178 F. E. Wright — Transmission of Light through 



This expression can be simplified, as was (34), by the intro- 

 duction of tg s 2 : 



cos <? 2 sin(^ + r 2 ) 



tg 8\ = - 



sin 3 ^(cot r 2 sin 8^—tg s 2 )+ sin <J 2 sin i cos i 



8' 



1 



= 





1 



8' 

 i 



= 



€ 2 



± 90' 



*'. 



= 



£ , 



± 90 



*- cos 8 smli + r.) . „ , 



or tg S\ — : — ^ — —-. r— ^ — ,: *' — r-i (36a) 



sm o^ sm(i + r J cos (i—9\)— s\n* r 2 tg s^ 



On comparing this relation with (355), it is evident that 



(SI) 



also 



This apparently new and important relation greatly simpli- 

 fies the labor of calculating the azimuths of the planes of 

 polarization of waves transmitted through a crystal plate. In 

 form it is similar to the relation deduced by Potier, 1 that in 

 case a wave W, within a crystal plate emerges into an isotropic 

 medium, the emergent wave is polarized at right angles to that 

 wave which, entering the crystal plate in the opposite direc- 

 tion, produces the so-called " Hilfswelle W " 3 of W. The 

 above relation states that the azimuth of the plane of polariza- 

 tion of the emergent wave ~W\ from W, is at right angles to 

 the uniradial azimuth e 2 of the wave W 2 . To calculate the 

 azimuths of the emergent waves W' 1? W\, it is only necessary, 

 therefore, to calculate the uniradial azimuths e 15 e 2 of the inci- 

 dent waves which produce the refracted waves W, and "W" a . 



Uniaxial Crystals. 



In the preceding pages the formulas for the transmission of 

 light through crystal plates have been developed for the most 

 general case, that of biaxial crystals. When applied to uni- 

 axial plates, these formulas become somewhat simpler, and 

 deserve brief consideration as they will be used in the observa- 

 tional part of this paper. The equation of the index surface 

 for uniaxial crystals referred to general coordinates is 



[o\x n + y n + z n ) - l][o, ,»'■ + a 22 y' 2 + a J* + 2a, 3 y'z' + 



2a 31 z'x' + 2a li x'y' — l] = 0. 



If, as usual, the plane of incidence be the x' z' plane, (y' = 0), 

 and the z' axis the normal to the plate, the positive direction 

 of z' being within the crystal plate, this equation can be written 



1 Journ. de Phys. (2), x, 354, 1891. 



2 F. E. Neumann, Berliner Akad. Abh., Math. Abt., 1835. 



