MAINTENANCE OF ELECTRIC CURRENTS BY MECHANICAL WORK. 



During the whole motion the current has also been decaying at a rate 

 which varies according to the value of L + 2M+N; but since M varies from 

 + .V to -J/, we may, in a rough theory, suppose that in the expression for 

 the decay of the current J/=0. 



If the secondary coil makes a semirevolution in time T, then the ratio of 

 the current X H after a semirevolution, to the current x, before the semirevolution, 



will be 



x -? 



'= 'r, 



a; 



L + N 

 where Tat R+~S ....................................... ^ '' 



and r is a ratio depending on the kind of commutator. 

 For the first kind, 



<" 



By increasing the speed, T may be indefinitely diminished, so that the 

 question of the maintenance of the current depends ultimately on whether r is 

 greater or less than unity. When r is greater than 1 or less than 1, the 

 current may be maintained by giving a sufficient speed to the machine ; it will 

 be always in one direction in the first case, and it will be a reciprocating current 

 in the second. 



When r lies between +1 and 1, no current can be maintained. 



Let there be p windings of wire in the first coil and q windings in the 

 second, then we may write 



L = lp', M=mpq, N=n<f ........................ (11), 



where I, m, n are quantities depending on the shape and relative position of 

 the coils. Since L 2M+N must always be a positive quantity, being the 

 coefficient of self-induction of the whole circuit, ln m 3 , and therefore LNM* 

 must be positive. When the commutator is of the first kind, the ratio r is 

 greater than unity, provided pm is greater than qn ; and when 



r -( l "fc) < 12 )' 



which is the maximum value of r. 



