(3) 



33() Prof. E. Ketteler on the Dispersion of Light 



To integrate these equations we put : — 



P = A cos 2tt /^ + j — ©J ; 



p'=AW27r(| + |-©Y 



Introducing these values, the equations are transformed into 

 the following : — 



m _e + cte 



where a/ f = j— 2 j is put for brevity. These conditions must, 



then, be satisfied between the constants of the expressions (3), 

 if they are to be admissible as integrals of equations (1). Eli- 

 minating a from them, we get, first, 





and, taking into account the relation / = wT, 

 9 / rnfe \ 



Lastly, we introduce the velocity of propagation v valid for 



e 

 the universal aether (m / = 0), for which v 2 = —.and, for abbre- 



viation, put 



^=L 2 — =D 

 k vie 



Then the refraction-ratio n receives the finally valid form 



^_i=_2_, ( 4 ) 



which corresponds to the above requirement, viz. that for an 

 infinitely great wave-length Z = T = co the refraction-ratio n 

 become = 1 ; while for an infinitely little wave-length we ob- 

 tain the limiting value n f2 = 1 — D, against which, even inas- 

 much as when D is positive it becomes less than 1, theoretic 

 objections are hardly admissible. 



