418 Does an Accelerated Electron Radiate Energy ? 



passes through the plane except at the moment when the 

 boundary crosses it. We consequently see that the only 

 radiation which the solution gives is, strictly speaking, not 

 from the electron at all, but is to be attributed ultimately 

 to the moving boundary which is postulated to be the limit 

 of the field. 



The limitation of the solution by a moving boundary seems 

 to be included, although perhaps tacitly, in the proof of 

 radiation; but a comparison with the unlimited solution 

 discussed in this paper raises the question whether the 

 boundary is essential in every case for the representation of 

 real motions. The arbitrary motion discussed in the proof 

 makes the case considered there fictitious in the sense pre- 

 viously explained ; but this point is only material in that it 

 makes it clear that an additional conception is involved in 

 the complete proof, which must necessarily concern itself 

 with a charge set in motion by an electromagnetic field. 

 Lorentz's equation is applied, and interpreted by assuming 

 that the electron will move in the same way as it would do 

 if it were a particle of given mass acted on by determinate 

 mechanical force. The retarded potential solution corre- 

 sponding to the resulting motion of the charge, superposed 

 on the external field which gives the motion, then forms the 

 complete solution of the problem, and the boundary is present 

 in it as before. 



The question whether the boundary is necessary or not 

 seems to be largely a question of the physical interpretation 

 made of the point law and of Lorentz's equation. The 

 conclusion that it is necessary is based on the conception 

 that the charges or nuclei of the electrons are first set into 

 motion by the operation of the field in their immediate 

 neighbourhood, and that the resulting changes in the field 

 are actually propagated outwards from them. But it does 

 not follow, from the mathematical fact that the changes in 

 the field at a point are the same as if the disturbances were 

 propagated from the charge, that the propagation is a 

 physical fact. The field variations at a point can also be 

 described in terms of the differential coefficients of the field 

 at a point in a way which does not bring in the charge at 

 all. Moreover, if we regard the nucleus of the electron 

 from a mathematical standpoint as a smiall closed surface 

 limiting the field and characterized by the constancy of the 

 flux of force over it, once the field is known at all points, 

 not only the field variations but also the motion of the 

 electrons is uniquely determined. It seems from first 

 principles as logical to consider the motion of the charges 



