( 130 ) 



At finite distance from their origin the fields E^ and E^ are of 

 identical structure. 



VI. In order to indicate the field E^ we assume a spherical 

 system of coordinates ^) and the double point in the origin along 

 the first axis of the system. Then the field E^ is the derivative of 

 a potential : 



cos (f 



The lines of force of this field run in the meridian plane. It can 

 be regarded as the sum of two fictitious "fields of a single agens- 

 point" constructed as derivative of a potential ?y„(7") to which, however, 

 must be assigned still complementary agens at infinity. 



VII. The field E^ of a small vortex-"— ^spjjgj.g according to the 

 space perpendicular to the axis of the double point just considered is 

 identical outside the origin to the field E^. Each line of force is now 

 however a closed vector tube with a line integral kn along itself. 

 We shall find for this field E^ a planivector potential //, lying in 

 the meridian plane and dependent only on r and (p. It appears then 



simply that this H is sx iX. 



Let s be an (n — 2)-dimensional element in the ?z — 2 coordinates 

 existing besides r and (p, then it defines for each r and (p an element 

 on the surface of an "—^.^pj^gi-g Qf ^ gj^e dh = C8 sink "~ -r sin ^~~g), 

 and for the entire SjJn what may be called a "meridian zone". 



We then obtain for the current of force -S, passing inside a 

 meridian zone between the axis of the system and a point P with 

 coordinates r and (p, if ds represents an arbitrary line element 

 through P in the meridian plane under an angle f with the direction 

 of force : 



d^ z=: dh . X ds sin f, 



whilst we can easily find as necessary and sufficient condition for H: 



d (Hdh) = dh . ds . X sin f ; 



SO we have but to take — for H. 



dh 



1) By this we understand in S'p» a system which with the aid of a rectangular 

 system of numbered axes determines a point by 1. r, its distance to the origin, 

 2. 0, the angle of the radius vector with Xi, 3. the angle of the projection of 

 the radius vector on the coordinate space X^ . . . X„ with X^, 4. the angle of 

 the projection of the last projection on the coordinate space X^ . . . X„ with X^ ; 

 etc. The plane through the Xj-direction and the radius vector we call the meri- 

 dian plane. 



