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

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.

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.

Fig. 2.

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.

Fig. 3.

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.

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]

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.

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).

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.

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.

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]

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.

Fig. 10.

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:—

'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.

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.

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.

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.

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 ½d; 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 1½d, 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.

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.

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.

Fig. 17.

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.

Fig. 18.

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.

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.

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.

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.

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.

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.

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.

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).

(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.

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.