158 Mr. A. B. Basset on an 



explained by making certain assumptions regarding the form 

 of these forces. 



The particular theory of this kind which I shall now con- 

 sider, and which on the whole is perhaps the most satisfactory, 

 is the theory of Lord Rayleigh* as modified by Sir W. 

 Thomson f , and which consists in supposing that double re- 

 fraction may be explained by assuming that X, Y, Z are equal 

 to —p\U, — p 2 v, —p^w, and that the velocity of propagation of 

 the pressural wave is so small that it may be treated as zero 

 without sensible error. This theory, so far as double re- 

 fraction is concerned, has been fully worked out by Glaze- 

 brook J, and has been applied by him§, and also by myself [| 

 to investigate the intensities of the reflected and refracted 

 waves, when the reflecting medium is a doubly-refracting 

 crystal. In order to deduce a theory of doubly-refracting media 

 which exhibit rotatory polarization, we shall assume that the 

 effect of the peculiar molecular structure of such media is to 

 introduce into the expressions for the forces the additional 

 terms which are given by the last three terms of (10) ; so 

 that our equations of motion are: — 



, .d 2 u ,dS _~ d fdv dw\ 



(P + Pi)W< = - n a^ +nV U+ d^{dz- dj)' 

 . .d 2 v f d8 — 2 d /dw du\ 



{p+p ^ = - n ^ +n ^ w+ *(^-f\ 

 KH ^ HBJ dt 2 dz v d<a\dy dx)> 



where u, v, w are the displacements, and p and n are the 

 density and rigidity of the aether in vacuo. 



When the medium is isotropic, p l = p 2 = p z • p 1= p 2 =p 3 ; if 

 therefore the axis of z is taken as the direction of propagation, 

 u and v will be functions of z and t alone, and w will be zero, 

 and (19) reduce to 





. . d 2 u 

 (P + Pi)^ 



,d 2 u 

 =n d? 



d 9 v 



+P dz 2 dt 





(P+Pi)^" 



,d 2 v 



= n d?- 



d 3 u 

 P dz 2 dt> 



ich are 



of the same form 



as (12). 





* Hon. J. W. Strutt, Phil. Mag. June 1871. 



t Phil. Mag. Nov. 1888, p. 114. 



t Ibid. Dec. 1888, p. 521. 



§ Ibid. August 1889, p. 110. 



II Proc. Lond. Math. Soc. vol. xx. p. 351. 



