History of the inductive sciences, from the earliest to the present time

by William Whewell

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 recently[36] 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.

[36] Phil. Trans. 1834, p. 2.

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.

[37] Neque diffiteor cum ipsa se mihi offerret . . . . me ad ipsam quodammodo exhorruisse. Tentamen Theor. Elect. p. 39.

Very recently, M. Mosotti[38] 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.

[38] Sur les Forces qui régissent la Constitution Intérieure des Corps. Turin. 1836.

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.