Crystalline Reflexion and Refraction. 147 



nothing, and shall suppose nothing, except what is involved in 

 the foregoing assumptions. But with respect to its physical 

 condition generally, we shall admit, as is most natural, that a 

 vast number of ethereal particles are contained in the differen- 

 tial element of volume ; and, for the present, we shall consider 

 the mutual action of these particles to be sensible only at dis- 

 tances which are insensible when compared with the length of a 

 wave. 



By putting together the assumptions we have made, it will 

 appear that when a system of plane waves disturbs the ether, the 

 vibrations are transversal, or parallel to the plane of the waves. 

 For all the particles situated in a plane parallel to the waves are 

 displaced, from their positions of rest, through equal spaces in 

 parallel directions ; and therefore if we conceive a closed surface 

 of any form, including any volume great or small, to be de- 

 scribed in the quiescent ether, and then all its points to partake 

 of the motion imparted by the waves, any slice cut out of that 

 volume, by a pair of planes parallel to the wave-plane and inde- 

 finitely near each other, can have nothing but its thickness 

 altered by the displacements ; and since the assumed preserva- 

 tion of density requires that the volume of the slice should not 

 be altered, nor consequently its thickness, it follows that the 

 displacements must be in the plane of the slice, that is to say, 

 they must be parallel to the wave-plane. And conversely, when 

 this condition is fulfilled, it is obvious that the entire volume, 

 bounded by the arbitrary surface above described, will remain 

 constant during the motion, while the surface itself will always 

 contain within it the very same ethereal particles which it en- 

 closed in the state of rest ; and all this will be accurately true, 

 no matter how great may be the magnitude of the displace- 

 ments. 



Let x, y, z be the rectangular co-ordinates of a particle before 

 it is disturbed, and x + 5, y + rj, z + its co-ordinates at the time t, 

 the displacements , TJ, being functions of #, y, * and t. Let 

 the ethereal density, which is the same in all media, be regarded 

 as unity, so that dxdydz may, at any instant, represent indif- 



