is dilated by heat in the direction of its axis; while it actually contracts, by a small amount, in directions perpendicular to it. The angles of the primitive form thus vary, the rhomboid becoming less obtuse, and approaching the form of the cube,— in crystals of which form there is no double refraction (69). Professor Mitscherlich accordingly conjectured, that the double-refracting energy of the crystal must, in these circumstances, be diminished; and the conjecture was verified by experiment. In fact, the extraordinary index in Iceland spar is found to increase considerably with the temperature, while the ordinary index undergoes little or no change.

We have seen (186) that the inclination of the optic axes, in biaxal crystals, is a simple function of the three principal elasticities of the vibrating medium, and that the plane of the axes is that of the greatest and least elasticities. If, then, these elasticities be altered by heat in different proportions, the inclination of the axes will likewise vary; and it may even happen that the plane of the axes will shift to a position at right angles to that which it formerly occupied. All these variations have been actually observed. Professor Mitscherlich found that, in sulphate of lime, the angle between the axes (which is about 60° at the ordinary temperature) diminishes on the application of heat; that, as the temperature increases, these axes approach until they unite; and that, on a still further augmentation of heat, they again separate, and open out in a perpendicular plane. Heat is found to dilate this crystal more in one direction than in another perpendicular to it.

CHAPTER XIII.

ROTATORY POLARIZATION.

(209) In the phenomena hitherto considered, the changes in the plane of polarization, which a polarized ray undergoes in reflexion or refraction, are determinate in amount, and are wholly independent of the distances traversed by the ray in either medium. There are certain cases, however, in which the change of the plane of polarization increases with the thickness of the medium traversed; and the plane is made to revolve, sometimes from left to right (like the hands on the dialplate of a clock), and sometimes in the opposite direction. This remarkable phenomenon was first observed by Arago.

When a polarized ray, of any simple colour, traverses a plate of Iceland spar, beryl, or any other uniaxal crystal, in the direction of its axis, it suffers no change of any kind. But when the ray traverses in the same manner a plate of rock-crystal, its plane of polarization is found to be altered at emergence; and the change increases with the thickness of the plate. In some crystals of this substance, the plane of polarization is turned from left to right, while in others it is turned in an opposite direction; and the crystals themselves are called right-handed or left-handed, according as they produce one or other of these effects.

(210) The phenomena of rotatory polarization in rockcrystal were analyzed with great diligence and success by M. Biot, and were reduced by him to the following general laws.

I. In different plates of the same crystal, the rotation of the plane of polarization is always proportional to the thickness

of the plate. The same thing holds, very nearly, in plates of different crystals.

II. When two plates are superposed, the effect produced is, very nearly, the same as that which would be produced by a single plate, whose thickness is the sum or difference of the thicknesses of the two plates, according as they are of the same or of opposite denominations.

III. The rotation of the plane of polarization is different for the different rays of the spectrum, and increases with their refrangibility. For a given plate, the angle of rotation is inversely as the square of the length of the wave. Thus, the angle of rotation, produced by a plate of rock-crystal whose thickness is a millimetre, is 17° for the extreme red of the spectrum, 30° for the rays of mean refrangibility, and 44° for the extreme violet.

Since the rays of different colours emerge polarized in different planes, it follows that if a beam of white light be let fall upon the crystal, and be received after emergence upon an analyzing plate, this will reflect a portion of the light in every position of the plane of reflexion; and this light will be beautifully coloured, the colour varying with the thickness of the crystal, and the position of the analyzing plate. the analyzing plate will reflect the rays of different colours in different proportions, depending on the positions of their planes of polarization with respect to the plane of reflexion; and the resulting colour will be a compound tint, which can be easily estimated.

For

(211) The curious distinction, which was found to subsist between different specimens of rock-crystal, has been connected by Sir John Herschel with a difference of crystalline form. The ordinary form of the crystal of quartz is the six-sided prism terminated by the six-sided pyramid. The solid angles, formed at the junction of the pyramid and prism, are sometimes replaced by small secondary planes, which are

oblique with reference to the original planes of the crystal; and the form of the crystal is then called plagiedral. In the same crystal these planes lean all in the same direction; and it is found that, when that direction is to the right (the apex of the pyramid being uppermost), the crystal is right-handed; and that, on the contrary, it is left-handed, when the planes lean in the opposite way.

Sir David Brewster subsequently discovered that the amethyst, or violet quartz, is made up of alternate layers of righthanded and left-handed quartz. This remarkable structure may be traced in the fracture of the mineral; for the edges of the layers crop out, and give to the fracture the undulating appearance which is peculiar to this mineral. But the structure in question is displayed in the most beautiful manner, when we expose a plate of this substance to polarized light.

The colours exhibited in polarized light likewise reveal the existence of crystals of quartz penetrating others in various directions, when no striæ, or other external appearances, indicate their presence.

(212) The connexion between the rotation of the plane of polarization and the crystalline form, discovered by Sir John Herschel in quartz, has since been observed in other substances. M. Pasteur has recently found that tartaric acid, and the tartrates, which are all plagiedral in the same direction, likewise deviate the plane of polarization to the same side. On the other hand, para-tartaric acid, and the para-tartrates, which have the same general form, are for the most part not plagiedral; while, in those salts of this class which are so, the facettes of the crystals are inclined sometimes to the right, and sometimes to the left,—and this difference is found to exist even in crystals belonging to the same specimen. M. Pasteur has found, accordingly, that the salts of the former class have no effect upon the plane of polarization; while those of the latter deviate the plane of polarization in the same direction as the facettes of the crystal.

This remarkable distinction among the para-tartrates has been traced by the same observer to their chemical composition. He has discovered that para-tartaric acid is composed of two distinct acids, which have the same general crystalline form; but which differ in this, that in one of them the facettes of the crystals are inclined to the right, and in the other to the left. These acids (one of which is the ordinary tartaric acid) accordingly deviate the plane of polarization—the former to the right, and the latter to the left, and by the same amount; and the difference in the optical properties of different specimens of the compound acid, and its salts, arises from the predominance of one or other of the component elements.

(213) The phenomena of rotatory polarization in rockcrystal, have been accounted for by the interference of two circularly polarized pencils, which are propagated along the axis with unequal velocities, one revolving from left to right, and the other in the opposite direction.

For a plane polarized ray is equivalent to two circularly polarized rays of half the intensity, in which the vibrations are in opposite directions. When a plane polarized ray, therefore, is incident perpendicularly upon a plate of rock-crystal, cut perpendicularly to the axis, it may be resolved into two such circularly polarized rays; and as these are supposed to be transmitted with different velocities, one of them will be in advance of the other when they assume a common velocity at emergence. They then compound a single ray, polarized in a single plane; and this plane, it can be shown, is removed from the plane of primitive polarization by an angle proportional to the interval of retardation, and therefore to the thickness of the crystal.

Thus the laws of rotatory polarization are completely explained; and it only remains to prove the truth of the assumption, that two circularly polarized pencils, whose vibrations are in opposite directions, are actually transmitted along