( J31 ) 



To ÜJid -2" we integrate the current of force inside the meridian 



zone passing- through the "—^spherical surface through P between the 



cosh r 

 axis of the system and 1\ As we ha\c (n — l)cos<p— for the 



force component perpendicular to that spherical surface we find: 



? 



ƒ* cosh r , 

 [ti — 1) cos <p —7 . sinh r cUp . c8 sink 't^-r siti ^—^(p ■=. ce sm ^*--^<fi coth r. 

 sink "r 

 



-2" cosh r 



II z= ~— =z -— si7i <p. 



dh sinh "—V 



VIII. If thus are given in different points a line vector L 



unity and an "— ^^ector W unity and if we put along their con- 



cosh r 

 nectine: line a line vectoi' , then the volume product il? of Z, IF 



and the vector along the connecting line is the "—-vector potential 

 in the direction of W caused by an elementary magnet with moment 

 unity in the direction of L. 



We know of if7(L, IF) that with integration of W along a closed 

 curved Si)n—2 Q it represents the current of force of a magnet unity 

 in the direction of L through Q, in other words the negative reci- 

 procal energy of a magnet unity in the direction of L and a 

 magnetic "—'scale with intensity unity, bounded by Q, hi other words 

 the force in the direction of Z by a magnetic "~'scale bounded 

 by Q, in othei words the force in the direction of Z by a vortex 

 system, regularly distributed over Q and perpendicular to Q. So we 

 can regard xp {L, W) as the force in the direction of L by a \'ortex 

 nnity, perpendicular to W. With this we have found for the force 

 of a plane vortex with intensity unity in the origin : 



cosh r 



— : sin (f, 



sinh "— 'r 



directed parallel to the operating vortex element and perpendicular 

 to the "meridian plane", if now we understand by that plane the 

 projecting plane on the vortex element ; whilst (p is here tlie angle of 

 the radiusvector with the aS/>„— 2 perpendicular to the vortex elemejit. 



IX. For the fictitious field of a vortex element in the origin intro- 

 duced in this way (which meanwhile lias vorticity everywhere in space) 

 we shall find a planivector potential, directed everywhere "parallel" 

 to the vortex element and of which the scalar value Ü is a function 

 of r only. 



Let us suppose a point to be determined by its azimuth parallel 



9* 



