WIRE OF VARIABLE DIAMETER. 87 



The parameter is thus a function of /. If, in like manner, we 

 consider U as a function of c, or of /, equation (24) gives 



= 4 

 we have, moreover, 



We get from these ratios 



(2S) 



P 



a IS. = 



These values of ^G , dl, and */R are those which correspond to the 

 layer bounded by two meridional curves, the parameters of which 

 have the values c and c + dc. The quotient 



dl c 2 



represents the specific action of the layer ; this action is inversely as 

 the square of c; that is to say, as the square of the distance of the 

 layer from the centre. 



Taking into account the internal cavity, the quantities G , /, and 

 R expressed as a function of <:, have the values 



(26) /= 



Jx = 



7T 



735. WIRE OF VARIABLE DIAMETER. Instead of using a wire 

 whose diameter was constant for the entire coil, it would be 

 more advantageous, while retaining the same channel, and the same 

 total resistance, to lessen the diameter of the wire in the first layers, 

 and then increase it progressively in the succeeding wires; in this way 



