DETERMINATION OF THE RATIO OF THE CONSTANTS. 455 



Let us place the origin of the co-ordinates at the centre of the 

 movable element ds', and the x axis in the direction of the element 

 itself. The action of an element ds of a closed circuit in which the 

 intensity is i is expressed, as we have seen, by 



= m * S (k-i) cos cos 0' + cos e . 



The co-ordinates of the element ds being x, y, z, and its distance 

 from the origin r, we have 



-, 



dr 



-, 



dx 



COS = - . 



ds 



The elementary action may then be written in the form 



hii 'dsds ' f x dr dx~\ 



= - (_!) + 



r 2 \_ rds ds\ 



and the projection of this force on the x axis is 



d*$ cos 6' = d^- = hii 'ds 1 \(k - i) + 1 

 r [_ r 4 r B J 



The component parallel to the x axis of the action of the closed 

 circuit on the element ds' is expressed by 



Integration by parts gives 



