Page:A History of Mathematics (1893).djvu/414

A function of fundamental importance in the mathematical theories of electricity and magnetism is the "potential." It was first used by Lagrange in the determination of gravitational attractions in 1773. Soon after, Laplace gave the celebrated differential equation,

$\scriptstyle {{\frac {\partial ^{2}V}{dx^{2}}}+{\frac {\partial ^{2}V}{dy^{2}}}+{\frac {\partial ^{2}V}{dz^{2}}}=0}$,

which was extended by Poisson by writing $\scriptstyle {-4\pi k}$ in place of zero in the right-hand member of the equation, so that it applies not only to a point external to the attracting mass, but to any point whatever. The first to apply the potential function to other than gravitation problems was George Green (1793–1841). He introduced it into the mathematical theory of electricity and magnetism. Green was a self-educated man who started out as a baker, and at his death was fellow of Caius College, Cambridge. In 1828 he published by subscription at Nottingham a paper entitled Essay on the application of mathematical analysis to the theory of electricity and magnetism. It escaped the notice even of English mathematicians until 1846, when Sir William Thomson had it reprinted in Crelle's Journal, vols. xliv. and xlv. It contained what is now known as "Green's theorem" for the treatment of potential. Meanwhile all of Green's general theorems had been re-discovered by Sir William Thomson, Chasles, Sturm, and Gauss. The term potential function is due to Green. Hamilton used the word force-function, while Gauss, who about 1840 secured the general adoption of the function, called it simply potential.

Large contributions to electricity and magnetism have been made by William Thomson. He was born in 1824 at Belfast, Ireland, but is of Scotch descent. He and his brother James studied in Glasgow. From there he entered Cambridge, and was graduated as Second Wrangler in 1845. William Thom-