Middle of the Nineteenth Century. 231 



the conductor is one to which, for various reasons which will 

 appear later, objection may be taken ; but it is an integral part 

 of Weber's theory, and cannot be excised from it. In fact, 

 if this condition were not satisfied, and if the law of force were 

 Weber's, electric currents would exert forces on electrostatic 

 charges at rest*; as may be seen by the following example. 

 Let a current flow in a closed circuit formed by arcs of two 

 concentric circles and the portions of the radii connecting their 

 extremities; then, if Weber's law were true, and if only one 

 kind of electricity were in motion, the current would evidently 

 exert an electrostatic force on a charge placed at the centre of 

 the circles. It has been shown,f indeed, that the assumption 

 of opposite electricities moving with equal and opposite veloci- 

 ties in a circuit is almost inevitable in any theory of the type 

 of Weber's, so long as the mutual action of two charges is 

 assumed to depend only on their relative (as opposed to their 

 absolute) motion. 



The law of Weber is not the only one of its kind; an alterna- 

 tive to it was suggested by Bernhard Eiemann (b. 1826, d. 1866), 

 in a course of lectures which were delivered^ at Gottingen 

 in 1861, and which were published after his death by 

 K. Hattendorff. Kiemann proposed as the electrokinetic 

 energy of two electrons e (x, y, z) and e\x f , y\ z') the expression 



this differs from the corresponding expression given by Weber 

 only in that the relative velocity of the two electrons is 

 substituted in place of the component of this velocity along 

 the radius vector. Eventually, as will be seen later, the laws 



* This remark was first made by Clausius, Journal fur Math. Ixxxii (1877), 

 p. 86: the simple proof given above is due to Grassmann, Journal fur Math. 

 Ixxxiii (1877), p. 57. 



t H. Lorberg, Journal fur Math. Ixxxiv (1878), p. 305. 



J Schicere, Elektricitat und Magnetismus, nach den Vorlesungen von B. Riemann : 

 Hannover, 1875, p. 326. Another alternative to Weber's law had been discovered 

 by Gauss so far back as 1835, but was not published until after his death: cf. 

 Gauss' Werke, v, p. 616. 



