gO MAINTENANCE OF ELECTRIC CURRENTS BY MECHANICAL WORK. 



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 



= Q (1), 



whence a-a*"**' ................................... (2), 



where x. is the initial value of the current. This expression shews that the 

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



L+2M+N 

 If we put ~ ~ r .............................. ' '' 



then x = x.e" ; ..................................... (4). 



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

 similar outward form, T 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 in- 

 crease. 



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

 secondary coil, which alters the value of M from M 1 to M s in a time t t <,, 

 during which the current changes from x, to x,. Integrating equation (1) with 

 respect to t, we get 



' l = ............ (5). 



(R + S) f' 



J ti 



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 t + N)x t ^(L+2M l + N)x l ................... (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 commutator, 

 let us suppose that, at a given instant, currents x and y exist in the two 

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



