Doubly Refracting Plates and Elliptic Analyzers 21 



ings, such that this is the case, since otherwise the final formulae 

 will give the reciprocals of tgw and tg^iV^, instead of the quan- 

 tities themselves. To insure the proper choice it is necessary 

 that 



cos(r- — n) . 



cos 2 7r N, 



>o 



If N t is not known beforehand with sufficient accuracy to de- 

 termine the sign of 003277-^, the direction of the major axis of the 

 ellipse must be determined roughly by some independent method. 



If the order of the compensator, N lf is accurately known in 

 advance, it is not necessary to read both compensator and nicol, 

 the reading of either one alone being sufficient to determine the 

 ellipticity of the incident light. The following equations are 

 readily obtained : 



tg 2 w=tg 2 it N x cos c (44) 



and 



sin2o)=sin27riV^cosw (45) 



For small ellipticities the first equation is preferable, and for 

 large, the second. 



The equations so far have been given in terms of the rotation 

 of the nicol relative to the compensator. It is sometimes con- 

 venient to read the rotation of the nicol relative to fixed axes. 

 Calling p and p' the two rotations of the nicol relative to fixed 

 axes, and v their difference : 



p=R—r p '=R'—r'=r—R 



v=p' — p=2(r — R)=c — u 

 Eliminating (c-\-n) between the equations: 





— and teir2V,=\\ . ) (43) 



11) si \sin(H-») y 



T~. cllH-l 15< 7T i V -V — ; — 



X.<gy 2 (c-\-n) & ' \sin(r+») 



the following equation is obtained : 



tgt>}=e_= 



f 

 \ tgfirArJ i± 



177 



(46) 



ter'ir^v; 



