124 Prof. S. P. Thompson on the 



If represent the intensity of the transmitted ordinary ray 

 and E that of the transmitted extraordinary ray, we have 



6 -^c 2 v 2 



U = g-^AV ( 16 ) 



whence 



logO_^CV 1 



logE f i 2 G 2 Y 2 V } 



Now the ratio of Vj to V 2 is known (§ 14), the velocity of 

 the ordinary ray V 2 being to that of the extraordinary ray Y x 

 in the ratio 1*8286 to 1 , 8504. If, therefore, the magnetic per- 

 meability were equal both along and across the axis of the 

 crystal, and if the electric conductivity were equal in both 

 directions, the relative intensities of the two transmitted rays 

 would depend only on the relative velocities ; and as V 1 is 

 greater than Y 2 , the ordinary ray should be more freely trans- 

 mitted than the extraordinary ray, which is contrary to obser- 

 vation. The conductivities therefore cannot be equal in fact. 



Billet's values (§13) for the refractive indices of tourma- 

 lines of different colours show slight differences, the colourless 

 tourmaline being apparently a little less refringent than the 

 coloured crystals. As in this case there was no opacity, the 

 presumption is that both C x and C 2 were = 0. If the fact 

 were confirmed by observation generally that the index of 

 refraction is less in crystals exhibiting no coloration, we 

 should be obliged to consider K as no longer independent of 

 C in the general equations of electromagnetic disturbances ; 

 and V, which is taken =(/LtK) - ^, would require a more com- 

 plicated formula for its complete expression. 



18. If, again, either the coefficient of magnetic induction or 

 the conductivity be greater along the axis of the crystal than 

 across it, then the ordinary ray should be transmitted more 

 freely than the extraordinary. This is not the fact with any 

 tourmalines; it is always the ordinary ray which suffers the 

 greater absorption. 



As I understand Plticker's experiment on the diamagnetism 

 of tourmaline (§7 ante), the crystal examined by that dis- 

 tinguished physicist possessed a greater magnetic inductive 

 capacity in a direction across the crystallographic axis than in 

 the direction of that axis. If this observation were also con- 

 firmed for tourmalines in general, we should have some reason 

 to expect that crystals possessing electric conductivity, even 

 if the conductivity were equal in all directions, should show 

 greater absorption for the ordinary ray; for if C 1 =C 2 , equa- 



