Page:On Faraday's Lines of Force.pdf/23

So that in the ordinary electrical problems the analogy in fluid motion is of this kind:

$V=-p,$
$X=-{\frac {dp}{dx}}=ku$,
$dm={\frac {k}{4\pi }}S$,

whole potential of a system $=-\Sigma Vdm={\frac {k}{4\pi }}W$, where $W$ is the work done by the fluid in overcoming resistance. The lines of forces are the unit tubes of fluid motion, and they may be estimated numerically by those tubes.

Theory of Dielectrics.

The electrical induction exercised on a body at a distance depends not only on the distribution of electricity in the inductric, and the form and position of the inducteous body, but on the nature of the interposed medium, or dielectric. Faraday^[1] expresses this by the conception of one substance having a greater inductive capacity, or conducting the lines of inductive action more freely than another. If we suppose that in our analogy of a fluid in a resisting medium the resistance is different in different media, then by making the resistance less we obtain the analogue to a dielectric which more easily conducts Faraday's lines.

It is evident from (23) that in this case there will always be an apparent distribution of electricity on the surface of the dielectric, there being negative electricity where the lines enter and positive electricity where they emerge. In the case of the fluid there are no real sources on the surface, but we use them merely for purposes of calculation. In the dielectric there may be no real charge of electricity, but only an apparent electric action due to the surface.

If the dielectric had been of less conductivity than the surrounding medium, we should have had precisely opposite effects, namely, positive electricity where lines enter, and negative where they emerge.

1. Series XI.