Magnetic Effect of Electromagnets. 255 



Let A = the outer diameter of tlie circular ends, 

 a = the inner „ „ „ 



h = the length of the bobbin, 



c s= the length of the straight sides between the cir- 

 cular ends, 

 S = the diameter of the wire, 



p = the radial thickness of the insulating covering, 

 and L = the length of the wire on the bobbin. 



Then 



_ h{K- a) 

 "^^ 2{h-\-2pY 



for each wdre being allo^ved a square, the length of Avhose sides 

 is equal to the diameter of the covered wire ; and 



But 



w^here \ is the specific resistance of the conducting material of 

 the wire, i. e. the resistance between opposite faces of the unit 

 cube of the conducting material. Therefore 



We had 



Put 



then 



^'=Sw^$f{<'^^-'^^'^ 



tE 



^=Y 



1. 



\n n/sh 



and it is required to make 6 a minimum with respect to 5. 

 Now 



cW 



dh 





