PROFESSOR IN BERLIN 289 



u. angewdt. Math., in 1873, ' On the Theory of Electrodynamics, 

 Part II : Critical/ Helmholtz partially devoted himself to re- 

 futing the objections that had been made to his former work. 

 He points out, in reply to Bertrand, that the expressions for 

 the potential of each pair of current-elements are not ex- 

 pressions of ultimate elementary forces, but refer in each 

 current-element, taking this as a solid body, to one force and 

 to a pair of forces ; the quantity, and to some extent the 

 direction, of these forces depend not merely upon the position 

 of the elements, but also upon the velocity of the electrical 

 currents, so that it should be as legitimate to speak of the 

 potential of two current-elements as of the potential of two 

 magnets. But he endeavoured, above all, to refute the ob- 

 jections of W. Weber to his argument, since even in the highly 

 special case of the motion of two particles of electricity along 

 the line joining them, in accordance with Weber's law, the 

 acceleration may become infinitely great, and at a less distance 

 the co-efficient of the acceleration, corresponding with the 

 mass, becomes negative. He further shows that on the 

 assumption of Weber's law for an electrified particle, which 

 is movable within a hollow sphere covered evenly with elec- 

 tricity, the case may occur in which the co-efficient of accelera- 

 tion becomes negative, thus producing perpetual motion ; and 

 he again points out that the differential equations proposed 

 by Kirchhoif for the motions of electricity on the assumption 

 of Weber's law would lead to an unstable equilibrium of 

 electricity in conductors. 



He then advanced a step farther in his comparison of 

 the different theories and their consequences, and set himself 

 the task of deriving Ampere's forces from the Potential Law 

 of F. E. Neumann. This was suggested to him by Riecke's 

 objection that when the potential of a closed current referred 

 to a current-element is deduced by means of Helmholtz's po- 

 tential expression, it follows that the action of a closed current 

 on the movable part of another current is not, as it must be 

 according to Ampere, perpendicular to the latter. Helmholtz 

 laid his conclusions before the Academy in a short note 

 entitled ' Comparison of the Laws of Ampere and Neumann for 

 Electrodynamic Forces ', on Feb. 6, 1873, while the full account 

 appeared the next year in the //. / Math., ' On the Theory 



