Transparent Inactive Crystal Plates. 209 



partly with and partly without the aid of the upper nicol (ana- 

 lyzer). In anisotropic crystals the planes of polarization of 

 light waves, transmitted along a given direction within the 

 crystal, are prescribed by the crystal structure. On entering 

 or emerging from a crystal plate, plane polarized light waves 

 transmitted obliquely usually suffer a slight rotation of the 

 azimuth of their plane of polarization. The amount of this 

 rotation is rarely more than a few degrees. In practical micro- 

 scope work but little attention has been given to this 

 phenomenon, but in accurate work it is a factor which must 

 be considered. 



In the foregoing pages the attempt has been made in Part 

 1 to present, in terms of the electromagnetic theory of light, 

 the general mathematical treatment of the transmission of 

 light waves through a transparent inactive crystal plate, spe- 

 cial attention being given to the rotatory effects of the boun- 

 dary surfaces of the crystal plate on the plane of polarization 

 of a transmitted wave. This problem was first solved in 1835 

 by J. MacCullagh and also by F. E. Neumann ; since their time 

 a number of investigators have made important contribu- 

 tions to its solution. Interest, however, has centered chiefly in 

 the reflexion of light waves by crystal surfaces and no con- 

 nected presentation of the mathematics covering the phenom- 

 ena of refraction in crystal plates appears to have been made. 

 This has been essayed in Part 1. The greater part of the 

 ground covered therein is familiar, but several of the formu- 

 las derived appear to be new, notably (325) and (37). Of 

 these (37) is important and states that the uniradial azimuths 

 of the plane of polarization of the emergent waves W, and W, 

 are 90° from the uniradial azimuths of the entering waves 

 which, on refraction, produce the waves W 2 and W\. In other 

 words, the positions of extinction on emergence for either one 

 of the two possible refracted waves, W, or W 2 , resulting from 

 a single plane polarized light wave, incident at the surface of 

 a crystal plate, are precisely 90° apart. The positions of 

 extinction for the two waves do not, however, coincide and 

 there is in general, therefore, no position of total extinction 

 for waves transmitted obliquely through a crystal plate. 



Both theory and the observations of Part 2 show that as a 

 general rale, a uniradial, plane polarized light wave, after 

 transmission through a bare crystal plate (preferably a cleav- 

 age plate so that the disturbing effects of surface films caused 

 by polishing are not serious), is still plane polarized, but its 

 plane of polarization has suffered a slight rotation depending 

 on the direction of transmission, and if examined under crossed 

 nicols does not appear perfectly dark in consequence. In thin 

 crystal plates the two refracted waves W 1 and W 2 overlap to a 



