( 364 ) 



the force caused by its motion. For tliis purpose the approximations, 

 mentioned in the beginning of the hist §, are not sufficient and we 

 have to resort to the rigorous formulae of § 3. Using the Jatler 

 always in the form of equations (17) und (18), I have succeeded 

 in my second paper in computing the force exerted on the electron 

 by its own field for any given translation, excluding simultaneous 

 rotations ; performing the integrations extended over the charge of 

 the electron I mei-ely had to use Green's theorem once more. 



I here put these formulae less explicitly ; whilst the final foi'mulae 

 there only contain one integration witli respect to the former time t, 

 I shall here refrain from performing the integration with respect to 

 .s' as w^ell as that with respect to t. This means a decided simplifi- 

 cation of the following calculation, at least in the simplest case of 

 stationary motion. 



Let S be the required force for the moment t, ^ the chord of the 

 path, traversed by the centre of the electi-on thiring the infer\'al from 

 t — T to ^ T the length of this chord; in the case of surface charge 

 we have according to the equation (48) and (50) of my second paper : 



2jt'a\- , r , 2 r t) si?i sT , . . ds 



Ü 



CC CO 



d r rslnsT _ _ . ds 



-\- Lim ^ I t> (/r I — -^^ fd?) sr sin as sin c>iT~ . . . (39) 



i^^a ^*tj 'J -L s 



(t 



in the case of bodily ciuirge according to eijuation (48) and (50') 

 2n'd'c ^ C 'J Z'v) sinsT /.si/ias — ascosasX' ds 







00 CO _ 



Ö r /*sm sTfsin as — as cos as\^ ds 



+ - h)^„^(/T ] sin est— . . (40) 



öj J T y a's' J s' ^ ^ 



Ü 



We are not allowed to pass to the limit r = a in (39) before 

 ])erfbrming the integration because the electrical intensity behaves 

 discontinuously at the surface of the electron, where charge is con- 

 centrated. The force 5" is determined tn' the foregoing state of motion, 

 that is by the path '4: and the velocity v<-t. It would seem from 

 the foregoing formulae, as if all the former states, from r =:: to 

 T = 00, contributed to the value of A ; in reality only the states 

 during a short interval preceding the time t come into account, as 

 is seen from the more explicit value of 5 given in the equations 

 (54) and (54') of my second paper. 



