Among the terms proportional to the squares of the velocities, how distinguish those which come from _T_ or from _U_? Consequently, how distinguish the two parts of energy? But still more; how define energy itself? We no longer have any reason to take as definition _T_ + _U_ rather than any other function of _T_ + _U_, when the property which characterized _T_ + _U_ has disappeared, that, namely, of being the sum of two terms of a particular form. But this is not all; it is necessary to take account, not only of mechanical energy properly so called, but of the other forms of energy, heat, chemical energy, electric energy, etc. The principle of the conservation of energy should be written: _T_ + _U_ + _Q_ = const. where _T_ would represent the sensible kinetic energy, _U_ the potential energy of position, depending only on the position of the bodies, _Q_ the internal molecular energy, under the thermal, chemic or electric form. All would go well if these three terms were absolutely distinct, if _T_ were proportional to the square of the velocities, _U_ independent of these velocities and of the state of the bodies, _Q_ independent of the velocities and of the positions of the bodies and dependent only on their internal state. The expression for the energy could be resolved only in one single way into three terms of this form. But this is not the case; consider electrified bodies; the electrostatic energy due to their mutual action will evidently depend upon their charge, that is to say, on their state; but it will equally depend upon their position. If these bodies are in motion, they will act one upon another electrodynamically and the electrodynamic energy will depend not only upon their state and their position, but upon their velocities. We therefore no longer have any means of making the separation of the terms which should make part of _T_, of _U_ and of _Q_, and of separating the three parts of energy. If (_T_ + _U_ + _Q_) is constant so is any function [phi](_T_ + _U_ + _Q_). If _T_ + _U_ + _Q_ were of the particular form I have above considered, no ambiguity would result; among the functions [phi](_T_ + _U_ + _Q_) which remain constant, there would only be one of this particular form, and that I should convene to call energy. But as I have said, this is not rigorously the case; among the functions which remain constant, there is none which can be put rigorously under this particular form; hence, how choose among them the one which should be called energy? We no longer have anything to guide us in our choice.