to be employed in testing with Wheatstone's Diagram. 31 

 called v'; thus 



1 + - 

 Q 



In case A = or — = constant, we again have U = \/g const., 



our former substitution ; in consequence of which, to produce the 

 maximum magnetic effect, we always have 



g=k, 

 or 



The resistance of the wire filling the given space must be equal to 

 the external resistance. 



But as the radial thickness of the insulating covering is always 



the same for wires of various diameters, — will be variable with 



Q 

 q, i. e. with g ; and consequently 



to produce the maximum magnetic effect for a given space ; or, 

 considering the insulating covering of wires, 



The resistance of the space must be not equal to the external 

 resistance. 



In order to find this function f(k) , we will suppose the space 

 equally filled up with wire ; and taking 8 as the radial thickness 

 of the insulating covering, we can put 



i q ' 



in which c is a constant, expressing the arrangement of the 

 convolutions in equally filling the space with wire*. 



This value of — substituted in the expression for U, and put- 



ting q = — -, we have 

 g\ 



V Tc 



•U= 



* Supposing we divide the sectional area A, by filling the space with 

 wire, into squares, we have 



c = 4; 

 or into hexagons, 



c = 3.4, &c. 



