446 ELEMENTARY ACTIONS. 



Although we have given the name elementary to the force which 

 we have defined, it cannot so be considered in the strict sense of 

 the word ; thus, as Ampere observes, " we cannot apply the term 

 elementary either to a force which is manifested between two 

 elements which are not of the same kind, or to a force which does 

 not act along the straight line joining the two points between which 

 it is exerted." 



464. RECIPROCAL ACTION OF A POLE AND OF A CURRENT. 

 Starting from this elementary law we shall prove as above (346) 

 that the components of the action of a unit pole, placed at the 

 origin of the co-ordinates, on a current element ds situated at a 

 point whose co-ordinates are x, y, and #, are 



^ = -^ 

 (3) dri = 



It may be observed that the moment dM. z of this force, in 

 reference to the z axis, is 



^M z = xdv) -yd% = \z (xdx +ydy) - (x 2 +/) dz . 

 The equation 



gives 



xdx +ydy + zdz = rdr. 



It follows that 



--\z rdr zdz - r* *' dz\ =- zc 

 2 ~r*[_ Z r r* ZL 



- Id ( - ) 

 r 



But - is the cosine of the angle, which the right line r makes 



with the z axis; we have then 



*/M z = - \d cos y, 



