Opacity of Tourmaline Crystals. 119 



corresponding components of vector-potential — one of these 

 functions varying with the electric conductivity of the medium, 

 the other with its dielectric capacity, and both being propor- 

 tional also to the magnetic inductive capacity. 



12. We have now four possible cases to consider: — 



(i) where K is very great and C relatively negligible, as in 

 non-conducting media ; 



(ii) where C is great and K relatively small, as in true con- 

 ductors of electricity ; 



(iii) w T here C and K are magnitudes of comparable order, 

 but having different values in different directions. 



(iv) where fi has values differing appreciably in different 

 directions. 



Although from Pliicker's experiments (see § 7 ante) it ap- 

 pears that fjL X and fjb 2 cannot be regarded as equal, yet their 

 values are both approximately so nearly equal to unity that we 

 are not in a position to discuss case (iv). 



13. Case i. {Non-conducting Substance), = 0. 

 Equations (2) become 



^ d 2 F d 2 F A 



dt 2 d< 

 ^ d 2 Q d 2 G 



/^K 3 



whence 



1 



/^K 2 



dt 2 



dz 2 " 



d 2 R 



dt 2 





d 2 ¥ 

 dz 2 = 



d 2 F 

 = dt 2 ' 



d 2 G 

 ' dz 2 



d 2 G 

 dt 2 



(4) 



(5) 



whence it follows that a plane wave in the plane (ay), 

 whose electric displacements are parallel to a, is propagated 

 with velocity Y x ; whilst displacements parallel to y are pro- 

 pagated in a wave whose velocity is Y 2 with the 

 values : — 



v 1= x 



following 



\Zfx 2 K 2 



(6) 



This agrees with the known fact that a wave of light is split on 

 passing through the crystal into two portions whose vibrations 



