Foi'ce of an Electromagnet Coil. 415 



if we except a slight variation due to the different proportion of 

 the space occupied by the insulating material according to the 

 size of the wire. 



In looking into this subject a short time since, I found two 

 other relations regarding electromagnet spirals or coils, equally 

 simple in their nature to that we have noticed, but not subject 

 to a similar anomaly. I believe these relations are new ; and 

 they are certainly interesting, if not of any very great practical 

 value. 



For the sake of clearness and brevity, it will be advisable to 

 give here two definitions of terms it is proposed to make use of. 



1. The minimum resistance of a battery is the resistance it 

 would have if all the positive and all the negative poles were 

 respectively joined together so as to form one element of large 

 surface. 



2. The reduced resistance of a given wire is the resistance of 

 a wire of uniform gauge, equal in volume and specific conducti- 

 vity to that of the given wire, and one metre in length. 



Let 



?• = the minimum resistance of the battery to be employed, 

 n = the number of elements to be joined in series, 

 e = the electromotive force of one element, 

 K,= the reduced resistance of the wire forming the magneti- 

 zing coil, 

 I = the length of the wire, 

 C = the strength of the current, 

 k = the conductivity of the wire, 



M= the maximum magnetizing force of a given combination; 

 then 



rn^ + ni^ ^^^ 



The condition of maximum effect is 



Therefore 



^=»v/l (2) 



and 



2rn^ 2rn 





The size of the frame on which the wire is wound being con- 

 stant, the number of convolutions will, of course, be proportional 



