MAINTENANCE OF ELECTRIC CURRENTS BY MECHANICAL WORK. 81 



current in the circuit the instant after completion; then the same equation (1) 

 gives 



(L + 2M+N)x' = (L+M)x + (N+H)y (7). 



The equation shews that the electromagnetic momentum of the completed 

 circuit is equal to the sum of the electromagnetic momenta of the separate coils 

 just before completion. 



The commutator may belong to one of four different varieties, according to 

 the order in which the contacts are made and broken. If A, B be the ends 

 of the first coil, and C, D those of the second, and if we enclose in brackets 

 the parts in electric connexion, we may express the four varieties as in the 

 following Table : 



(1) (2) (3) (4) 



(AC) (BD) (AC) (BD) (AC) (BD) (AC) (BD) 

 (ABCD) (ABC) (D) (A) (BCD) (A) (B) (C) (D) 



(AD) (BC) (ABCD) (ABCD) (AD) (BC) 



(AD) (BC) (AD) (BC) 



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

 the operation is complete, two equal currents in opposite directions are com- 

 bined into one. In this case, therefore, y= x, and 



(L+ZM+N}x' = (L-N)x (8). 



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

 pendent currents can be excited, the electrical equations are much more com- 

 plicated, and contain as many independent variables as there can be independent 

 electromagnetic quantities. I shall therefore, for the sake of preserving simplicity, 

 avoid the consideration of the iron cores, except in so far as they simply in- 

 crease the values of L, M, and N. 



I shall also suppose that the secondary coil is at first in a position 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 + N 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 + N. 



VOL. II. ll 



