760 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
where in the last term SjT refers to the change of T due to change of material con¬ 
figuration only. Hence 
8 J T cZi = I S -j- I 
the terms in | . . . | referring to the beginning and end of the time. 
Thus we derive, and that in Maxwell’s manner but rather more rigorously, 
Faraday’s law of the induced electromotive force (— E^) under the form 
d 
dt 
(Lii] H" M13I2 +•••)—“ 
dt di^ 
55. As already mentioned, for currents flowing round complete conducting circuits 
devoid of viscosity, the values of i^, tg, . . . are constant, by a sort of constraint or 
rather by the constitution of the medium, throughout all time; and the electromotive 
forces E^, Eg, . . . here determined have no activity. But if, as in actual electric 
currents, the strengths are capable of change owing to the circuits being completed 
by displacement currents in the dielectric or across a voltaic battery thus constituting 
gaps through which additional displacement can so to speak flow into the conductoi-s, 
or owing to viscous effects in the conductors carrying them which must also involve 
such discontinuity, then the forces E^, Eg, . . . here deduced from the energy-function 
will have an active existence, and the phenomena of electrodynamic induction will 
occur. Alteration of the strength of a current implies essentially incompleteness of 
the inelastic circuit round which it travels, and may be produced either by change of 
displacement across a dielectric portion of the circuit, or through the successive 
bi’eaches of the effective elasticity of the aether which are involved in electric trans¬ 
mission across an electrolyte, and also probably in transmission through ordinary 
media which are not ideal perfect conductors. In short, the existence of electro¬ 
dynamic induction leads to the conclusion that currents of conduction always flow in 
open circuits ; if the circuit were complete, there would be no means available for the 
medium to get a hold on the current circulating in it. On this view the Amperean 
current circulating in a vortex atom is constant throughout all time, and unaffected 
by electrodynamic induction, so that there is apparently no room for WEBiER’s 
explanation of diamagnetisn. 
56. The vorticity in a circuit, that is, the current flowing round it, can thus be 
changed only by an alteration of the displacement across a break in the conducting 
cpiality of the circuit, or by the transfer of electric charge across an electrolyte, in 
which case it is elastic rupture of the medium that is operative. Such an alteration 
of current will be evidenced by, and its amount will be derivable from, the change in 
the energy-function of the dielectric medium, in the manner above described. When 
