( 265 ) 



sin Vp (I -f- y cot r) =z ziz l. 



Potential of a single agens point : 



2 



— . y . cot r. 

 rr 



Vector potential of an elementary circular current; 



2 . I -^ y cotr 



— sin (f . ; . 



ct sin r 



So also force of an element of current : 



2 . \ -\- y cotr 



sin If . ; . 



ct sin r 



Linevector potential of an element of current : 



, . cos i-fi \ ^^ ct { r' 



according? to tiie racliusvector : 1- — 



Ct \ cos^ A r sin r si?i^ ^ r 



2 ' oc/t ƒ ot/t -Q 



sinq\ i/3' 2r—ct \r 



normal to the racliusvector: 1- 



TT— 1- 



Ct ( cos^ I r sin r sin^ ^ r ' 

 IX. For the elliptic plane we find : 

 Potential of an agens double point : 



cos ff cot r. 

 Equation of the boundary lines of force : 



sin (fi z=z dz sin r, or ff =. 



Potential of a single agens point : 



— I sin r. 

 Scalar value of the plani vector potential of a double point of rotation: 



sin (p 

 sin r 

 Thus also force of a rotation element : 



sin cp 

 siïi r 

 Planivector potential of a rotation element : 



I cot ^ r. 

 We notice that the duality of both potentials and both derivatives 

 existing for the spherical Sj),, has disappeared again in these results. 

 The reason of this is that for tiie representation on the sphere a 

 divergency in the elliptic plane becomes two equal divergencies in 

 opposite points with equal signs ; a rotation two equal rotations in 

 opposite points with different signs; for the latter we do not find 

 the analogous potential as for the former ; the latter can be found 

 here according to the Schering potential formula. 



With this is connected immediately that in the elliptic plane the 

 field of a single rotation (in contrast to that of a single divergency) 

 has as such possibility of existence, so it can be regarded as unity 



18 



Proceedings Royal Acad. Amsterdam. Vol. IX. 



