( 252 ) 

 arbitrary gradient distribution holds 



lX = \T/ f ^^—F{r)dt (i) 



The "field of a single agens point" has however divergencies every- 

 where on the sphere. 



VI. Out of the field E^ we deduce in an analogous way as under 

 B § VI the field E^ of a rotation double point normal to the agens- 

 doublepoint of the field E^. As scalar value of the plani vector potential 

 we find there: 



^ sin (p cot I r, 

 as we had to expect, completely dual to the scalar potential of the 

 field E,. 



As fictitious force field of a unity-rotationelement we deduce out 

 of this (in the manner of B § VI) -. 



è cot ^ r, 

 directed normally to the radiusvector. For the rest this force field has 

 rotation everywhere in Sp^. 



VII. Out of this we find (comp. under B ^ VII) for the scalar 

 value of the planivector potential of a rotation-element: 





^cot h rdr:z^F (r), 

 SO that for an arbitrary 2X: 



. r w 2A 



And an arbitrary vector field is the \7 of a potential 



VX 



F (r) dr. 



s 



2jr 



E. The spherical Sp^. 



I. The purpose is in the first place to find E^; we shall compose 

 it of some singular potential functions with simple divergency distri- 

 butions, and which are easy to construct. 



Let us suppose a principal 'sphere B with poles P^ and P^, and 

 on ^ a principal circle C with poles Q, and Q, determining on B 

 meridian circles M cutting C in points H. 



