As the results to which we have now arrived are of continual use in the developement and connec tion of electrical phenomena, it is necessary to re duce them to a kind of theorem, which we shall enunciate in the following manner : When a conducting and insulated body B, in its natural state, is placed near another body A, elec trified and insulated, the electricity distributed over the surface of A acts, by influence, on the two com bined electricities of B, decomposes a quantity pro portional to the intensity of its action, and resolves it into its two constituent principles. Of the two electricities thus liberated, it repels that of the same and attracts that of a different name with itself. The first diffuses itself over that part of the surface of B which is farthest from A, and the second over that which is nearest.' Both being now at liberty, they act in their turn on the free, and even on the com bined electricities of A, which, by this re-action, are partly decomposed, and, if A is also a conductor, are separated. This new separation produces a new de composition of the combined electricity of B, and the same process goes on until the quantities of each principle, liberated upon the two bodies, attain an equilibrium, by a balance of all the attractive and repulsive forces which they exert' on one another, in consequence of the similar or contrary nature of each.
Having thus discovered, in general, the attractive and repulsive properties belonging to the two elec tricities, the vitreous and the resinous,—having dis. covered their natural state of combination in bodies, —their separation by the influence of a body at a distance, and the general consequences which result from these new properties, we must, according to the philosophical method now adopted in the scien ces, endeavour to submit them to calculation; so as to ascertain exactly the detail of the facts, and to anticipate, for example, in regard to each of the electrified bodies which we cause mutually to act on one another, what will be, on any point of its surface, the quantity and the nature of the electri city.
But as we have found that the effects of these mutual influences, such as we have observed them, arise from actions between the electrical principles themselves, it is easy to conceive that We cannot ar. rive at their cause without determining the nature and the mode of action of these principles; or, what is the same thing to us, imagining, according to the phenomena observed, some calculable mode of ae, tion which will represent exactly the phenomena, and which can be verified, if not immediately as to its physical existence, at least indirectly, but with certainty, in its conwquences.
But if we consider the extreme facility with which the two electricities, the vitreous and the resinous, diffuse themselves in conducting bodies, and advance towards their surfaces where they are retained by the pressure of the air; if we consider the perfect mobility with which these two principles approach and recede from each other, unite themselves, or separate, without losing any of their original pro perties ; it will be obvious, that the most probable idea we can obtain of their nature, is to regard them as fluids of perfect fluidity, whose particles are en dowed with attractive and repulsive powers, and which arrange themselves in the bodies where they can move with liberty, in such a manner as to be in equilibrio, by virtue of all the interior and exterior forces which act upon them.
It is easy to see that each of these fluids must pos. sees in itself a cause of repulsion, which tends to se parate its particles from each other. For, if we sup. pose a certain quantity of vitreous or of resinous electricity, introduced into a sphere of metal where its motions are free, we know that it will diffuse it self entirely at the surface, where it will form a stra• turn of a very small thickness. If we augment the diameter of the sphere, the electrical stratum will always recede more and more from its centre, dimi nishing at the same time its thickness. If we at last withdraw altogether the pressure of the air, the elec tricity will be completely dissipated. These effects indicate with certainty a repulsive action exerted between the electrical particles of the same nature, and all the phenomena in which the combined elec tricities are separated from each other by influence at a distance, confirm completely this result; and at the same time also demonstrate the existence of a re ciprocal attraction between the electricities of a dif ferent nature.
We see also from these phenomena that the at tractions and repulsions become weaker in propor tion as the distance increases; but according to what law ? Among all those which can be tried, there is one which represents and reproduces completely all the phenomena; it is that GC the inverse ratio of the squares of the distances. Adopting this law, then, the constitutions of the two electrical principles will be comprised in the following enunciation : Each of the two electrical principles is a fluid, whose particles, perfectly mutually repel each other, and at tract those of the otherrI pnciple, with forces recipro cally as the square of the distance. Also at equal distances the attractive power is equal to the repulsive. This equality is necessary in order that in a body, in the natural state, the two combined electricities may not exert any action at a distance.