II. ON THE MATHEMATICAL THEORY OF ELECTRICITY IN EQUILIBRIUM.
I.-ON THE ELEMENTARY LAWS OF STATICAL ELECTRICITY.*[1]
[From Cambridge and Dublin Mathematical Journal, Nov. 1845. Reprinted Philosophical Magazine, 1854, second half-year, with additional Notes of date March 1854.]
25. The elementary laws which regulate the distribution of electricity on conducting bodies have been determined by means of direct experiments, by Coulomb, and in the form he has given them, which is independent of any hypothesis,[2] they have long been considered as rigorously established. The problem of the distribution of electricity in equilibrium on a conductor of any form was thus brought within the province of mathematical analysis; but the solution, even in the simplest cases, presented so much difficulty that Coulomb, after having investigated it experimentally for bodies of various forms, could only compare his measurements with the results of his theory by very rude processes of approximation. Without, however, giving rigorous solutions in particular cases, he examined the general problem with great care, and left nothing indefinite in the conditions to be satisfied, so that it was entirely by analytical difficulties that he was stopped. As an example of the
- ↑ This paper is a translation (with considerable additions) of one which appeared in Liouville's Journal de Mathématiques, 1845, p. 209.
- ↑ Coulomb has expressed his theory in such a manner that it can only be attacked in the way of proving his experimental results to be inaccurate. This is shown in the following remarkable passage in his sixth memoir, which follows a short discussion of some of the physical ideas then commonly held with reference to electricity. "Je préviens pour mettre la théorie qui va suivre à l'abri de toute dispute systématique, que dans la supposition des deuxfluides électriques, je n'ai d'autre intention que de présenter avec le moins d'élémens possible, les resultats du calcul et de l'expérience, et non d'indiquer les véritables causes de l'électricité. Je renverrai, à la fin de mon travail sur l'électricité, l'examen des principaux systèmes auxquels les phénomènes électriques ont donné naissance."-Histoire de l'Académie, 1788, p. 673.
