Theory of Radiation . 239 



electric pulses which collectively constitute the radiation from 

 the body. When we resolve, by Fourier's theorem, this 

 radiation into its constituent harmonic vibrations, we find that 

 the amount of light of any given period depends upon the 

 ratio of that period to the time occupied by a collision. It 

 was shown, moreover, that this radiation would not conform 

 to the Second Law of Thermodynamics unless the time 

 occupied by a collision varied inversely as the kinetic energy 

 of the corpuscle before it came into collision, and in addition, 

 that the time of collision of a corpuscle moving with a given 

 speed must be constant and independent of the nature of the 

 molecule against which the corpuscle collides. I showed 

 that the first of these conditions would be satisfied if the 

 forces exerted during the collision between a corpuscle and 

 a molecule varied inversely as the cube of the distance 

 between them ; the second condition will be satisfied if the 

 collision is regarded as taking place, not between 1he 

 corpuscle and the molecule as a whole, but as between 

 the corpuscle and systems dispersed through the molecules., 

 these systems being of the same character in whatever 

 molecules they may be found, and repelling the corpuscle 

 with forces varying inversely as the cube of the distance 

 between them. Forces of this type would be exerted by 

 electric-doublets of constant moment with their negative 

 ends pointing to the corpuscles. 



In this paper I shall consider more in detail the collision 

 theory of radiation when the forces exerted during collision 

 vary inversely as the cube of the distance between the 

 colliding bodies. In the paper already quoted it is shown 

 (see Phil. Mag. xiv. p. 225) that if E^ be the energy per 

 unit volume of the radiant energy with frequencies between 

 q and q + dg, 



where m is the mass of a corpuscle, V the velocity of light 

 in vacuo, K the specific inductive capacity of the luminous 

 body, and 



/-» + » 

 <£i= 1 f(\) cos q\ . d\ 



where /(X) is the acceleration of the corpuscle at the 

 time X. 



We shall first find/(\) when the repulsion varies inversely 

 as the cube of the distance. If x be the distance of the 



