Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/245

 which, of course, is a function of the position of the element ds from which r is measured, then the electromotive force induced in any circuit-element ds by any alteration in the currents which give rise to a is

The induction of currents is therefore governed by the vector a; this, which is generally known as the vector-potential, has from Neumann's time onwards played a great part in electrical theory. It may be readily interpreted in terms of Faraday's conceptions; for (a.ds) represents the total number of unit lines of magnetic force which have passed across the line-element ds prior to the instant t. The vector-potential may in fact be regarded as the analytical measure of Faraday's electrotonic state.

While Neumann was endeavouring to comprehend the laws of induced currents in an extended form of Ampère's theory, another investigator was attempting a still more ambitious project: 110 less than that of uniting electrodynamics into a coherent whole with electrostatics.

Wilhelm Weber (b. 1804, d. 1890) was in the earlier part of his scientific career a friend and colleague of Gauss at Göttingen. In 1837, however, he became involved in political trouble. The union of Hanover with the British Empire, which had subsisted since the accession of the Hanoverian dynasty to the British throne, was in that year dissolved by the operation of the Salic law; the Princess Victoria succeeded to the crown of England, and her uncle Ernest-Augustus to that of Hanover. The new king, who was a pronounced reactionary, revoked the free constitution which the Hanoverians had for some time enjoyed; and Weber, who took a prominent part in opposing this action, was deprived of his professorship. From 1843 to 1849, when his principal theoretical researches in electricity were made, he occupied a chair in the University of Leipzig.

The theory of Weber was in its origin closely connected with the work of another Leipzig Professor, Fechner, who in 1845 introduced certain assumptions regarding the nature of