Page:Reprint of Papers on Electrostatics and.pdf/38

 II. ON THE MATHEMATICAL THEORY OF ELECTRICITY IN EQUILIBRIUM.

I.-ON THE ELEMENTARY LAWS OF STATICAL ELECTRICITY.*

[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, 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