FORCE 691 



their internal state. The expression for the energy could be decom- 

 posed in one way only into three terms of this form. But this is not 

 the case. Let us consider electrified bodies. The electro-static en- 

 ergy due to their mutual action will evidently depend on their charge 

 i. e., on their state; but it will equally depend on their position. 

 If these bodies are in motion, they will act electro-dynamically on one 

 another, and the electro-dynamic energy will depend not only on their 

 state and their position, but on their velocities. We have therefore 

 no means of making the selection of the terms which should form part 

 of T, and U, and Q, and of separating the three parts of the energy. 

 If T+U+Q is constant, the same is true of any function whatever, < 

 (T+U+Q). 



If T+U+Q were of the particular form that I have suggested above, 

 no ambiguity would ensue. Among the functions $ (T+U+Q) which 

 remain constant, there is only one that would be of this particular 

 form, namely the one which I would agree to call energy. But I 

 have said this is not rigorously the case. Among the functions that 

 remain constant there is not one which can rigorously be placed in 

 this particular form. How then can we choose from among them 

 that which should be called energy? We have no longer any guide 

 in our choice. 



Of the principle of the conservation of energy there is nothing left 

 then but an enunciation : There is something which remains con- 

 stant. In this form it, in its turn, is outside the bounds of experi- 

 ment and reduced to a kind of tautology. It is clear that if the world 

 is governed by laws there will be quantities which remain constant. 

 Like Newton's laws, and for an analogous reason, the principle of the 

 conservation of energy being based on experiment, can no longer be 

 invalidated by it. 



This discussion shows that, in passing from the classical system to 

 the energetic, an advance has been made, but it shows, at the same 

 time, that we have not advanced far enough. 



Another objection seems to be still more serious. The principle of 

 least action is applicable to reversible phenomena, but it is by no 

 means satisfactory as far as irreversible phenomena are concerned. 

 Helmholtz attempted to extend it to this class of phenomena, but he 

 did not and could not succeed. So far as this is concerned all has yet 

 to be done. The very enunciation of the principle of least action is 

 objectionable. To move from one point to another, a material mole- 

 cule, acted upon' by no force, but compelled to move on a surface, will 

 take as its path the geodesic line i.e., the shortest path. This mole- 

 cule seems to know the point to which we want to take it, to foresee 

 the time that it will take it to reach it by such a path, and then to 

 know how to choose the most convenient path. The enunciation of 

 the principle presents it to us, so to speak, as a living and free entity. 



