400 Mr. Clerk Maxwell on the Maintenance of Electric [March 14, 



which M = 0, and that it turns into a position in which M=— -M, which 

 will increase the current in the ratio of L + N to L— 2M-f-N. 



The commutator is then reversed. This will diminish the current in a 

 ratio depending on the kind of commutator. 



The secondary coil is then moved so that M changes from M to 0, which 

 will increase the current in the ratio of L + 2M+N to L+N. 



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 +M to — M, we may, in a rough theory, suppose that in the expres- 

 sion for the decay of the current M=0. 



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

 the current x^, after a semirevolution to the current before the semirevo- 

 lution, will be 



T 



where 



L + N 



^==RTs' • • 



and 7' is a ratio depending on the kind of commutator. 

 For the first kind, 



'•=L-2M+N- 0») 



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

 question of the maintenance of the current depends ultimately on whether 



?• 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 reciproca- 

 ting current in the second. 



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



Let there hep windings of wire in the first coil and q windings in the 

 second, then we may write 



L=lp-', M=inpq, 'N=nq-, (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, In—irir, and therefore 

 LN— M m.ust 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 



'-('--'&' 



which is the maximum value of r. 



