536 M. Helmholtz on the Theory of Electrodynamics. 



as much ; so that we can make it as great as we please, in spite 

 of continually increasing distance of the acting mass. We have 

 here, therefore, by no means to do with actions at molecular 

 distances, but with distant actions of the Weberian forces. 



The case I previously indicated, in which the mass (ju attains 

 infinite velocity, rests on the fact that this must always happen 

 as often as, under the action of an accelerating force, it arrives 

 at any place where the coefficient [fju—pe] representing the mass 

 becomes =0, because the mass zero receives infinite acceleration 

 from a finite force. Besides, in the present memoir, I have 

 shown that neither is it necessarily at molecular distances that 

 this takes place, nor does it require an infinite initial velocity, if 

 only sufficiently large electrical masses are chosen, and if upon 

 the whole path of the two masses an exterior force acts which 

 impels them towards each other and is powerful enough to over- 

 come their electrostatic repulsion. 



The objections raised by W. Weber against one of the physi- 

 cally impossible consequences which, in my earlier memoir, are 

 deduced from his theory are thus removed. 



In his most recent electrodynamic researches, M. C. Neu- 

 mann has expressed his concurrence in Weber^s objections, and, 

 for his own part, has endeavoured to remove from the theory 

 the deficiencies pointed out by me, in that he has introduced 

 an alteration into Weber^s expression for very small distances. 

 From what has just been said it is evident that such an altera- 

 tion cannot obviate the physical impossibilities mentioned. 



Also, for electric currents, no introduction of molecular pro- 

 cesses, motions, or forces can get rid of the unstable equih- 

 brium, because when the dimensions are increased n-fold and the 

 electric densities unchanged the work-equivalent of the mole- 

 cular processes increases only as n^, but that of the potentials 

 as n^ or n^y according to whether they proceed from surfaces 

 or spaces ; so that the latter, if they represent a quantity of 

 work which is smaller than in the resting equilibrium of elec- 

 tricity, always obtain the preponderance with a sufficient aug- 

 mentation. When everywhere equal quanta of positive and 

 negative electricity move in opposite directions, the quantities 

 Pn vanish, but the electrodynamic potential ( — Q) may become 

 less than zero. That such a distribution of electric densities and 

 currents may occur has been shown in my earlier memoir, quite 

 independently of the differential equations which regulate the 

 course of the currents. 



Given a current-distribution which represents a less quantity 

 of work than that of electric equilibrium, such a flow can only 

 by the application of exterior work be brought to rest, and 

 must otherwise, by withdrawal of work, such as takes place 



