THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
753 
breaches of linearity of the current are at the condensers themselves, and these 
may be made negligible by taking the dielectric plates very thin. In this way a 
steady current can be realized in a conductor devoid of resistance, without the aid 
of any complicated electromotive source.* 
47. Now we have to inquire what account the dynamical theory gives of this 
steady current. In the first place, the motion is very slow in comparison with the 
velocity of electric propagation ; therefore the interior of the dielectric is at each 
instant sensibly in an equilibrium condition, for the same kind of reason that moving 
a body slowly to and fro does not start any appreciable sound waves in the 
atmosphere. Thus at each instant the vector [f, g, h) is derived as above from a 
potential function V ; and at the surface of any of the conductors (supposed here of 
insensible resistance) it is directed along the normal, if the medium is isotropic. It 
is, in fact, in the more familiar electric language, at each instant the electric displace¬ 
ment determined by the charges which exist in a state of equilibrium on the faces of 
the condensers and on the connecting wires. This electric displacement in the 
dielectric field is, owing to the condensing action, very small compared with the 
charges involved, except between the plates of the condensers and close to the thin 
conducting wire. Imagine a closed surface which passes between the plates of one 
of the condensers, and intersects the conducting wire at a place P. As the vector 
(/ g, h) is by its nature as a rotation circuital, its total flux through any surface must 
be null, if we imagine the elastic continuity of the medium inside the conductors to 
be restored, and such an electric displacement at the same time imparted along the 
wire as will leave the state of the field unaltered and thus no disturbance inside 
the conductors. And this flux must remain null when the plates of the condenser 
are slightly brought together; or rather we have to contemplate such a flow of 
displacement along the wire as will make it remain null. The movement of the 
plates wiU, however, very considerably alter the large flux across that portion of the 
* Cf. “ A mechanical representation of a vibrating electrical system and its radiation,” ‘ Proc. Camb. 
Phil. Soc.,’ 1891. 
MDCCCXCIV.—A. 5 D 
