I r 



cos (f 2 



( 254 ) 



of the solid angle about P), whilst this integral field has as only 



divergency a magnetic scale in B with intensity proportional to 

 cos (p. 



Effecting the integration we obtain : 



■n 



/(r) =z 2jr j sin <p cos (p ta7i~^ [cos (p tan r] dip. 







Ir ] 

 — cot r 4- ^— - , 

 sin r ) 



and for the corresponding potential function (y) we find : 



Ir ) 

 — cot r -\ — : I . 

 sin^ r] 



III. If we take the difference of the field (^) multiplied by ^ and 

 the field (y) multiplied by — the magnetic scale in B disappears 

 and we have left the field (d) : 



— r 



. \- cot r\ , 



Jt \ sin ^r ) 



which field has as only divergency two double points in P^ and P, 

 of which in the opposite points equal poles correspond. 



The sum of this field (rf) and the field («) multiplied by h must 

 now give a field having as divergency a single double point with 

 unity-moment in Pj, i. o. w. the field ^j. 



We therefore find on the half hypersphere between Pj and B: 



1 ijt — r ) 



— cos (p I — ; 1- cotr\ 



jr ( sill ^r ) 



and on the half hypersphere between P^ and B : 



1 \—r ) 



— cos (p I -; \-cotr\ , 



n { sin ^r ) 



or if we define on both halves the coordinates 7^ and <p according to 



Pi and Pj Qi we obtain the following expression holding for both halves: 



1 ijt — r I 



~ cos (p I — : \- cotr) :ir '^^ ( v ^^^ ^ • 



3t ( sin ^r ) 



IV. To break up this field into two fictitious "fields of a single 

 agens point" (having however divergency along the whole hypersphere) 



we take for the latter | ip (?•) c?r = F^ (r). 



