364 Mr. H. A. Rowland on Magnetic Distribution. 



This only attains a maximum when - = co , or the rod is infi- 

 nitely long compared with its diameter. 



The second case is rather indefinite, seeing it will depend 

 upon whether the body attracted is large or small. When it is 

 small, we require to make the surface-density a maximum, the 

 weight being constant. We find 



e • +1 



which attains a maximum as before when - = oo . When the 



a 



attracted body is large, the attraction will depend more nearly 



upon the linear density, 



which is a maximum when -7 = — -. 



a p 



For the third case we have the value of Q" at the centre of the 

 bar from equation (6), 



£ (^ Cil -1)2 



The condition for a maximum gives in this case 



b _ 1-65 



d p 



For the last case, in which the magnetic moment for a given 

 length is to be. made a maximum, we find 



-=\L. 

 d p 



This last result is useful in preparing magnets for determining 

 the intensity of the earth's magnetism, and shows that the mag- 

 nets should be made short, thick, and hard for the best effect*. 

 But for all ordinary purposes the results for the second and 

 third cases seem most important, and lead to nearly the same 



* Weber recommends square bars eight times as long as they are broad, 

 and tempered very hard. (Taylor's Scientific Memoirs, vol. ii. p. 86.) 



