( 251 ) 



So there is no oX possible with nowhere divergency, thus no ^X 

 having nowhere rotation and nowiiere divergency, and from this 

 ensues : 



^ A linevector distribution in a spherical Spn is determined uniformly 

 by its rotation and its divergency. 



III. The general vector distribution in a spherical Spn must thus 

 be obtainable again as an arbitrary integral of : 



1. fields E^, whose second derivative consists of two equal and 

 opposite scalar values close to each other. 



2. fields E^, whose first derivative consists of planivectors distri- 

 buted regularly in the points of a small "--sphere and perpendicular 

 to that "—-sphere. 



At finite distance from their origin the fields E^ and E^ have 

 an identical structure. 



IV. For the spherical Sp^ there exists a simple way to find 

 the field E^ namely conform representation by stereographic pro- 

 jection of a Euclidean plane with a doublepoint potential, which 

 double point is situated in the tangential point of the sphere and the 

 plane. If we introduce on both surfaces as coordinates the distance 

 to the double point and the angle of the radiusvector with the 

 doublepoint-axis — in the plane q and (p, on the sphere r and <p — 

 we have : 



^ Q ^= tan 4 r. 

 cos (f 



The potential in the plane: — becomes on the sphere: 



Q 



\cos (p cot \ r. 

 This potential shows nothing particular in the centre of projection 

 on the sphere, so it is really the potential to be found of a single 

 double point, the field E^. (If we place in the opposite point of 

 the double point an other double point in such a way that tiie 

 unequal poles correspond as opposite points, we find as potential 



cos <p 

 ^ COS (f, {cot \ r-]rtan { r) = — — , which is the Schering potential of a 



sm r ^ 



double point). 



V. Here too we can meanwhile break up the field of a double 

 point into two fictitious "fields of a single eigens point"; for this 



■K 



we have but to take \\cot^rdrz=:~lsin^^r^F{r)', so that for an 



r 



17* 



