[33] Mém. A. P. 1785, pp. 569, 578.
The law of force being determined for the particles of the electric fluid, it now came to be the business of the experimenter and the [207] mathematician to compare the results of the theory in detail with those of experimental measures. Coulomb undertook both portions of the task. He examined the electricity of portions of bodies by means of a little disk (his tangent plane) which he applied to them and then removed, and which thus acted as a sort of electric taster. His numerical results (the intensity being still measured by the torsion-balance) are the fundamental facts of the theory of the electrical fluid. Without entering into detail, we may observe that he found the electricity to be entirely collected at the surface of conductors (which Beccaria had before shown to be the case), and that he examined and recorded the electric intensity at the surface of globes, cylinders, and other conducting bodies, placed within each other’s influence in various ways.
The mathematical calculation of the distribution of two fluids, all the particles of which attract and repel each other according to the above law, was a problem of no ordinary difficulty; as may easily be imagined, when it is recollected that the attraction and repulsion determine the distribution, and the distribution reciprocally determines the attraction and repulsion. The problem was of the same nature as that of the figure of the earth; and its rigorous solution was beyond the powers of the analysis of Coulomb’s time. He obtained, however, approximate solutions with much ingenuity; for instance, in a case in which it was obvious that the electric fluid would be most accumulated at and near the equator of a certain sphere, he calculated the action of the sphere on two suppositions: first, that the fluid was all collected precisely at the equator; and next, that it was uniformly diffused over the surface; and he then assumed the actual case to be intermediate between these two. By such artifices he was able to show that the results of his experiments and of his calculations gave an agreement sufficiently near to entitle him to consider the theory as established on a solid basis.
Thus, at this period, mathematics was behind experiment; and a problem was proposed, in which theoretical numerical results were wanted for comparison with observation, but could not be accurately obtained; as was the case in astronomy also, till the time of the approximate solution of the Problem of Three Bodies, and the consequent formation of the Tables of the Moon and Planets on the theory of universal gravitation. After some time, electrical theory was relieved from this reproach, mainly in consequence of the progress which astronomy had occasioned in pure mathematics. About 1801, [208] there appeared in the Bulletin des Sciences,[34] an exact solution of the problem of the distribution of electric fluid on a spheroid, obtained by M. Biot, by the application of the peculiar methods which Laplace had invented for the problem of the figure of the planets. And in 1811, M. Poisson applied Laplace’s artifices to the case of two spheres acting upon one another in contact, a case to which many of Coulomb’s experiments were referrible; and the agreement of the results of theory and observation, thus extricated from Coulomb’s numbers, obtained above forty years previously, was very striking and convincing.[35] It followed also from Poisson’s calculations, that when two electrized spheres are brought near each other, the accumulation of the opposite electricities on their nearest points increases without limit as the spheres approach to contact; so that before the contact takes place, the external resistance will be overcome, and a spark will pass.
[34] No. li.
[35] Mém. A. P. 1811.
Though the relations of non-conductors to electricity, and various other circumstances, leave many facts imperfectly explained by the theory, yet we may venture to say that, as a theory which gives the laws of the phenomena, and which determines the distribution of those elementary forces, on the surface of electrized bodies, from which elementary forces (whether arising from the presence of a fluid or not,) the total effects result, the doctrine of Dufay and Coulomb, as developed in the analysis of Poisson, is securely and permanently established. This part of the subject has been called statical electricity. In the establishment of the theory of this branch of science, we must, I conceive, allow to Dufay more merit than is generally ascribed to him; since he saw clearly, and enunciated in a manner which showed that he duly appreciated their capital character, the two chief principles,—the conditions of electrical attraction and repulsion, and the apparent existence of two kinds of electricity. His views of attraction are, indeed, partly expressed in terms of the Cartesian hypothesis of vortices, then prevalent in France; but, at the time when he wrote, these forms of speech indicated scarcely anything besides the power of attraction. Franklin’s real merit as a discoverer was, that he was one of the first who distinctly conceived the electrical charge as a derangement of equilibrium. The great fame which, in his day, he enjoyed, arose from the clearness and spirit with which he narrated his discoveries; from his dealing with electricity in the imposing form of thunder and lightning; and partly, perhaps, from his character as an [209] American and a politician; for he was already, in 1736, engaged in public affairs as clerk to the General Assembly of Pennsylvania, though it was not till a later period of his life that his admirers had the occasion of saying of him
Eripuit cœlis fulmen sceptrumque tyrannis;
Born to control all lawless force, all fierce and baleful sway,
The thunder’s bolt, the tyrant’s rod, alike he wrenched away.
Æpinus and Coulomb were two of the most eminent physical philosophers of the last century, and labored in the way peculiarly required by that generation; whose office it was to examine the results, in particular subjects, of the general conception of attraction and repulsion, as introduced by Newton. The reasonings of the Newtonian period had, in some measure, anticipated all possible theories resembling the electrical doctrine of Æpinus and Coulomb; and, on that account, this doctrine could not be introduced and confirmed in a sudden and striking manner, so as to make a great epoch. Accordingly, Dufay, Symmer, Watson, Franklin, Æpinus and Coulomb, have all a share in the process of induction. With reference to these founders of the theory of electricity, Poisson holds the same place which Laplace holds with reference to Newton.