46 L. B. Tuckerman 



These are of the form : 



a cos n — /? sin n=y 



{3cos?i J r asin?i—o 



Squaring both and adding, a 2 +/? 2 =y 2 , which is an equation inde- 

 pendent of n. Substituting values for a, /? and y, and arranging 

 according to powers of t: 



/ 2 (i — sin 2 2irN x sec 2 2 77) 



— 2 / cos £ sin 2 7r TV, cos 2?^^ sec 2 2 ?7 



-f- [1- — (1 — cos 2 rsin 2 2 7rA r 1 )sec 2 2r/]=o 



Solving for t: 



cos csin 2 it N x cos 2 ir N Y sec 2 2 77 ± tg 2 7? 1 ' 1 — sin^ TrA 7 , sec 2 2-g sin 2 c 

 1 ■ — sin 2 2 7r A^ sec 2 2 77 



^__ (84) 



which is of the form : /=^ 1 cosf-^2 1 : — ^sinV 



where k 15 k 2 and k 3 are constants depending only on A^ and 77. 



If 77 is small the equation approaches the equation for Stokes's 



analyzer, 



/ =tg 2 7T ACCOST 



As 2tt A 7 , approaches — > this approaches the form, /=cc . o, so that 



the equation becomes illusory for compensators which are approxi- 

 mately quarter-wave plates and are required for measuring large 

 ellipticities. The value of t varies less with changes of c, the more 

 nearly t=tg2irN 1 which gives the condition for greatest accuracy 

 in determining /. 



When 2irA\ is near — > a usable equation may be obtained by 



eliminating c instead of n. Arranged according to cose and sin*:, 

 the equations (73) and (74) are of the form: 



a cos c -j- /3 sin c -\- y =0 

 8 cos c -j- € sin c -j- £=0 



Solving for cos c and sin c, squaring, adding and clearing of 

 fractions : 



202 



