of the transmitted light will undergo no further diminution. For, when the transmitted light becomes wholly polarized, no portion of it whatever will be reflected by any of the succeeding plates, its plane of polarization being perpendicular to the plane of incidence; it is therefore transmitted without diminution through them, whatever be their number. The case is different, however, when the light is incident on the pile at any other than the polarizing angle; and it follows therefore that the intensity of the light transmitted through a thick pile is greatest, when it is incident at the polarizing angle.

(150) There are certain crystals which, like the pile of transparent plates, possess the property of polarizing the transmitted light. This property depends upon a peculiarity in the absorbing powers of double-refracting crystals,—namely, that the absorption of a polarized ray varies with the position of its plane of polarization with respect to the crystal. Thus, tourmaline absorbs a polarized ray more rapidly when the plane of polarization is parallel to the axis, than when it is perpendicular to it. But a ray of common light falling upon this crystal may be divided into two, one polarized in a plane passing through the axis, and the other in a plane perpendicular to it ; and as the former of these is absorbed more rapidly than the latter, the transmitted light will be partially polarized in the plane perpendicular to the axis of the crystal. When the plate is sufficiently thick, the latter portion alone will be sensible, and the ray emerges wholly polarized in the perpendicular plane.

The tourmaline, accordingly, is of much use in experiments on polarized light, not only in affording a ready test of polarization, but also in producing a polarized beam. It has the disadvantages, however, that the polarization of the emergent light is never perfect, and that its intensity is much weakened by absorption- both the rays being absorbed in

their passage through the crystal, though with unequal energies.

The polarization produced by double refraction is the most complete of any; while the intensity of the polarized pencils is greater than in any other case, being very nearly one-half of the intensity of the original light. The intensity of the light reflected from a plate of glass, at the polarizing angle, is not more than theth part of that of the incident light.

(151) M. Haidinger has observed a remarkable phenomenon of polarized light, by which it may be recognised by the naked eye, and its plane of polarization ascertained. This phenomenon consists in the appearance of two brushes, of a pale orange-yellow colour, the axis of which coincides always with the trace of the plane of polarization; these are accompanied, on either side, by two patches of light, of a complementary or violet tint. In order to see them, the plane of polarization of the light must be turned quickly from one position to another, so as to shift the position of the brushes. Thus, they may be observed by looking for a few moments at one of the images of a circular aperture, formed by a rhomb of Iceland spar, and then at the other, and so alternately. They gradually disappear when the eye continues directed to them in the same position; but they may be made to reappear by shifting that position, or the plane of polarization on which it depends.

The most probable explanation of this phenomenon seems to be that given by M. Jamin, in which it is ascribed to the refracting coats of the eye. When polarized light falls upon a pile of parallel plates, the proportion of the refracted to the incident light varies with the plane of polarization, being a minimum when that plane coincides with the plane of incidence, and a maximum when it is perpendicular to it. These variations are nothing at a perpendicular incidence: they are greatest when the angle of incidence is equal to the angle

of polarization. Accordingly, when the polarized light is incident obliquely on the plates, the refracted light should exhibit two dark brushes, enlarging from the centre to the circumference, in the plane of polarization; and two bright brushes in the perpendicular plane.

In the preceding explanation, the incident light is supposed to be homogeneous. When white light is used, the intensities of its several components, in the refracted pencil, will vary with the refractive indices, and consequently the brushes will be coloured. M. Jamin has shown that the effect of a single refracting surface will be to produce two yellow brushes, whose axis is in the plane of polarization.

CHAPTER IX.

TRANSVERSAL VIBRATIONS-THEORY OF REFLEXION AND REFRACTION OF POLARIZED LIGHT.

(152) HAVING in the preceding chapter stated the principal facts of polarization, we may proceed to consider their connexion with the physical theory.

It is strange that the department of optics, in which the wave-theory now stands unrivalled, should be the very one which Newton selected as affording the most decisive evidence against it:" Are not," says he, "all hypotheses erroneous, in which light is supposed to consist in pressure, or motion, propagated through a fluid medium? for pressures or motions, propagated from a shining body through an uniform medium, must be on all sides alike; whereas it appears that the rays of light have different properties in their different sides." In this objection Newton seems to have had his thoughts fixed upon that species of undulatory propagation, whose laws he himself had so sagaciously unfolded. sound is propagated through air, the vibrations of the particles of the air are performed in the same direction in which the wave advances; and if the vibrations of the ether which constitute light had been of the same kind, the objection would be insuperable. For, if the particles of the ether vibrated in the direction of the ray itself, the ray could not bear a different relation to the different parts of the surrounding space.

When

But the case is altered, if the vibrations of the ethereal particles be performed in a transverse direction. Let us suppose the direction of the vibrations to be perpendicular to that of the ray: then it is obvious that if that direction be

vertical, for example, while the ray advances horizontally, the ray will bear a relation to the parts of space above and below, different from that which it bears to those parts which are on the right hand and on the left. Such is, in fact, the mode of vibration which is now assumed to belong to the ether, in the wave-theory, the ethereal molecules being supposed to vibrate in the plane of the wave; and we shall find that, with the help of this assumption, all the complicated phenomena of polarization and double refraction are explained in the fullest and most complete manner.

The principle of transversal vibrations, as it is called, seems to have first occurred to Hooke, and was announced, in 1672, in his Micrographia. Young and Fresnel arrived at the same principle independently; and the latter has reared upon its basis the noblest fabric which has ever adorned the domain of physical science,-Newton's system of the universe alone excepted.

(153) In order to conceive the manner in which an undulation may be propagated by transversal vibrations, let us imagine a cord stretched in a horizontal position, one end being attached to a fixed point, and the other held in the hand. If the latter extremity be made to vibrate, by moving the hand up and down, each particle of the cord will, in succession, be thrown into a similar state of vibration; and a series of waves will be propagated along it with a uniform velocity. The vibrations of each succeeding particle of the cord, being similar to that of the first, will all be performed in the same plane, and the whole will represent the state of the ethereal particles in a polarized ray.

Now if, after a certain number of vibrations in the vertical plane, the extremity of the cord be made to vibrate in another plane, and then in another, and so on, in rapid succession,-each particle of the cord will, after a time proportional to its distance from the extremity, assume in suc