COIL OF MAXIMUM ACTION FOR A GIVEN SOURCE. 83 



volume of the channel is proportional to the length of the wire. 

 From this it follows that 



_T? 



p R' 



The problem is then to make the expression - + - a minimum, 



-rry" I 



which is given by the condition 



pdy Rtf/ _dy n ,dl 



2-4 + -70 - = 0, or 2 R-^- + R'- = 0. 

 Try 3 / 2 y I 



We have further, by equation (19), U being a constant, 



2dy dl 

 + T = 0; 



y + z I 



and therefore 



- 



that is to say, that the resistance of the coil should be to the external 

 resistance as the diameter of the bare ivire is to the diameter of the 

 covered wire* 



This result is independent of the shape of the channel. 



732. The total resistance of the wire being determined by one of 

 the preceding conditions, we might calculate the length and diameter 

 of the wire with which the coil must be covered. 



In the first case we have 



pl 



we deduce from this 



* SCHWENDLER. Phil. Mag., Vol. xxix. 1867. 



G 2 



