Middle of the Nineteenth Century. 225 



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 



(a. ds). 



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 Ampere's theory, 

 another investigator was attempting a still more ambitious 

 project : no less than that of uniting electrodynamics into a 

 coherent whole with electrostatics. 



Wilhelm Weber (6. 1804, d. 1890) was in the earlier part of 

 his scientific career a friend and colleague of Gauss at Gottingen. 

 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 

 1845f introduced certain assumptions regarding the nature of 



* Cf. pp. 212, 272. t Ann. d. Phys. Lxiv (1845), p. 337. 



Q 



