( 124 ) 



The divergency in the origin of this field is 2jr. 



The scalar distribution lcoth\r has thus the potential property. 

 (This was not the case for the field of a single agens point in the 

 Euclidean Sp^. 



IV. In the following we presuppose again for the given vector 

 distribution the field property (which remains equally defined for 2 

 and for n dimensions as for 3 dimensions); no vector field is possible 

 that has nowhere rotation and nowhere divergency; so each vector 

 field is determined by its rotation and its divergency and we have 

 first of all for a gradient distribution : 



1 r \2/ qX 



qX ■=. \i/ I AL I coth \r dr, 



^ J 2:7r 



lx=^^/J 



\V oX 



\L^F,{r)dr (J) 



V. For the field E^ of an agens double point we find the gradient 

 of the potential: 



cos ip 

 sink r 



It can be broken up into "fields of a single agens point" formed 

 as a derivative of a potential / coth \ r. 



VI. Identical outside the origin to the above field E^ is the field 

 E^ of a double point of rotation, whose axis is perpendicular to the 

 axis of the agens double point of the field E^. For that field E^ we 

 find as scalar value of the planivector potential in a point P the total 

 current of force between P and the axis of the agens double point, 

 that is : 



sin if) coth r. 



So if are given a vector unity V and a scalar unity S and if 

 we apply along their connecting line a vector coth r, the volume 

 product ^ of V, S and the vector along the connecting line is the 

 scalar value of the planivector potential in S by a magnet unity 

 in the direction of V. 



Of tp we know that when summing up S out of a positive scalar 

 unity S^ and a negative S^ it represents the current of force of a 

 magnet unity in the direction of V passing between S^ and S„ in 

 other words the negative reciprocal energy of a magnet unity in the 

 direction of V and a magnetic strip S^ S^ with intensity unity, in 



