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diff --git a/14000-0.txt b/14000-0.txt new file mode 100644 index 0000000..d7afa72 --- /dev/null +++ b/14000-0.txt @@ -0,0 +1,7100 @@ +*** 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 *** |