244 COMPARISON OF THE ELECTRIC THEORY OF LIGHT 



and dielectric capacity may be expressed in a form which will furnish 

 a more rigorous test, as not involving extrapolation. 



We have seen on page 242 how we may determine numerically 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}Qgl TrPW 

 4 "dlogX p* 



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

 tude and period in vacuo, I becomes X, F remains the same, and for G 

 we may write G'. This gives 



(30) 



f 'JJ- 



Dividing, we get 



G = cnogZ_ ^ 

 G'~cnogX X 2 = 



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

 specific dielectric capacity of the body which we are considering, 

 G'/K is the dielectric elasticity of the body and Gy2K is the potential 

 energy of the body (per unit of volume), due to a unit of ordinary 

 electrostatic displacement. But Gh 2 /4> is the potential energy in a 

 train of waves of amplitude h. Since the average square of the dis- 

 placement 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 experi- 

 ment the displacement 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 



?=&' < 32 > 



K> 

 and 



/7/"\2\ 



(33) 



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



n- 2 = a-6X- 2 , (34) 



I/a, which is the square of the index of refraction for an infinite 

 wave-length, would be identical with the second member of (33). 



Another similarity between the electrical and optical properties of 

 bodies consists in the relation between conductivity and opacity. 

 Bodies in which electrical fluxes are attended with absorption of 

 energy absorb likewise the energy of the motions which constitute 



