}•■ 



Electromagnetic Theory of Quartz. 159 



In the case of quartz, pi = p 2 ; p 1 =p 2 = y the axis of the 

 quartz being the axis of z. If therefore we put 



"70 + Pi) = a \ n 'fo + /°s) = ** Q =Pl n '> 

 (19) become 



S-('-»-S^4(2-f>~ 



^ 2 /n2 <^\ 2 d /^ ^\ 



Solving these equations in exactly the same way as we 

 solved (16), we shall obtain 



(V s -a 2 n 2 )\ + aHnv + (2nrq/r)a 2 n 2 fj,= 0, 



(V>-a 2 )fJL+ {2t7rq/r)a 2 n{lv-nX) = 0, 

 (Y« _ c 2/2) v + cs^\ - tfnrq/ryinii = 0. 



Multiplying the first and third by l/a 2 , n/c 2 respectively 

 and adding, we obtain 



which requires either that 



V = 0, or l\/a 2 + nv/c 2 = 0. 



The first equation corresponds to the pressural wave, 

 whilst the second determines the direction of vibration in the 

 optical wave. 



Eliminating \, fi, v from (21) we shall obtain 



(V 2 -a 2 )(Y 2 -aV-c 2 / 2 )=^^(aV + c 2 Z 2 )a 2 n 2 , . (22) 



which determines the velocity of propagation of the two 

 waves. 



The right-hand side of this equation is not quite the same 

 as (17), but the difference is not very large, since a 2 —c 2 is 

 a small quantity. It might, however, be possible to determine 

 experimentally which formula is the more exact representative 

 of the facts. 



7. Boussinesq* has proposed to explain rotatory polariza- 

 tion by the introduction of the terms 



dv dw dw dii dil dv ,~ ns 



»*-*&**-»-&**-*■& ■ ,(23) 



• LiouviUe, deuxi&me s^rie, vol. xiii. p. 313. 



