THEORY OF GRAMME'S MACHINE. 713 



The potential of the original field being V - F#, the resultant 

 potential is 



The component N of the field along the direction r is 



which gives, for r = a that is to say, at the surface of the cylinder, 



N = 2F = 2F sin a ; 

 r 



this is a value double the component, which would be due to the 

 original field alone. 



If L is the length of the cylinder, 



/"'(a) = 2FL# sin a, 



/(a) = |/(aXa = 2FL0(i - cos a), 

 J o 



n?f(v) cos 



The equation which defines the angle of lead (1265) becomes 



W 2 47T 



and, if the magnetisation M of the ring may be considered as 

 proportional to the current, 



