88 PROPERTIES OF CIRCULAR CURRENTS. 



we should increase the number of windings of the first layers, which 

 are especially efficacious, and diminish the number of the more 

 distant ones which are less so. 



Supposing that we fix the values R, R', and U, we may propose 

 to ourselves to determine the diameter y + z of the wire for each of 



the similar layers of thickness dc so as to make the expression 

 s~* 



FO=E R + R? a maximum - 



Let us consider one of these layers corresponding to the two 

 values c and c + dc of the parameter. If we vary the diameter of the 

 wire the constant of the coil will vary from ^G , the resistance from 

 */R, and the magnetic action at the centre will experience a variation 



GO 



R + l 



from which, disregarding infinitely small quantities of the second 

 order, 



G 



pGo__^R_l 

 '[G O R + R'J 



R + R' 

 The condition of the maximum of SF is evidently 



. WJ.X 



dy 

 If we refer to expressions (25), we find 



d . 



d JK <- 



~T U& NO t 



dy TT 2 y(y + z) 3 



