24 L. B. Tuckerman 



which reduces to 

 i— e- 



K-\ -— -° [C0S2(0, i) ( I— k)C0S2(0, l')]=0 



~\ 



Writing (o, i)=(o, i')- — (1,1'), expanding and collecting terms 



2 



~k- — [ [ — k— cos 2(1,1')] cos 2 (o, i' ) +sin 2 ( i , i ' ) sin 2 ( o, i ' ) =o 



i c' * 



Writing ,? o =tga> and solving for cos 2(0, 1') and sin 2(0, i'), this 

 gives after some reduction: 



, a sec 2 w— bV c — tQ^ 2 2i 



COS2(0, I )=H ; 



c-\-\ 



(47) 



^sec2a>-j-#l / V — tff-2w 

 sin 2(0, 1 )= — 



c-\-i 



where 



a= — [1 — k — cos2(i, 1')] 



£=— sin 2 (1, 1') 



K 



2 sin 2 2(i 1' ) 



C =—,( l K )[l COS 2(l,l')] =4(1 x) r ■ ^ y^r 



K [(l+O i 1 K „) COS2 ( 1 ' 1 )J 



If (o, i')=(o, i') for e=o, and a=(o, 1') — (o, i') : where a 

 represents the error in setting when ellipticity is present. 



V C sec 2 0) — Vc — tg 2 2w . ox 



Sin2a= (48) 



C-\-l 



Substituting ^ o =tgw and expanding in ascending powers of e o , 



2 „ ■ 2 c+i , 2 (V+i) 2 +i 6 



, 2 ( t +iy+3(c+-i), (49) 





Vc 



2 (f+l) 4 +IO(r+l) 2 +2(r+l)+I , 



Vc c 



If k=o, <r=oo and a=o for all values of e o . It is evident that if 

 *=o, the setting is independent of the ellipticity of the incident 



180 



