40 ON MAGNETISM. 



which produces the angular momentum opposite watch- 

 hands 



y. sin . 8. /%.c (c 2 + 2c#.cos + 2 / 2 )~ T ~. 



Now when c is very large, it will suffice to retain the 

 first efficient term in the expansion, which gives 



or 



m 0.8 < 



The integral of this, through the whole needle, will be 



In like manner, the attraction of the mass of N of blue 

 magnetism will produce an angular momentum in the 

 same direction represented by 



and the total angular momentum will be 



Let the quantity in the bracket be called E: then the 

 total angular momentum = 



EB. sin 6. 



It is evident that, under the action of this force, 

 the needle B will vibrate according to the same law as 

 a common pendulum. 



It will be remarked that the conditions here sup- 

 posed correspond to those of the Earth's horizontal 

 magnetic influence as observable at any one place. 

 We know nothing of the precise action of the Earth's 

 magnetism, except that, for any one place, it may be 



