Electromagnetic Theory of Quartz. 155 



by (4) ; whence the equations of magnetic induction are 



d? Hy\dy dx) dz\dx dz) 47Tfjidco\dz dyP 



#* - A* A( C R_ *V C 2 A /*?_ *Y + JL A/* _ ^ ^ ( n ) 



</£ 2 ~~ ck \<fo flty/ tfce I//*/ dx) ±7TfjL dco \dx dz r 



^-■m^L( c h da \ A 2 — /— ^Yj 1 d l da d ^\ 

 dt 2 ~~ dx\dx dz) dy\dz dy) 4tt/j, dco\dy dx)' 



4. We shall now briefly consider the propagation of light 

 in an isotropic medium. In this case p^ =p 2 =P3, A = B = C. 

 If therefore the axis of z is the direction of propagation, h = 0, 

 and / and g are functions of z and t alone; whence (10) 

 become 



di 1 dz 2 ^ p dz 2 dt' 



(12) 



dt 2 dz 2 P dz 2 di 



To solve these equations, assume 



/=LeT^-*) 3 g = 'Ke ± r ( ^- t )- . . . (13) 



where L and M are complex constants, t is the period of the 

 particular light considered, and Y is the velocity of propaga- 

 tion in the medium. 



Substituting in (12), we obtain 



(V 2 -A 2 )L+2^M/t=0, 



(V 2 -A 2 )M-2*7r ? L/T=0; 

 whence 



M = +*L, 



Y 2 = A 2 ±'27rp/r (14) 



If the incident light is represented by 

 /= L cos 2irt/T, g = ; 



and if V : , Y 2 denote the greater and lesser values of V, we 



shall obtain in real quantities, 



/= ^Lcos^f^ 1\ +^Ijcos~(~ — A 



It? ( z \ . T . 27r / z \ 



1T . 2tt 



