Opacity of Tourmaline Crystals. 123 



and 



_2ttV 1 



whence 



2ttV 2 



n 2=~\ 9 



2 a ? 



(11) 



(12) 



we may write equations (9) in the form 



F = €-** COS (H^-frs), 1 



G = €T** cos (n 2 t - q 2 z); i K } 



in which case the expressions (9) will satisfy the differential 

 equations (3), provided that 



2p 1 2 1 =47r/x 1 C 1 n 1J 1 ^ ^ ^ 



2p 2 <7 2 ==47r/* 2 2 w 2 . / 

 It follows at once that the coefficients of absorption are 

 p 1 =2irfi 1 C 1 Y l ,') 

 p 2 = 2^ 2 C 2 Y 2 J ■■'•■' W 



Here Ox and C 2 are volume-coefficients of conductivity, and 

 would require to be replaced by their values IJbzRi and b/lzR 2 

 if a given rectangular plate of the substance, of length I 

 (parallel to of), breadth b, and thickness z, were measured, and 

 found to have resistances of E 2 and E 2 respectively in direc- 

 tions parallel to x and y. In the actual case of the tourmaline, 

 however, in which no measurements of resistance have yet 

 been made, the volume-conductivities Ci and C 2 may stand for 

 conductivities in general. And the proportions of the incident 

 (unpolarized) light transmitted by the crystal will be as 

 follow : — 



Ordinary ray (polarized in a plane (xz) of principal sec- 

 tion ; electric displacements parallel to y, magnetic displace- 

 ments parallel to os), 



proportion transmitted — e^ 2p2Z = e" 4 ^-^-^^. 



Extraordinary ray (polarized in a plane (yz) perpendicular 

 to the optic axis ; electric displacements parallel to a } mag- 

 netic displacements parallel to y), 



proportion transmitted = e- a Pi" = e- 4,r ' i > c ' v i". 



