474 Royal Society : — Mr. Clerk Maxwell on the 



between the augmentation of the power of a weak magnet by means 

 of an inductive action produced by itself, and that accumulation of 

 power shown in the static electric machines of Holtz and others 

 which have recently excited considerable attention, in which a very 

 small quantity of electricity directly excited is, by a series of inductive 

 actions, augmented so as to equal, and even exceed, the effects of 

 the most powerful machines of the ordinary construction. 



March 14, 1867. — Lieut. -General Sabine, President, in the Chair. 



The following communication was read : — 



" On the Theory of the Maintenance of Electric Currents by Me- 

 chanical Work without the use of Permanent Magnets." Bv J. 

 Clerk Maxwell, F.R.S. 



The machines lately brought before the Royal Society by Mr. 

 Siemens and Professor Wheatstone consist essentially of a fixed and 

 a moveable electromagnet, the coils of which are put in connexion 

 by means of a commutator. 



The electromagnets in the actual machines have cores of soft iron, 

 which greatly increase the magnetic effects due to the coils ; but, in 

 order to simplify the expression of the theory as much as possible, I 

 shall begin by supposing the coils to have no cores ; and, to fix our 

 ideas, we may suppose them in the form of rings, the smaller revol- 

 ving within the larger on a common 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), 



S=R*+^(L*+My), 



9 = Sy+i?(M*+Ny), 



where x and y are the currents, £ and rj 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 rela- 

 tive position. In the electromagnetic 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 + 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 



(R + SVr+-(L + 2M + N>==0, . . . . (1) 

 dt 



whence 



R+S t 

 X = CC^e L+2M + N , (2) 



* Phil. Trans. 1865, p. 469. 



