on the principles of the wave theory, and he succeeded in doing so. He made highly important observations on the distinctive character of the two beams transmitted by the spar. Newton, reflecting on the observations of Huyghens, came to the conclusion that each of the beams had two sides; and from the analogy of this two sidedness with the two endedness of a magact, wherein consists its polarity, the two beams came subsequently to be described as polarized.

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

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

A moment's reflection will show, if what has been stated be correct, that, on placing a second plate of tourmaline with its axis parallel to the first, the light will pass through both; but that, if the axes be crossed, the

FIG. 10.

FIG. II.

light that passes through the one plate will be quenched by the other, a total interception

of the light being the consequence. The image of a plate of tourmaline, t t (Fig. 10), is now before you. I place parallel to it anot er plate, t't': the green of the crystal is a little deepened, nothing more. By means of an endless screw, I now turn one of the crystals gradually round; as long as the two plates are oblique to each other, a certain portion of light gets through; but, when they are at right angles to each other, the space common to both is a space of darkness, as shown in Fig. 11.

Let us return to a single plate; and let me say that it is on the green light transmitted by the tourmaline that you are to fix your attention. We have now to illustrate the twosidedness of that green light. The light surrounding the green image being ordinary light, is reflected by a plane glass mirror in all directions; the green light, on the contrary, is not so reflected. The image of the tourmaline is now horizontal; reflected upwards, it is still green; reflected sideways, the image is reduced to blackness, because of the incompetency of the green 1 ght to be reflected in this direction. Making the plate of tourmaline vertical and reflecting it as before, in the upper image the light is quenched; in the side image you have now the green. Picture the thing clearly. I the one case the mirror receives the impact of the edges of the waves, and the green light is q.enched. In the other case the sides of the waves strike the mirror, and t e green light is reflected. To render the extinction complete, the light must be received upon the mirror at a special angle. What this angle is we shall learn presently.

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

And now let us try to make substantially the experiment of Malus. I receive the beam from the lamp upon this plate of glass and reflect it through the spar. Instead of two images, you see but one. So that the light, when polarized, as it now is, can only get through the spar in one direction, and consequently produce but one image. Why is this? In the Iceland spar, as in the tourmaline, all the vibrations of the ordinary light

are reduced to two planes at right angles to conclude? That the green light will be each other; but, unlike the tourmaline, both transmitted along the latter, which is parallel beams are transmitted with equal facility by to the tourmaline, and not along the former, the spar. The two beams, in short, emerg- which is perpendicular to it. Hence we may ent from the spar are polarized, their direc-infer that one image of the tourmaline will tions of vibration being at right angles to each other. When, therefore, the light was polarized by reflection, the direction of vibration in the spar which corresponded to the

show the ordinary green light of the crystal, while the other image will be black. Let us test our reasoning by experiment: it is verified to the letter. (Fig. 12.)

being thus polarized, if they be suitably re- so increase the quantity as to render the transceived upon a plate of glass at the polarizing mitted beam, for all practical purposes, perangle, one of them will be reflected, the fectly polarized. Indeed, bundles of glass This is the conclusion of reason plates are often emp'oyed as a means of furfrom our previous knowledge; but you ob-nishing polarized light. serve that reason is justified by experiment. (Figs. 15 and 16.)

other not.

One word more.

When the tourmalines are crossed, the space where they cross each I have said that the whole of the beam re- other is black. But we have seen that the flected from glass at the polarizing angle is least obliquity on the part of the crystals perpolarized; a word must now be added regard- mits light to get through both. Now suping the larger portion of the light transmittedose, when the two plates are crossed, that by the glass. The transmitted beam contains a quantity of polarized light equal to that of tl e reflected beam; but this quantity is only a fraction of the whole transmitted light. By taking two plates of glass instead of one, we

FIG 15.

we interpose a third plate of tourmaline between them, with its axis oblique to both. A portion of the light transmitted by the first plate will get through this intermediate one. But, after it has got through, its plane of vibration is changed: it is no longer perpendicular to the axis of the crystal in front. Hence it will get through that crystal. Thus, by reasoning, we infer that the interposition of a third plate of tourmaline will in part abolish the darkness produced by the perpendicular crossing of the other two plates. I have not a third plate of tourmaline; but the talc or mica which you employ in your stoves is a more convenient substance, which acts in the same way. Between the crossed tourmalines I introduce a film of this crystal. You see the edge of the film slowly descending, and as it descends between the tourmalines, light takes the place of darkness. The darkness, in fact, seemed scraped away as if it were something material. This effect has been called and improperly called-depolarization.

(B is the birefracting spar, dividing the incident light into the two beams, o and e. G is the mirror). The beam is here reflected laterally. When the reflection is upwards, the other beam is reflected, as shown in Fig. 16.

FIG. 16.

LECTURE IV.

Chromatic Phenomena produced by Crystals on Polarized Light: The Nicol Prism: Polarizer and Analyzer: Action of thick and thin Plates of Selenite: Colors dependen: on Thickness: Resolution of Pɔlarized 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 Colors: 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.

We now stand upon the threshold of a new and splendid optical domain. We have to examine, this evening, the chromatic phenomena produced by the action of crystals, and double-refracting bodies gene: ally, upon polarized light. 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. But we have better apparatus now. You have seen the two beams emer

augment the quantity of the transmitted polar-gent from Iceland spar, and have proved ized light; and, by taking a bundle of plates, we them to be polarized. If we could abolish

one of these beams, we might employ the other for experiments on polarized light.

These beams, as you know, are refracted differently, and from this we are able to infer that under some circumstances the one may be totally reflected, and the other not. An optician, named Nicol, cut a crystal of Iceland spar in two in a certain direction. He polished the severed urfaces, 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. The invention of the Nicol prism was a great step in practical optics, and quite recently such prisms have been constructed of a size which enables audiences like the present to witness the chromatic phenomena of polarized light to a degree altogether unattainable a short time ago. The two prisins here before you belong to my excellent friend, Mr. William Spottiswoode, and they were manufactured by Mr. Ladd. I have with me another pair of very noble prisms, still larger than these, manufactured for me by Mr. Browning, who has gained so high and well-merited a reputation in the construction of spectroscopes.

heart's-ease, the colors of which you might safely defy the artist to reproduce. By turning the front Nicol ninety degrees round, we pass through a colorless phase to a series of colors complementary to the former ones. Here, for example, is a rose tree with red flowers and green leaves; turning the prism ninety 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. principle of interference, duly applied and interpreted, explains them all.

The

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 agent which makes the impression. It is with the agent that we have to occupy ourselves at present. That agent is the motion of a substance which fills all space, and surrounds the atoms and molecules of bodies. To this interstellar and interatomic medium definite mechanical properties are ascribed, and we deal with it as a body possessed of these p operties. 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, resolution, and interference of its vibrations, we deduce all the phenomena displayed by crystals in polarized light.

These two Nicol prisms play the same part as the crystals of tourmaline. Placed with their directions of vibration parallel, the light passes through both. When these directions are crossed, the light is quenched. Introducing a film of mica between the Let us take, as an example, the crystal of prisms, the light is in part restored. But tourmaline, with which we are now so familnotice, when the film of mica is thin, you iar. Let a vibration cross this crysta, oblique have sometimes not only light, but colored to its axis; we have seen by experiment that light. Our work for some time to come will a portion of the light will pass through. be the examination of these colors. With How much, we determine in this way: Draw this view, I will take a representative crystal, a straight line representing the intensity of one easily dealt with; the crystal gypsum, or the vibration before it reaches the tourmaline, selenite, which is crystallized sulphate of and from the two ends of this line draw two lime. Between the crossed Nicols I place a perpendiculars to the axis of the crystal; the thick plate of this crystal; like the mica, it distance between the feet of these two perrestores the light, but it produces no color.pendiculars will represent the intensity of the With my penknife I take a thin splinter from transmitted vibration. this crystal and place it between the prisms; its image on the screen glows with the richest colors. Turning the prism in front, these colors gradually fade, disappear, but by continuing the rotation until the vibrating sections of the prisms are parallel, vivid colors again appear, but these colors are complementary to the former ones.

Follow me now while I endeavor to make clear to you what occurs when a film of gypsum is placed between the Nicol prisms. But, at the outset, let us establish still further the analogy between the action of the prisms and that of two plates of tourmaline. The plates are now crossed, and you see that by turning the film round, it may be placed Some patches of the splinter appear of one in a position where it has no power to abolish color, some of another. These differences the darkness. Why is this? The answer is are due to the different thicknesses of the that in the gypsum there are two directions, film. If the thickness be uniform, the color at right angles to each other, which the waves is uniform. Here, for instance, is a stellar of light are constrained to follow, and that shape, every lozenge of the star being a film now one of these directions is parallel to one of gypsum of uniform thickness. Each of the axes of the tourmaline, and the other lozenge, you observe, shows a brilliant uni-parallel to the other axis. When this is the form color. It is easy, by shaping our films so as to represent flowers or other objects, to exhibit such objects in colors unattainable by art. Here, for example, is a specimen of

case, the film exercises no sensible action upon the light. But now I turn the film so as to render its direction of vibration oblique to the axes; then you see it has the power,

demonstrate in the last lecture, of restoring | other. You can readily imagine that in this