124 



ON MAGNETISM. 



Fig. 41. 



This, in every case of the magnetic end directed towards 

 the compass, represents truly the entire action, tending 

 (with the poles as supposed in the figure) to draw the 

 red end of the compass towards A. And, when A is 

 contained in a horizontal plane passing through B, the 

 expression gives the force which tends to disturb the 

 red end of the compass in the horizontal plane. 



But when the direction of A 

 is inclined to the horizon, take the 

 vertical plane passing through A as 

 in Figure 41 ; the force which A 

 exerts on the red end of the compass 

 is that just found, but it acts in 

 the direction BA : and the hori- 

 zontal part of it will be obtained 

 by multiplying by sin <, or will be 



ca 



. sin <f>. 



52. The disturbing magnet is horizontal; it is 

 directed end-on to the vertical axis of the compass, and 

 is not necessarily at the same elevation as the compass. 



This state of things is represented in Figure 42. 



The attraction of the blue end is - 5 -. 



c + a 2ca sm <f> 



the horizontal part of this is 



a(c sin <j> - a) (c 2 + a 2 - 2ca sin 0)~^ 

 The horizontal repulsion of the red end is 



a(c sin <f> + a) (c 2 + a 2 + 2ca sin c)~i 



: and 



