﻿of Radiation in ant/ Material System. 517 



theory of radiation therefore it is implied, though not always 

 explicit, that the radiation does not exhaust the whole 

 electromagnetic field, part is always attached to the electric 

 charge in the immediate neighbourhood. The distinction 

 is here made precise and expressed in formula? through 

 which the interaction of matter and radiation can be 

 studied. In a previous paper (Phil. Mag., January 1911) 

 I made no attempt to distinguish in the whole field that 

 part which is properly associated with the moving electrons. 

 It was there shown .that the complete system of matter and 

 " aether " forms a Lagrangian dynamical system having an 

 infinity of degrees of freedom. But the only term associated 

 with the material part which appears in the energy is 

 merely potential and due to the electrostatic field. Kinetic 

 energy there is none unless it arises outside the pale of 

 electromagnetics. Without some such source of energy the 

 Lagrangian system cannot he reduced to Hamilton's form 

 mid the ordinary statistical methods cannot be applied. 

 Even granted its existence, it would be unsafe to assume that 

 taken in isolation the purely material energy has the 

 character of that known to us. Our experience cannot 

 separate it as our mathematics do. The theory 1 give in this 

 paper avoids the difficulty, it does not so divide where nature 

 has joined together. But on the other hand, there is set up 

 the new distinction between electromagnetic energy credited 

 to the account of the material system and the energy of 

 radiation. This too is an arbitrary distinction however great 

 its practical importance. The price paid for insisting upon 

 it is that our formula? no longer represent the action of a 

 single dynamical system. Instead there appear to be two 

 such systems each disturbed by external forces due to the 

 other. And when a charge moves with translational velocity 

 comparable to that of light it does not interact dynamically 

 with other charges, the aether in fact intervenes between 

 them. The methods used in this paper assume therefore 

 that the square of the velocity of a charge divided by the 

 square of the velocity of light is negligible. 

 The equations of the electromagnetic field are 



(v*4f 2 )F + 4^ = o. . . . (ii) 



(v*-4J)* + 4^=0 (12) 



^ + DivF=0 (13) 



