74 PROPERTIES OF CIRCULAR CURRENTS. 



occupies a fraction nfry 2 of the surface of the square, and the total 

 section, including the envelope, a fraction n\-xy\ or n\Try\i +S 2 ) of the 

 same surface. Each of these fractions is a maximum when the wires 

 are in contact; the side of the square is then equal to the diameter of 



the wire, and the value of the last fraction is - . 



4 



The ratio of the total volume of the wire to that of the channel 

 is equal to that of the sections ; when the wires are in contact we 

 have 



V'_V(l+S) 2 _7T 



u~ ~~D~~ ~I' 



which gives for the weight of the wire 



4(1 +S) 2 



u. 



It follows from this that if 8 is constant that is to say, if the 

 thickness of the insulator is a constant fraction of the radius of the 

 wire, the weight of the metal for a given volume of the channel is 

 independent of the diameter of the wire ; this weight is moreover 

 proportional to the volume of the channel. 



In the case of a uniform coiling we have 



(4) / 



and, when the wires are in contact, 



The volume of the channel U being given, the total length of the 

 wire varies then inversely as the square of the diameter of the in- 

 sulated wire ; for a wire of a given diameter the length varies as the 

 volume of the channel. 



726. RESISTANCE. The resistance of the coil is 



(5) R-4- 



Try 2 



