Doubly Refracting Plates and Elliptic Analyzers 13 



in equation (11) the value o and finding P v Q v AT, and S v Let- 

 ting the 2^ (o, 1)= — 9 a , this gives: 



Px=P. 



Q, = Q n COS2(o, l)=P : — / COS2(9 



i—e 2 



Ki=— Qo sm2 (o,i)=p—-—°sm2e o (17) 



x °\4-e i 



2e 



S X =S=P 



x ~r c 



P and 5 are therefore invariant for any rotation of the axes. 



When the direction of propagation and the plane of the ordi- 

 nary vibration are given, P, Q, K and S completely define the 

 properties of any completely polarized light. In fact, only three 

 of them are necessary since there exists between them the 

 equation : 



Q 2 +K+S=P 2 (18) 



From equations (17) any of the ordinary constants of the light 

 may easily be obtained. The following are the more important 

 ones : 



The ordinary and extraordinary intensities, / and /: 



I=P+Q J=P-Q (19) 



The phase lag of the extraordinary on the ordinary vibration : 



5 



<£=arctg-^ (20) 



The intensities of the light in the major and minor axes of the 

 ellipse, I m and J m : 



(21) 



J=P-VP l -S l 



The angle 6 which the major axis of the ellipse makes with the 

 plane of the ordinary vibration : 



0=i^arctg*^ (22) 



169 



