164 NOTES ON MAGNETISM. 



Then the distance of the particle in question from P is 

 2rs cos#)^, and consequently its action on Pis 



r 2 + s 2 2rs cos ' 



magnetic attraction being supposed to follow the ordinary law. 

 The component of this action along cD, is 



muds , n x 



(r cos 6 s). 



2rs cos 0)* 

 This is approximately equal to 



j- (1 + 3 - cos 0) (r cos s) ds, 



or to ^ {r cos + (3 cos 2 1) s} ds; 



and therefore the total action of AB on P, parallel to cZ>, is 

 wcos0 f 3cos 2 0-l 



f , , 3 cos 2 (9-1 r 

 l/tas + w ^ l/isas, 



the integrals being taken along the whole length of the magnet. 

 Consequently 



since the aggregate magnetism of a magnet, each element being 

 taken with its proper sign, is zero. Again, ffisds being the 

 moment of the magnetism of AB> is the measure of its magnetic 

 power, or what we have called M. 



Consequently the action parallel to cD is 



2 0-l) (1). 



-r 



The action of the element at 5, perpendicular to cD, is 



= r sin 0, 



or, approximately, 



Hp (1 + 3 - cos 0) sin 6ds. 

 The total action perpendicular to cD is, therefore, 



sin0cos0 (2). 



