160 The Rev. H. Lloyd on the mutual Action of permanent Magnets. 



the law of the force being similar to that of gravity, 1. e. directly as the pro- 

 duct of the magnetic masses, and Inversely as the square of their distance. 

 Let this force be resolved In the direction of the axes of coordinates. The 

 portion parallel to the axis of x Is 



mq{a — x) 



and that parallel to the axis of ^ Is . 



mqy 



and the sums of these portions, taken throughout the entire length of the 

 magnet, are the components of the total action. 



Let the distance oq = r, and the angle moq = 0, 



0^ = r cos 0, y = /■ sin ; 

 and substituting, the components of the force exerted by q on m are 



mq (a — /•cos0) mqr sin <f) 



(a* — 2 ar cos + r^)i ' (a^ — 2 ar cos + ^i ' 



Hence If ^ and F denote the components of the total force exerted by the magnet 

 Ns on M, we have 



+1 -+/ 

 v-^C (a - r cos (f>)qdr y_^ smtf^grdr 



^-™ (o^_2arcos0+Ol' (a^ — 2 ar cos + r^)! ' ^^ 



I being half the length of the magnet. The quantity q being an unknown function 

 of r, it is manifest that the integration of these formulae cannot be effected 

 in finite terms. 



