2S2 



A. TAN AK AD ATE. 



Let ^ 1} l)e the co-ordinates of 

 any one of the poles, i-eferred to 

 anij position of thi current as origin, 

 ,so that, if X, 11 he the co-ordinates 

 of the current, 



^ + X ^ a and j) -\- y ^= b 



Then p = y' ^'^ + j)' is the dis- 

 tance of any pole from the current. 



The potential energy of unit 

 current and four unit poles is 



V 



9.^ 



2jtan ^ — T- + const 



\ «--J r -♦" 



\1/ '-:i i , 



^ _ 



_ À 



S 



s 



Fiçj. 5. 



= 2^d + const (1) 



^4 meaning summation for the four distinct poles, and 6 heing 

 the angle between any of the polar distances and the axis of ^, I' 

 then reduces to the algebraic sum of the two angles subtended by the 

 two parallel lines of length 2 h placed 2 a apart. This is the same as 

 the potential energy of unit pole and two parallel magnetic strips of 

 infinite length placed 2 a apart, the breadth of each being 2 b. The 

 solid angles «i and cji of the usual notation become two spherical 

 wedges. The two magnetic strips may be replaced by two equal 

 pairs of parallel currents, placed along the edges of the strips, as 

 will be evident à priori, since the action of a, unit current upon 

 four unit poles must be the same as that of four currents 

 upon a unit pole so far as the dynamical aspect is concerned. 

 This latter was the combination I used in making an experimental 

 verification of the result. 



From (1) the equation 



2j Ö ^ C07lSt. 



gives the equipotential surfaces, and 



2_| log p = const. 



