334 CONSTITUTION OF MAGNETS. 



From the figure we have 



co.*--* 



From the extremities P' and P" of the elements ds' let perpen- 

 diculars P'A and P"A' be drawn to the tangent to the curve ; we get 



PA =rcos<9, 



from which we deduce 



OS 



On the other hand, the distance AA' is the projection of the 

 element ds' on the tangent at P to the curve j, which gives 



A , jt 



AA =- v ^ , ds = ds cos e , 



OS 



and, therefore, 



M r~ 



COS = , 



V ^f 05 



The elementary action may then be written 



~&,r 3 



'^y^y'F <) 2 ^ i ^r ^r 

 * ?>s~ds' 2^s^)s' 



We have further 



ayr 



_ _^ ^ _ i g^gr __ ^_ r 



' 2 N /rt)j()j / ^r^r^s^s' 2r^r^ 



