Read LECTURE IV. of Six Lectures on Light Delivered In The United States In 1872-1873, free online book, by John Tyndall, on ReadCentral.com.

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.

Se. Action of Crystals on Polarized Light: the Nicol Prism.

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

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

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

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

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

Se. Colours of Films of Selenite in Polarized Light.

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

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

Se. Colours of Crystals in Polarized Light explained by the Undulatory Theory.

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

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

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

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

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

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

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

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

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

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

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

Se. Colours produced by Strain and Pressure.

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

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

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

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

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

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

Se. Colours of Unannealed Glass.

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

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

Se. Circular Polarization.

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

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

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

Se. Complementary Colours of Bi-refracting Spar in Circularly Polarized Light. Proof that Yellow and Blue are Complementary.

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

Se. The Magnetization of Light.

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

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

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

Se. Iris-rings surrounding the Axes of Crystals.

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

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

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

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

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

Se. Power of the Wave Theory.

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

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

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

Se. The Blue of the Sky.

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

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

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

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

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

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

Se. Artificial Sky.

But we have it in our power to imitate far more closely the natural conditions of this problem. We can generate in air artificial skies, and prove their perfect identity with the natural one, as regards the exhibition of a number of wholly unexpected phenomena. It has been recently shown in a great number of instances by myself that waves of ether issuing from a strong source, such as the sun or the electric light, are competent to shake asunder the atoms of gaseous molecules. The apparatus used to illustrate this consists of a glass tube about a yard in length, and from 21/2 to 3 inches internal diameter. The gas or vapour to be examined is introduced into this tube, and upon it the condensed beam of the electric lamp is permitted to act. The vapour is so chosen that one, at least, of its products of decomposition, as soon as it is formed, shall be precipitated to a kind of cloud. By graduating the quantity of the vapour, this precipitation may be rendered of any degree of fineness, forming particles distinguishable by the naked eye, or particles which are probably far beyond the reach of our highest microscopic powers. I have no reason to doubt that particles may be thus obtained whose diameters constitute but a very small fraction of the length of a wave of violet light.

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

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

Se. Polarization of Skylight.

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

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

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

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

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

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

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

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

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

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