WIRE OF VARIABLE DIAMETER. 89 



from this follows, for the desired condition, 



(27) ,'- const 



If the thickness of the insulator is in a constant ratio with the 

 diameter of the wire, the equation reduces to 



c 



- = const ; 



y 



that is to say that the diameter of the wire in each layer should be 

 proportional to the linear dimensions of this layer. If the thickness 

 z is constant, equation (27) shows that the diameter of the wire 

 increases a little less rapidly than the parameter c. 

 In the first hypothesis, if we put 



we shall have y + z = a (i+S)c; the expressions for dG Q and 

 (25) will acquire the form 



N dc 



- 



TT ' 4 a 4 (i+ 8)2'^ * 



We may allow for the central cavity if we assume that it is 

 bounded by a curve of parameter a ; we get then 



We see that the influence of the external layers diminishes very 

 rapidly when the thickness of the coil increases, and that the 

 maximum action is virtually inversely as the parameter of the curve 

 which bounds the cavity. 



