Doubly Refracting Plates and Elliptic Analyzers 25 



light, and depends only on the azimuth of its major axis, the mi- 

 nor axis always bisecting the angle between the principal azi- 

 muths of the two halves of the analyzing system. If k^o the 

 setting depends not only on the azimuth of the major axis, but 

 also upon the ellipticity of the incident light. The series for 

 sin 2 a is rapidly convergent, and for small values of e o and k 

 may be written : 



°-=-y=^ (50) 



V c. 



Or expressed- in degrees : 



i,745X 10 2 1 c 



I (l + ie o y— (i— K ")C0S2(l,l') 



e- 



3,49Xio- 2 1/i-k o sin 2 (1,1') 



The coefficient k is infinite for 2^ (1, i')=o, falls to a minimum for 



cos 2(1,1') = 



and then rises again as ^ ( 1,1') increases. For the Lippich half 

 nicol this minimum, ^ (i,i')=i5.8°, lies outside the range of 

 practical use. The series is, of course, not convergent for 

 large values of k, but it gives sufficiently accurate results for all 

 practical values of 2£(i,i'). The value of k, for the Lippich half 

 nicol (k=.o8) is plotted in the curve, figure 2. Plotted on the 

 same scale, the value of k, for the Brace sensitive strip (k o =o) 

 could not be distinguished from the axis of abscissae. For the 

 Brace sensitive strip a is negligible, but for the Lippich half nicol 

 it may be appreciable in accurate work even with -small elliptici- 

 ties. If 2^(i,i / ) = i° and <? o =.oo85, then a = .oi°, the error intro- 

 duced by neglecting it being greater for smaller values of 2^( 1 , 1') and 

 larger values of e o . Care must therefore be taken in using the 

 Lippich half nicol to ensure the absence of ellipticity, or, if pres- 

 ent, to eliminate the error produced by it. In measurements on 

 naturally rotating substances this error can only be eliminated by 

 reversing the angle between the two halves of the field [changing 



181 



