( 350 ) 



t' =i±Qr., and certainly ^? = O stands for ^' := ± oo according to the 

 definition of F. Fiirtiier we snppose, tbat the first integral on the 

 right vanishes also, on acconnt of the nature of the potential (p. In 

 order to understand this, we ma}' perform the integration with 

 respect to t', as follows: 



I V Z-— c at = — — I V c at :=: — 

 J on Oft J r 



d?i 



where (f^ means the value of (p for that t', for wiiich the argument 



r 

 of F vanishes viz. t' = t . Similarly we show : 



c 



1 



ƒ 



-|- 00 



dv Ö 1 1 or 1 d(pg 



—-(pcdt =^0^ s ^T 



On On r r On c Ot 



If the electron was at rest originally, for instance until the moment 

 tg, we can in any case expand the bordering surface o so far, that 

 the value t' just now defined gets less than /„. In this case g)(, becomes 



the electrostatical potential of the electron and -j— = 0. The surface 



integral in question is then reduced to tlie following expression 



ƒ 



On r r On 



which we know by the potential theory to vanish, if it is calculated 

 for a surface sufficiently distant. 



So you keep in equation (6) only tlie second member on the left 

 and on the right, and you have : 



-|-00 -j-* 



I c dt' I Qv dS = 4rr j </) F { — c [t — t')) c dt' . 



00 QO 



Perform the integration on the right in the way used repeatedly 

 and denote for short ^vith (p the value at the point A at the time t. 

 We get conclusively : 



4:.t(p = fcdt' C^F{r—c{t—t'))dS (7) 



00 



77k? scalar potential is represented here by a quadruple integral, 

 viz. a time-integral and a space-integral. 



