This supposes only that the body and the balls of the balance are perfectly insulated, and lose none of their electricity while the experiments last. This constancy can never be made to hold with rigour, but we can correct its effect in a very simple man ner. For this purpose, compare all the points al, sr, of the body with a single point, which we shall denote by M. To compare the state of w, begin by touching M with the proof plane, and determine by means of the torsion balance, the intensity of the re pulsive force. Then, having deprived the fixed ball of the electricity which had been communicated to it in this experiment, touch sr with the proof plane, and determine, in like manner, the repulsive force which results. Observe the time that elapses be tween these two comparisons, and suppose, for ex ample, that it is a minute. In a minute after the se cond experiment, try again the state of M, and take the mean of the two values of the repulsive force, which this point will have furnished. The second will be weaker than if M and in had been both tried at the same time; but the first will be stronger ; and if the waste is very slow, as the precautions we have indicated suppose it to be, the arithmetical mean be tween the two results will be the same that would' have been obtained at the intermediate instant, that is to say, when the observation was made upon the point w. This corrective process, so simple and so exact, was imagined and employed by Coulomb, who, in general, has left but little to be added as to the use of his ingenious The method of which we have explained, may be employed to discover the disposi tion of electricity, not only at the surface of bodies, but even in their interior. For this purpose, it is sufficient to pierce in the body a small canal, ter minating on its surface, and to plunge the proof plane to the bottom of this canal, when the body is electrified and insulated. In this manner the re markable result has been obtained, that whatever be the external figure and substance of the body, pro vided it be a conductor, the electricity will remain nowhere in its interior. It will confine itaelf entire ly to its surface, where it will form a stratum infi nitely thin; and this fact, demonstrated by Coulomb, forms another capital basis for the theory.
In regard to the distribution on the surface, it de pends on the form of the body. In spheres, for ex ample, the electricity is distributed in a spherical stra tum of a constant thickness. On an ellipsoid of re volution, the thickness is variable. The exterior sur face of the stratum is that of the body itself, and the quantities of electricity at the extremities of the greater axis are proportional to its length. Lengthen, then, considerably, the ellipsoid, and the thickness of the stratum will augment at the extre mities of its greater axis in the same proportion. If the resulting force of repulsion is then sufficiently powerful to overcome the resistance which the am bient air presents to it, the electricity will escape by the points; and this gives the reason that it escapes at the corners of all angular bodies. in general, what ever be the exterior form of the electrified body, this form constitutes the exterior surface of the elec trical stratum. As to the interior surface, it always differs infinitely little from the first. But its deter.
mination can only be expressed by analytical condi tions, deduced from theory, and which experiment demonstrates to be conformable to the truth.
The method of alternate contacts serves also to measure another phenomenon of capital importance. This is the developement of electricity in conduct ing bodies by the inluence at a distance, of bodies already electrified. a body A, for example, which we shall suppose, for greater simplicity, to be spherical, has been electrified and insulated, if we then bring within a certain distance of it a body B, a conductor of electricity, and equally well insulated, but not previously electrified ; this latter, as it ap proaches the other, begins to give signs of electrici ty ; it ceases, however, to do so when we remove it again to a great distance, and it recovers this virtue, or loses it, according as we expose it to, or with draw it from, the influence of the body already elec trified. The philosophers who first discovered this
fact supposed, in order to explain it, that every elec trified body sent forth electrical emanations, which spread around it like an atmosphere, and electrified every conducting body which one might plunge in. to it. But as this effect is produced even through bodies such as glass, for example, which do not al low the electricity to pass through their substance, it is evident, that, if we wish not to go beyond the facts, we ought not to view this but as a certain influence exerted at a distance, like what is ob served in the celestial attraction, and in the mag netic attractions and repulsions. Now, to study the effects and the laws of this influence, we must place the conducting and insulated body B, be. fore the electrified body A, and so near it as to give evident signs of electricity; then touch different points of its surface with the proof plane, and study with the electric balance the nature and the quanti ty of the electricity which is developed in each of them. In making this experiment we find the following result: The electricity developed in B is not every where of the same nature; it is similar to that of A in the portion of B which is most dis tant from A, and different in that which is nearest. if A, for example, is charged with vitreous electri city, the anterior part of B, that towards A, is in the resinous, the posterior, in the vitreous state ; and between these two extremes each of the two elec tricities extends in a certain zone, which may be de termined by the proof plane. But in all cases the to tal quantities of the different electricities distributed over these zones have the remarkable property of being exactly equal, so that, if left to themselves, they would neutralize each other's effect. This supposes that B, before being submitted to the in fluence of A, was in the natural state; but if it has already received a certain quantity of electricity, we then find that the sums of the vitreous And re sinous electricities which itsee under the in fluence of A, do not differ other but by this primitive quantity ; and hence we re-obtain it entire when we withdraw B from the influence of A, and deliver it to its natural state of electrical equilibrium. In every case, however, as it is ral to expect, this constancy only holds when we suppose the body B to lose none of its primitive or acquired electricity, either by the contact of the air, or the imperfection of the insulating supports. It is understood, therefore, that we correct the effect of these two sources of waste, by the laws already men.. tioned, which are determined for each of them by experiment. With the same condition we may study the electricity of A by the proof plane, either when it is abandoned to itself, or when it acts on B; and in this manner, we find that this action takes away from it absolutely nothing of its primitive electricity ; i but that when B is near A, and influenced by it, A is also influenced in its turn, so that the' electricity we have given it is distributed in a different manner ; and if the distance of B is small, or the reciprocal action energetic, the electricity ceases even to be of the same nature over all the surface of A. The part nearest to B takes the contrary electricity to that which the anterior part of B possesses, and the more distant takes the opposite. word, every thing here.is reciprocal, in regard to the two bodies, and the effects are only in proportion to the differ ence of their form, and of the quantities of external electricity which they primitively possessed.