Doubly Refracting Plates and Elliptic Analysers 



37 



For a match, Q 3 — Q'3— o, or from (53) 

 -cos 2 (o, 1 ) sin 2 ( 1 , 2 ) sin 2 ( 2, 3 ) 



»!.+<, 



2e 



°i+e* o 



. . ( COS 2 7r A 7 , 



COS2 7tA^ 2 ) 



— Sin 2(0, i) COS2(l,2)sill2(2,3) COS27TA 7- ! (cos2rr A, 



— COS2 7riV 2 ) 



H-sin2(o,i) sin2(2,3) sin2 7rA^ 1 (sin2 7rA r , 



— sin2 7riV'.,) 

 + COS 2 ( 1 , 2 ) sin 2 ( 2, 3 ) sin 2 7T A", ( COS 27T A, COS 27T A 77 ,,) 



+ . • • • sin2(2,3)cos27rA^(sin27rA^ — sin27rA 7 ' 2 ) 



Substituting N. i =N J r A N, N'=N—\A r , 2^(0,1) = ^, expanding, 

 cancelling like terms and dividing by 



^ sin 2 ( 2, 3 ) cos 2 7r A^sin 2 7r A A 7 ^.- 



eives : 



(64) 



-}-COS2l/'sin2(l,2) .... tg27rA r 



-j-sin 2^1 COS 2 (l,2) COS27ryV, tg27T N 



-psin2t/' sin 2ttN y 



— cos 2 ( 1 , 2 ) sin 2 7r N x tg 2 7r A 7- 



+ ..'.. COS27rA r 1 



The equation is independent of the angle (2,3), and consequently 

 the match is independent of. the azimuth of the analyzing nicol, 

 although the sensibility depends upon it. 



If the half shade is balanced, tg2 7rA^==o, and 



-sin 2 4 1 tg 2 7r yVj 



or 



(65) 

 ) (66) 



e= — ^tg2 7rA 7 ' 1 sin2i/'( 1— ^ tg 2 2 7rA r 1 sin 2 2i/'+ . . 



If the halfshade is not balanced and small cllipticitics are to be 

 measured it is as before convenient to fix the halfshade, this time 

 at 45 to the major axis of the incident light. Then: 



*(o,2)=- 



• 4 



193 



