Doubly Refracting Plates and Elliptic Analyzers 59 



That is: the errors in e o due to errors in the determination of X 

 and if/, and the errors in o due to errors in the determination of 

 e x and A\ are at the most of the second order and hence negli- 

 gible. 

 If in addition 0^=0: 



de de „ 



— - = — = sec <«> 



de Y 971-vYj 



and (113) 



d$ dd 



der i -dj =sec20i » 



In the second case, Wj=o and therefore, 



5(0^,0^) = ] COS-2(u o ' — COS^WV, 



where | sin 2 w o | ^> | sin 2 it A\ | 



Then : 



de 



— sec 2 w sec2w COS2 7TA 7 ; 

 de, ' 



3^ 3^„ / — 9 ~> r? 9 / \ 



— — ?=— -2= — 1 cos^2w — cos-27ryV . sec"w sec2u) o (114) 



and 



3^"„ 9 jr 



- — ^-=sec' : w o tg 2 w o cot 2 7r A , 



7T A\ 



30 



— ^^l'cOS^W COS 1 2irJV . sec 2 2i 



3# 30 



ZQ^ 1 — g-^=sec-2co o cos 2irA\ (115) 



30 



:l/cOS 2 2to o COS' 2 2 7rA 7 1 . tg2 U> SeC2 to CSC 2 7T A 7 , 



If in addition, N 1 =%, cos2 7rA r 1 =cot2 7rA r 1 =o, csc27rA r 1 =i, and 

 locos' 2 2 w y — cos 2 2'n-A 7 1 =cos 2 w u , then; 



3^ 3d- 30 dB , ^ 



^-=^t7=^=I-^t'=0 ( I l6) 



3<?j 3Af 3d, d\\i 



That is: the errors in e due to errors in the determination of e, and 

 A 7 ", and the errors in 6 due to errors in the determination of 0., are 



1 o 1 



at the most of the second order, and hence negligible. 



215 



