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.

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

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.

The reception of the Coulombian theory (so we most call it, for the Æpinian theory implies one fluid only,) has hitherto not been so general as might have been reasonably expected from its very beautiful accordance with the facts which it contemplates. This has partly been owing to the extreme abstruseness of the mathematical reasoning which it employs, and which put it out of the reach of most experimenters and writers of works of general circulation. The theory of Æpinus was explained by Robison in the Encyclopædia Britannica; the analysis of Poisson has recently been presented to the public in the Encyclopædia Metropolitana, but is of a kind not easily mastered even by most mathematicians. On these accounts probably it is, that in English compilations of science, we find, even to this day, the two theories of one and of two fluids stated as if they were nearly on a par in respect of their experimental evidence. Still we may say that the Coulombian theory is probably assented to by all who have examined it, at least as giving the laws of phenomena; and I have not heard of any denial of it from such a quarter, or of any attempt to show it to be erroneous by detailed and measured experiments. Mr. Snow Harris 210 has recently36 described some important experiments and measures; but his apparatus was of such a kind that the comparison of the results with the Coulombian theory was not easy; and indeed the mathematical problems which Mr. Harris’s combinations offered, require another Poisson for their solution. Still the more obvious results are such as agree with the theory, even in the cases in which their author considered them to be inexplicable. For example, he found that by doubling the quantity of electricity of a conductor, it attracted a body with four times the force; but the body not being insulated, would have its electricity also doubled by induction, and thus the fact was what the theory required.

Though it is thus highly probable that the Coulombian theory of electricity (or the Æpinian, which is mathematically equivalent) will stand as a true representation of the law of the elementary actions, we must yet allow that it has not received that complete evidence, by means of experiments and calculations added to those of its founders, which the precedents of other permanent sciences have led us to look for. The experiments of Coulomb, which he used in the establishment of the theory, were not very numerous, and they were limited to a peculiar form of bodies, namely spheres. In order to form the proper sequel to the promulgation of this theory, to give a full confirmation, and to ensure its general reception, we ought to have experiments more numerous and more varied (such as those of Mr. Harris are) shown to agree in all respects with results calculated from the theory. This would, as we have said, be a task of labor and difficulty; but the person who shall execute it will deserve to be considered as one of the real founders of the true doctrine of electricity. To show that the coincidence between theory and observation, which has already been proved for spherical conductors, obtains also for bodies of other forms, will be a step in electricity analogous to what was done in astronomy, when it was shown that the law of gravitation applied to comets as well as to planets.

But although we consider the views of Æpinus or Coulomb in a very high degree probable as a formal theory, the question is very different when we come to examine them as a physical theory;—that is, when we inquire whether there really is a material electric fluid or fluids.

Question of One or Two Fluids.—In the first place as to the question whether the fluids are one or two;—Coulomb’s introduction of 211 the hypothesis of two fluids has been spoken of as a reform of the theory of Æpinus; it would probably have been more safe to have called his labors an advance in the calculation, and in the comparison of hypothesis with experiment, than to have used language which implied that the question, between the rival hypotheses of one or two fluids, could be treated as settled. For, in reality, if we assume, as Æpinus does, the mutual repulsion of all the particles of matter, in addition to the repulsion of the particles of the electric fluid for one another and their attraction for the particles of matter, the one fluid of Æpinus will give exactly the same results as the two fluids of Coulomb. The mathematical formulæ of Coulomb and of Poisson express the conditions of the one case as well as of the other; the interpretation only being somewhat different. The place of the forces of the resinous fluid is supplied by the excess of the forces ascribed to the matter above the forces of the fluid, in the parts where the electric fluid is deficient.

The obvious argument against this hypothesis is, that we ascribe to the particles of matter a mutual repulsion, in addition to the mutual attraction of universal gravitation, and that this appears incongruous. Accordingly, Æpinus says, that when he was first driven to this proposition it horrified him.37 But we may answer it in this way very satisfactorily:—If we suppose the mutual repulsion of matter to be somewhat less than the mutual attraction of matter and electric fluid, it will follow, as a consequence of the hypothesis, that besides all obvious electrical action, the particles of matter would attract each other with forces varying inversely as the square of the distance. Thus gravitation itself becomes an electrical phenomenon, arising from the residual excess of attraction over repulsion; and the fact which is urged against the hypothesis becomes a confirmation of it. By this consideration the prerogative of simplicity passes over to the side of the hypothesis of one fluid; and the rival view appears to lose at least all its superiority.

Very recently, M. Mosotti38 has calculated the results of the Æpinian theory in a far more complete manner than had previously been performed; using Laplace’s coefficients, as Poisson had done for the 212 Coulombian theory. He finds that, from the supposition of a fluid and of particles of matter exercising such forces as that theory assumes (with the very allowable additional supposition that the particles are small compared with their distances), it follows that the particles would exert a force, repulsive at the smallest distances, a little further on vanishing, afterwards attractive, and at all sensible distances attracting in proportion to the inverse square of the distance. Thus there would be a position of stable equilibrium for the particles at a very small distance from each other, which may be, M. Mosotti suggests, that equilibrium on which their physical structure depends. According to this view, the resistance of bodies to compression and to extension, as well as the phenomena of statical electricity and the mutual gravitation of matter, are accounted for by the same hypothesis of a single fluid or ether. A theory which offers a prospect of such a generalization is worth attention; but a very clear and comprehensive view of the doctrines of several sciences is requisite to prepare us to estimate its value and probable success.

Question of the Material Reality of the Electric Fluid.—At first sight the beautiful accordance of the experiments with calculations founded upon the attractions and repulsions of the two hypothetical fluids, persuade us that the hypotheses must be the real state of things. But we have already learned that we must not trust to such evidence too readily. It is a curious instance of the mutual influence of the histories of two provinces of science, but I think it will be allowed to be just, to say that the discovery of the polarization of heat has done much to shake the theory of the electric fluids as a physical reality. For the doctrine of a material caloric appeared to be proved (from the laws of conduction and radiation) by the same kind of mathematical evidence (the agreement of laws respecting the elementary actions with those of fluids), which we have for the doctrine of material electricity. Yet we now seem to see that heat cannot be matter, since its rays have sides, in a manner in which a stream of particles of matter cannot have sides without inadmissible hypotheses. We see, then, that it will not be contrary to precedent, if our electrical theory, representing with perfect accuracy the laws of the actions, in all their forms, simple and complex, should yet be fallacious as a view of the cause of the actions.

Any true view of electricity must include, or at least be consistent with, the other classes of the phenomena, as well as this statical electrical action; such as the conditions of excitation and retention of 213 electricity; to which we may add, the connexion of electricity with magnetism and with chemistry;—a vast field, as yet dimly seen. Now, even with regard to the simplest of these questions, the cause of the retention of electricity at the surface of bodies, it appears to be impossible to maintain Coulomb’s opinion, that this is effected by the resistance of air to the passage of electricity. The other questions are such as Coulomb did not attempt to touch; they refer, indeed, principally to laws not suspected at his time. How wide and profound a theory must be which deals worthily with these, we shall obtain some indications in the succeeding part of our history.

But it may be said on the other side, that we have the evidence of our senses for the reality of an electric fluid;—we see it in the spark; we hear it in the explosion; we feel it in the shock; and it produces the effects of mechanical violence, piercing and tearing the bodies through which it passes. And those who are disposed to assert a real fluid on such grounds, may appear to be justified in doing so, by one of Newton’s “Rules of Philosophizing,” in which he directs the philosopher to assume, in his theories, “causes which are true.” The usual interpretation of a “vera causa,” has been, that it implies causes which, independently of theoretical calculations, are known to exist by their mechanical effects; as gravity was familiarly known to exist on the earth, before it was extended to the heavens. The electric fluid might seem to be such a vera causa.

To this I should venture to reply, that this reasoning shows how delusive the Newtonian rule, so interpreted, may be. For a moment’s consideration will satisfy us that none of the circumstances, above adduced, can really prove material currents, rather than vibrations, or other modes of agency. The spark and shock are quite insufficient to supply such a proof. Sound is vibrations,—light is vibrations; vibrations may affect our nerves, and may rend a body, as when glasses are broken by sounds. Therefore all these supposed indications of the reality of the electric fluid are utterly fallacious. In truth, this mode of applying Newton’s rule consists in elevating our first rude and unscientific impressions into a supremacy over the results of calculation, generalization, and systematic induction.39

214 Thus our conclusion with regard to this subject is, that if we wish to form a stable physical theory of electricity, we must take into account not only the laws of statical electricity, which we have been chiefly considering, but the laws of other kinds of agency, different from the electric, yet connected with it. For the electricity of which we have hitherto spoken, and which is commonly excited by friction, is identical with galvanic action, which is a result of chemical combinations, and belongs to chemical philosophy. The connexion of these different kinds of electricity with one another leads us into a new domain; but we must, in the first place, consider their mechanical laws. We now proceed to another branch of the same subject, Magnetism.

~Additional material in the 3rd edition.~