Transparent Inactive Crystal Plates. 191 



tion of these two images do not coincide exactly and there is, 

 therefore, no position of total extinction for this area. In a 

 thin or weakly hirefracting plate, the margins indicated in fig. 

 8b hecome very narrow and all observations are practically 

 confined to this area of overlap. In the microscopic examina- 

 tion of thin sections this is always the case ; it is evident, 

 therefore, that in tilted, thin crystal plates there is no position 

 of total extinction, strictly speaking, but a region of minimum 

 illumination which may extend over several degrees. The 

 emergent light is not strictly plane polarized but shows ellipti- 

 cal polarization and cannot, therefore, be totally extinguished 

 by the upper nicol in any position. 



Still another feature deserves mention. In the actual deter- 

 mination of the uniradial azimuths outlined above, it was 

 often noted that for certain positions of the plate, even the 

 margins of fig. 8b did not extinguish properly because of 

 repeated internal reflexions. A wave, I (fig. 2), entering at the 

 uniradial azimuth produces a single refracted wave, W 1 ; from 

 this w T ave, in turn, one emergent wave, ¥', and two reflected 

 waves, W ia , W lb are formed. Each of these reflected waves 

 produces one refracted wave R, a and two reflected waves W' ia , 

 W" ia ; of these W, a is parallel with the first refracted wave 

 W„ while "W" ia is parallel with the second possible refracted 

 wave W 2 , which w r ould result from the initial wave I if the 

 azimuth of its plane of polarization were not uniradial. The 

 first wave W ia produces an emergent wave (not indicated in 

 fig. 2), the azimuth of whose plane of polarization is parallel 

 with that of W, ; from the second wave W' 1& a second emerg- 

 ent wave is produced, whose line of propagation is parallel with 

 that of the first, but whose plane of polarization coincides with 

 that of W 2 and not with that of W\. In this case the effect 

 produced is precisely that of an overlap of the two images ; 

 there is no position of total extinction but only a region of 

 minimum illumination occasionally covering several degrees. 

 Accurate measurements under such conditions are impossible. 



If thin plates be used for the observations, as in thin section 

 work, this effect must always be present, and consequently 

 there are under these conditions no points of total extinction 

 for obliquely transmitted light waves, but only regions of 

 minimum illumination which may extend over several degrees 

 and on which only approximate measurements can then be 

 made. In the thick plates employed in the present experi- 

 ments, a portion of the exposed area was usually free from the 

 effects of total reflexion and on these portions the positions of 

 extinction were determined. And even there an abrupt shift 

 of the faint margin due to a weak, repeatedly reflected wave, 

 was often observed near the positions of total extinction of one 



