424 Prof. Lorenz on the Theory of Light. 



The integral 



J: 



1 



can be transformed in the same way. If we put 



s=Jf (oy*-i), 



where the integration has reference only to the portion of the 

 space -so"! occupied by the molecules, we obtain 



and hence 



Sr »-o S-2P- P P 



2 , p 1 S-2P-pP 2 



3 r 1 + pP 



Since, according to our supposition, the last term is very small, 

 the refractive power is nearly constant, namely 



r 2 — 1 

 M=- -=P. 



P 

 If we take into consideration the last term also, the refractive 

 power assumes nearly the form 



M=Q-|, 



where Q and R are two positive constants. The refractive 

 power therefore diminishes with the refractive index. 

 The above formula, 



holds good for mixtures as for substances in general. If the 

 densities and volumes of the several constituents were originally 

 P\> P<2> Pa - ' • anc ^ v \> v< 2> v 3 • • • ) while the volume of the mixture 

 is v, the constituents possess in the mixture the densities p ] — , 

 p 2 - 2 , . . . The constants P x , P 2 , . . . of the constituents, however, 

 do not alter with the density ; thus we also have 



Now vp, VjPjj Vcfi 2 , . . . are proportional to the weights of the 

 mixture and of its several constituents; we thus obtain, if 

 Pi Pv P& • • • are these weights, 



