DETERMINATION OF THE FUNCTIONS F(r) AND/(r). 453 



VI. The action of a closed current on an element of current is 

 perpendicular to the element. The arrangement of this latter experi- 

 ment is the same as that for the action of magnets on currents 

 (463, IV.) 



Consider the three similar currents of the first experiment (V.) 

 For the position of equilibrium, the distances to the centre of 



Fig. no. 



similitude of the three homologous points, A, B, C (Fig. no) of 

 the circles, satisfy the ratio 



OA OB OC 



from which is deduced 



and therefore 



OB - OC = B C = OA m (i - m), 



AB 



For three homologous elements of current #, b, and c, the lengths 

 will be ds t mdS) and m z ds ; the distance of the two former being r, 

 that of the second to the third will be mr. 



If we assume that each intermediate element such as b is in 

 equilibrium between the two others a and c, which correspond to it, 

 the entire current S' will be in equilibrium between the two similarly 

 placed currents S and S". It does not seem that this condition is 

 always necessary, but it is evidently sufficient, and it enables us to 

 determine the form of the two functions ~F(r) and/(r). 



