888 Prof. E. Ketteler on the Dispersion of Light 



and. after integrating, 



m 2 in , e 2 / e 2 e' /2 , A 



Comparison with equation (5 a) shows immediately that the 

 '.filled is the following : — 



In 



(5 b), 'we obtain 



condition to be fulfilled is the following 



p 



If we omit the first factor and substitute for - its value from 



and also 



i 1 



L 2 L 



The condition sought is therefore no other than the disper- 

 sion-formula itself ; and accordingly it forms the requisite com- 

 plement to the theorem of the refracting force as the ratio of the 

 vires vivse of the corporeal and wthereal particles. 



4. Media which would in strictness satisfy for the entire 

 compass of the radiation the simple formula of dispersion 

 hitherto developed have not yet been observed. From this it 

 will be inferred that by far the preponderating number of sub- 

 stances possess, instead of one, several zones with a complex 

 refraction-ratio (absorption-streaks). In regard to the treat- 

 ment of these media, the vibrating corporeal masses will have 

 to be analyzed into as many optic o-chemical elements as there 

 are absorption-streaks present. If the number were 11, we 

 should get n differential equations for the vibrations of the 

 11 different corporeal qualities of the masses mf, and, besides, 

 for the vibrations of the aether the deformation-equation of the 

 aether of space increased by n additional terms. We should 

 thus obtain : — 



1 



d<2 P / . . , \<Pp 



, d 2 p' 2 , d 2 9 ' 2 



2 ~aW ~" 2 2 lhF + " 2fC2 P< 



Integration and the elimination of a would now give 



