754 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
surface which lies between them ; and the total flux for the other part of the surface 
not near the wire is as we have seen of trifling amount; therefore the alteration just 
mentioned must be considered to be balanced by an intense alteration of the above 
ideal flux in the immediate neighbourhood of the surface of the wire, in fact along 
its very surface if it is a perfect conductor. Immediately this change of the capacity 
of the condenser is over, the vector {f, g, h) will be back in its equilibrium condition 
in wdiich it is, at each point of the surface of the wire, directed along the normal. 
As {/, g, h) represents the electric displacement in the field, the intense flux here 
contemplated, close to or on the surface of the wire, when the capacity is undergoing 
change, is the current in the wire. But all these circumstances concerning it have 
been made out from the dynamics alone, electric phraseology being employed only to 
facilitate the quotation of known analytical theorems about potential functions, and 
about how their distribution througli space is connected with the forms of surfaces 
to which their fluxes are at right angles, and over which they therefore have them¬ 
selves constant values. 
If now while a current is flowing round the circuit, the two condensers are imagined 
to he instantaneously removed, and the wire made continuous, wm shall be left with 
an ordinary circuital current, which in the absence of dissipative resistance will flow 
on for ever. 
48. The argument in the above rests on the fact that there is circuital change of an 
elastic displacement djclt [f, g, li) distributed throughout the dielectric, while the 
medium is discontinuous at the surface of the perfectly conducting wire because 
disj)lacement cannot be sustained inside the wire. When we for purposes of calculation 
imagine the elastic quality to extend across the section of the wire, and so avoid 
consideration of the discontinuity in the medium, we must imagine as above a flow of 
rotational displacement along the wire so long as the capacity of one of the condensers 
is being altered; and the velocity in the field will be deducible, by the ordinary 
formuloe for a continuous medium, from this ideal flow together with the actual 
changes of displacement throughout the dielectric. For a perfect conductor the 
circumstances will be exactly represented by confining this flow to its surface; what 
is required to make the analytical formulae applicable, without modification on 
account of discontinuity in the medium, is simply the addition of such an ideal flow 
at the places of discontinuity as shall render the displacement {f, g, h) circuital 
throughout the field, without disturbing its actual distribution in the volume of the 
media. 
The kinetic and potential energies of the medium may in fact either be calculated 
for the actual configuration, when they will involve surface integral terms extended 
over the surfaces of discontinuity, or they may be calculated as for a continuous 
medium if we take into account a flow of displacement along these surfaces, such as 
we wovdd require to introduce by some agency if the medium were perfectly 
continuous, in order to establish the actually existing state of motion throughout it; 
