1867.] 



Currents by Mechanical TVorJc. 



399 



Let us next ascertain the effect of a sudden change of position in the se- 

 condary coil, which alters the value of M from to in a time t, — t^, 

 during which the current changes from ^\ to Integrating equation (1) 

 with respect to t, we get 



(K + S) I %^^^+(L + 2M,+NK-(L + 2M, + NK = 0. . (5) 



If we suppose the time so short that we may neglect the first term in com- 

 parison with the others, we find, as the effect of a sudden change of position, 



(L + 2M, + N).r, = (L -f 2M^ + N)^, (6) 



This equation may be interpreted in the language of the dynamical theory, 

 by saying that the electromagnetic momentum of the circuit remains the 

 same after a sudden change of position. To ascertain the effect of the com- 

 mutator, let us suppose that, at a given instant, currents x and 7/ exist in 

 the two coils, that the two coils are then made into one circuit, and that x' 

 is the current in the circuit the instant after completion ; then the same 

 equation (1) gives 



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



This equation shows that the electromagnetic momentum of the com- 

 pleted circjiitis 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 combined into one. In this case, therefore, y=~x, and 



(L + 2M + N)a^'= (L - N).r (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 

 comphcated, and contain as many independent variables as there can be in- 

 dependent 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 increase the values of L, M, and N. 



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



