SURFACE AND MAGNETIC MOMENT OF A COIL. 75 



When the wires touch, considering that zn^y'i and /=fU, 



4, 



(6) 





From which it follows that if 8 is constant, and if the volume of 

 the channel, and therefore also the weight of metal, is given, the 

 resistance varies inversely as the fourth power of the diameter of the 

 wire. For a given wire the resistance varies as the volume of the 

 channel. 



This latter conclusion is manifest. We get the first result directly 

 by observing that, if we make the diameter of the wire one-half, its 

 section is one-fourth, and for the same volume of the channel the 

 length is four times as great ; the resistance is then sixteen times 

 as great. 



727. SURFACE. MAGNETIC MOMENT. The magnetic moment 

 of a cylindrical coil (495) for unit current, is equal to the total 

 surface comprised by the different windings. If the coil consists of 

 a single layer comprising n turns of radius a, we shall have 



S = mra 2 . 



If the coil consists of several layers, the surfaces corresponding 

 to each are added together ; this calculation amounts to determining 

 the sum of the squares of a series of terms which vary in arithmetical 

 progression. 



If r is the smallest radius, the value of any given radius is 



which gives 



t s = t*+2 



Let p be the number of layers, the sum of the squares of the radii is 



The radius d^ of the mean circle is given then by the equation 



2a 2a2 



(7) ai = r' +2r Q + -. 



P P 



