142 J. W. Gibbs — Comparison of the Electric Theory of 



trie capacity, although in other cases thej are quite different, 

 the correspondence is generally regarded as corroborative, in 

 some degree, of the theory. But the relation between refrac- 

 tive power and dielectric capacity may be expressed in a form 

 which will furnish a more rigorous test, as not involving ex- 

 trapolation. 



We have seen on page 140 how we may determine numeri- 

 cally the ratio of the two first terms of equation (25). We 

 thus easily get the ratio of the first and last term, which gives 



Gh* d\og I TtFlVf 



In the corresponding equation for a train of waves of the same 

 amplitude and period in vacuo, I becomes X, F remains the 

 same and for G we may write Q'. This gives 



G'A 2 ttF/VA 2 , . 



(30) 



Dividing, we get 



G d log I r d(l a ) 



4 p % 



(31) 



G' " cHogA A 2 " r/(A 2 )" 



Now G' is the dielectric elasticity of pure ether. If K is 

 the specific dielectric capacity of the body which we are con- 

 sidering, G'/K is the dielectric elasticity of the body and G'/2K 

 is the potential energy of the body (per unit of volume), due 

 to a unit of ordinary electrostatic displacement. But GA 2 /4 

 is the potential energy in a train of waves of amplitude h. 

 Since the average square of the displacement is A 5 / 2, the po- 

 tential energy of a unit displacement such as occurs in a train 

 of waves is G/2. Now in the electrostatic experiment the dis- 

 placement distributes itself among the molecules so as to make 

 the energy a minimum. But in the case of light the distribu- 

 tion of the displacement is not determined entirely by statical 

 considerations. Hence 



G ^ G 



2~ ~ 2K' 



K > — 



- G' 



(32) 



and 



t^ ^> d (A 2 ) 



K = TTTl^Y (33) 



d{F) 



should 



n-* = a-bl- 2 , (34) 



It is to be observed that if we should assume for a dispersion- 

 formula 



