Electromagnetic Tlieory of Quartz. 157 



travelling parallel to the axis of y. Our equations thus far 

 represent observed facts. 



Since everything is symmetrical about the axis, we may 

 without loss of generality assume that the axis of y is parallel 

 to the wave- front, and we may therefore put 



/= S\, g = Sya, li = S v, 



where I, n are the direction-cosines of the wave-front, \, fi, v 

 are those of the direction of displacement, and r is the period. 

 Substituting in (16) we obtain 



(V 2 - AV)\ f C 2 lnv + (2iirp/r)n 2 fi=Q, 



(V 2 -A>-(2^t)X = 0, 

 (V 2 -C 2 l 2 )v + AnnX-(2tTTp l 'r)ln f i = 0; 



whence eliminating X, \i, v and putting 6 for the angle which 

 the normal to the wave-front makes with the axis, we obtain 



(V 2 _A 2 ) (V 2 -A 2 cos 2 6-0 2 sin 2 6>) = (4tt 2 //t 2 )cos 2 6, . (17) 



which determines the velocity of propagation of waves of 

 period r. Putting 6 = 0, we get 



V 2 = A 2 ±27r/.?/T (18) 



which gives the values of V when the wave is travelling in 

 the direction of the axis. In this case equations (16) reduce 

 to (12), so that the rotation of the plane of polarization is 

 given by (15). 



6. The elastic solid theory of double refraction which was 

 proposed by Green is, I believe, universally admitted at the 

 present time to be unsatisfactory ; and accordingly during 

 recent years numerous theories have been proposed, which 

 attempt to explain optical phenomena by a quasi-elastic solid 

 theory, based upon assumptions respecting the mutual re- 

 action of aether and matter ; and it will therefore be instructive 

 to ascertain whether the terms by which we have endeavoured 

 to explain rotatory polarization on the electromagnetic theory, 

 will also explain this phenomenon on the quasi-elastic solid 

 theory. 



The fundamental idea of all such theories is, that the statical 

 properties of the aether in transparent media are the same as 

 in vacuo, but that the motion of the aether is modified by the 

 presence of ponderable matter, the effect of which may be 

 represented by forces X, Y, Z ; and phenomena such as 

 double refraction, rotatory polarization and the like, are 



