418 Dr. A. H. Bucherer on a JSew Principle 



accelerated. The form of" equation (10) suggests putting for 

 the increase of the electromagnetic energy of A in virtue of 

 its acceleration : 



This equation, which holds for quasistationary motions, 

 is compatible with our principle of relativity but does not 

 follow from it. 



§ 4. We consider an electron in motion, and we inquire 

 after its electromagnetic masses. Let fii denote its longitu- 

 dinal and iA t its transversal mass. External forces acting in 

 the direction of motion will increase its electromagnetic 

 energy W. Proceeding exactly as in mechanics we can put 



w= i^ = JL £. fl]W + i* fflW (i 2) 



u on iTu oujJJ ottuw duJJJ 



Now the right member of this equation has been evaluated 

 by Gr. F. C. Searle for the case of a charged sphere. Sup- 

 posing an electron to be a rigid charged sphere, we find by 

 an easy calculation the same expression as Abraham derived 

 lor the longitudinal mass. 



We can connect the electromagnetic masses of the electron 

 with the quantity of motion M 



The first term of the right member represents the longi- 

 tudinal force, while the second member represents the 

 transverse force. 



From mechanics we know 



fn^w, f" 7 



L u ou 1 



M 



But the general expression for the transverse force is 



1 dt U **» 



where R denotes the radius of curvature. 

 And 



Therefore 



dM l _ u 



fit 



= -J ^ du (14) 



Substituting the value of fju t we find the same value for 

 fi t as was obtained by Abraham. 



