INVESTIGATION BY POTENTIALS. 35 



7O -t 



or -j- . - {(c -f b cos 6 x') sin - (e+6sin 0-y') cos 0J : 

 CUT T 



dS 1 dr Id8 



or T-.T -f~T^) ory- 7/1 j 

 dr &r d<9 & d0 



and the angular momentum opposite to watch-hands 



_dS 



~ d6' 



(d) Thus we have all the forces that we require, 

 expressed in terms of a single function S m , which we 

 must now proceed to develope. If the force of attrac- 

 tion between a pole of magnet A and a pole of needle 



B = a/3 x r~, which must be taken for one part of -j , 



ar 



then the corresponding part of 8= . -. x r"" 1 " 1 " 1 . Let 



the disturbing magnet A be inclined at the angle <f> to 

 the axis of x\ then for the right-hand pole, x = a cos <, 

 y = a sin <. And, supposing the similar poles of the 

 two magnets to be on the same side, the complete 

 value of S will be 



m 1 



-m+l 



VI * 



{(cbcos0-acos(j)y+(e-bsm6asin<f)) 



(e) For applying this method to specific cases, 

 such as those of Articles 14, 15, 16, 17, 18, it is neces- 



32 



