Theory of the Equivalent of Refraction. 183 



The conceptions and propositions of the undulatory theory arc 

 fully in accord with the Newtonian refractive power. Thus 

 Lorenz finds* 



r 1+Dcc 



a formula which also involves the idea of the refractive power. 



Secondly, the previous formula (I.) agrees with the deductions 

 in the chapter on dispersion* According to Ca'uchy, to whom 

 we owe our present theory of dispersion, 



v 2 = a l -\-aJi i '\ r . . . 



For empty space, in which we must assume the dispersion to 

 be a minimum, 



v 2 =a 1 . 



For every other medium in which there is dispersion the ve- 

 locity diminishes ; the velocity a 1} for so-called empty space, is 

 diminished. Accordingly 



v l ^=a 1 — a 2 k 2 . 

 By means of 



^, 2 =1 + const. f~ 2 J, 



we obtain a formula agreeing with the formula (I.) used by me. 



Apart from these theoretical propositions, the relations demon- 

 strable numerically appear to speak in favour of Newton's refrac- 

 tive power. 



In consequence of the equations 



/ x*-l=2( f t-l) + G* l) 2 

 and M = 2m + Dm 2 , 



m=iM-JDM 2 + ... 



The two formulae (I.) and (V.) are inseparably connected, inas- 

 much as the values of Newton and Biot's refractive powers form 

 mutually sums and differences which are influenced only in a se- 

 condary degree by the variable element, the density. Hence it 

 is easy to perceive that the constancy of the one formula partly 

 involves the constancy of the other. In all cases in which, as in 

 gases, the density is small, m and ^M coincide. A similar agree- 

 ment is shown in those cases where the variation of density is 

 very trifling throughout the members of long series of bodies. 

 For the latter reason, which must by no means be neglected, the 

 homologous series in organic chemistry will not serve to deter- 

 mine between the above formulae. 



In order, however, to determine whether the one or the other 



* Poggendorff' s Annalen. 



