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 X.

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

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

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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. When 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.

But the case is altered, if the vibrations of the ethereal particles be performed in a transverse direction. Let us sup

pose 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.

(180) 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 succession all these varied vibrations; and the whole cord, instead of taking the form of a plane curve, as in the last case, will be thrown into a species of helical curve, depending on the nature of the original disturbance. Such is the condition of the ethereal particles in a ray of common, or unpolarized light.

When, therefore, we admit a connexion to subsist among the particles of the ether, such as that which holds among the particles of the cord, there is no difficulty in conceiving how a vibration may be propagated in a direction perpendicular to that in which it is executed. It is true, the particles of the ether are not chained together by cohesive forces, like those of the cord; but the attractive forces which subsist among them are of the same kind, and may be shown to produce a similar effect. In fact, let us conceive the ether to be composed of separate molecules, which act on one another according to some law varying with the distance. When any row or line of such molecules is similarly displaced, through a space which is small compared with the separating intervals, the molecules of the succeeding row will be moved in the same direction by the forces developed with the change of distance; so that the vibrations of the particles composing the first row will be communicated to those of the second, and thus the vibratory motion will be propagated in a direction perpendicular to that in which it takes place. The rapidity of the propagation will depend on the magnitude of the force developed by the displacement.

To account for the fact, that there are no sensible vibrations in a direction normal to the wave, we have only to suppose the repulsive force between the molecules to be very great, or the resistance to compression very considerable.

For, in this case, the force which resists the approach of two strata of the fluid is much greater than that which opposes their sliding on one another.

(181) But the existence of transversal vibrations—and of transversal vibrations only—is a necessary consequence of the laws of interference of polarized light, if the theory of waves be admitted at all. It has been experimentally proved, by Fresnel and Arago, that two rays oppositely polarized compound a single ray whose intensity is constant, whatever be the phases of vibration in which they meet. But theory shows, that the intensity of the light resulting from the union of two rays oppositely polarized will be constant, and independent of the phase, only when the vibrations normal to the wave are evanescent.

This conclusion is easily extended to the case of common, or unpolarized light. In unpolarized light, therefore, as in polarized, the vibrations are only in the plane of the wave; but in the latter, these vibrations are all parallel to a fixed line, while in the former they take place in every possible direction in the plane of the wave. The phenomenon of polarization consists simply in the resolution of these vibrations into two sets, in two rectangular directions, and the subsequent separation of the two systems of waves thus produced. When the resolved vibrations are not separated, but one of them is diminished in any ratio, the light is said to be partially polarized.

(182) We have stated that the vibrations of the molecules of the ether, in a polarized ray, are all parallel to a fixed direction in the plane of the wave. This fixed direction may be either parallel or perpendicular to the plane of polarization; and there is nothing in the phenomena, hitherto discovered, to determine the choice between these two positions.