290 HERMANN VON HELMHOLTZ 



of Electrodynamics, Part III : Electrodynamic Forces in 

 Moving Conductors.' His further ' Criticism of Electrody- 

 namics/ published in 1874 in Poggendorff's Annalen, is directed 

 solely against the objections raised to his mathematical theory 

 of electrodynamics. 



The Potential Law of F. E. Neumann (which Helmholtz in 

 a letter to Schering calls one of the most brilliant achievements 

 of mathematical physics) was designed and well fitted to 

 comprise the whole department of electrodynamic motive 

 forces included under Ampere's Law, as well as the electro- 

 dynamic induction produced by the movement of conductors, 

 and alteration of current intensity, under a single and very 

 simple law. This, however, according to Neumann's proof, 

 could only, in the case of closed currents, coincide with 

 Ampere's law (which was actually correct in this instance), on 

 the assumption that the two conductors in question were 

 moved without alteration of form or magnitude. In order 

 to express the law of the electrodynamic motive forces for 

 conductors of three dimensions, Helmholtz analyses the latter 

 into conducting threads, which everywhere follow the direction 

 of the lines of current present, so that no electricity can escape 

 from one of the threads to its neighbours. Now since Ampere's 

 law only recognizes forces which act from current-element to 

 current-element, Helmholtz was able to show that when in 

 applying the law of potential other forces are taken into 

 account which act between the ends of the current and the 

 current-elements, and between the current-ends of the two 

 conductors themselves, then, from the potential set up by the 

 current-elements, motive forces may be derived for two open 

 parts of the current, which, for these portions of the current, 

 can be brought into the form which Ampere has given them. 

 If, as in the motion of the so-called rotation apparatus, points 

 of slip make their appearance, Helmholtz regards them as 

 current-ends, and in his opinion the solution in these cases 

 is found without difficulty, if we suppose that the discontinuous 

 displacement which is theoretically assumed as the limiting 

 case at the point of slip is in reality only the limit of what is 

 physically speaking a perpetual continuous displacement. 



In Part III of the Theory of Electrodynamics, as above, 

 Helmholtz not only gives a full account of these results, but 



