4<76 Royal Society : — Mr. Clerk Maxwell on the 



In the first kind the circuit of both coils remains uninterrupted ; 

 and when the operation is complete, two equal currents in opposite 

 directions are combined into one. In this case, therefore, y=— x, 

 and 



(L + 2M + N)a?'=(L-N> (8) 



When there are iron cores in the coils, or metallic circuits in which 

 independent currents can be excited, the electrical equations are 

 much more complicated, and contain as many independent variables 

 as there can be independent electromagnetic quantities. I shall 

 therefore, for the sake of preserving simplicity, avoid the consider- 

 ation of the iron cores, except so far as they simply increase the 

 values of L, M, and N. 



I shall also suppose that the secondary coil is at first in a posi- 

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

 M= — M, which will increase the current in the ratio of L-fN to 

 L-2M + 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-fN. 



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 -f M to — M, we may, in a rough theory, suppose 

 that in the expression 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 v after a semirevolution, to the current x before 

 the semirevolution, will be 



T 



x, ■=. 

 -l — e T r t 

 x 



where 



L + N 



r= R + S' * ' (9) 



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

 For the first kind, 



r= L-2M+N • (10) 



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 -f I 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 2 , M=mpq, N = nq 2 , (11) 



where I, m, n are quantities depending on the shape and relative posi- 

 tion of the coils. Since L — 2M -f N must always be a positive quan- 



