( 3fi7 ) 



Tn ordoi- lo ovaln.ito lliis i]ile»nxl wo divido i< into one part 

 IVüin O to II (jiuiiitity f to he conveiiicntly choscji and another tVoin 

 8 to 00. In the second part we express the i)rodnet of the sines by 

 the düFerence of the cosines: 



OC - OO 00 



I sm rs sui as — z=: I .nn rs sm a-t 1 I cos (r — a) s I cos (r 4- a) .^ 



ds 



s 



In the second and tliird integral we introdnce tlie new variable 

 of inlegralion j) = (r — a) s and p =z {7'-\-rf) s respectively. Then the 

 difference of these two integrals becomes : 



00 00 '.(r-\-a) '/r-\-a) 



1 r dp 1 r dp 1 r dp 1 i^dp 



I cos p I COS p Z= I COS p = I 1- 



••^J P ^J P 2 J. ^ p 2j p^ 



'•[r~n) <'■+"; -'('■-") <'• — rO 



1 rcosp — 1 1 r-\-a. f p dp 



2 J p 2 r — a J 2 p 



z(r—a) -(r — n) 



or, if we snni \\\) : 



Jds f . , ds 1 r-\-a f . p dp 

 sii) rs sni as -- = I sin 7's sni as 1 lor; I siii'^ . 

 s J s 2 ' r- a J 2 p 



Ü <'•-«) 



Now if we choose e sufticiently small, the first and second integral 

 of the right-hand side may be made as small as we like. Namely in 

 both cases we ha\'e to integrate an entirely finite function within 

 two limits indefinitel}' close to each other. Therefore for any given 

 r and a (r ^ a) there results rigorously : 



I 



ds 1 ?'-(-« 



,nn rs sin as — = — log , (46) 



8 2 r — a 







Making r converge to a, our integral becomes positively logarithmic 

 infinite. It follows, that the force necessary to act on the electron 

 in order to maintain its uniform motion also becomes infinite. 



The .stationary motion of an electron^ charged uniforuihj over 

 its surface, icith a velocity exceeding that of light, is actually ini' 

 possible; it would require an infinitely great expense of force and 

 energy. 



