126 



ON MAGNETISM. 



53. The disturbing magnet is vertical. 



In Figure 43, the horizontal part of the attraction 



Fig. 43. 



of the blue pole is a . c . sin < . (c 2 + a 2 2ca cos $)"-, 

 and that of the repulsion of the red pole is 

 a . c sin </> (c 2 + a 2 4- 2ca cos <)~^. 



If these be expanded to the first power of a, the result- 

 ant attraction is found to be 



. 

 3- . sin <j) . cos <f>. 



With a given value of c, it is therefore greatest 

 when (j> = 45. 



With a given horizontal distance h, which makes 



sn 



~ , the force is 



- . air < . cos 



