﻿of lladiation in any Material System-. 519 



I define 1\, as that solution of: the equation 



(v-^+^vgf) . . . («) 



which is normal at the surface S. tc~ l is a length large 

 compared with the radius of action of the intermolecular 

 forces but small in comparison with the wave-length of the 

 radiation involved. The phenomena of gases show that 

 neighbouring molecules do not affect each other sensibly till 

 the distance between their centres is of the order 10 -8 ; it 

 would be sufficient we shall find to take k -1 equal to 10 _G 

 or even 10 ~ 7 . 



*-=f?('°-iv *).<•■ 



(25) 



Ihus the value of F given by (25) at any point is con- 

 tributed entirely by elements of volume dv which are within 

 distances of the point small compared with the wave-length. 

 Substitute from (17) in (11) 



(v-^5)^^o) + 4^=vgf) • (20) 



Now the elements of the integrals in (2d) and (27) are 

 identical so long as£ - ' cr =l 



- (>«-i^H"-i^),., 



The first condition means that r is to be small compared 

 with k" 1 . The second that the distribution and velocity of 

 the charge within the molecular radius r are not to alter 

 appreciably during the time it takes light to travel that 

 distance. This is of course ensured in any steady distri- 

 bution of electric currents. It also holds if the velocity U is 

 small compared with the velocity of light, and if the rate of 

 change of II is such that the radiation emitted is of wave- 

 length large compared with the distance r. Under these 

 conditions (25) and (27) show that all that part of 1^ + 1^ 

 which arises from the charge within the molecular radius is 

 included in F . Thus the inter-atomic forces are removed 

 from Fj, and it represents the radiation proper, a force 

 producing only a small disturbance in the motion of the 

 material system *. 



* See Phil, Mag. Julj 1911, p. 69. 



