Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/162

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Now is the resultant due to the combined action of the external system and the electrification of the surface . Hence the effect of the pressure on each element of the inside of the surface considered as a rigid body is equivalent to this combined action.

But the actions of the different parts of the surface on each other form a system in equilibrium, therefore the effect of the pressure on the rigid shell is equivalent in all respects to the electric attraction of on the shell, and this, as we have before shewn, is equivalent to the electric attraction of on considered as a rigid system.

If we had supposed the pressure to act on the outside of the shell, the resultant effect would have been equal and opposite, that is, it would have been statically equivalent to the action of the internal system on the external system .

Let us now take the case of two electrified systems and , such that two equipotential surfaces and , which we shall call and respectively, can be described so that is exterior to , and surrounds , and lies within .

Then if and represent the resultant force at any point of and respectively, and if we make

and

the mechanical action between and is equivalent to that between the shells and , supposing every point of pressed inwards, that is, towards with a pressure , and every point of pressed outwards, that is, towards with a pressure .

105.] According to the theory of action at a distance the action between and is really made up of a system of forces acting in straight lines between the electricity in and that in , and the actual mechanical effect is in complete accordance with this theory.

There is, however, another point of view from which we may examine the action between and . When we see one body acting on another at a distance, before we assume that the one acts directly on the other we generally inquire whether there is any material connexion between the two bodies, and if we find strings, or rods, or framework of any kind, capable of accounting for the observed action between the bodies, we prefer to explain the action by means of the intermediate connexions, rather than admit the notion of direct action at a distance.

Thus when two particles are connected by a straight or curved rod, the action between the particles is always along the line joining them, but we account for this action by means of a system of