POLAEIZATION TRANSVERSAL VIBRATIONS. 85 



the nature of the fluid, during which the pressure is not the same 

 in all directions. In the case of very rapid motions this time must 

 be taken into account, and the equations of motion of fluids will no 

 longer be those furnished by the principle of D'Alembert.* 



M. Poisson has shown also that a disturbance produced in a 

 limited portion of a solid body will give rise to two waves, which 

 will be propagated with different velocities. He proves further 

 that, whatever be the initial motions of the disturbed particles, the 

 vibrations in one of these waves will finally be radial, or in the 

 direction of the motion propagated, while those of the other are 

 perpendicular to that direction, or transversal. The first are at- 

 tended with dilatations proportionate to the absolute velocities of 

 the molecules, and the waves thus propagated are similar to 

 those which take place in fluids. The transversal vibrations, on 

 the other hand, are unaccompanied by any change of density in 

 the medium. M. Poisson does not seem to think that this result 

 can justify the hypothesis of transversal vibrations in the ethereal 

 fluid; though he admits that the properties attributed to the ether 

 are in some respects analogous to those of a solid body. 



The propagation of transversal vibrations appears to be now 

 established, as a necessary consequence of dynamical principles, by 

 the able researches of M. Cauchy.f I shall shortly have occasion 

 to allude more particularly to the important conclusions arrived at 

 by this mathematician, in applying the general laws of the propa- 

 gation of motion in elastic media to the case of light. For the 

 present it will be sufficient to observe that the form of the wave- 

 surface, obtained in the course of these investigations, is a curved 

 surface of three sheets ; and that, consequently, a ray of light on 

 entering any medium will be, in general, subdivided into three 

 rays, the directions of the vibrations being determined in each. 

 When the elasticity of the ether, in this medium, is the same in all 

 directions, these three rays will have a common direction, and two 

 of them a common velocity. They are thus reduced to two a 

 single and a double ray coincident in direction, the vibrations of 

 the former being parallel to that direction, and those of the latter 

 perpendicular to it. If the initial vibrations in the system in ques- 

 tion are contained in a plane perpendicular to the direction of the 



* Annales da CJiimie, torn. xliv. 



f " Memoire sur la Theorie de la Lumicrc." Mm. Inst., torn. x. 



