Doubly Refracting Plates and Elliptic Analyzers 39 



ing edges of the Lippich and the halfshade cross each other at 

 an angle (preferably 90 ), dividing the field into four parts. 

 They should be placed as nearly in the same plane as possible, in 

 order that both may be at the same time in focus in the observ- 

 ing telescope. A match of intensity of the two halves of the 

 Lippich will be called a "Lippich match" ; of the two halves of 

 the halfshade, a "halfshade match." ' A complete match is both 

 a Lippich and a halfshade match. The setting is always made 

 for a complete match. 



Expressed in terms of the light which emerges from the com- 

 pensator (P o , Q v K v Sx), the condition for a halfshade match is 

 from (14) : 



— QjSin2(i,2) sin2(2,3) (cos27rA^ — cos2ttN\) 

 +/lj cos 2 (1,2) sin 2 (2, 3) (cos27riV 2 — cos2tt N' 2 ) 

 +Sj sin 2(2,3) (sin 2 7r A, — sin 2 7rA r ' 2 )=o 



Expanding in terms of N and AN and simplifying, this reduces 

 to 



[Q,sin2(i,2)- K t cos 2(1,2 )]tg 271-iy-f-S! =0 

 Similarly the condition for a Lippich match is from (14) : 



kP + Q,j + COS2(l,2) .... [cos2(2,3) — C 1 — K ) cos 2 ( 2 > 3')] 

 | — sin 2 ( i, 2) cos 2 7tA^, [sin 2 (2,3) — (1 — *) sin 2 (2,3')] 



+AT 1 l +sin2(i,2) .... [cos2(2,3) — (1 — fc)cOS2(2,3')] 

 |+cos2(i,2)cos2 7rA^ 2 [sin2 (2,3) — (1 — k) sin 2 (2,3')] 



-j-S, sin 2 7T N 2 [sin 2(2,3) — ( 1 — k ) sin 2 ( 2, 3' )] =0 



Expanding in terms of N and A.V and introducing the con- 

 dition of a simultaneous halfshade match, the terms containing 

 sin 2 7r A A 7 " become zero, and it reduces to: 



195 



