Reflection and Refraction of Light. 153 



Physique. Later volumes of the Comptes Rendus contain 

 re-statements of it ; and in 1850 an extension of the method 

 was made to rotatory isotropic media* and to anisotropic 

 mediaf ; but this later work was never completed. 



II. 



Cauchy's final method^ of determining the conditions at the 

 interface of the media depended on finding the relations 

 which must exist between the known values of the displace- 

 ments in the interior of the medium, and the values, consistent 

 with the conditions of the problem, which these displacements 

 take when the change in the form of the equations of motion 

 near the interface is taken into account. 



Treating the aether as an isotropic elastic solid, for which 

 the density is p, and the coefficients of compressibility and 

 rigidity are k, n, the equations of motion are 



where 



&£ d8^ 

 d 2 rj d8 , ~ 

 d*Z dS 



Pdfi =m Tz +nVi ' . 



(1) 



n. 



dx dy dz 



Sir W. Thomson § has shown that all possible solutions of these 

 equations are included in 



f. d(j) t dcj) y defy 



t=£ +u ' v= a% +v > ^r +w > 



where (/>, u,v,w are some functions of x, y, z y t and u, v, w such 



that - — h t- + i— = ; further that, making these substitu- 

 dx dy dz ° 



tions, equations (1) may be replaced by 



d 2 6 , , x^g. d?u ~ d% ^ 9 



_^=( m + n)V 2 0, p~ m =n\/ <2 u, p- m =n\/\ 



' ' vv ^ r dt*~ 



dhv 

 p^=n^w. 



So that there are two modes of waves possible : a condensa- 



* C. R. xxxi. pp. 160, 225. t Ibid. xxxi. pp. 257, 297. 



\ Ibid. viii. pp. 374, 432, 459. § Baltimore Lectures, p. 32. 



Phil. Mag. S. 5. Vol. 23. No. 141. Feb. 1887. M 



