Doubly Refracting Plates and Elliptic Analyzers 23 



Soleil Biquartz. 1 



Poynting Biquartz. 2 



Poynting Sugar Cell. - 



Of these halfshade analyzing systems, all except the last three 

 analyze the light in two directions making a slight angle with 

 each other. The last three do not properly come under the gen- 

 eral theory here given, but an elementary consideration shows 

 that the emergent intensities are the same as if the biquartz or 

 sugar cell were removed and the two halves of the analyzing 

 nicol rotated in the opposite direction through the same angles 

 as those produced by the rotation of the quartz or sugar. The 

 theory is then identical (for monochromatic light) with that of 

 the split nicols. 



In the first two systems, the intensities of the emergent light 

 when the incident light is unpolarized are not the same but have 

 the ratio 1 — * where : 



K=siir(i,i')+K o cos" 2 (i, 1') 



a£(i,i') being the angle • between the two halves of the analysing 

 system, and 1 — k , the ratio when 2^(1, i')=o. For the Brace Sen- 

 sitive Strip k=o, and for the Lippich half nicol *=.o8. The 

 theory of the other systems may be obtained from that of the first 

 two by making k=o. 



Referring the incident light to its major axis (16) : 



P=P 



M o M 

 Qo=Po-J-T 



**o i-\-e\ 



For a match of intensity of the two halves of the field : 



JVr-Q^O-" XP'.+QY) 



or from (n) 



P 



1—e 2 Krmt , „ 1— e 2 



» +p <>r+/ cos2(o ' I)=(I ~ K)[/>0+p< 'r+?; cos2(o ' 1 ' )] 



'Soleil, . C. R., vol. 20, p. 1805, 1845. 



2 Poynting, J. H. Phil. Mag. (5), vol. 10, pp. 18-21, 1880. 



179 



