42 PROFESSOR KELLAND ON THE POLARIZATION OF LIGHT 



Let us abbreviate eSx+fdy by ki, e8x-fdy by kr, e,8x+f8y by k,e, and 

 e' 8 x +/8y by k' o ; then we have the following values of 8 1, &c. 



* T O T 9 ^ Z 1 rf I . 



o I = 2 1 sm 2 H --- sm k z 

 2 



T . T , . k i 1 d I' . 

 o I'= 21'sin 2 + -- smkt 

 2 e rfz 



X E> o r> 9 ^ r 1 a? R .* , 



oR= 2Rsm 2 H --- smkr 



2 e dx 



d R'= -2 R'sin 2 + - sin k r 

 2 e dx 



%T> n /-i mtx ..% \ 1 afR, mS* . , 



oR / = R 7 (l e cosfoy) + - ^e smfoy 



2 e' afa; 



", 5* f S \.1'*1/ , J X ,. 5> 



cos/dy) + - -i e ' sin/Oy 



f a y 



By substituting these results in the increments of equations (1) and (2), we 

 shall obtain 



d a = 2 I sin d> sin 2 + 2 R sin d> sin 2 H --- sin d> sin k i 

 2 2 e dx 



1 d R . i . , n /i S * j- % \ d R 1 m Jr. 

 



. i . , n /i * j- % \ m Jr. .. 



--- - sm <p sin* r R x (1 e cosfoy) + -^e smfoy 



e dx ay f 



n ( a ki nn . 9 kr Idl . IdR . 1 



38= { 2 Ism 2 2Rsm 2 -- 1- -- smki + - - smkr } cos d> 

 2 2 edx e dx 



. ki n -n, . .k r I dl' . 1 rfR' . 



5'y=-2rsin 2 + 2R'sm ! -+- - smki --- s 

 2 2 e dx edx 



8 a t = 2T,sin( / cos 6 sin 2 -^- + 2 T' sin <' sin & sin 2 _ + -- sin (p / cos 6 sin k, e 



1 rf T' . /i, m /i , S ..Jx L di. m, > x . .. s> 



' '-- ' -~ sm/Oy 



f$ t = 2 T cos (f), cos sin 2 -^- + 2 T' cos <p' sin & sin 2 



1 // T \ d T' 



H cos (b cos ^ sin k . e cos 0' sin 6' sin K o 



e, dx e ax 



S 7,= - 2 T sin 6 sin 2 ^- 2 T' cos # sin 2 ^ 



(40 



