[From the Proceedings of the Royal Society, No. 91, 1867.] 



XXIX. On the Theory of the Maintenance of Electric Currents by Mechanical 

 Work without the use of Permanent Magnets. 



THE machines lately brought before the Royal Society by Mr Siemens 

 and Professor Wheatstone consist essentially of a fixed and a moveable electro- 

 magnet, 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 revolving 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), 



-^ t 



~ 



where x and y are the currents, 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 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. 



* Philosophical Transactions, 1865, p. 469. 



