( 363 ) 



8 

 The number -- = 1,6 here takes the place of j/2 = 1,4 . . . in 

 o 



equation (35). 



I. If the point in question is situated in region I, there are no 

 positive roots r^ and t.^ ; here therefore stands : 



<p = 0. 



II. In region II, wliere onl}- the pair t/, t," is to be considered, 

 Ave liave according to (13) and (14) in the first instance the following 

 expression : 



While T goes from t/ to t/', our variable u passes from — 1 to 

 a certain value u^ <^ 1 and returns to — 1. 



du 

 At the turning-point u^^, for which —^=0, the square root on 



dt 



the right of (27) vanislies also (see (25) and (27)) and changes its 

 sign. So the integral, extended forwards from — 1 to u,„ equals the 

 integral, extended backwards from ii^ to — 1, and we get instead 

 of (37) : 



«0 



— ii^)dti 



—1 

 Here it would no longer be permitted to put a = 0, as, bj^ ne- 

 glecting it, the denominator would become very small in the whole 

 of region II and the value of the integral would become very in- 

 exact. We content ourselves with stating, that ti„ grows continually 

 from — 1 to -j- 1 and therefore (f increases continually from to 

 the high value given by (35), as we traverse the region II 

 from its front border, the cone K^, to its back border, the cone /v's. 

 It is hardly worth while computing the manner of tfiis increase 

 in detail, as the whole of the region II (the so called border of 

 shadow) is of the same thickness as the diameter of the electron. 



§ 5. IVie force exerted on ike electron bi/ ii.s o/vn field, e^ijjecialli/ 

 if the velocity ii stationary and e.nceeds that of light. 



Whilst in general only such parts of the held would be of inlei'est, 

 that are at a great distance from the electron, viz. a distance great 

 in comparison with the ivkMus of the eleclro]), we need jusi ilio Held 

 in the interior or at (he surface of the electron in order to calculate 



25 

 rrocccdiiigs Royal Acad. Amsterdam, Vol. VII. 



«0 



3£ r (1— u^ 



4.mfi = — , - - ' . . . (38) 



