44 L. B. Tuckcrman 



Solving for tgir N^. 



sin r tg 2 7? ±: 1 sin'-<:tg-277+sin(c+^)sin(<: — n) 



tQf 7T iV. 7 ; ■ 



& a sin(V+;z) 



Letting 



sinr sinr 



1 sin(^-(-»)sin(t — «) 1 sin' 2 *: — sin 2 « 

 where the square root is given its positive value : - 



sin( c — n ) 



, r bllllt— It) 5 \ , . 



tQ-TTN.—X ~. Utg277 1 I^-rt-tSf-277) (78) 



Al sin(V+») & ' B U w } 



The square root 1 i^ r a z tg-2r) must also be given its positive value. 

 If (] is small and the ellipticity of the incident light is also not too 

 small this may be expanded in a series: 



!sin(*r — n) , / o o / 1 1 



tg ^ N =^^-—^(i-atg2 V ^l4a'tg 2 2 V —y8ahg i 2 V + . . .) 



(79) 



If the ellipticity of the incident light is small the coefficient a be- 

 comes large, and for the value /— tg2>? is infinite. For these 

 values tg7ri\f is given by the series: 



v __ sin (c—?i ) _ 1 1 . .„ . 



^ 1Tl 1_ 2sin7tg27 ? ^ 1 4«'-tg 2 277 8a i tg i 2r j ^~ 



In the equation (77), substitute, 



2 to: 7r N, 



sin2 7riV,=- 



1 i + tg^TV; 

 and 



at i— tg-vA 7 ; 



COS 2 7T A'. = ; — ^— T7 



1 I+tg-TTiX 



Then 



— cos c sin « ( 1 — tg 2 7r yVj ) +sin c cos // ( 1 + tg 2 it N x ) 

 2smntgirJV 1 



sin (c — u) -f- sin(r+«) tg 2 ?r A^ 



2sin7Ztg7rAf 



200 



