1884.] homogeneous polarized light seen in a uniaxal crystal. 79 



But by equation a, Prop. II., 



OQ^nTT + p* 



OP 2 = nir - p 2 . 

 :. Area EE'QF'FPE=±J2p 2 d0 =fp 2 d0. 



Fig. 1. 



The limits are = \ sin -1 h to 6 = ~ ~ \ sm ' &> an( ^ as m ^ as ^ 



proposition p 2 is independent of n. 



Therefore the area is independent of n. Thus the area between 

 the first and second ovals will be the same as between the nth and 

 n + 1th ovals. 



Cor. I. Let T k denote the area between tangents and ovals of 

 k p intensity. 



By the preceding 



f A sin -1 k 



T k = ' P *d0. 



J ism- 1 /* 



By Prop. VII. if A k denote the area of an oval of intensity k 



--Jsin-ifc 



p 2 dd. 



A = Z \Z - sin * k - 



6 L z J ^ ^sin-i/o 



Therefore 



T m + A m = 



a — sin A; 



CW. II. A Prop, similar to Prop. VIII. holds if instead of 

 areas between consecutive ovals the areas between ovals whose 

 difference of order is constant be taken. 



