41 6 Prof. E. Ketteler on the Dispersion of Light 



perpendicular to the ray ; and so far they do not behave 

 otherwise in anisotropic than in isotropic media. 



d. On the other hand, again, on account of the difference 

 intimated, it does not appear indispensable that the corporeal 

 and sethereal particles should vibrate in parallel directions. 

 We preliminarily leave it undecided whether the vibrations of 

 the former, so far as they have generally a regular direction, 

 are perpendicular to the ray or to the normal. 



This supposed, let e be the constant of deformation of pure 

 aether; and let E, W, K be the constants of the additional 

 forces, originating from the resistance of the corporeal parti- 

 cles and acting perpendicular to the ray. 



Consequently, as regards the equation of motion of the 

 aethereal particles vibrating perpendicular to the normal, we 

 have, if e acts exactly in this direction and to e the increment 

 E cos S (understanding by 8 the angle between the ray and 

 the wave-normal) is added, 



mg=(, + EcosS)g. . . . (15 a) 



On the other hand, for the corporeal particles the previous 

 differential equation 



m W^M+*<>' ■ ■ ■ • < 15 >) 



remains afterwards as before ; and in it W and K are to be 

 referred to a direction perpendicular to the ray. We also 

 again make the assumption that 



E = «e, W = *e f , K = *k (16) 



To integrate these equations, we imagine the actual excur- 

 sion p (A) as a component of the virtual excursion p (A =£l), 

 and put 



Po =acos2^ + |-©) = ^g 



p' = ®'cos2J 1 t + f-@\ 



(17) 



Here, consequently, as may be particularly remarked, the 

 abscissae x also are referred to the direction of the ray ; and 

 just so the V are the internal wave-lengths measured in the 

 same direction, not in the direction of the normal. 



If, finally, we denote the ray-velocity by a (in contradi- 

 stinction to the w^ave-velocity co), and put, besides the sine- 

 sin e v 

 ratio n = — — = -, the ratio of velocities nf— , we obtain for 

 sin r co a 



