Prof. Lorenz on the Theory of Light. 423 



where p is the density of the substance, remains nearly constant 

 for the same body at different densities, and that the refractive 

 power of mixtures can be calculated from those of their separate 

 constituents by the formula 



Mp=M,/» 1 + M a # l + ... 



if jo is the weight of the mixture, and the marked letters are 

 taken as applying to the several constituents of the mixture. An 

 additional law, which seems not to have been remarked, appears 

 from the same table of refractive powers (loc. cit. p. 211), namely, 

 that the refractive power always and without exception decreases 

 somewhat with the refractive index. It was precisely the pre- 

 sent theory which first drew my attention to this point. 



The above-mentioned empirical laws can in fact all be deduced 

 from our theory, but only on the supposition that bodies are 

 made up of transparent particles or molecules separated by in- 

 terstices in which the velocity of light is the same as in a vacuum. 

 The molecules must likewise, so far as these laws remain appli- 

 cable, be unalterable, in the sense that any alteration of the body 

 affects merely the size of these interstices and the arrangement 

 of the molecules themselves. 



In the integral \ r^ 



we may therefore separate the elements which belong to the 

 empty spaces surrounding the molecules. Since the velocity of 

 light (<w) is here equal to 0, and therefore 



we obtain 



3 9 "o« + J^;v o 2 ) 



Q 



if we allow the integration now to extend only to the unalterable 

 portion of the space ot 1? occupied by the molecules. 



If p is put for the density of the substance, then pix { remains 

 a constant quantity, which may be denoted by c, for all altera- 

 tions of density. According to this, we obtain 



^=Q- 2 (l+ P P), 



where 



=J?(oy- 



i). 



a quantity which is independent of the density of the substance. 



