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1. a component C/i normal to the radius vector, according to the 

 formula : 



U 



cos 



i-=-— i— - fcos^(n-2)irXn{r)dr-{- 

 (p cos ^(n— -i; ^r ^ 



+ • .(n 2) 1 r^' '^""'^ ^ ^' • ^» (^) ^^'^ 



TT — r 



2. a component f/, through the radius vector, according to the 

 formula : 



u 1 r 



sm (f cos ^vn—'i) 1 r j 



r 



- . J ,, , fcosKn-2)ir.Xn{r)dr. 

 sm ^K^^—^J \r ^ 

 ■K — r 



If we regard this planivector potential as function of the vortex 

 element and the coordinates with respect to the vortex element and 

 represent that function by (r,, then 



2X=\y I '^ ^^ ' ^^ dx {II) 



^^ J k. 



holds for an arbitrary flux in the elliptic Spn- 



And regarding an arbitrary vector field as caused by the two 

 derivatives (the magnets and the vortex systems) propagating them- 

 selves through the space to a potential, we write: 



='ƒ 



kji 



VIII. In particular for the elliptic Sp^ the results are: 

 Potential of an agens double point: 



cos cp J. 2 COS w i(è^— ^) , I 



-\- cotr) ^ 



shi^ r \ S^ rr I sin V 



or if we put \:x — rz=y -. 



2cosip \ y \ 



7t sm r 



Equation of the boundary lines of force: 



