THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
761 
there is no break in the conducting circuit, the current in it is restricted by the 
constitution of the medium to remain constant; and therefore an electromotive force 
E round the circuit, of the kind here determined, can do no work ; it is not operative 
in the phenomena. The induction of a current on itself, due to change of form of its 
circuit, is bound up with the continued maintenance of the current by feed from 
batteries or other sources included in the circuit, in opposition to dissipation in the 
conductors which is connected with a sort of transfer by discharge from molecule to 
molecule within their substance : in an ideal perfectly conducting circuit there would 
be no such induction. A case wdiich strikingly illustrates these remarks is the 
maintenance of a continuous current by a dynamo without any source other than 
mechanical work. The very essence of this action consists in the rhythmical make 
and break of the two circuits of the dynamo in synchronism with their changes of 
form, so that they are inteidocked during one portion of the cycle and unlocked during 
the remainder. Such lockings and unlockings of the circuits may of course be produced 
by sliding contacts, but these are equivalent for the present purpose to breaches in 
the continuity of the conductors. The original apparatus of Faraday’s rotations 
(Maxwell, “ Treatise,” Vol. II., § 486), which was the first electromotor ever 
constructed, and which driven backwards would act also as a dynamo, illustrates 
this point in its simplest form. Without some arrangement which allows the two 
circuits to cut across each other in this manner, there could be no induction of a 
continuous current, but only electric oscillations in the dielectric field, which could 
however be guided along conducting wires, as in alternate-current dynamos. The 
phenomena of electric currents in ordinary conducting circuits are thus more general 
than the phenomena of vortex-rings in hydrodynamics, or of atomic electric currents, 
in that the strengths of the currents in them are not constrained to remain constant ; 
an additional displacement current can, so to speak, flow into a conductor at any 
of its breaches of continuity. The variables of the problem are thus more numerous, 
and the energy-function leads to more equations connecting them. 
57. We might now attempt to proceed, by including the mechanical energy of the 
material conductors in the same function as the electro-kinetic energy, thus deducing 
that the energy gained by altering the co-ordinate is (cZT/c/c^^) in other words 
that the displacement is oj^posed by a force equal to cZT/c/(^p This would make 
currents flowing in the same direction along parallel wires repel each other, and in fact 
generally the force thus indicated is just the opposite to the reality. 
The expression T represents completely the energy of the system so far as electro¬ 
motive disturbances are concerned, as has been proved above. But we have no right 
to assume that the energy of the system, so far as to include movements of the 
conductors and mechanical forces, can be completely expressed by this formula with 
only the electric co-ordinates and the sensible co-ordinates of the matter involved in it; 
lor the mechanism that links them together is too complicated to be treated other¬ 
wise than statistically. We may however proceed as in the electrostatic problem ; a 
MDCCCXCIV.—A. 5 E 
