﻿Motion of the Lorentz Electron. 49 



given out in quanta, which represent the differences between 

 the energies in two steady states of: motion. 



When, however, the numerical value of the appropriate 

 constants in the formula of Ritz is considered, it is found 

 that the magnetic forces set up by the atom are not in 

 themselves sufficient to account for more than a small 

 fraction of the effect that would be necessary to give the 

 observed distribution of lines in spectral series. 

 University of London, King's College. 



VI. On the Motion of the Lorentz Electron. By G. A. 

 Schott, B.A., D.Sc, Professor of Applied Mathematics, 

 University College of Wales, Aberystwyth*. 



URINGr a theoretical investigation of the origin of 



D 



X-rays I found it necessary to take into account the 

 effect on the motion of the electron of the reaction due to its 

 own radiation, and from this point of view examined some 

 simple cases of motion in order to gain a clear idea of the 

 result to be expected. The following communication in- 

 cludes these preliminary studies, but is also intended to serve 

 as an introduction to a more complete investigation to be 

 published later. 



The Equations of Motion and Energy of the Electron. 



1. The vector-equation of motion of the electron may be 

 written in the following form | 



G-K = F (1) 



where 



2e 2 v 2e 2 {vv)v 2g 2 (vv)v 2e 2 (vv) 2 v 



K ~ 3c(c 2 -^) + oc(c 2 -v 2 ) 2 + c(c 2 -v 2 ) 2 + c(c 2 -v 2 ) 3 ' W 



G denotes the electromagnetic momentum of the electron in 

 the form due to Lorentz, K the reaction due to radiation, 

 i. e. the radiation pressure in the form due to Abraham t, 

 and F the external mechanical force. If we accept the 

 Principle of Relativity for accelerated as well as for uniform 



* Communicated b} r the Author. 



t Schott, 'Electromagnetic Radiation,' pp. 175, 176, 246 (quoted 

 below as E. R.). 



X Abraham, Theorie der Elektrizitat, ii. p. 123. 



Phil Mag. S. 6. Vol. 29. No. 169. Jan. 1915. E 



