170 Mr. J.Walker on Cauchy's Theory of 



whence from (14) 



A, _ 2aV^IC __ _ 



2a i/^1 C y 



^■(a-a 1 ')tr 1 + ^(a-tf l f jUi 



and writing for U 1; U 2 , a, a/, a 2 ', & their values in terms of 

 the angles of incidence and refraction, 



r-i—r 



sin 2t sin -^— 2 . [cos 2R-M sin2R • - 1] 



A /= -*/~l -^ ^-= C, 



D[sin 2 0>R)-sin 2 ^-^ 2 J 



D sin (i - R) sin (t + R) + D' sin 2 ^p 



D|rin 8 (i + R)-sin^^ 8 J 



where 



D = cos (i-R) + M sin (i-R) */ -1, 



D' = cos (z + R)-Msin (i + R) V^, 



R = - x 2 , the mean angle of refraction. 



Omitting squares and products of the small quantities 

 M, sin , the formulae become 



sin 2i sin 1 9 2 . cos 2R 



A/= " v/ ~ 1 [cos(^-R) + Msin(^-R) V-l] sin 2 (i + R) ' 

 p _ ' sin(i*-R) p 

 U '"~~sin(i + R) U 



Hence the reflected ray will be in general elliptically pola- 

 rized, except for an angle of incidence such that the angle of 

 mean refraction is tt/4, in which case the reflected ray will be 

 plane-polarized with vibrations perpendicular to the plane of 

 incidence. In all cases the component perpendicular to the 

 plane of incidence is practically the same as if the medium 

 had no rotating power, the other component being very small. 



