H. A. Rowland — Studies on Magnetic Bhtrihutioyi. 105 



4th. The magnetic moment, the length being constant and 

 the diameter variable. 



Either of these inay be considered as a measure of the power 

 of the bar according to the view we take. The magnetic 

 moment of a bar is easily found to be 



(19) 



*^=i;^.^ 



I2-.T 



+-^P 



(1! 



and if y is the weight of a uni 



t of voh 



Lime of the steel and W 



the weight of the magnet, we 



have fit 



lally 





-..l^cl 



^4 





(2( 



where 0=^=;,V/^'. 









This only attains a maxim i: 



im wher 



4==^'^ 



.r the rod is ini 



nitely long compared with its diameter. 



The second case is rather indefinite, seeing that 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 



^o=;;.^R>7^^,' • • • (^^) 



which attains a maximum as before when - — co . When the 

 attracted body is large, the attraction will depend more nearly 

 upon the linear density 



_ ^ iW'^i 



which is a maximum when - 





h 1-65 



