( 366 ) 



The value of the integral, still to be calculated, is a mere niiniber, 



namely -, as one sees, on introducing the new variable p = a,s and 

 4 



transforming as follows (note, that the expressions taken in [ ] 

 disappear) : 



i{smp-pcospy~ = -]^ ^--, ]^-^-jsinp{mip-pcosp)-^^ = 



• ü 



00 ao 



rsinpisinp—pcosp)! If, , . , , . , s^^P 



\ 4~? 4 J ('^^^'P^'^^'P—P'^^'P^ + P^'^t P)—, = 







00 ^ 



1 f /I sm2p pcos2p'\ 1 rd sin2p 1 /' sin2p\ 1 



iJU '~j^-^ "T^j'^^'^'sJ^ P ^^^^\ p y~4' 



p = 



Tims the force exerted hy its oum jield on an electron bodily charged 

 and moving with a velocity exceeding that of light becomes: 



*--'« = ^t('-.47 <"> 



This force acts cojitrary to the movement. The opposite force is 

 to be exerted in order to maintain the motion and to balance the 

 loss of energy caused bv radiation. The force is absolutely finite and 

 and remains so for v = oc. For v = c we have 5 = 0, a value which 

 is connected continually to the case of velocity less than that of light; 

 for V = Qp we get 



4rr 4 rr 

 this equals the attraction oi two point charges -^ in the distance a, 



according to Coulomb's Law. 



Although the stationary motion initJi velocity exceeding that of light 

 is no free possible movement of the electron, yet this motion is not 

 impossible from a physical point of vieni as requiring (even if the 

 velocity is infinite) in every moment only a finite expense of force 

 ami also for every fnite path only a. finite expense of ivorlt. 



We finish by studying the motion of a surface charge with a 

 velocity exceeding that of light, returning to equations (41) and (43). 

 These give us with r ]> c : 



00 



4 jr a' ^ ?;'—(•" T • r • . ds 

 ^ =: Lirn I sin rs sm as — . . . . \^'^} 



