M. Helmholtz on the Theory of Electrodynamics, 535 



and let V denote the potential energy of the remaining forces 

 which act upon the inert masses ; then the equation which, in 

 Weber^s sense, expresses the conservation of the force becomes 



42[(/i„-j»„eJ?^] +P + V-Q=const. 



The sum here occurring, which occupies the place of the vis viva, 

 and which shall be denoted by L, differs from the ordinary form 

 of this expression by the necessarily positive squares of qn being 

 not merely multiplied by the necessarily positive inert masses 

 ^ji, but, instead of the latter, the differences (fin—^npn) entering 

 as coefficients of the squares. These differences, however, 

 may become negative, since fin can at all events be reduced to 

 what even Weber and C. Neumann regarded as an extraordi- 

 narily little inert mass of the electrical quantum e^, while the 

 quantity^,,, a function formed after the manner of potential 

 functions, may proceed from as great electrical masses as we 

 please. If, now, 6'„^m >/>t„, the point Cn would possess a qicasi ne- 

 gative mass. Acceleration of its motion icoukl co7Tespond to a 

 diminution of the vis viva. If the vis viva L consisted of a num- 

 ber of positive and negative terms of this kind, it might con- 

 serve an unchanged final value while its negative and its positive 

 terms alike augmented ad infinitum. 



These relations are represented most simply when only one of 

 the masses fju is supposed to be in motion, and the rest spread 

 over and adherent to a spherical surface surrounding the mass 

 fi (perhaps the surface of an insulator). Then p and P become 

 constants independent of the position of the point iju in the 

 sphere; further, Q=Oj and the equation reduces itself to 



■J (yLt -- ep) 5-^ + V = const. 



If, now, the quantum of the electricity on the sphere is great 

 enough, so that ep >fjL, then g^ and V must increase and diminish 

 together. If fx moves in a direction opposite to the force repre- 

 sented by y, y augments and the velocity q must increase. If on 

 the contrary, /uu moves in the direction of the force, the velocity di- 

 minishes. If jjb moves in a prescribed path against a force which 

 constantly resists it (for example, against friction), its velocity 

 must increase continually and ad infinitum, with which produc- 

 tion of heat ad infinitum would be connected. If in its course 

 the mass impinges again and again continually against a greater 

 inert elastic mass, it will drive this onward, and at each impact 

 increase its own velocity, so as to make the next collision more 

 forcible. This would evidently give Si perpetuum mobile. 



It may here be remarked that, if the linear dimensions of the 

 spherical electric layer be increased ?i-fold, but the density be 

 preserved unaltered, the quantityjo will be augmented to ?z times 



