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, Sylvester, Maxwell, Clifford, and J. J. Thomson are a group of great men who were Second Wranglers at Cambridge. At the age of twenty-two W. Thomson was elected professor of natural philosophy in the University of Glasgow, a position which he has held ever since. For his brilliant mathematical and physical achievements he was knighted, and in 1892 was made Lord Kelvin. His researches on the theory of potential are epoch-making. What is called "Dirichlet's principle" was discovered by him in 1848, somewhat earlier than by Dirichlet. We owe to Sir William Thomson new synthetical methods of great elegance, viz. the theory of electric images and the method of electric inversion founded thereon. By them he determined the distribution of electricity on a bowl, a problem previously considered insolvable. The distribution of static electricity on conductors had been studied before this mainly by Poisson and Plana. In 1845 F. E. Neumann of Königsberg developed from the experimental laws of Lenz the mathematical theory of magneto-electric induction. In 1855 W. Thomson predicted by mathematical analysis that the discharge of a Leyden jar through a linear conductor would in certain cases consist of a series of decaying oscillations. This was first established experimentally by Joseph Henry of Washington. William Thomson worked out the electro-static induction in submarine cables. The subject of the screening effect against induction, due to sheets of different metals, was worked out mathematically by Horace Lamb and also by Charles Niven. W. Weber's chief researches were on electrodynamics. Helmholtz in 1851 gave the mathematical theory of the course of induced currents in various cases. Gustav Robert Kirchhoff[97] (1824–1887) investigated the distribution of a current over a flat conductor, and also the strength of current in each branch of a network of linear conductors.

The entire subject of electro-magnetism was revolutionised