of Light and the Theory of a Quasi-labile ^ther. 251 



polation in some cases agree strikingly with the specific dielec- 

 tric capacity, although in other cases they are quite differentj 

 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 w'ill furnish a more rigorous test, as not involving- 

 extrapolation. 



We have seen on page 249 how we may determine nume- 

 rically 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^ __ dhgl irFlVi^ 

 4 ~dlog\ p^ ^ -^ 



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

 amplitude and period m vacuo, I becomes \, F remains the 

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



•^''^ -^^^''^ (30) 



Dividing, we get 



p"- 

 G_ _ dlogl l^ _ d(l^) 



^'dlogW^'diX^) ^^^^ 



Now Gr' is the dielectric elasticity of pure aether. 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 Gh'^/'i 

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

 Since the average square of the displacement is h^/2, the 

 potential energy of a unit displacement such as occurs in a 

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

 the displacement distributes itself among the molecules so as 

 to make the energy a minimum. But in the case of light the 

 distribution of the displacement is not determined entirely by 

 statical considerations. Hence 



(32) 



and K><^) (33) 



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

 formula _2 ,,_„ ,0 4N 



n^ = a — b\-^, (34) 



