in Singly and Doubly Refracting Media. 341 



and L w = oo , equation (7) can also be written thus, 



and this relation will, as an empirical one, equally well repre- 

 sent the connexion between index of refraction and wave-length 

 provided only the number of terms be made dependent on ex- 

 periment. As for the rest, the hyperbolic character of the 

 particular curves permits n to be exchanged for its reciprocal 

 value co ; and thus the formula 



may lay claim to equal admissibility ; I have proved and con- 

 firmed it in the most comprehensive manner. 



From the result of this trial I here conversely draw the 

 conclusion that just so the theoretical formula (7) accords per- 

 fectly with the best measurements hitherto made extending over 

 an interval of two octaves. 



5. If we proceed to the discussion of the vires vivce in 

 this more general case also, it will suffice, in the first place, to 

 point out that generalizing ihe method of reasoning carried 

 out under § 3 leads at once to the corresponding relation 



o -. 2}mV 2 

 n z — \— l — 



mp l 

 Self-evidently, instead of the vires vivce of the single molecules, 

 we can bring into it the vis viva of the entire corporeal mass ; 

 we have then to put 



In regard to the compatibility of the same with the above 

 differential equation, by an analogous procedure we obtain 



mp 



dl 



w# -« & +2 * b&^v'JJ + V), AH) 



and the condition-equation becomes 



or 



S^p 2 [e + (6 / -^ 2 )^] = 0. 



Now, as the medium under consideration (a mixture of gases, 

 suppose, or a solution of salts) is composed quite arbitrarily of 

 several simple constituents, each of which is characterized by 

 e, e r , k' , and a, and we do not assume that these constituents 

 individually exert reciprocal action upon one another, the fore- 



