( 820 ) 



R 

 and 



U imist be observed that the i)i'odiK't Jcl \=^ a function of ?/? and 



that, for reasons of syniraetrv, the vector © lias the direction of the 



translation. In general, representing bv r> the velocity of this motion, 

 we have the vector equation 



®r=-^^kUM (28) 



b 7t c^ U 



Now, e\'ery change in the motion of a system will entail a cor- 

 responding change in the electromagnetic momentum and will there- 

 fore require a certain force, which is given in direction and mag- 

 nitude by 



^=iü <^^> 



Strictly speaking, the formula (28) may only be applied in the 

 case of a uniform rectilinear translation. On account of this circum- 

 stance — though (29) is always true — the theory of rapidly A'arying 

 motions of an electron becomes \'ery complicated, the more so, because 

 the hypothesis of § 8 would imply that the direction and amount of 

 the deformation are continually changing. It is even hardly probable 

 that the form of tlie electron will be determined solely by the 

 velocity- existing at the moment considered. 



Nevertheless, provided the changes in the state of motion be suf- 

 ficiently slow, we shall get a satisfactory approximation by using (28) 

 at every instant. The application of (29) to such a (jua.si-stationari^ 

 translation, as it has been called by Abraham '), is a very simple 

 matter. Let, at a certain instant, jj be the acceleration in the direction 

 of the path, and j^ the acceleration perpendicular to it. Then the force 

 S will consist of two components, having the directions of these acce- 

 lerations and which are given by 



Sj = m, ii and g, = m, j„ 

 if 



m, = —-vf,— , and m, = --— kl . . . . (30) 



Hence, in phenomena in which there is an acceleration in the 



') Abrah.ui, Wied. Ann, 10 (190:3), p. 105. 



