Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/163

internal forces in the substance of the rod. The existence of these internal forces is deduced entirely from observation of the effect of external forces on the rod, and the internal forces themselves are generally assumed to be the resultants of forces which act between particles of the rod. Thus the observed action between two distant particles is, in this instance, removed from the class of direct actions at a distance by referring it to the intervention of the rod ; the action of the rod is explained by the existence of internal forces in its substance ; and the internal forces are explained by means of forces assumed to act between the particles of which the rod is composed, that is, between bodies at distances which though small must be finite.

The observed action at a considerable distance is therefore explained by means of a great number of forces acting between bodies at very small distances, for which we are as little able to account as for the action at any distance however great.

Nevertheless, the consideration of the phenomenon, as explained in this way, leads us to investigate the properties of the rod, and to form a theory of elasticity which we should have overlooked if we had been satisfied with the explanation by action at a distance.

106.] Let us now examine the consequence of assuming that the action between electrified bodies can be explained by the intermediate action of the medium between them, and let us ascertain what properties of the medium will account for the observed action.

We have first to determine the internal forces in the medium, and afterwards to account for them if possible.

In order to determine the internal forces in any case we proceed as follows :

Let the system $M$ be in equilibrium under the action of the system of external forces $F$. Divide $M$ by an imaginary surface into two parts, $M_{1}$ and $M_{2}$, and let the systems of external forces acting on these parts respectively be $F_{1}$ and $F_{2}$. Also let the internal forces acting on $M_{1}$ in consequence of its connexion with $M_{2}$ be called the system $I$.

Then, since $M_{1}$ is in equilibrium under the action of $F_{1}$ and $I$, it follows that $I$ is statically equivalent to $F_{1}$ reversed.

In the case of the electrical action between two electrified systems $E_{1}$ and $E_{1}$, we described two closed equipotential surfaces entirely surrounding $E_{2}$ and cutting it off from $E_{1}$, and we found that the application of a certain normal pressure at every point of the inner side of the inner surface, and on the outer side of the outer surface,