334 Prof. E. Ketteler on the Dispersion of Light 



and treat first of one whose ponderable molecules are arranged 

 isotropically and are optically simple in their chemical quality, 

 so that its dispersion-curve exhibits only a single absorption- 

 streak. 



This presupposed, let m, m f be the masses contained in the 

 unit of volume of the ethereal and corporeal particles, and p, 



J k 2 72 / 



p' the relative excursions. Then m-7-£, m f ^r are the forces 

 r dt- dr 



acting upon them, measured by the acceleration. On the 



other hand these forces will be composed in the following 



manner. 



If e is the constant of the elastic deformation of the pure 



aether, so that, for this, 



d 2 p drp 



dr dar 



where x is to be referred to the direction of propagation, then, 



for the interior of a ponderable medium, to the force e y-V 



another is added, arising from the reciprocal action of the cor- 

 poreal particles. This, on account of the infinitely less mass 

 and minuteness of the aether particles, as well as their facility 



of displacement, will likewise be a deformation-force E — ^ *, 



of which the characteristic (at present unknown) E is there- 

 fore added as increment to e. We may perhaps suppose that 

 by the resistance of the corporeal particles a like effect is pro- 

 duced as if the tension of the aether were altered. We have con- 

 sequently, for the motion of the aether particles in the interior, 



,ng=(, + E)g. ..... (1 A ) 



On the other hand, with respect to the vibrations of the 

 more discretely distributed corporeal particles, the assumption 

 is a priori admissible, that their amplitudes are much less than 

 those of the aether particles. We further consider the presence of 

 the former solely as a hindrance to the free motion of the aether. 

 Now the force acting on the corporeal particles may either 

 depend on the curvature of the wave-line uniting themf, or on 



* At least, as the sequel will show, it is equivalent to such a force. 



t If the corporeal particles of a medium effected no resistance at all to 

 the motion, the equation for it would he the same as if the masses m and 

 m' -were firmly united to one another — that is, 



(m-\-m') —§ =e — '£-. 

 K J dt* dx 2 



Even this extreme case the theory will have to take into account. 



