( 480 ) 



means of a suitable choice of the value of v» and a, and now it is 

 the place of the electron which must be such that the etjuation is 

 satisfied. Tf the electron stood still the equation would cease to be 

 satisfied in a following moment because of the propagation of the field- 

 forces, it must therefore sulfer a displacement in such a way that 

 the relation continues to be satisfied. So the eciuation determines the 

 velocity, though the velocity itself does not occur in it. 



This remark may perha|)s serve to elucidate the results of Som- 

 MKRFKLD coucemiug the motion with a velocity greater than that 

 of light, and this is principally my aiui \vith ihis comninnication. 

 In the following I shall denote a velocity, greater than that of light, 

 with 25 and one smaller with ». 



We see at once that the supposition of Sommrrpeld that the velo- 

 city of an electron moving with '1^ will suddenly decrease to i> when 

 the external foi'ce is suddeidy suppressed, cannot l)e accurate. For 

 if ^ve take t) to be the sum of two })arts b^ the external field and 

 b, the held of the electron itself, then we have at the momem t 

 before the suppression of the external field: 



JJj Q(^.i-^.)dS=0. 



But as i> I'cquires an external force, I I I ? b, (IS is not zero, so 



neither can | I I C> b.> '^'"^ '^^ zero. 'J'his last (piaulity is independent 



of the velocity at the uiomeut f itself, and so it cannot l)e made to 

 disappear bv any choice of the velocity, and tlioi-o is no possible 

 way in Avhich ecpiatioii ( Vd) can be satisfied. 



If we imagine the velocity of an electron moving with '^ momcn- 

 tarilv to decrease to r, then the required external force will not 

 suddenly becouie zero, but at the first instaul it remains unchanged, 

 and onlv gradually it varies in accordance with the new mode of 

 motion. This thesis applies to every discontinuity in the velocity 

 provided the nu)tion be rectilinear and the electron have the required 

 symmetry. Por the case that the initial velocity is zero it follows 

 from Sommrrfrld's complete calculation of the force. We see again 

 the conformableuess of the dynamics of an electron with a theory 

 of mechanics in which no inertia is assumed : the foi'ce required for 

 a discontinuous change in the velocity is not only not infinite, but 

 even zero; the foire, which acts before the discontinuity, remains 

 unchanged at the moment of the discontinuity. 



We cannot be astonished at the fact that w^e do not find a possible 



