﻿• Motion of the Lorentz Electron. 55 



7. In order to apply the new hypothesis to our prohlem 

 we must find the acceleration. From (18) together with 

 the expressions given in § 4 we obtain 



• IV 



Again we find from (23) 



>'={B-( T Fe-^/ r ) 6 r (27) 



Hence applying our new hypothesis we obtain 



B=Xo , =F , (28) 



where the suffix is used to denote initial values. Substituting 

 this value in (23) . . . (25) we get finally 



x =| FdT-e T ( T Fe-rdT + F {eT-l), (29) 



Jo Jo 



x=\ r smh jT T FdT-e 7 ( T Fe-ldT+F (e' r -rl)\dT, (30) 



i=[ T cosh{ J Fdr-A T Fe-TdT + F (e T -l) \dr. (31) 



Jo Wo Jo ~> 



We also find from (19) and (29) 



R= JF -f r Fe-^T}V (32) 



In order better to appreciate the import of our hypothesis 

 Ave shall now apply the solutions (29) ... (32) to the particular 

 case of a uniform force. 



8. Example — Motion of a Lorentz electron in a uniform 

 electrostatic field parallel to the line of motion. I have already 

 treated this example elsewhere *, but without taking the 

 radiation pressure into account. 



In the present problem F is a constant, so that Ave may 

 omit the zero suffix as no longer necessary. Then we find 



^ = Ft, F.v= cosh% — 1, Ft= sinh^;, K = F-. . (33) 



Eliminating ^ between the second and third of these equa- 

 tions, Ave obtain precisely the same relation between a and t 

 as we do Avhen Ave neglect radiation. This surprising result 

 is a direct consequence of the hypothesis of §6 : in order to 



* E. R. p. 181. 



