results as if we suppose two fluids; thus, if an electrized body, overcharged with the single fluid, act upon a ball, it drives the electric fluid in the ball to the further side by its repulsion, and then attracts the ball by attracting the matter of the ball more than it repels the fluid which is upon the ball. If we suppose two fluids, the positively electrized body draws the negative fluid to the nearer side of the ball, repels the positive fluid to the opposite side, and attracts the ball on the whole, because the attracted fluid is nearer than that which is repelled. The verification of either of these hypotheses, and the determination of their details, depended necessarily upon experiment and calculation. It was under the hypothesis of a single fluid that this trial was first properly made. Epinus of Petersburg published, in 1759, his Tentamen Theoria Electricitatis et Magnetismi; in which he traces mathematically the consequences of the hypothesis of an electric fluid, attracting all other matter, but repelling itself; the law of force of this repulsion and attraction he did not pretend to assign precisely, confining himself to the supposition that the mutual force of the particles increases as the distance decreases. But it was found, that in order to make this theory tenable, an additional supposition was required, namely, that the particles of bodies repel each other as much as they attract the electric fluid. For if two bodies, A and B, be in their natural electrical condition, they neither attract nor repel each other. Now, in this case, the fluid in A attracts the matter in B and repels the fluid in B with equal energy, and thus no tendency to motion results from the fluid in A; and if we further suppose that the matter in A attracts the fluid in B and repels the matter in B with equal energy, we have the resulting mutual inactivity of the two bodies explained; but without the latter supposition, there would be a mutual attraction: or we may put the truth more simply thus; two negatively electrized bodies repel each other; if negative electrization were merely the abstraction of the fluid

5 Robison, vol. iv. p. 18.

which is the repulsive element, this result could not follow except there were a repulsion in the bodies themselves, independent of the fluid. And thus Epinus found himself compelled to assume this mutual repulsion of material particles; he had, in fact, the alternative of this supposition, or that of two fluids, to choose between, for the mathematical results of both hypotheses are the same. Wilcke, a Swede,

who had at first asserted and worked out the Æpinian theory in its original form, afterwards inclined to the opinion of Symmer; and Coulomb, when, at a later period, he confirmed the theory by his experiments and determined the law of force, did not hesitate to prefer the theory of two fluids, because,' he says, 'it appears to me contradictory to admit at the same time, in the particles of bodies, an attractive force in the inverse ratio of the squares of the distances, which is demonstrated by universal gravitation, and a repulsive force in the same inverse ratio of the squares of the distances; a force which would necessarily be infinitely great relatively to the action of gravitation.' We may add, that by forcing us upon this doctrine of the universal repulsion of matter, the theory of a single fluid seems quite to lose that superiority in the way of simplicity which had originally been its principal recommendation.

The mathematical results of the supposition of Epinus, which are, as Coulomb observes, the same as of that of the two fluids, were traced by the author himself, in the work referred to, and shown to agree, in a great number of cases, with the observed facts of electrical induction, attraction, and repulsion. Apparently this work did not make its way very rapidly through Europe; for in 1771, Henry Cavendish stated8 the same hypothesis in a paper read before the Royal Society; which he prefaces by saying, 'Since I first wrote the following paper, I find that this way of accounting for the phenomena of electricity is not new.

6 Mém. Ac. P. 1788, p. 671.

7 Ac. P. 1788, p. 672.

8 Phil. Trans. 1771, vol. lxi,

Epinus, in his Tentamen Theoria Electricitatis et Magnetismi, has made use of the same or nearly the same hypothesis that I have; and the conclusions he draws from it agree nearly with mine as far as he goes.'

The confirmation of the theory was, of course, to be found in the agreement of its results with experiment; and in particular, in the facts of electrical induction, attraction, and repulsion, which suggested the theory. Epinus showed that such a confirmation appeared in a number of the most obvious cases; and to these, Cavendish added others, which, though not obvious, were of such a nature that the calculations, in general difficult or impossible, could in these instances be easily performed; as, for example, cases in which there are plates or globes at the two extremities of a long wire. In all these cases of electrical action, the theory was justified. But in order to give it full confirmation, it was to be considered whether any other facts, not immediately assumed in the foundation of the theory, were explained by it; a circumstance which, as we have seen, gave the final stamp of truth to the theories of astronomy and optics. Now we appear to have such confirmation, in the effect of points, and in the phenomena of the electrical discharge. The theory of neither of these was fully understood by Cavendish, but he made an approach to the true view of them. If one part of a conducting body be a sphere of small radius, the electric fluid upon the surface of this sphere will, it appears by calculation, be more dense, and tend to escape more energetically, in proportion as the radius of the sphere is smaller; and, therefore, if we consider a point as part of the surface of a sphere of imperceptible radius, it follows from the theory that the effort of the fluid to escape at that place will be enormous; so that it may easily be supposed to overcome the resisting causes. And the discharge may be explained in nearly the same manner; for when a conductor is brought nearer and nearer to an electrized body, the opposite electricity is more and more accumulated by attraction on the side next to the electrized body; its tension becomes greater by the increase of its

quantity and the diminution of the distance, and at last it is too strong to be contained, and leaps out in the form of a spark.

The light, sound, and mechanical effects produced by the electric discharge, made the electric fluid to be. not merely considered as a mathematical hypothesis, useful for reducing phenomena to formulæ (as for a long time the magnetic fluid was), but caused it to be at once and universally accepted as a physical reality, of which we learn the existence by the common use of the senses, and of which measures and calculations are only wanted to teach us the laws.

The applications of the theory of electricity which I have principally considered above, are those which belong to conductors, in which the electric fluid is perfectly moveable, and can take that distribution which the forces require. In non-conducting or electric bodies, the conditions to which the fluid is subject are less easy to determine; but by supposing that the fluid moves with great difficulty among the particles of such bodies, that nevertheless it may be dislodged and accumulated in parts of the surface of such bodies, by friction and other modes of excitement; and that the earth is an inexhaustible reservoir of electric matter,the principal facts of excitation and the like receive a tolerably satisfactory explanation.

The theory of Epinus, however, still required to have the law of action of the particles of the fluid determined. If we were to call to mind how momentous an event in physical astronomy was the determination of the law of the cosmical forces, the inverse square of the distance, and were to suppose the importance and difficulty of the analogous step in this case to be of the same kind, this would be to mistake the condition of science at that time. The leading idea, the conception of the possibility of explaining natural phenomena by means of the action of forces, on rigorously mechanical principles, had already been promulgated by Newton, and was, from the first, seen to be peculiarly applicable to electrical phenomena; so that the very material step of clearly proposing the problem,

often more important than the solution of it, had already been made. Moreover the confirmation of the truth of the assumed cause in the astronomical case depended on taking the right law; but the electrical theory could be confirmed, in a general manner at least, without this restriction. Still it was an important discovery that the law of the inverse square prevailed in these as well as in cosmical attractions.

It was impossible not to conjecture beforehand that it would be so. Cavendish had professed in his calculations not to take the exponent of the inverse power, on which the force depended, to be strictly 2, but to leave it indeterminate between 1 and 3; but in his applications of his results, he obviously inclines to the assumption that it is 2. Experimenters tried to establish this in various ways. Robison, in 1769, had already proved that the law of force is very nearly or exactly the inverse square; and Mayer10 had discovered, but not published, the same result. The clear and satisfactory establishment of this truth is due to Coulomb, and was one of the first steps in his important series of researches on this subject. In his first paper11 in the Memoirs of the Academy for 1785, he proves this law for small globes; in his second Memoir he shows it to be true for globes one and two feet in diameter. His invention of the torsion-balance, which measures very small forces with great certainty and exactness, enabled him to set this question at rest for ever.

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 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

9 Works, iv. p. 68.

10 Biog. Univ. art. Coulomb, by Biot. 11 Mém. A. P. 1785, pp. 569, 578.