M, Helmholtz on the Theory of Electrodynamics. 533 



ried out carefully and intelligently, retains its value even if it 

 should only teach that no way exists except the high road. 



It was through Weber's hypothesis that a question of the 

 highest significance for the principles of natural science was for 

 the lirst time tested in the problems of facts, viz. whether ele- 

 mentary forces, incapable of further analysis, must be assumed 

 dependent not merely on the position, but also on the motion of 

 the acting points. In my work ' On the Conservation of Force,'' 

 I had stated that forces which depend only on the distance and 

 the velocities, and therefore only on the coordinates of the points, 

 and on their first differential quotient, must necessarily infringe 

 the universal natural law of the conservation of energy, which 

 law proves everywhere true also in electrodynamic phenomena. 

 At that time, however, I had not considered this still more com- 

 plicated case set up by the Weberian law, in which the forces 

 depend on the coordinates and on the first and second differen- 

 tial quotients ; and this case is certainly compatible with a some- 

 what extended form of the law of the conservation of energy. If 

 we, as has always hitherto been done, name vis viva or actual 

 energy the sum of the moved inert masses multiplied each by 

 half the square of its velocity, then, in the usual form of the law, 

 the quantity which I have called quantity of tensio7i-force, and 

 the English physicists potential energy^ is a function of the coor- 

 dinates of the moved points only ; and the law of the conserva- 

 tion of energy afiirms that the sum of the actual and potential 

 energy remams constant in every motion of a mass-system not 

 influenced from without. 



If, however, under the action of external forces a self-repeating 

 cyclical process takes place, at the end of which all the points 

 of the system have exactly the same position, and the whole the 

 same vis viva, as at the beginning, the sum of the work received 

 from without and the work given out must be equal to zero, so 

 that by no repetition of the process can work be permanently 

 gained or destroyed. If the former were the case, there would be 

 possible a perpetually continuous gain of work without a pro- 

 gressive alteration of the mass-system, and a perpetuum mobile 

 might be constructed. 



Weber's extension of the law of energy makes also the value 

 of the potential energy a function not merely of the position, but 

 also of the velocities of the mass-points. Under this assumption 

 also, by no cyclical process which brings back not merely all the 

 masses of the system to their initial positions, but also each one 

 to its initial velocity, can more work be given out than is re- 

 ceived from without, because those quantities of actual and po- 

 tential energy which constitute the measure of the work are the 

 same at the end of every such cyclical process as at the beginning. 



