Double Refraction of Quartz. 115 



Whence the vibrations, after emerging from the second plate, 

 are (omitting ^-^) : 



In Oo\ 2k". cosT+0 . sin f + ^® 



-2A.sina + 0.cos£ + ^-^. 



In o>'„ 2F. sin a + . sin £ + ?^ 



A 



+ 2F cos a + . cos f + 



2tt9 



In E'e\ -k°{\-¥)cosa + <f>.sm % + 



47T0 



+ /<■ (l - £ 2 ) sin a + . cos £ + 



4^9 



In e>'„ (1 -#*) . sin a + . sin £ + 



4*-9 



+ £ (1 — £ c ) COS a + <p . COS £ + 



4tt9 



X 



Adding together the vibrations in the same direction, we find 

 (omitting the factor -, — %— V 



Vibration parallel to Oo 1 



= 1 -A*. COS a + 0. sin £ + /<•. (I -k s ).sma + (f>.COS% 



+ 4^.cos7T^.sinf + ^-2^(l-F).sin^T^.cos?+^- 



-*(1-*) co.a + ^.rinf + i^ + *(i_^). sin ^T^.cos? + 4 ^ 



p2 



