60 PROFESSOR KELLAND ON THE POLARIZATION OF LIGHT 



sin q> sin , 

 add together (1) and (4), and 



I-RTcos0 Tsinfr 



sin' *' V 1 ' 4 



By this equation and (2) we get 



Put (*-l)T,sin0 = wTcos0 ..... (8) 



then 21=T cos 



- 

 sm (p, cos / sin <jf)' cos 



=/T-T' suppose; . . . . . (9) 



- 

 sm 9, cos 9 / sin <' cos 



=w'T-'T' suppose ...... (10) 



R' I' 



Let us also denote, as before, - by cot a, y by -cot. 



Then if we write R cot a and I cot a for E' and F, and afterwards put for 

 R and I their values given above, we obtain from (3), 



-(m T-w T) cot u-(nt T-' T') cot a=2 T sin + 2 T' cos & 



and -(mT^ W TOcot. C ^ + (m'T- M 'T';cota C ?i|=2T C -^' S m0 + 2T' C -?i$'cos^ 



sin <p sin <p sin <p y sm <p' 



From the first, 



T{2 sin 6 -f- i cot u + m' cot a} = T'{ 2 cos & + w cot w + ' cot a}. 



From the second, 



T'{2 cos O' cot (f)' n cot u cot + M' cot a cot (f)} = 



T( 2 sin 6 cot (j) l m cot a cot (f) + m? cota cot(>}. 



By multiplying these equations together we get 



(2 sin 6 + m cot u -f m' cota) (2cos# cotfi ncot a cot (f) + n' cot a cot 0) 

 = (2 cosfl' + wcotw + w' cota) (2 sin 6 cot0 y wzcot cot0 + z' cota cot </>). 



But when the incident light is common light, this expression will give rise to 

 two, of which one is the coefficient of cot u, and the other that part of the expres- 

 sion which does not contain . 

 These are respectively, 

 m (2 cos & cot 0' + n' cot a cot 0) cot</> (2sin0 + i' cota) 



= n (2 sin 6 cot<t>, + m' cota cot<p~) m cot <p ( 2 cos & + n' cota), 

 and (2 sin 6 + m' cot a) (2 cos & cot (j)' + n' cot a cot 0) = 



( 2cos ft + n' cot a) ( 2sin 6 cot^ + w' cot a cot (/>) ; 



