416 On the Magnetizing Force of an Electromagnet Coil. 

 to the length of the wire ; we may therefore say 



M=A = !V^^=Vj = ^=. . (4) 

 2m 2m 2r 2^1ir ^ ^ 



The maximum magnetizing force, therefore, varies directly as 

 the electromotive force of one element of the battery, and in- 

 versely as the square root of the product of the reduced resist- 

 ance of the coil-wire into the minimum battery resistance. 



The volume of the wire used in the coil being constant, its 

 reduced resistance will vary inversely as its conductivity, or 



Then 



^^-i^ (^) 



Supposing the dimensions of the helix to remain constant, 

 and the combination to be always arranged to give the maximum 

 effect, we learn from this equation : — 



1st. That, the battery remaining the same, the magnetizing force 

 will vary directly as the square root of the conductivity of the wire. 



2ndly. That, the conductivity of the wire remaining constant, 

 the magnetizing force will vary inversely as the square root of the 

 minimum battery resistance; or since, if the battery consist of a 

 number of cells, equal in ail respects, the minimum battery resist- 

 ance will be inversely as the number of cells employed, the magne- 

 tizing force will vary directly as the square root of that number. 



It must be remembered that we are dealing, in the above re- 

 lations, with the magnetizing powers of the helices, and not with 

 the amount of magnetism developed by them ; this magnetism, 

 however, according to the laws of Lenz and Jacobi, varies as the 

 magnetizing force within wide limits — that is, so long as we are 

 not approaching too near to the maximum magnetic force the 

 iron is capable of receiving. 



While we are upon this subject, it might perhaps be well to 

 point out a very useful application of equation (5) in my paper 

 published in the Philosophical Magazine for February 1870, 

 page 113. 



We have frequently to wind a coil of given size with wire, and 

 at the same time it is necessary that the coil should have some 

 given resistance; the question arises, what must be the size of 

 the wire ? A slight modification of the equation above men- 

 tioned will enable us to answer this question without difficulty. 



