34 



L. B. Tuckcrman 



sin 2 6 



+ COS 2 2i/' X.g2irN 

 -f-sin 2 2i/' tg2 7rA ; 'cOS2 7rA r 2 



+sin2i/' .... sin27rA r 2 



2<? | + COS 2 2l/' 



"+sin 2 2i/'. . . . cos27rVV 2 

 — sin 2i/'tg27rA ; 'sin27r N 2 



=o 



Substituting i — sin 2 2i^ for cos 2 21^, 2 sin 2 7r TV,, for \—cos2ttN v col- 

 lecting terms and solving for j-- 



2e . .ts:27rA r -^sin2 7r7y,sin2t/' — 2sin 2 7riy. ts:2 7r7Vsin 2 2i/' . „. 



V=sin20-^ — - r 2 - — z^-. .- & ., . .. , (58) 



1 — e\ 1 — sin2 7ri'V 2 tg2 7riVsin2i/' — 2sur7rYv sin'^i/' 



If the ellipticity of the incident light is zero, the numerator of 

 this expression is zero, from which : 



tg2irA r = — sin27riV, sin 2 ^-|- 2 sin 2 71- tV, tg2 7rA 7 "sin 2 2i/' (59) 



where the second term may usually be neglected. Or 



sin27rA^ sin 2^ 



tg2TTjV- 



(60) 



1 — 2sin 2 7TiV 2 sin 2 2^ 



which may be expanded in a series : 



tg 2irJV= — .sin 27r7VT,sin 2^(1 + 2 sin 2 7r N 2 sin 2 2 \p 



+4sin 4 7r7V r 2 sin 4 2^+ . . . . ) (61) 



This is the condition of the apparatus in the work done by Elmen, 1 

 Morse, 2 Hagenow, 3 and McComb, 4 on the electric double refraction 

 of liquids. In their work the electric field is placed parallel to 

 the principal azimuth of the halfshade, so that the liquid may be 

 considered as part of the halfshade. N then represents the re- 

 tardation of the liquid plus the average order of the mica half- 

 shade itself. 



'Elmen, G. W. Phys. Rev., vol. 20, p. 54, 1905. 

 -Morse, L. B. Fhys. Rev , vol. 23, p. 252, 1906. 

 3 Hagenow, C. F. Phys. Rev., vol. 27, p. 196, 1908. 

 'McComb, H. E. Phys. Rev., vol. 27, p. 336, 1908. 



190 



