If this pressure is everywhere less than the resist ance which the air opposes, the electricity is retained in the vase of air, and cannot escape. But if the pressure, in certain points of. the surface, comes to exceed the resistance of the air, then the vase breaks, and the fluid escapes through the opening. This is what happens towards the extremities of the points, and on the sharp corners of angular bodies. For it can be demonstrated, that at the summit of a cone, for example, the pressure of the electric fluid would become infinite, if the electricity were allowed to accumulate there. At the surface of an elonga ted ellipsoid of revolution, the pressure does not become infinite at any point; but it will be so much the more considerable at the two poles, as the axis which joins them is greater in relation to the diame ter of the equator. According to the theorems already cited, this pressure will be to that which takes place at the equator of the same body, as the ' square of the axis of the poles is to the square of the axis of the equator; so that, if the ellipsoid is very much elongated, the electric pressure may be very feeble at the equator, while at the poles it will surpass the resistance of the air. Hence, also, when we electrify a metallic bar, which has the form of a very long ellipsoid, the electric fluid runs principally towards its two extremities, and escapes by these points, in consequence of its excess of pressure above the resistance of the air which opposes it. In gene ral, the indefinite increase of the electric pressure in certain points of electrified bodies, furnishes a na tural and exact explanation of the i faculty which points possess, of dissipating with rapidity into the non-conducting air the electric fluid with which they are charged.
If the nature of the electrified body were such that the electricity could not move freely in it, the excess of pressure, of which we have been speaking, would exert itself against the particles themselves of the body which envelope the electric stratum; or, in general, against those which, either by their affinity, or by any other mode of resistance, would oppose its dissipation.
Having determined, according to the theory, the manner in which electricity disposes itself in a single conducting body, insulated and unaffected by any external influence, let us pass to the more compli cated case, where several electrified and conducting bodies act mutually on each other; and as it is ne cessary to make choice of bodies whose form renders the phenomena accessible to calculation, let us con eider two spheres of some conducting substance, both electrified and placed in presence of each other at any distance.
The disposition of electricity in these circumstan ces, and in all those where several electrified bodies are submitted to their mutual influence, depends on a general principle, evident in itself, and which has the valuable advantage of reducing all these ques tions to a mathematical condition. The following is its enunciation, which we take from the treatise of M. Poisson.
If several electrified bodies • are placed near each other, and if they arrive at a permanent state of electricity, it is necessary in this state that the re sulting effect of the actions of the electric strata which cover them, upon any point taken in the interior of these bodies, be nothing. For if this resulting force
were not nothing, the combined electricity which i exists at the point in question would be decomposed, and the electrical state would change, contrary to the supposition which we have made of its perm nency.
This principle, translated into the language of the calculus, furnishes immediately as many equations as we consider bodies, and as there are unknown quantities in the problem. But their resolution often surpasses the powers of analysis. M. Poisson, how ever, who has so happily discovered the general key of this theory, has at last surmounted all the analy tical difficulties, for the case of two spheres placed in contact or near to each other, and primitively charged with any quantities of electricity. The formulae to which he has arrived afford a great number of re sults which can be verified by experiment, and which form so many severe tests of the justness of the theory. Besides the interest which such verification must always present, we will obtain in them the far ther advantage of fixing our ideas with precision on the most delicate phenomena which electricity pro, duces.
Suppose, first, the two spheres in contact, and charged with either electricity, vitreous or vesinons; calculation shows that there is no free electricity at the point of contact. From thence the thickness'of the electric stratum goes on increasing on each of the spheres, according to a law which depends on the relation of their radii, but it attains always its maxi mum on the opposite side, on the line of the two centres. If we separate the two spheres, each of them preserves the same quantity of electricity which it has attained during the contact, and these quan tities have to each other a relation which the calcu lation assigns according to the proportion of the radii.
The verification of these results is effected with the greatest 'facility, by means of the small proof plane, and by the general method of alternate con tacts explained above. In this manner the indica tions of the theory are found to be confirmed by experiment in their minutest details; that is to say, that, on introducing into the theoretical formulae the diameters of khe spheres on which we operate, or only the relations of these diameters, the calculus shows in advance, and as exactly even as the obser vations themselves, the law of the distribution of electricity over the two spheres, as well as the pro portion of its intensity on each. There is no occasion, even for this purpose, of new experiments ; for we may take those which have been already made by Coulomb, and have for a long time been published in the Transactions e Me Academy of Sciences ; and, accordingly, it is with these previous results, whose priority, indeed, gives them all the authenticity of an incontestible fact, that M. Poisson has compared the numbers given by his theory.