II. — The Transmission of Light through Doubly Refracting 

 Plates with Applications to Elliptic Analyzing Systems 



BY L. B. TUCKERMAX, JR. 



The importance of the measurement of elliptically polarized 

 light in the study of electro- and magneto-optic phenomena and 

 the optical properties of various substances, has caused many 

 different methods to be devised for the accurate measurement of 

 ellipticity. Among these, the various halfshade methods offer 

 the advantage of convenience combined' with high sensibility. 

 No adequate general discussion of these halfshade methods has, 

 however, as yet been published, and this lack has probably con- 

 tributed in part to the comparatively small use of halfshade 

 methods by investigators. This paper is an attempt to supply this 

 lack. 



In discussing some halfshade systems it is necessary to know 

 the effect of three or more successive doubly refracting plates. 

 The direct calculation of "this effect is laborious, and the general 

 theorem given b)' Mallard is almost as cumbersome. The kine- 

 matical analogy due to Poincare, an analogy whose simplicity 

 and convenience make it invaluable in obtaining qualitative or 

 roughly quantitative results, does not lend itself readily to the 

 analytical discussion here desired. I have obtained a . general 

 theorem which combines comparative simplicity with ease of 

 application. The first part of the paper gives the derivation of 

 the general theorem and a discussion of its interpretation. The 

 second part consists of the application of the theorem to various 

 halfshade analyzers. No attempt has been made to discuss, ex- 

 cept incidentally, the effects of chromatic dispersion or lack of 

 plane parallelism in the light, although such effects are notice- 

 able and even important in practice. 



University Studies, Vol. IX. No. 2. April 1909. 



157 



