( 479 ) 



For such a motion tlie equations (/)...(/)") are therefore sufficient 

 to determine the motion. If the motion is not (|uasi stationary tlien 

 the equations (/)... {IV) are not sufficient, and we must make use 

 of equation (F), which may be written: 



9U + l[(i^+lvjr])I^]L'5=:0 . . (Va) 



SSI' 



tlie integral i>eing taken 'throughout tlie electron. 



If we wish to state tlie meaning of this formula with the aid of 



the conceptions force and mass, we may say : the real mass of the 



electron being zero, it is impossible that a force should act on it. 



We may, however, set these conceptions aside, and simply state : the 



electron places itself and moACS in the electric field in such a way, 



that the relation (I"^) is permanently satisfied. 



d\> 

 It is true, this oci nation has the form : force = without m — 



dt 



in the righthand member. Yet it may serve to determine the motion. 



This is owing to the fact that the expression of the force itself 



contains the velocity i"» and the angular velocity ji. In general we 



may choose such values for these quantities that the equation (F") 



is satistied. To some extent therefore we return with the dynamics 



of an electron to the standpoint of mechanics before Galilei : the 



forces do not determine the acceleration but the velocity. If we 



might assume ^ and l^ to be given throughout all space and at all 



times, b and g would be determined by the place of the electron, and 



we should get a diiferential equation of the first order for the 



determination of the motion of the electron. 



The question is in reality less simple, because b and () depend on 

 the former motion of the electron. This causes a time-integral of a 

 function of v* and <\ to occur in the equation of motion of the electron. 

 So we get integral ecpiations as Sommerfeld has used in his treatises 

 "Zur Elektronentheorie I, II and III". ^) In some cases the integrations 

 may be effected, and then we get functional equations. 



If the electron moves rectilinearly without rotation, and if it 

 moreover has an axis of symmetry the direction of which coincides 

 with the direction of the translation, then the terms of equation 

 {Va) which contain i> or j] disappear and the equation reduces to: 



Iff' 



Q^JSz=zO. 



In this case il is no longer possible to satisfy the equation by 



1) Göttinger Nachrichten 1904, p. 99 and 363 and 1905 p. 201. 



