36 L. B. Tuckerman 



i + 2tg 2 7rA r (i — ^sin 2 2 0J — sin 2 7rA r 2 +>^sin27r7V 2 tg27rA r cos 2 2^sin2i/' 



+ 2sin 2 7rA r 2 (i — ^sin 2 2^)sin 2 2^ 



In practice, can not differ much from 45 °, if the sensibility is satis- 

 factory, so that in the correction factor, the assumption may be 

 made: sin2 0=r, cos 2 0=o. It then becomes: 



. i-f-tgVA 7 — si n 2 77 A 7- ,, cos 2 2 1// 



The correction factor may be neglected if both tg 2 7r A 7 " and sin^A^ 

 are negligible in comparison with 1. Then: 



e =sin 2 tg it N„ ( sin 2 \\i — sin 2 if/ o ) ( 63 ) 



Since complementary values of \j/ o give the same value of sin 2^, \f/ o 

 is readily obtained by making two independent settings for a match 

 on plane polarized light and subtracting j4 their sum from 90 °. 



The value of \p o may evidently be used (equation 61) to calibrate 

 an unknown compensator in terms of a known halfshade and vice 

 versa. 



This is the arrangement and the formula used by Skinner and 

 Tool' in their work on the optical properties of magnetic metals. 

 In their work, sin 20=i. 



B. »->"■ Compensator s->- Elliptic Halfshade «s->- Nicol 



For this arrangement the symbols have the following signifi- 

 cance : 



Order of compensator z= ^ T v 



Order of the one-half of halfshade =A',. 



Order of other half of halfshade =jV' 2 . 



Angle between major axis of incident light and principal azimuth 



of compensator=2^(o, 1). 

 Angle between compensator and halfshade=^(i,2). 

 Angle between halfshade and nicol =2^(2,3). 



'Skinner, C. A., and Tool, A. Q. Phil. Mag. (6), vol. 16, pp. 833-62, 

 1908. 



192 



