION THROUGH ICE-LENS</li>
+<li>IGNITION OF DIAMOND</li>
+<li>SEARCH FOR THE RAYS HERE EFFECTIVE</li>
+<li>SIR WILLIAM HERSCHEL'S DISCOVERY OF DARK SOLAR RAYS</li>
+<li>INVISIBLE RAYS THE BASIS OF THE VISIBLE</li>
+<li>DETACHMENT BY A RAY-FILTER OF THE INVISIBLE RAYS FROM THE
+VISIBLE</li>
+<li>COMBUSTION AT DARK FOCI</li>
+<li>CONVERSION OF HEAT-RAYS INTO LIGHT-RAYS</li>
+<li>CALORESCENCE</li>
+<li>PART PLAYED IN NATURE BY DARK RAYS</li>
+<li>IDENTITY OF LIGHT AND RADIANT HEAT</li>
+<li>INVISIBLE IMAGES</li>
+<li>REFLECTION, REFRACTION, PLANE POLARIZATION, DEPOLARIZATION,
+CIRCULAR<br />
+&nbsp;&nbsp;&nbsp;&nbsp;POLARIZATION, DOUBLE REFRACTION, AND
+MAGNETIZATION OF RADIANT HEAT.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<h3>&sect; 1. <i>Range of Vision and of Radiation</i>.</h3>
+<p>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&mdash;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 <i>evolution</i>, 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
+<a name="Page_160" id="Page_160"></a><span class="pagenum">[Pg
+160]</span>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.</p>
+<p>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&mdash;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&mdash;the yellow rays are found to be the most
+active.</p>
+<p>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.</p>
+<h3>&sect; 2. <i>Ultra-violet Rays: Fluorescence</i>.</h3>
+<p>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 con<a name="Page_161" id=
+"Page_161"></a><span class="pagenum">[Pg 161]</span>verted 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.</p>
+<p>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&mdash;on those of sulphate of
+quinine, for example&mdash;they compel those molecules, or their
+constituent atoms, to vibrate; and the peculiarity is, that the
+vibrations thus set up are <i>of slower period</i> 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.</p>
+<p><a name="Page_162" id="Page_162"></a><span class="pagenum">[Pg
+162]</span>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 <i>Thallene</i>, produces a very striking
+elongation of the spectrum, the new light generated being of
+peculiar brilliancy.</p>
+<p>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 <i>Fluorescence</i>.</p>
+<p>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-<a name=
+"Page_163" id="Page_163"></a><span class="pagenum">[Pg
+163]</span>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
+<i>molecules</i>, not of <i>particles</i>. The medium before you is
+not a turbid medium, for when you look through it at a luminous
+surface it is perfectly clear.</p>
+<p>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 Dupr&eacute;, 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.</p>
+<p>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 <i>Lignum
+Nephriticum,</i> because the inhabitants of the country where it
+grows <a name="Page_164" id="Page_164"></a><span class=
+"pagenum">[Pg 164]</span>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 <i>Lignum,
+Nephriticum</i>, 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.'</p>
+<p>'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.'<a name="FNanchor_21_21" id=
+"FNanchor_21_21"></a><a href="#Footnote_21_21" class=
+"fnanchor">[21]</a></p>
+<p><a name="Page_165" id="Page_165"></a><span class="pagenum">[Pg
+165]</span>Goethe in his 'Farbenlehre' thus describes the
+fluorescence of horse-chestnut bark:&mdash;'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.'<a name=
+"FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22"
+class="fnanchor">[22]</a> 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.</p>
+<h3>&sect; 3. <i>The Heat of the Electric Beam. Ignition through a
+Lens of Ice. Possible Cometary Temperature</i>.</h3>
+<p>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 <a name="Page_166" id=
+"Page_166"></a><span class="pagenum">[Pg 166]</span>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.</p>
+<div class="figcenter" style="width: 365px;"><img src=
+"images/fig48.jpg" width="365" height="268" alt="Fig. 48." title=
+"" /> <b>Fig. 48.</b></div>
+<p>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 (<i>m</i> <i>m'</i>, 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.</p>
+<p><a name="Page_167" id="Page_167"></a><span class="pagenum">[Pg
+167]</span>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.</p>
+<p>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 <a name="Page_168" id=
+"Page_168"></a><span class="pagenum">[Pg 168]</span>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 <i>absorption</i>
+takes place that heat is thus produced: and heat is always a result
+of absorption.</p>
+<p>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.</p>
+<p>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 <a name="Page_169"
+id="Page_169"></a><span class="pagenum">[Pg 169]</span>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.</p>
+<h3>&sect; 4. <i>Combustion of a Diamond by Radiant Heat</i>.</h3>
+<p>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:&mdash;'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 3&frac12; 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.'</p>
+<p>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 <a name=
+"Page_170" id="Page_170"></a><span class="pagenum">[Pg
+170]</span>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.</p>
+<h3>&sect; 5. <i>Ultra-red Rays: Calorescence</i>.</h3>
+<p>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
+<i>light</i> 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 <i>light</i> is not
+absorbed by the white paper, and therefore does not burn the paper;
+but there is something over and above the light which <i>is</i>
+absorbed, and which provokes combustion. What is this
+something?</p>
+<p><a name="Page_171" id="Page_171"></a><span class="pagenum">[Pg
+171]</span>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, M&uuml;ller, 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 <i>filtered</i> 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.</p>
+<p>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, <a name="Page_172" id=
+"Page_172"></a><span class="pagenum">[Pg 172]</span>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.</p>
+<p>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.</p>
+<p>The invisible heat, emitted both by dark bodies and by luminous
+ones, flies through space with the velosity of light, and is called
+<i>radiant heat</i>. Now, radiant heat may be made a subtle and
+powerful explorer of molecular condition, and, of late years, it
+has given a new <a name="Page_173" id="Page_173"></a><span class=
+"pagenum">[Pg 173]</span>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 <i>diathermancy</i>, or
+perviousness to radiant heat.</p>
+<p>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.</p>
+<p>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 <a name="Page_174" id="Page_174"></a><span class=
+"pagenum">[Pg 174]</span>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.</p>
+<p>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 <i>lowered</i> the refrangibility, so
+as to render the non-visual rays visual, and to this change he gave
+the name of <i>Fluorescence</i>. Here, by the intervention of the
+platinum, the refrangibility is <i>raised</i>, so as to render the
+non-visual visual, and to this change I have given the name of
+<i>Calorescence</i>.</p>
+<p>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.</p>
+<p>The important part played by these ultra-red rays <a name=
+"Page_175" id="Page_175"></a><span class="pagenum">[Pg
+175]</span>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
+<i>boils</i>. 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.</p>
+<p>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.<a name="Page_176" id=
+"Page_176"></a><span class="pagenum">[Pg 176]</span></p>
+<h3>&sect; 6. <i>Identity of Light and Radiant Heat. Reflection
+from Plane and Curved Surfaces. Total Reflection of Heat</i>.</h3>
+<p>The growth of science is organic. That which today is an
+<i>end</i> becomes to-morrow a <i>means</i> 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 &OElig;rsted, 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 <i>thermo-electric pile</i>, 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.</p>
+<p>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 <a name="Page_177" id=
+"Page_177"></a><span class="pagenum">[Pg 177]</span>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.</p>
+<p>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&deg;. 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&mdash;the substantial
+<i>identity of light and radiant heat</i>.</p>
+<p>That they are identical in <i>all</i> respects cannot of course
+be the case, for if they were they would act in the same manner
+upon all instruments, the <i>eye</i> 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 <a name="Page_178" id="Page_178"></a><span class=
+"pagenum">[Pg 178]</span>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 (<i>m</i> <i>n</i>), 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.</p>
+<div class="figcenter" style="width: 425px;"><img src=
+"images/fig49.jpg" width="425" height="288" alt="FIG 49." title=
+"" /> <b>FIG 49.</b></div>
+<p>As regards reflection from curved surfaces, the identity also
+holds good. Receiving the beam from our electric lamp on a concave
+mirror (<i>m</i> <i>m</i>, 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.</p>
+<p><a name="Page_179" id="Page_179"></a><span class="pagenum">[Pg
+179]</span>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
+<i>a</i> <i>b</i> <i>c</i> is the section. It meets the hypothenuse
+at an obliquity greater than the limiting angle,<a name=
+"FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23"
+class="fnanchor">[23]</a> 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.</p>
+<div class="figcenter" style="width: 500px;"><img src=
+"images/fig50.jpg" width="500" height="310" alt="Fig. 50." title=
+"" /> <b>Fig. 50.</b></div>
+<h3>&sect; 7. <i>Invisible Images formed by Radiant Heat.</i></h3>
+<p>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 <a name="Page_180" id="Page_180"></a><span class=
+"pagenum">[Pg 180]</span>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.)</p>
+<div class="figcenter" style="width: 219px;"><img src=
+"images/fig51.jpg" width="219" height="215" alt="Fig. 51." title=
+"" /> <b>Fig. 51.</b></div>
+<h3>&sect; 8. <i>Polarization of Heat</i>.</h3>
+<p>Whether radiant heat be capable of polarization or not was for a
+long time a subject of discussion. B&eacute;rard 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 <a name=
+"Page_181" id="Page_181"></a><span class="pagenum">[Pg
+181]</span>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.</p>
+<div class="figcenter" style="width: 421px;"><img src=
+"images/fig52.jpg" width="421" height="296" alt="Fig. 52." title=
+"" /> <b>Fig. 52.</b></div>
+<p>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&deg;. 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.</p>
+<p><a name="Page_182" id="Page_182"></a><span class="pagenum">[Pg
+182]</span>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&deg;. 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.</p>
+<p>Removing the mica and restoring the needle once more to 0&deg;,
+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.</p>
+<h3>&sect; 9. <i>Double Refraction of Heat</i>.</h3>
+<p>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 <a name="Page_183" id=
+"Page_183"></a><span class="pagenum">[Pg 183]</span>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&deg;, and then rises
+again to 90&deg; in the second position. This proves the double
+refraction of the heat.</p>
+<div class="figcenter" style="width: 408px;"><img src=
+"images/fig53.jpg" width="408" height="383" alt="Fig. 53." title=
+"" /> <b>Fig. 53.</b></div>
+<p>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&deg;, rising, however, again
+<a name="Page_184" id="Page_184"></a><span class="pagenum">[Pg
+184]</span>to 90&deg; after a rotation of 360&deg;. 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.</p>
+<h3>&sect; 10. <i>Magnetization of Heat</i>.</h3>
+<p>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&deg;, the
+excitement of the magnet causes a far greater positive augmentation
+of the light, though the augmentation is not so well <i>seen</i>
+through lack of contrast, because here, at starting, the field is
+illuminated.</p>
+<p>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 <a name="Page_185" id=
+"Page_185"></a><span class="pagenum">[Pg 185]</span>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.</p>
+<p>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 <i>obscure</i> 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.</p>
+<h3>&sect; 11. <i>Distribution of Heat in the Electric
+Spectrum</i>.</h3>
+<p>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.</p>
+<div class="figcenter" style="width: 600px;"><img src=
+"images/fig54.jpg" width="600" height="287" alt=
+"SPECTRUM OF ELECTRIC LIGHT." title="" /> <b>SPECTRUM OF ELECTRIC
+LIGHT.</b></div>
+<p>When this instrument is brought to the violet end <a name=
+"Page_186" id="Page_186"></a><span class="pagenum">[Pg
+186]</span><a name="Page_187" id="Page_187"></a>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.</p>
+<p>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.</p>
+<p>But in verification, as already stated, consists the strength of
+science. Determining in the first place <a name="Page_188" id=
+"Page_188"></a><span class="pagenum">[Pg 188]</span>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 <i>diffraction</i>,
+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.</p>
+<hr style="width: 65%;" />
+<div><a name="Page_189" id="Page_189"></a><span class="pagenum">[Pg
+189]</span></div>
+<h2><a name="LECTURE_VI" id="LECTURE_VI"></a>LECTURE VI.</h2>
+<table border="0" cellpadding="0" cellspacing="0" summary="">
+<tr>
+<td>
+<div style="font-size: smaller;">
+<ul style="list-style: none;">
+<li>PRINCIPLES OF SPECTRUM ANALYSIS</li>
+<li>PRISMATIC ANALYSIS OF THE LIGHT OF INCANDESCENT VAPOURS</li>
+<li>DISCONTINUOUS SPECTRA</li>
+<li>SPECTRUM BANDS PROVED BY BUNSEN AND KIRCHHOFF TO BE
+CHARACTERISTIC</li>
+<li>OF THE VAPOUR</li>
+<li>DISCOVERY OF RUBIDIUM, CAESIUM, AND THALLIUM</li>
+<li>RELATION OF EMISSION TO ABSORPTION</li>
+<li>THE LINES OF FRAUNHOFER</li>
+<li>THEIR EXPLANATION BY KIRCHHOFF</li>
+<li>SOLAR CHEMISTRY INVOLVED IN THIS EXPLANATION</li>
+<li>FOUCAULT'S EXPERIMENT</li>
+<li>PRINCIPLES OF ABSORPTION</li>
+<li>ANALOGY OF SOUND AND LIGHT</li>
+<li>EXPERIMENTAL DEMONSTRATION OF THIS ANALOGY</li>
+<li>RECENT APPLICATIONS OF THE SPECTROSCOPE</li>
+<li>SUMMARY AND CONCLUSION.</li>
+</ul>
+</div>
+</td>
+</tr>
+</table>
+<p>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, <a name="Page_190" id="Page_190"></a><span class=
+"pagenum">[Pg 190]</span>the carbon-vapour would yield a few bands
+of colour with spaces of darkness between them.</p>
+<p>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&mdash;that
+corresponding to this particular green&mdash;is emitted by the
+thallium-vapour.</p>
+<p>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
+<i>colour</i> from the other, it is equally impossible to confound
+the <i>spectrum</i> of incandescent silver-vapour with that of
+<a name="Page_191" id="Page_191"></a><span class="pagenum">[Pg
+191]</span>thallium. In the case of silver, we have two green bands
+instead of one.</p>
+<p>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.</p>
+<p>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 <i>resistance</i> 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.<a name=
+"FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24"
+class="fnanchor">[24]</a></p>
+<p>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 <a name="Page_192" id=
+"Page_192"></a><span class="pagenum">[Pg 192]</span>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&mdash;an alloy of copper and zinc&mdash;gives the
+bands of both metals, perfectly unaltered in position or
+character.</p>
+<p>But we are not confined to the metals themselves; the
+<i>salts</i> 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.</p>
+<p>When, therefore, Bunsen and Kirchhoff, the illustrious founders
+of <i>spectrum analysis</i>, 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 <a name="Page_193" id=
+"Page_193"></a><span class="pagenum">[Pg 193]</span>it now stands
+among chemical substances as the metal <i>Rubidium</i>. They
+subsequently discovered a second metal, which they called
+<i>C&aelig;sium</i>. 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 <i>Thallium</i>, and obtained
+the salts of the metal which yielded it. The metal itself was first
+isolated in ingots by M. Lamy, a French chemist.</p>
+<p>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 <i>pure</i> 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.</p>
+<p>(The positions of the principal lines, lettered according to
+Fraunhofer, are shown in the annexed sketch <a name="Page_194" id=
+"Page_194"></a><span class="pagenum">[Pg 194]</span>(fig. 55) of
+the solar spectrum. A is supposed to stand near the extreme red,
+and J near the extreme violet.)</p>
+<div class="figleft" style="width: 82px;"><img src=
+"images/fig55.jpg" width="82" height="600" alt="Fig. 55." title=
+"" /> <b>Fig. 55.</b></div>
+<p>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.</p>
+<p>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 <a name="Page_195" id=
+"Page_195"></a><span class="pagenum">[Pg 195]</span>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.</p>
+<p>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 <i>produce</i> 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.</p>
+<p>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.</p>
+<p>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 <a name="Page_196" id=
+"Page_196"></a><span class="pagenum">[Pg 196]</span>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.</p>
+<p>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. &Aring;ngstr&ouml;m and Thal&eacute;n 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:&mdash;</p>
+<table border="0" cellpadding="2" cellspacing="0" summary="">
+<tr>
+<td align='left'>Calcium</td>
+<td align='right'>75</td>
+</tr>
+<tr>
+<td align='left'>Barium</td>
+<td align='right'>11</td>
+</tr>
+<tr>
+<td align='left'>Magnesium</td>
+<td align='right'>4</td>
+</tr>
+<tr>
+<td align='left'>Manganese</td>
+<td align='right'>57</td>
+</tr>
+<tr>
+<td align='left'>Titanium</td>
+<td align='right'>118</td>
+</tr>
+<tr>
+<td align='left'>Chromium</td>
+<td align='right'>18</td>
+</tr>
+<tr>
+<td align='left'>Nickel</td>
+<td align='right'>33</td>
+</tr>
+<tr>
+<td align='left'>Cobalt</td>
+<td align='right'>19</td>
+</tr>
+<tr>
+<td align='left'>Hydrogen</td>
+<td align='right'>4</td>
+</tr>
+<tr>
+<td align='left'>Aluminium</td>
+<td align='right'>2</td>
+</tr>
+<tr>
+<td align='left'>Zinc</td>
+<td align='right'>2</td>
+</tr>
+<tr>
+<td align='left'>Copper</td>
+<td align='right'>7</td>
+</tr>
+</table>
+<p>The probability is overwhelming that all these substances exist
+in the atmosphere of the sun.</p>
+<p>Kirchhoff's discovery profoundly modified the conceptions
+previously entertained regarding the constitution of the sun,
+leading him to views which, though <a name="Page_197" id=
+"Page_197"></a><span class="pagenum">[Pg 197]</span>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 <i>clouds</i>, 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.</p>
+<p>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 <a name="Page_198" id="Page_198"></a><span class=
+"pagenum">[Pg 198]</span>he found to he considerably strengthened
+by the passage of the solar light through the voltaic arc.</p>
+<p>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 <i>generated</i> 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.</p>
+<p>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 a&euml;rial 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.</p>
+<p>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 <i>radiation</i> or <i>emission</i> of sound from the fork. A
+few days ago, on sound<a name="Page_199" id=
+"Page_199"></a><span class="pagenum">[Pg 199]</span>ing 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 <i>absorption</i> 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.</p>
+<p>I have now to bring before you, on a suitable scale, the
+demonstration that we can do with <i>light</i> 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 <a name="Page_200" id="Page_200"></a><span class=
+"pagenum">[Pg 200]</span>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.<a name="FNanchor_25_25" id=
+"FNanchor_25_25"></a><a href="#Footnote_25_25" class=
+"fnanchor">[25]</a></p>
+<p>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.</p>
+<p>In front of the slit (at L, fig. 56) through which the beam
+issues is placed a Bunsen's burner (<i>b</i>) 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 <a name="Page_201" id="Page_201"></a><span class=
+"pagenum">[Pg 201]</span>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.</p>
+<div class="figright" style="width: 441px;"><img src=
+"images/fig56.jpg" width="441" height="252" alt="Fig. 56." title=
+"" /> <b>Fig. 56.</b></div>
+<p>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:&mdash;'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
+<a name="Page_202" id="Page_202"></a><span class="pagenum">[Pg
+202]</span>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 Pl&uuml;cker, have also given us
+beautiful drawings of spectra obtained from the same source.</p>
+<p>'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
+&Aring;ngstr&ouml;m. 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 <i>reversal</i> 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.'</p>
+<p><a name="Page_203" id="Page_203"></a><span class="pagenum">[Pg
+203]</span>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.</p>
+<p>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 <a name=
+"Page_204" id="Page_204"></a><span class="pagenum">[Pg
+204]</span>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.</p>
+<p>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.</p>
+<p>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
+<a name="Page_205" id="Page_205"></a><span class="pagenum">[Pg
+205]</span>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
+<i>Chromosphere</i>.</p>
+<p>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.<a name="Page_206" id="Page_206"></a><span class=
+"pagenum">[Pg 206]</span></p>
+<h3>SUMMARY AND CONCLUSION.</h3>
+<p>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&mdash;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.</p>
+<p>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 <i>know</i>. 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 <a name="Page_207" id=
+"Page_207"></a><span class="pagenum">[Pg 207]</span>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&mdash;I might say, indeed, for more than fifteen hundred
+years&mdash;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.</p>
+<p>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.</p>
+<p>Up to his demonstration of the composition of white light,
+Newton had been everywhere triumphant&mdash;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 <a name="Page_208" id=
+"Page_208"></a><span class="pagenum">[Pg 208]</span>went hand in
+hand, and that you could not abolish the one without at the same
+time abolishing the other. Here Dollond corrected him.</p>
+<p>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.</p>
+<p>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
+<a name="Page_209" id="Page_209"></a><span class="pagenum">[Pg
+209]</span>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.</p>
+<p>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.</p>
+<p>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 <a name="Page_210" id="Page_210"></a><span class="pagenum">[Pg
+210]</span>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.</p>
+<p>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.</p>
+<p>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 <a name="Page_211" id="Page_211"></a><span class=
+"pagenum">[Pg 211]</span>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.'</p>
+<p>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.'</p>
+<hr style='width: 45%;' />
+<p>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 <a name="Page_212"
+id="Page_212"></a><span class="pagenum">[Pg 212]</span>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.</p>
+<p>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,<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href=
+"#Footnote_26_26" class="fnanchor">[26]</a> 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 <a name="Page_213" id=
+"Page_213"></a><span class="pagenum">[Pg 213]</span>the last
+results of their labours, and then rested from them for ever.</p>
+<p>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&mdash;your
+Henry or your Draper, for example&mdash;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
+<i>use</i> 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 <i>may</i> 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.</p>
+<p>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 <a name="Page_214" id="Page_214"></a><span class=
+"pagenum">[Pg 214]</span>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.</p>
+<p>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&mdash;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 <a name="Page_215" id="Page_215"></a><span class="pagenum">[Pg
+215]</span>analyzed, what are industrial America and industrial
+England?</p>
+<p>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.</p>
+<p>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.</p>
+<p>Both England and America have reason to bear those things in
+mind, for the largeness and nearness of <a name="Page_216" id=
+"Page_216"></a><span class="pagenum">[Pg 216]</span>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&mdash;nay, if you fail to secure
+for him free scope and encouragement&mdash;you not only lose the
+motive power of intellectual progress, but infallibly sever
+yourselves from the springs of industrial life.</p>
+<p>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.</p>
+<p>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 <a name="Page_217" id="Page_217"></a><span class=
+"pagenum">[Pg 217]</span>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&mdash;they spread themselves so
+largely and umbrageously before the public eye&mdash;that they
+often shut out from view those workers who are engaged in the
+quieter and profounder business of original investigation.</p>
+<p>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.</p>
+<p>The ancients discovered the electricity of amber; and Gilbert,
+in the year 1600, extended the discovery <a name="Page_218" id=
+"Page_218"></a><span class="pagenum">[Pg 218]</span>to other
+bodies. Then followed Boyle, Von Guericke, Gray, Canton, Du Fay,
+Kleist, Cun&aelig;us, 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. &OElig;rsted
+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.</p>
+<p>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
+G&ouml;ttingen, 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&mdash;nay, its
+applicability to telegraphic purposes demonstrated&mdash;by men
+whose sole reward for their labours was the noble <a name=
+"Page_219" id="Page_219"></a><span class="pagenum">[Pg
+219]</span>excitement of research, and the joy attendant on the
+discovery of natural truth.</p>
+<p>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.</p>
+<p>Pasteur, one of the most illustrious members of the Institute of
+France, in accounting for the disastrous <a name="Page_220" id=
+"Page_220"></a><span class="pagenum">[Pg 220]</span>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 <i>applied science</i>. 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 <i>in our day the
+reign of theoretic science yielded place to that of applied
+science</i>. 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. <i>We have science, and the applications of science</i>,
+which are united together as the tree and its fruit.'</p>
+<p>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 <a name="Page_221" id=
+"Page_221"></a><span class="pagenum">[Pg 221]</span>issues though
+born of their own deeds. These rising workshops, these peopled
+colonies, those ships which furrow the seas&mdash;this abundance,
+this luxury, this tumult&mdash;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.'</p>
+<p>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.</p>
+<p>Among the many problems before them they have <a name="Page_222"
+id="Page_222"></a><span class="pagenum">[Pg 222]</span>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&mdash;in a spirit, indeed, the reverse of
+unfriendly&mdash;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.</p>
+<p>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.'<a name="FNanchor_27_27" id=
+"FNanchor_27_27"></a><a href="#Footnote_27_27" class=
+"fnanchor">[27]</a> 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; <a name="Page_223" id=
+"Page_223"></a><span class="pagenum">[Pg 223]</span>and it is
+there, he contends, that you collect the treasures of the
+intellect, without taking the trouble to create them.</p>
+<p>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&mdash;whether
+scientific genius cannot find, in the midst of you, a tranquil
+home.</p>
+<p>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 <a name="Page_224" id="Page_224"></a><span class=
+"pagenum">[Pg 224]</span>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.</p>
+<p>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.</p>
+<p>Drawn by your kindness, I have come here to give these lectures,
+and now that my visit to America has <a name="Page_225" id=
+"Page_225"></a><span class="pagenum">[Pg 225]</span>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&mdash;not sown broadcast, believe me, it is sown thus
+nowhere&mdash;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&mdash;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.</p>
+<div><a name="Page_226" id="Page_226"></a><span class="pagenum">[Pg
+226]</span></div>
+<hr style="width: 65%;" />
+<div><a name="Page_227" id="Page_227"></a><span class="pagenum">[Pg
+227]</span></div>
+<h2><a name="APPENDIX" id="APPENDIX"></a>APPENDIX.</h2>
+<h3><a name="ON_THE_SPECTRA_OF_POLARIZED_LIGHT" id=
+"ON_THE_SPECTRA_OF_POLARIZED_LIGHT"></a>ON THE SPECTRA OF POLARIZED
+LIGHT.</h3>
+<p>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:&mdash;</p>
+<div class="blockquot">
+<p>'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 <a name="Page_228" id="Page_228"></a><span class=
+"pagenum">[Pg 228]</span>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&deg;, all trace of
+colour disappears; and also that when the angle amounts to 90&deg;,
+colour reappears, not, however, the original colour, but one
+complementary to it.</p>
+<p>'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&deg; 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&deg;. Thus we have
+from the spectroscope a complete account of what has taken place to
+produce the original colour and its changes.</p>
+<p>'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.</p>
+<p>'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 <a name="Page_229" id=
+"Page_229"></a><span class="pagenum">[Pg 229]</span>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.</p>
+<p>'These experiments were made more than thirty years ago by the
+French philosophers, MM. Foucault and Fizeau.</p>
+<p>'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>i.e.</i> 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 <i>vice vers&acirc;</i>, precisely in such
+a direction as to give rise to the tints seen by direct
+projection.</p>
+<p>'The kind of polarization effected by the quartz plates is
+called circular, while that effected by the other class of <a name=
+"Page_230" id="Page_230"></a><span class="pagenum">[Pg
+230]</span>crystals is called plane, on account of the form of the
+vibrations executed by the molecules of &aelig;ther; and this leads
+us to examine a little more closely the nature of the polarization
+of different parts of these spectra of polarized light.</p>
+<p>'Now, two things are clear: first, that if the light be
+plane-polarized&mdash;that is, if all the vibrations throughout the
+entire ray are rectilinear and in one plane&mdash;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&deg;; 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>i.e.</i> 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>i.e.</i> 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 <a name=
+"Page_231" id="Page_231"></a><span class="pagenum">[Pg
+231]</span>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.</p>
+<p>'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 <i>vice vers&acirc;</i>), we have
+only to turn the plate round through 90&deg;. 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&deg; 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<a name=
+"FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28"
+class="fnanchor">[28]</a>.</p>
+<p>'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.</p>
+<p><a name="Page_232" id="Page_232"></a><span class="pagenum">[Pg
+232]</span>'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&mdash;that is, as if they were one plate of
+crystal&mdash;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&deg;,
+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&deg; 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&deg;, 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&deg;.</p>
+<p>'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.</p>
+<p>'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.</p>
+<p><a name="Page_233" id="Page_233"></a><span class="pagenum">[Pg
+233]</span>'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.</p>
+<p>'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 <i>vice vers&acirc;</i>, according to the position
+of the plates.</p>
+<p>'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.'</p>
+</div>
+<hr style='width: 45%;' />
+<p>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 <i>iris-rings</i>,
+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, <a name="Page_234" id=
+"Page_234"></a><span class="pagenum">[Pg 234]</span>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.</p>
+<p>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&mdash;the
+fan opening out at the red end of the spectrum.</p>
+<hr style='width: 45%;' />
+<h3><a name="MEASUREMENT_OF_THE_WAVES_OF_LIGHT" id=
+"MEASUREMENT_OF_THE_WAVES_OF_LIGHT"></a><i>MEASUREMENT OF THE WAVES
+OF LIGHT.</i></h3>
+<p>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 <i>the length</i> of a wave of
+light.</p>
+<div class="figright" style="width: 313px;"><img src=
+"images/fig57.jpg" width="313" height="196" alt="Fig. 57." title=
+"" /> <b>Fig. 57.</b></div>
+<p>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 differ<a name="Page_235" id="Page_235"></a><span class=
+"pagenum">[Pg 235]</span>ence 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,<a name=
+"FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29"
+class="fnanchor">[29]</a> 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.</p>
+<p>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 <i>d</i>. The
+distance, C <i>d</i>, between the foot of this perpendicular and
+the other edge is the length of a wave of the light. The angle C D
+<i>d</i>, 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 <i>d</i> is so
+small that it sensibly coincides with the arc of the circle. Hence
+the length of the semicircle is to the length C <i>d</i> of the
+wave as 180&deg; to <a name="Page_236" id=
+"Page_236"></a><span class="pagenum">[Pg 236]</span>1'38", or,
+reducing all to seconds, as 648,000" to 98". Thus, we have the
+proportion&mdash;</p>
+<div class="blockquot">
+<p>648,000 : 98 :: 4.248 to the wave-length C <i>d</i>.</p>
+</div>
+<p>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.</p>
+<div class="footnotes">
+<p class="center">FOOTNOTES:</p>
+<div class="footnote">
+<p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href=
+"#FNanchor_1_1"><span class="label">[1]</span></a> Among whom may
+be especially mentioned the late Sir Edmund Head, Bart., with whom
+I had many conversations on this subject.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href=
+"#FNanchor_2_2"><span class="label">[2]</span></a> At whose hands
+it gives me pleasure to state I have always experienced honourable
+and liberal treatment.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href=
+"#FNanchor_3_3"><span class="label">[3]</span></a> One of the
+earliest of these came from Mr. John Amory Lowell of Boston.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href=
+"#FNanchor_4_4"><span class="label">[4]</span></a> It will be
+subsequently shown how this simple apparatus may be employed to
+determine the 'polarizing angle' of a liquid.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href=
+"#FNanchor_5_5"><span class="label">[5]</span></a> From this
+principle Sir John Herschel deduces in a simple and elegant manner
+the fundamental law of reflection.&mdash;See <i>Familiar
+Lectures</i>, p. 236.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href=
+"#FNanchor_6_6"><span class="label">[6]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href=
+"#FNanchor_7_7"><span class="label">[7]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href=
+"#FNanchor_8_8"><span class="label">[8]</span></a> 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
+<i>all</i> the other colours of the spectrum may be obtained.</p>
+<p>Some years ago Sir Charles Wheatstone drew my attention to a
+work by Christian Ernst W&uuml;nsch, Leipzig 1792, in which the
+author announces the proposition that there are neither five nor
+seven, but only three simple colours in white light. W&uuml;nsch
+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 <i>simple</i>
+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 <i>simple</i> 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 <i>simple</i> colour. He also finds that yellow and indigo
+blue produce <i>white</i> 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, W&uuml;nsch
+very emphatically distinguishes the mixture of pigments from that
+of lights. Speaking of the generation of yellow, he says, 'I say
+expressly <i>red and green light</i>, because I am speaking about
+light-colours (Lichtfarben), and not about pigments.' However
+faulty his theories may be, W&uuml;nsch'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. (<i>Popular Lectures</i>, p.
+249. The paper of Helmholtz on the mixture of colours, translated
+by myself, is published in the <i>Philosophical Magazine</i> for
+1852. Maxwell's memoir on the Theory of Compound Colours is
+published in the <i>Philosophical Transactions</i>, vol. 150, p.
+67.)</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href=
+"#FNanchor_9_9"><span class="label">[9]</span></a> 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:&mdash;</p>
+<div class="blockquot">
+<p>'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.'&mdash;(<i>Maclaurin: An
+Account of Sir I. Newton's Philosophical Discoveries. Written 1728;
+second edition</i>, 1750; pp. 18, 19.)</p>
+</div>
+</div>
+<div class="footnote">
+<p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href=
+"#FNanchor_10_10"><span class="label">[10]</span></a> 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 <i>circular</i> motion of the
+particles. This, as proved by the brothers Weber, is the real
+motion in the case of water-waves.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href=
+"#FNanchor_11_11"><span class="label">[11]</span></a> Copied from
+Weber's <i>Wellenlehre</i>.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href=
+"#FNanchor_12_12"><span class="label">[12]</span></a> See
+<i>Lectures on Sound</i>, 1st and 2nd ed., Lecture VII.; and 3rd
+ed., Chap. VIII. Longmans.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href=
+"#FNanchor_13_13"><span class="label">[13]</span></a> <i>Boyle's
+Works</i>, Birch's edition, p. 675.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href=
+"#FNanchor_14_14"><span class="label">[14]</span></a> Page 743.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href=
+"#FNanchor_15_15"><span class="label">[15]</span></a> The beautiful
+plumes produced by water-crystallization have been successfully
+photographed by Professor Lockett.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href=
+"#FNanchor_16_16"><span class="label">[16]</span></a> 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 <i>wetted</i> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href=
+"#FNanchor_17_17"><span class="label">[17]</span></a> This
+beautiful law is usually thus expressed: <i>The index of refraction
+of any substance is the tangent of its polarizing angle</i>. 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href=
+"#FNanchor_18_18"><span class="label">[18]</span></a> Whewell.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href=
+"#FNanchor_19_19"><span class="label">[19]</span></a> Removed from
+us since these words were written.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href=
+"#FNanchor_20_20"><span class="label">[20]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href=
+"#FNanchor_21_21"><span class="label">[21]</span></a> <i>Boyle's
+Works</i>, Birch's edition, vol. i. pp, 729 and 730.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href=
+"#FNanchor_22_22"><span class="label">[22]</span></a> <i>Werke</i>,
+B. xxix. p. 24.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href=
+"#FNanchor_23_23"><span class="label">[23]</span></a> Defined in
+Lecture I.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href=
+"#FNanchor_24_24"><span class="label">[24]</span></a> This
+circumstance ought not to be lost sight of in the examination of
+compound spectra. Other similar instances might be cited.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href=
+"#FNanchor_25_25"><span class="label">[25]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href=
+"#FNanchor_26_26"><span class="label">[26]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href=
+"#FNanchor_27_27"><span class="label">[27]</span></a> 'Il faut
+reconna&icirc;tre que parmi les peuples civilis&eacute;s de nos
+jours il en est pen chez qui les hautes sciences aient fait moins
+de progr&egrave;s qu'aux &Eacute;tats-Unis, ou qui aient fourni
+moins de grands artistes, de po&euml;tes illustres et de
+c&eacute;l&egrave;bres &eacute;crivains.' (<i>De la
+D&eacute;mocratie en Am&eacute;rique</i>, etc. tome ii. p. 36.)</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href=
+"#FNanchor_28_28"><span class="label">[28]</span></a> 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.</p>
+</div>
+<div class="footnote">
+<p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href=
+"#FNanchor_29_29"><span class="label">[29]</span></a> The
+millimeter is about 1/25th of an inch.</p>
+</div>
+</div>
+<hr style="width: 65%;" />
+<div><a name="Page_237" id="Page_237"></a><span class="pagenum">[Pg
+237]</span></div>
+<h2><a name="INDEX" id="INDEX"></a>INDEX.</h2>
+<div>Absorption, principles of, <a href="#Page_199">199</a><br />
+<br />
+Airy, Sir George, severity and conclusiveness of his proofs,
+<a href="#Page_209">209</a><br />
+<br />
+Alhazen, his inquiry respecting light, <a href="#Page_14">14</a>,
+<a href="#Page_207">207</a><br />
+<br />
+Analyzer, polarizer and, <a href="#Page_127">127</a><br />
+&mdash;&mdash;recompounding of the two systems of waves by the
+analyzer, <a href="#Page_129">129</a><br />
+<br />
+&Aring;ngstr&ouml;m, his paper on spectrum analysis, <a href=
+"#Page_202">202</a><br />
+<br />
+Arago, Fran&ccedil;ois, and Dr. Young, <a href=
+"#Page_50">50</a><br />
+&mdash;&mdash;his discoveries respecting light, <a href=
+"#Page_208">208</a><br />
+<br />
+Atomic polarity, <a href="#Page_93">93-96</a><br />
+<br />
+Bacon, Roger, his inquiry respecting light, <a href=
+"#Page_14">14</a>, <a href="#Page_207">207</a><br />
+<br />
+Bartholinus, Erasmus, on Iceland spar, <a href=
+"#Page_112">112</a><br />
+<br />
+B&eacute;rard on polarization of heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Blackness, meaning of, <a href="#Page_32">32</a><br />
+<br />
+Boyle, Robert, his observations on colours, <a href=
+"#Page_65">65</a>, <a href="#Page_66">66</a><br />
+&mdash;&mdash;his remarks on fluorescence, <a href=
+"#Page_163">163</a>, <a href="#Page_164">164</a><br />
+<br />
+Bradley, James, discovers the aberration of light, <a href=
+"#Page_21">21</a>, <a href="#Page_22">22</a><br />
+<br />
+Brewster, Sir David, his chief objection to the undulatory theory
+of light, <a href="#Page_47">47</a><br />
+<br />
+Brewster, Sir David, his discovery in biaxal crystals, <a href=
+"#Page_209">209</a><br />
+<br />
+Brougham, Mr. (afterwards Lord), ridicules Dr. T. Young's
+speculations, <a href="#Page_50">50</a>, <a href=
+"#Page_51">51</a><br />
+<br />
+C&aelig;sium, discovery of, <a href="#Page_193">193</a><br />
+<br />
+Calorescence, <a href="#Page_174">174</a><br />
+<br />
+Clouds, actinic, <a href="#Page_152">152-154</a><br />
+&mdash;&mdash;polarization of, <a href="#Page_155">155</a><br />
+<br />
+Colours of thin plates, <a href="#Page_64">64</a><br />
+&mdash;&mdash;Boyle's observations on, <a href="#Page_65">65</a>,
+<a href="#Page_66">66</a><br />
+&mdash;&mdash;Hooke on the colours of thin plates, <a href=
+"#Page_67">67</a><br />
+&mdash;&mdash;of striated surfaces, <a href="#Page_89">89</a>,
+<a href="#Page_90">90</a><br />
+<br />
+Comet of 1680, Newton's estimate of the temperature of, <a href=
+"#Page_168">168</a><br />
+<br />
+Crookes, Mr., his discovery of thallium, <a href=
+"#Page_193">193</a><br />
+<br />
+Crystals, action of, upon light, <a href="#Page_98">98</a><br />
+&mdash;&mdash;built by polar force, <a href="#Page_98">98</a><br />
+&mdash;&mdash;illustrations of crystallization, <a href=
+"#Page_99">99</a><br />
+&mdash;&mdash;architecture of, considered as an introduction to
+their action upon light, <a href="#Page_98">98</a><br />
+&mdash;&mdash;bearings of crystallization upon optical phenomena,
+<a href="#Page_106">106</a><br />
+<br />
+Crystals, rings surrounding the axes of, uniaxal and biaxal,
+<a href="#Page_145">145</a><br />
+<br />
+Cuvier on ardour for knowledge, <a href="#Page_220">220</a><br />
+<br />
+De Tocqueville, writings of, <a href="#Page_215">215</a>, <a href=
+"#Page_222">222</a>, <a href="#Page_223">223</a><br />
+<a name="Page_238" id="Page_238"></a><span class="pagenum">[Pg
+238]</span><br />
+Descartes, his explanation of the rainbow, <a href=
+"#Page_24">24</a>, <a href="#Page_25">25</a><br />
+&mdash;&mdash;his ideas respecting the transmission of light,
+<a href="#Page_43">43</a><br />
+&mdash;&mdash;his notion of light, <a href=
+"#Page_207">207</a><br />
+<br />
+Diamond, ignition of a, in oxygen, <a href=
+"#Page_169">169</a><br />
+<br />
+Diathermancy, <a href="#Page_173">173</a><br />
+<br />
+Diffraction of light, phenomena of, <a href="#Page_78">78</a><br />
+&mdash;&mdash;bands, <a href="#Page_78">78</a>, <a href=
+"#Page_79">79</a><br />
+&mdash;&mdash;explanation of, <a href="#Page_80">80</a><br />
+&mdash;&mdash;colours produced by, <a href="#Page_89">89</a><br />
+<br />
+Dollond, his experiments on achromatism, <a href=
+"#Page_28">28</a><br />
+<br />
+Draper, Dr., his investigation on heat, <a href=
+"#Page_172">172</a><br />
+<br />
+Drummond light, spectrum of, <a href="#Page_195">195</a><br />
+<br />
+<br />
+Earth, daily orbit of, <a href="#Page_74">74</a><br />
+<br />
+Electric beam, heat of the, <a href="#Page_168">168</a><br />
+<br />
+Electricity, discoveries in, <a href="#Page_217">217</a>, <a href=
+"#Page_218">218</a><br />
+<br />
+Emission theory of light, bases of the, <a href=
+"#Page_45">45</a><br />
+&mdash;&mdash;Newton espouses the theory, and the results of this
+espousal, <a href="#Page_77">77</a><br />
+<br />
+Ether, Huyghens and Euler advocate and defend the conception of an,
+<a href="#Page_48">48</a>, <a href="#Page_58">58</a><br />
+&mdash;&mdash;objected to by Newton, <a href=
+"#Page_58">58</a><br />
+<br />
+Euler espouses and defends the conception of an ether, <a href=
+"#Page_48">48</a>, <a href="#Page_58">58</a><br />
+<br />
+Eusebius on the natural philosophers of his time, <a href=
+"#Page_13">13</a><br />
+<br />
+Expansion by cold, <a href="#Page_104">104</a><br />
+<br />
+Experiment, uses of, <a href="#Page_3">3</a><br />
+<br />
+Eye, the, its imperfections, grown for ages towards perfection,
+<a href="#Page_8">8</a><br />
+&mdash;&mdash;imperfect achromatism of the, <a href=
+"#Page_29">29</a>, <a href="#Footnote_6_6"><i>note</i></a><br />
+<br />
+<br />
+Faraday, Michael, his discovery of magneto-electricity, <a href=
+"#Page_218">218</a><br />
+<br />
+'Fits,' theory of, <a href="#Page_73">73</a><br />
+&mdash;&mdash;its explanation of Newton's rings, <a href=
+"#Page_74">74</a><br />
+&mdash;&mdash;overthrow of the theory, <a href=
+"#Page_77">77</a><br />
+<br />
+Fizeau determines the velocity of light, <a href=
+"#Page_22">22</a><br />
+<br />
+Fluorescence, Stokes's discovery of, <a href=
+"#Page_161">161</a><br />
+&mdash;&mdash;the name, <a href="#Page_174">174</a><br />
+<br />
+Forbes, Professor, polarizes and depolarizes heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Foucault, determines the velocity of light, <a href=
+"#Page_22">22</a><br />
+&mdash;&mdash;his experiments on absorption, <a href=
+"#Page_197">197</a>, <a href="#Page_198">198</a><br />
+<br />
+Fraunhofer, his theoretical calculations respecting diffraction,
+<a href="#Page_87">87</a><br />
+&mdash;&mdash;his lines, <a href="#Page_193">193</a><br />
+&mdash;&mdash;&mdash;their explanation by Kirchhoff, <a href=
+"#Page_193">193</a><br />
+<br />
+Fresnel, and Dr. Young, <a href="#Page_50">50</a><br />
+&mdash;&mdash;his theoretical calculations respecting diffraction,
+<a href="#Page_87">87</a><br />
+&mdash;&mdash;his mathematical abilities and immortal name,
+<a href="#Page_210">210</a><br />
+<br />
+<br />
+Goethe on fluorescence, <a href="#Page_165">165</a><br />
+<br />
+Gravitation, origin of the notion of the attraction of, <a href=
+"#Page_92">92</a><br />
+&mdash;&mdash;strength of the theory of, <a href=
+"#Page_148">148</a><br />
+<br />
+Grimaldi, his discovery with respect to light, <a href=
+"#Page_56">56</a><br />
+<a name="Page_239" id="Page_239"></a><span class="pagenum">[Pg
+239]</span> &mdash;&mdash;Young's generalizations of, <a href=
+"#Page_56">56</a><br />
+<br />
+<br />
+Hamilton, Sir William, of Dublin, his discovery of conical
+refraction, <a href="#Page_209">209</a><br />
+<br />
+Heat, generation of, <a href="#Page_6">6</a><br />
+&mdash;&mdash;Dr. Draper's investigation respecting, <a href=
+"#Page_171">171</a><br />
+<br />
+Helmholtz, his estimate of the genius of Young, <a href=
+"#Page_50">50</a><br />
+&mdash;&mdash;on the imperfect achromatism of the eye, <a href=
+"#Page_29">29</a>, <a href="#Footnote_6_6"><i>note</i></a>,
+<a href="#Page_31">31</a><br />
+&mdash;&mdash;reveals the cause of green in the case of pigments,
+<a href="#Page_37">37</a><br />
+<br />
+Henry, Professor Joseph, his invitation, <a href=
+"#Page_2">2</a><br />
+<br />
+Herschel, Sir John, his theoretical calculations respecting
+diffraction, <a href="#Page_87">87</a><br />
+&mdash;&mdash;first notices and describes the fluorescence of
+sulphate of quinine, <a href="#Page_165">165</a><br />
+&mdash;&mdash;his experiments on spectra, <a href=
+"#Page_201">201</a><br />
+<br />
+Herschel, Sir William, his experiments on the heat of the various
+colours of the solar spectrum, <a href="#Page_171">171</a><br />
+<br />
+Hooke, Robert, on the colours of thin plates, <a href=
+"#Page_67">67</a><br />
+&mdash;&mdash;his remarks on the idea that light and heat are modes
+of motion, <a href="#Page_68">68</a><br />
+<br />
+Horse-chestnut bark, fluorescence of, <a href=
+"#Page_165">165</a><br />
+<br />
+Huggins, Dr., his labours, <a href="#Page_205">205</a><br />
+<br />
+Huyghens advocates the conception of ether, <a href=
+"#Page_48">48</a>, <a href="#Page_58">58</a><br />
+&mdash;&mdash;his celebrated principle, <a href=
+"#Page_83">83</a><br />
+<br />
+Huyghens on the double refraction of Iceland spar, <a href=
+"#Page_112">112</a><br />
+<br />
+<br />
+Iceland spar, <a href="#Page_109">109</a><br />
+&mdash;&mdash;double refraction caused by, <a href=
+"#Page_110">110</a><br />
+&mdash;&mdash;this double refraction first treated by Erasmus
+Bartholinus, <a href="#Page_112">112</a><br />
+&mdash;&mdash;character of the beams emergent from, <a href=
+"#Page_114">114</a><br />
+&mdash;&mdash;tested by tourmaline, <a href=
+"#Page_116">116</a><br />
+&mdash;&mdash;Knoblauch's demonstration of the double refraction
+of, <a href="#Page_185">185</a><br />
+<br />
+Ice-lens, combustion through, <a href="#Page_167">167</a><br />
+<br />
+Imagination, scope of the, <a href="#Page_42">42</a><br />
+&mdash;&mdash;note by Maclaurin on this point, 43 <i>note</i><br />
+<br />
+<br />
+Janssen, M., on the rose-coloured solar prominences, <a href=
+"#Page_204">204</a><br />
+<br />
+Jupiter, Roemer's observations of the moons of, <a href=
+"#Page_20">20</a><br />
+<br />
+Jupiter's distance from the sun, <a href="#Page_20">20</a><br />
+<br />
+<br />
+Kepler, his investigations on the refraction of light, <a href=
+"#Page_14">14</a>, <a href="#Page_207">207</a><br />
+<br />
+Kirchhoff, Professor, his explanation of Fraunhofer's lines,
+<a href="#Page_193">193</a><br />
+&mdash;&mdash;his precursors, <a href="#Page_201">201</a><br />
+&mdash;&mdash;his claims, <a href="#Page_203">203</a><br />
+<br />
+Knoblauch, his demonstration of the double refraction of heat of
+Iceland spar, <a href="#Page_185">185</a><br />
+<br />
+<br />
+Lactantius, on the natural philosophers of his time, <a href=
+"#Page_13">13</a><br />
+<br />
+Lamy, M., isolates thallium in ingots, <a href=
+"#Page_193">193</a><br />
+<a name="Page_240" id="Page_240"></a><span class="pagenum">[Pg
+240]</span><br />
+Lesley, Professor, his invitation, <a href="#Page_2">2</a><br />
+<br />
+Light familiar to the ancients, <a href="#Page_5">5</a><br />
+&mdash;&mdash;generation of, <a href="#Page_6">6</a>, <a href=
+"#Page_7">7</a><br />
+&mdash;&mdash;spherical aberration of, <a href=
+"#Page_8">8</a><br />
+&mdash;&mdash;the rectilineal propagation of, and mode of producing
+it, <a href="#Page_9">9</a><br />
+&mdash;&mdash;illustration showing that the angle of incidence is
+equal to the angle of reflection, <a href="#Page_10">10</a>,
+<a href="#Page_11">11</a><br />
+&mdash;&mdash;sterility of the Middle Ages, <a href=
+"#Page_13">13</a><br />
+&mdash;&mdash;history of refraction, <a href=
+"#Page_14">14</a><br />
+&mdash;&mdash;demonstration of the fact of refraction, <a href=
+"#Page_14">14</a><br />
+&mdash;&mdash;partial and total reflection of, <a href=
+"#Page_16">16-20</a><br />
+&mdash;&mdash;velocity of, <a href="#Page_20">20</a><br />
+&mdash;&mdash;Bradley's discovery of the aberration of light,
+<a href="#Page_21">21</a>, <a href="#Page_22">22</a><br />
+&mdash;&mdash;principle of least time, <a href=
+"#Page_23">23</a><br />
+&mdash;&mdash;Descartes and the rainbow, <a href=
+"#Page_24">24</a><br />
+&mdash;&mdash;Newton's analysis of, <a href="#Page_26">26</a>,
+<a href="#Page_27">27</a><br />
+&mdash;&mdash;synthesis of white light, <a href=
+"#Page_30">30</a><br />
+&mdash;&mdash;complementary colours, <a href=
+"#Page_31">31</a><br />
+&mdash;&mdash;yellow and blue lights produce white by their
+mixture, <a href="#Page_31">31</a><br />
+&mdash;&mdash;what is the meaning of blackness? <a href=
+"#Page_32">32</a><br />
+&mdash;&mdash;analysis of the action of pigments upon, <a href=
+"#Page_33">33</a><br />
+&mdash;&mdash;absorption, <a href="#Page_34">34</a><br />
+&mdash;&mdash;mixture of pigments contrasted with mixture of
+lights, <a href="#Page_37">37</a><br />
+&mdash;&mdash;W&uuml;nsch on three simple colours in white light,
+<a href="#Page_39">39</a> <a href=
+"#Footnote_8_8"><i>note</i></a><br />
+&mdash;&mdash;Newton arrives at the emission theory, <a href=
+"#Page_45">45</a><br />
+&mdash;&mdash;Young's discovery of the undulatory theory, <a href=
+"#Page_49">49</a><br />
+&mdash;&mdash;illustrations of wave-motion, <a href=
+"#Page_58">58</a><br />
+&mdash;&mdash;interference of sound-waves, <a href=
+"#Page_58">58</a><br />
+&mdash;&mdash;velocity of, <a href="#Page_60">60</a><br />
+&mdash;&mdash;principle of interference of waves of, <a href=
+"#Page_61">61</a><br />
+&mdash;&mdash;phenomena which first suggested the undulatory theory
+<a href="#Page_62">62-69</a><br />
+&mdash;&mdash;soap-bubbles and their colours, <a href=
+"#Page_62">62-65</a><br />
+&mdash;&mdash;Newton's rings, <a href="#Page_77">69-77</a><br />
+&mdash;&mdash;his espousal of the emission theory, and the results
+of this espousal, <a href="#Page_77">77</a><br />
+&mdash;&mdash;transmitted light, <a href="#Page_77">77</a><br />
+&mdash;&mdash;diffraction, <a href="#Page_77">77</a>, <a href=
+"#Page_89">89</a><br />
+&mdash;&mdash;origin of the notion of the attraction of
+gravitation, <a href="#Page_92">92</a><br />
+&mdash;&mdash;polarity, how generated, <a href=
+"#Page_93">93</a><br />
+&mdash;&mdash;action of crystals upon, <a href=
+"#Page_98">98</a><br />
+&mdash;&mdash;refraction of, <a href="#Page_106">106</a><br />
+&mdash;&mdash;elasticity and density, <a href=
+"#Page_108">108</a><br />
+&mdash;&mdash;double refraction, <a href="#Page_109">109</a><br />
+&mdash;&mdash;chromatic phenomena produced by crystals in
+polarized, <a href="#Page_121">121</a><br />
+&mdash;&mdash;the Nicol prism, <a href="#Page_122">122</a><br />
+&mdash;&mdash;mechanism of, <a href="#Page_125">125</a><br />
+&mdash;&mdash;vibrations, <a href="#Page_125">125</a><br />
+&mdash;&mdash;composition and resolution of vibrations, <a href=
+"#Page_128">128</a><br />
+&mdash;&mdash;polarizer and analyzer, <a href=
+"#Page_127">127</a><br />
+&mdash;&mdash;recompounding the two systems of waves by the
+analyzer, <a href="#Page_129">129</a><br />
+&mdash;&mdash;interference thus rendered possible, <a href=
+"#Page_131">131</a><br />
+&mdash;&mdash;chromatic phenomena produced by quartz, <a href=
+"#Page_139">139</a><br />
+&mdash;&mdash;magnetization, of, <a href="#Page_141">141</a><br />
+&mdash;&mdash;rings surrounding the axes of crystals, <a href=
+"#Page_143">143</a><br />
+&mdash;&mdash;colour and polarization of sky, <a href=
+"#Page_149">149</a>, <a href="#Page_154">154</a><br />
+&mdash;&mdash;range of vision incommensurate with range of
+radiation, <a href="#Page_159">159</a><br />
+&mdash;&mdash;effect of thallene on the spectrum, 162<br />
+<a name="Page_241" id="Page_241"></a><span class="pagenum">[Pg
+241]</span> &mdash;&mdash;fluorescence, <a href=
+"#Page_162">162</a><br />
+&mdash;&mdash;transparency, <a href="#Page_167">167</a><br />
+&mdash;&mdash;the ultra-red rays, <a href="#Page_170">170</a><br />
+&mdash;&mdash;part played in Nature by these rays, <a href=
+"#Page_175">175</a><br />
+&mdash;&mdash;conversion of heat-rays into light-rays, <a href=
+"#Page_176">176</a><br />
+&mdash;&mdash;identity of radiant heat and, <a href=
+"#Page_177">177</a><br />
+&mdash;&mdash;polarization of heat, <a href=
+"#Page_180">180</a><br />
+&mdash;&mdash;principles of spectrum analysis, <a href=
+"#Page_189">189</a><br />
+&mdash;&mdash;spectra of incandescent vapours, <a href=
+"#Page_190">190</a><br />
+&mdash;&mdash;Fraunhofer's lines, and Kirchhoff's explanation of
+them, <a href="#Page_193">193</a><br />
+&mdash;&mdash;solar chemistry, <a href=
+"#Page_195">195-197</a><br />
+&mdash;&mdash;demonstration of analogy between sound and, <a href=
+"#Page_198">198</a>, <a href="#Page_199">199</a><br />
+&mdash;&mdash;Kirchhoff and his precursors, <a href=
+"#Page_201">201</a><br />
+&mdash;&mdash;rose-coloured solar prominences, <a href=
+"#Page_204">204</a><br />
+&mdash;&mdash;results obtained by various workers, <a href=
+"#Page_205">205</a><br />
+&mdash;&mdash;summary and conclusion, <a href=
+"#Page_206">206</a><br />
+&mdash;&mdash;polarized, the spectra of, <a href=
+"#Page_227">227</a><br />
+&mdash;&mdash;measurement of the waves of, <a href=
+"#Page_234">234</a><br />
+<br />
+Lignum Nephriticum, fluorescence of, <a href=
+"#Page_164">164</a><br />
+<br />
+Lloyd, Dr., on polarization of heat, <a href="#Page_180">180</a>,
+<a href="#Page_209">209</a><br />
+<br />
+Lockyer, Mr., on the rose-coloured solar prominences, <a href=
+"#Page_205">205</a><br />
+<br />
+Lycopodium, diffraction effects caused by the spores of, <a href=
+"#Page_88">88</a><br />
+<br />
+<br />
+Magnetization of light, <a href="#Page_141">141</a><br />
+<br />
+Malus, his discovery respecting reflected light through Iceland
+spar, <a href="#Page_115">115</a><br />
+&mdash;&mdash;discovers the polarization of light by reflection,
+<a href="#Page_208">208</a><br />
+<br />
+Masson, his essay on the bands of the induction spark, <a href=
+"#Page_202">202</a><br />
+<br />
+Melloni, on the polarization of heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Metals, combustion of, <a href="#Page_5">5</a>, <a href=
+"#Page_6">6</a><br />
+&mdash;&mdash;spectrum analysis of, <a href=
+"#Page_190">190</a><br />
+&mdash;&mdash;spectrum bands proved by Bunsen and Kirchhoff to be
+characteristic of the vapour of, <a href="#Page_192">192</a><br />
+<br />
+Mill, John Stuart, his scepticism regarding the undulatory theory,
+<a href="#Page_149">149</a><br />
+<br />
+Miller, Dr., his drawings and descriptions of the spectra of
+various coloured flames, <a href="#Page_201">201</a><br />
+<br />
+Morton, Professor, his discovery of thallene, <a href=
+"#Page_162">162</a><br />
+<br />
+Mother-of-pearl, colours of, <a href="#Page_90">90</a><br />
+<br />
+<br />
+Nature, a savage's interpretation of, <a href="#Page_4">4</a><br />
+<br />
+Newton, Sir Isaac, his experiments on the composition of solar
+light, <a href="#Page_26">26</a><br />
+&mdash;&mdash;his spectrum, <a href="#Page_27">27</a><br />
+&mdash;&mdash;dispersion, <a href="#Page_27">27</a><br />
+&mdash;&mdash;arrives at the emission theory of light, <a href=
+"#Page_45">45</a><br />
+&mdash;&mdash;his objection to the conception of an ether espoused
+and defended by Huyghens and Euler, <a href="#Page_58">58</a><br />
+&mdash;&mdash;his optical career, <a href="#Page_70">70</a><br />
+&mdash;&mdash;his rings, <a href="#Page_69">69-77</a><br />
+&mdash;&mdash;his rings explained by the theory of 'fits,' <a href=
+"#Page_73">73</a><br />
+&mdash;&mdash;espouses the emission theory, <a href=
+"#Page_77">77</a><br />
+&mdash;&mdash;effects of this espousal, <a href=
+"#Page_77">77</a><br />
+&mdash;&mdash;his idea of gravitation, <a href=
+"#Page_92">92</a><br />
+&mdash;&mdash;his errors, <a href="#Page_208">208</a><br />
+<br />
+Nicol prism, the, <a href="#Page_122">122</a><br />
+<br />
+<br />
+Ocean, colour of the, <a href="#Page_35">35</a><br />
+<a name="Page_242" id="Page_242"></a><span class="pagenum">[Pg
+242]</span><br />
+&OElig;rsted, discovers the deflection of a magnetic needle by an
+electric current, <a href="#Page_176">176</a><br />
+<br />
+Optics, science of, <a href="#Page_4">4</a><br />
+<br />
+<br />
+Pasteur referred to, <a href="#Page_219">219</a><br />
+<br />
+Physical theories, origin of, <a href="#Page_41">41-44</a><br />
+<br />
+Pigments, analysis of the action of, upon light, <a href=
+"#Page_33">33</a><br />
+&mdash;&mdash;mixture of, contrasted with mixture of lights,
+<a href="#Page_37">37</a><br />
+&mdash;&mdash;Helmholtz reveals the cause of the green in the case
+of mixed blue and yellow pigments, <a href="#Page_37">37</a><br />
+&mdash;&mdash;impurity of natural colours, <a href=
+"#Page_37">37</a><br />
+<br />
+Pitch of sound, <a href="#Page_59">59</a><br />
+<br />
+Pl&uuml;cker, his drawings of spectra, <a href=
+"#Page_202">202</a><br />
+<br />
+Polariscope, stained glass in the, 130,<a href=
+"#Page_131">131</a><br />
+&mdash;&mdash;unannealed glass in the, <a href=
+"#Page_136">136</a><br />
+<br />
+Polarity, notion of, how generated, <a href="#Page_93">93</a><br />
+&mdash;&mdash;atomic, <a href="#Page_93">93-96</a><br />
+&mdash;&mdash;structural arrangements due to, <a href=
+"#Page_96">96</a><br />
+&mdash;&mdash;polarization of light, <a href=
+"#Page_112">112</a><br />
+&mdash;&mdash;tested by tourmaline, <a href=
+"#Page_116">116</a><br />
+&mdash;&mdash;and by reflection and refraction, <a href=
+"#Page_119">119</a><br />
+&mdash;&mdash;depolarization, <a href="#Page_120">120</a><br />
+<br />
+Polarization of light, <a href="#Page_112">112</a><br />
+&mdash;&mdash;circular, <a href="#Page_140">140</a><br />
+&mdash;&mdash;sky-light, <a href="#Page_149">149</a>, <a href=
+"#Page_157">157</a><br />
+&mdash;&mdash;of artificial sky, <a href="#Page_156">156</a><br />
+&mdash;&mdash;of radiant heat, <a href="#Page_180">180</a><br />
+<br />
+Polarizer and analyzer, <a href="#Page_127">127</a><br />
+<br />
+Poles of a magnet, <a href="#Page_93">93</a><br />
+<br />
+Powell, Professor, on polarization of heat, <a href=
+"#Page_180">180</a><br />
+<br />
+Prism, the Nicol, <a href="#Page_122">122</a><br />
+<br />
+<br />
+Quartz, chromatic phenomena produced by, <a href=
+"#Page_139">139</a><br />
+<br />
+<br />
+Radiant heat, <a href="#Page_172">172</a><br />
+&mdash;&mdash;diathermancy, or perviousness to radiant heat,
+<a href="#Page_173">173</a><br />
+&mdash;&mdash;conversion of heat-rays into light rays, <a href=
+"#Page_174">174</a><br />
+&mdash;&mdash;formation of invisible heat-images, <a href=
+"#Page_179">179</a><br />
+&mdash;&mdash;polarization of, <a href="#Page_180">180</a><br />
+&mdash;&mdash;double refraction, <a href="#Page_182">182</a><br />
+&mdash;&mdash;magnetization of, <a href="#Page_184">184</a><br />
+<br />
+Rainbow, Descartes' explanation of the, <a href=
+"#Page_24">24</a><br />
+<br />
+Refraction, demonstration of, <a href="#Page_14">14</a><br />
+<br />
+Refraction of light, <a href="#Page_106">106</a><br />
+&mdash;&mdash;double, <a href="#Page_109">109</a><br />
+<br />
+Reflection, partial and total, <a href="#Page_20">16-20</a><br />
+<br />
+Respighi, results obtained by, <a href="#Page_205">205</a><br />
+<br />
+Ritter, his discovery of the ultraviolet rays of the sun, <a href=
+"#Page_159">159</a><br />
+<br />
+Roemer, Olav, his observations of Jupiter's moons, <a href=
+"#Page_20">20</a><br />
+&mdash;&mdash;his determination of the velocity of light, <a href=
+"#Page_21">21</a><br />
+<br />
+Rubidium, discovery of, <a href="#Page_193">193</a><br />
+<br />
+Rusting of iron, what it is, <a href="#Page_5">5</a><br />
+<br />
+<br />
+Schwerd, his observations respecting diffraction, <a href=
+"#Page_87">87</a><br />
+<br />
+Science, growth of, <a href="#Page_176">176</a>, <a href=
+"#Page_203">203</a><br />
+<br />
+Scoresby, Dr., succeeds in exploding gunpowder by the sun's rays
+conveyed by large lenses of ice, <a href="#Page_167">167</a><br />
+<br />
+Secchi, results obtained by, <a href="#Page_205">205</a><br />
+<br />
+Seebeck, Thomas, discovers thermo-electricity, <a href=
+"#Page_176">176</a><br />
+&mdash;&mdash;discovers the polarization of light by tourmaline,
+<a href="#Page_208">208</a><br />
+<br />
+Selenite, experiments with thick and thin plates of, <a href=
+"#Page_124">124</a><br />
+<a name="Page_243" id="Page_243"></a><span class="pagenum">[Pg
+243]</span><br />
+Silver spectrum, analysis of, <a href="#Page_190">190</a>, <a href=
+"#Page_191">191</a><br />
+<br />
+Sky-light, colour and polarization of, <a href="#Page_149">149</a>,
+<a href="#Page_154">154</a><br />
+&mdash;&mdash;generation of artificial skies, <a href=
+"#Page_152">152</a><br />
+<br />
+Snell, Willebrord, his discovery, <a href="#Page_14">14</a><br />
+&mdash;&mdash;his law, <a href="#Page_15">15</a>, <a href=
+"#Page_24">24</a><br />
+<br />
+Soap-bubbles and their colours, <a href="#Page_63">63</a>, <a href=
+"#Page_65">65</a><br />
+<br />
+Sound, early notions of the ancients respecting, <a href=
+"#Page_51">51</a><br />
+&mdash;&mdash;interference of waves of, <a href=
+"#Page_58">58</a><br />
+&mdash;&mdash;pitch of, <a href="#Page_59">59</a><br />
+&mdash;&mdash;analogies of light and, <a href=
+"#Page_56">56</a><br />
+&mdash;&mdash;demonstration of analogy between, and light, <a href=
+"#Page_198">198</a>, <a href="#Page_199">199</a><br />
+<br />
+Sonorous vibrations, action of, <a href="#Page_134">134</a><br />
+<br />
+Spectrum analysis, principles of, <a href="#Page_189">189</a><br />
+<br />
+Spectra of incandescent vapours, <a href="#Page_190">190</a><br />
+&mdash;&mdash;discontinuous, <a href="#Page_191">191</a>, <a href=
+"#Page_192">192</a><br />
+&mdash;&mdash;of polarized light, <a href="#Page_227">227</a><br />
+<br />
+Spectrum bands proved by Bunsen and Kirchhoff to be characteristic
+of the vapour, <a href="#Page_192">192</a><br />
+&mdash;&mdash;its capacity as an agent of discovery, <a href=
+"#Page_193">193</a><br />
+&mdash;&mdash;analysis of the sun and stars, <a href=
+"#Page_193">193</a><br />
+<br />
+Spottiswoode, Mr. William, <a href="#Page_123">123</a>, <a href=
+"#Page_227">227</a><br />
+<br />
+Stewart, Professor Balfour, <a href="#Page_202">202</a><br />
+<br />
+Stokes, Professor, results of his examination of substances excited
+by the ultra-violet waves, <a href="#Page_161">161</a><br />
+&mdash;&mdash;his discovery of fluorescence, <a href=
+"#Page_162">162</a><br />
+&mdash;&mdash;on fluorescence, <a href="#Page_165">165</a><br />
+&mdash;&mdash;nearly anticipates Kirchhoff's discovery, <a href=
+"#Page_198">198</a>, <a href="#Page_202">202</a><br />
+<br />
+Striated surfaces, colours of, <a href="#Page_89">89</a><br />
+<br />
+Sulphate of quinine first noticed and described by Sir John
+Herschel, <a href="#Page_165">165</a><br />
+<br />
+Sun, chemistry of the, <a href="#Page_195">195</a><br />
+<br />
+Sun, rose-coloured solar prominences, <a href=
+"#Page_204">204</a><br />
+<br />
+<br />
+Talbot, Mr., his experiments, <a href="#Page_201">201</a><br />
+<br />
+Tartaric acid, irregular crystallization of, and its effects,
+<a href="#Page_131">131</a><br />
+<br />
+Thallene, its effect on the spectrum, <a href=
+"#Page_162">162</a><br />
+<br />
+Thallium, spectrum analysis of, <a href="#Page_190">190</a>,
+<a href="#Page_191">191</a><br />
+&mdash;&mdash;discovery of, <a href="#Page_193">193</a><br />
+&mdash;&mdash;isolated in ingots by M. Lamy, <a href=
+"#Page_193">193</a><br />
+<br />
+Theory, relation of, to experience, <a href="#Page_91">91</a><br />
+<br />
+Thermo-electric pile, <a href="#Page_176">176</a><br />
+<br />
+Thermo-electricity, discovery of, <a href="#Page_176">176</a><br />
+<br />
+Tombeline, Mont, inverted image of, <a href="#Page_19">19</a><br />
+<br />
+Tourmaline, polarization of light by means of, <a href=
+"#Page_112">112</a><br />
+<br />
+Transmitted light, reason for, <a href="#Page_77">77</a><br />
+<br />
+Transparency, remarks on, <a href="#Page_167">167</a><br />
+<br />
+<br />
+Ultra-violet sun-rays, discovered by Ritter, <a href=
+"#Page_159">159</a><br />
+&mdash;&mdash;effects of, <a href="#Page_160">160</a><br />
+<br />
+Ultra-red rays of the solar spectrum, <a href=
+"#Page_171">171</a><br />
+&mdash;&mdash;part played by the, <a href="#Page_173">173</a><br />
+<br />
+Undulatory theory of light, bases of the, <a href=
+"#Page_47">47</a><br />
+&mdash;&mdash;Sir David Brewster's chief objection to the, <a href=
+"#Page_47">47</a><br />
+<br />
+Undulatory theory of light, Young's foundation of the, <a href=
+"#Page_49">49</a><br />
+<a name="Page_244" id="Page_244"></a><span class="pagenum">[Pg
+244]</span> &mdash;&mdash;phenomena which first suggested the,
+<a href="#Page_62">62</a>, <a href="#Page_69">69</a><br />
+&mdash;&mdash;Mr. Mill's scepticism regarding the, <a href=
+"#Page_143">143</a><br />
+&mdash;&mdash;a demonstrated verity in the hands of Young, <a href=
+"#Page_210">210</a><br />
+<br />
+<br />
+Vassenius describes the rose-coloured solar prominences in 1733,
+<a href="#Page_204">204</a><br />
+<br />
+Vitellio, his skill and conscientiousness, <a href=
+"#Page_14">14</a><br />
+&mdash;&mdash;his investigations respecting light, <a href=
+"#Page_207">207</a><br />
+<br />
+Voltaic battery, use of, and its production of heat, <a href=
+"#Page_6">6</a>, <a href="#Page_7">7</a><br />
+<br />
+<br />
+Water, deportment of, considered and explained, <a href=
+"#Page_105">105</a>, <a href="#Page_106">106</a><br />
+<br />
+Waves of water, <a href="#Page_51">51</a><br />
+&mdash;&mdash;length of a wave, <a href="#Page_52">52</a><br />
+&mdash;&mdash;interference of waves, <a href=
+"#Page_53">53-55</a><br />
+<br />
+Wertheim, M., his instrument for the determination of strains and
+pressures by the colours of polarized light, <a href=
+"#Page_134">134</a><br />
+<br />
+Wheatstone, Sir Charles, his analysis of the light of the electric
+spark, <a href="#Page_202">202</a><br />
+<br />
+Whirlpool Rapids, illustration of the principle of the interference
+of waves at the, <a href="#Page_55">55</a><br />
+<br />
+Willigen, Van der, his drawings of spectra, <a href=
+"#Page_202">202</a><br />
+<br />
+Wollaston, Dr., first observes lines in solar spectrum, <a href=
+"#Page_193">193</a><br />
+&mdash;&mdash;discovers the rings of Iceland spar, <a href=
+"#Page_209">209</a><br />
+<br />
+Woodbury, Mr., on the impurity of natural colours, <a href=
+"#Page_37">37</a><br />
+<br />
+W&uuml;nsch, Christian Ernst, on the three simple colours in white
+lights, <a href="#Page_39">39</a> <a href=
+"#Footnote_8_8"><i>note</i></a><br />
+&mdash;&mdash;his experiments, <a href="#Page_39">39</a> <a href=
+"#Footnote_8_8"><i>note</i></a><br />
+<br />
+<br />
+Young, Dr. Thomas, his discovery of Egyptian hieroglyphics,
+<a href="#Page_49">49</a><br />
+&mdash;&mdash;and the undulatory theory of light, <a href=
+"#Page_49">49</a><br />
+&mdash;&mdash;Helmholtz's estimate of him, <a href=
+"#Page_50">50</a><br />
+&mdash;&mdash;ridiculed by Brougham in the 'Edinburgh Review,'
+<a href="#Page_50">50</a><br />
+&mdash;&mdash;generalizes Grimaldi's observation on light, <a href=
+"#Page_56">56</a>, <a href="#Page_57">57</a><br />
+&mdash;&mdash;photographs the ultra-violet rings of Newton,
+<a href="#Page_160">160</a><br /></div>
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
+
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+</body>
+</html>
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@@ -0,0 +1,7493 @@
+The Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Six Lectures on Light
+       Delivered In The United States In 1872-1873
+
+Author: John Tyndall
+
+Release Date: November 10, 2004 [EBook #14000]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK SIX LECTURES ON LIGHT ***
+
+
+
+
+Produced by Clare Boothby, Stephen Schulze and the PG Online
+Distributed Proofreading Team.
+
+
+
+
+
+
+
+
+
+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, Caesium, 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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 _a 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 deg., for example, water reflects 22
+rays, at 60 deg. it reflects 65 rays, at 80 deg. 333 rays; while at an
+incidence of 891/2 deg., 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 481/2 deg., for flint glass 38 deg.41', and for
+diamond 23 deg.42'. Thus all the light incident from two complete
+quadrants, or 180 deg., in the case of diamond, is condensed into an
+angular space of 47 deg.22' (twice 23 deg.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.
+
+
+Sec. 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.
+
+
+Sec. 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 421/2 deg. 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 421/2 deg.
+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 421/2 deg., but of 401/2 deg., 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 deg.. 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.
+
+
+Sec. 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 Wuensch, 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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
+laminae, 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.
+
+
+Sec. 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.
+
+
+Sec. 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 1/2_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 11/2_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.
+
+
+Sec. 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.]
+
+
+Sec. 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
+
+
+Sec. 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 Caesar 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.
+
+
+Sec. 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 spiculae branch from the trunk, and from these
+branches others shoot; but the angles enclosed by the spiculae 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 spiculae
+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 deg. 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 deg. Fahr. Crystallization has virtually here
+commenced, the molecules preparing themselves for the subsequent act
+of solidification, which occurs at 32 deg., 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 deg.. 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 deg. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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 deg. 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 521/2 deg.; for glass, as already
+stated, 58 deg.; while for diamond it is 68 deg..
+
+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.
+
+
+Sec. 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 Sec.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.)
+
+
+Sec. 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.
+
+
+Sec. 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.
+
+
+Sec. 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.]
+
+
+Sec. 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.]
+
+
+Sec. 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.
+
+
+Sec. 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.]
+
+
+Sec. 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]
+
+
+Sec. 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 deg. 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.
+
+
+Sec. 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]
+
+
+Sec. 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 Bruecke 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.
+
+
+Sec. 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 21/2 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.
+
+
+Sec. 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 deg. 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.
+
+
+Sec. 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.
+
+
+Sec. 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
+Dupre, 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.
+
+
+Sec. 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.
+
+
+Sec. 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 31/2 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.
+
+
+Sec. 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,
+Mueller, 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.
+
+
+Sec. 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 deg.. 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.]
+
+
+Sec. 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.]
+
+
+Sec. 8. _Polarization of Heat_.
+
+Whether radiant heat be capable of polarization or not was for a long
+time a subject of discussion. Berard 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 deg.. 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 deg.. 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 deg., 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.
+
+
+Sec. 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 deg., and
+then rises again to 90 deg. 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 deg., rising, however, again to 90 deg. after a
+rotation of 360 deg.. 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.
+
+
+Sec. 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 deg., 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.
+
+
+Sec. 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, CAESIUM, 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 _Caesium_. 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. Angstroem and Thalen 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 aerial
+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 Pluecker, 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 Angstroem. 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, Cunaeus, 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 Goettingen, 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 deg., all trace
+    of colour disappears; and also that when the angle amounts to 90 deg.,
+    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 deg. 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 deg.. 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 versa_, 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 aether; 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 deg.; 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 versa_), we have only to turn
+    the plate round through 90 deg.. 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 deg.
+    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 deg., 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 deg. 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 deg., 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 deg..
+
+    '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 versa_, 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 deg. 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 Wuensch, Leipzig 1792, in which the author announces
+the proposition that there are neither five nor seven, but only three
+simple colours in white light. Wuensch 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, Wuensch 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, Wuensch'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 reconnaitre que parmi les peuples civilises de
+nos jours il en est pen chez qui les hautes sciences aient fait moins
+de progres qu'aux Etats-Unis, ou qui aient fourni moins de grands
+artistes, de poetes illustres et de celebres ecrivains.' (_De la
+Democratie en Amerique_, 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
+
+Angstroem, his paper on spectrum analysis, 202
+
+Arago, Francois, 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
+
+Berard 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
+
+Caesium, 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
+----Wuensch 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
+
+Pluecker, 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
+
+Wuensch, 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
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Six Lectures on Light, by John Tyndall
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