( 256 ) 



We choose c:=0, and we find a,s vector potential V of a unity- 

 element of current : 



^-> .... l|JiL_A|=^,H. 



jt ^cos' 4 r smr] 



directed parallel to the element of current. The function i^^ (r) vanishes 

 in the opposite point. 



. For an arbitrary flux now holds: 



-I '.„' 



lX=sr/J)l^^FAr)dr (//) 



And finally the arbitrary vector field X is the V of the potential: 



F. The spherical Spn- 



I. To find the field E^ we set to work in an analogous way as 

 for the spherical Sp^. The principal sphere B becomes here a. 

 "-^sphere B; the principal circle C of the points H a principal 

 «— ^sphere C of the points H. 



For the potential («) is found: 



cos w 



for the potential (/?) : 



cos ip 



- - s^w"~"' r 



this field (j3) has in the sphere B a magnetic "— ^scale. 



The potential (y) is integrated out of fields tan~ ^ \ cos ip tan r \ 

 according to cos (p, the first zonal "—^spherical harmonic on B. This 

 integration furnishes when dw represents the element of the w-dimen- 

 sional solid angle about P: 



cos<pf{r), 



where : 



ït 



f(r) =. I cos<ptan~^ I cos <ptanr\ dw =■ ^/j— 1 1 sin^~^(p cos(ptan~^ | cos(ptanr\ dcp = 



n 



k,i—i f , tan r d<p 



I sm "O) - 



-ij ^1 



n — \J \-\- tan ^r cos ^(p 







[hn defined as under C § III). 



