124 HENRY A. ROWLAND 



M 4rr 2 fl' 1 2~rl4-c-rt h ( 19 ) 



and if ? is the weight of a unit of volume of the steel and W is the 

 weight of the magnet, we have finally 



M- -* 



This only attains a maximum when - oo , or the rod is infinitely 



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 con- 

 stant. We find 



which attains a maximum as before when -, oo When the attracted 



CL 



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), 



The condition for a maximum gives in this case 



5 _ 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 



b_-l 

 d~ p' 



This last result is useful in preparing magnets for determining the 



