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



supposing the coils to have no cores, and, to fix our ideas, we may suppose 

 them in the form of rings, the smaller revolving within the larger on a com- 

 mon diameter. 



The equations of the currents in two neighbouring circuits are given in 

 my paper ''On the Electromagnetic Field"*, and are there numbered (4) 

 and (5), 



where x and y are the currents, i, and 77 the electromotive forces, and R 

 and S the resistances in the two circuits respectively. L and N are the 

 coefficients of self-induction of the two circuits, that is, their potentials on 

 themselves when the current is unity, and M is their coefficient of mutual 

 induction, which depends on their relative position. In the electromag- 

 netic system of measurement, L, M, and N are of the nature of lines; and 

 R and S are velocities. L may be metaphorically called the " electric 

 inertia" of the first circuit, N that of the second, and L + 2M-f N that of 

 the combined circuit. 



Let us first take the case of the two circuits thrown into one, and the two 

 coils relatively at rest, so that M is constant. Then 



whence 



(Il + S>+^(L + 2M + N>=0, (1) 



X = XQe L+2M + N J (2) 



where is the initial value of the current. This expression shows that the 

 current, if left to itself in a closed circuit, will gradually decay. 

 If we put 



TfS-=^' ....... (3) 



then 



x=x^e r , (^4) 



The value of the time 7 depends on the nature of the coils. In coils of 

 similar outward form, r varies as the square of the linear dimension, and 

 inversely as the resistance of unit of length of a wire whose section is the 

 sum of the sections of the wires passing through unit of section of the coil. 



In the large experimental coil used in determining the B.A. unit of re- 

 sistance in 1864, T was about '01 second. In the coils of electromagnets 

 T is much greater, and when an iron core is inserted there is a still greater 

 increase. 



Phil. Trans, 1865, p. 469. 



