The imposing simplicity of Mayer's principle likewise contributes to strengthen our faith. In a law deduced immediately from experiment, like Mariotte's, this simplicity would rather seem to us a reason for distrust; but here this is no longer the case; we see elements, at first sight disparate, arrange themselves in an unexpected order and form a harmonious whole; and we refuse to believe that an unforeseen harmony may be a simple effect of chance. It seems that our conquest is the dearer to us the more effort it has cost us, or that we are the surer of having wrested her true secret from nature the more jealously she has hidden it from us. But those are only little reasons; to establish Mayer's law as an absolute principle, a more profound discussion is necessary. But if this be attempted, it is seen that this absolute principle is not even easy to state. In each particular case it is clearly seen what energy is and at least a provisional definition of it can be given; but it is impossible to find a general definition for it. If we try to enunciate the principle in all its generality and apply it to the universe, we see it vanish, so to speak, and nothing is left but this: _There is something which remains constant_. But has even this any meaning? In the determinist hypothesis, the state of the universe is determined by an extremely great number _n_ of parameters which I shall call x_{1}, x_{2},... x_{_n_}. As soon as the values of these _n_ parameters at any instant are known, their derivatives with respect to the time are likewise known and consequently the values of these same parameters at a preceding or subsequent instant can be calculated. In other words, these _n_ parameters satisfy _n_ differential equations of the first order. These equations admit of _n_ - 1 integrals and consequently there are _n_ - 1 functions of x_{1}, x_{2},... x_{_n_}, which remain constant. _If then we say there is something which remains constant_, we only utter a tautology. We should even be puzzled to say which among all our integrals should retain the name of energy. Besides, Mayer's principle is not understood in this sense when it is applied to a limited system. It is then assumed that _p_ of our parameters vary independently, so that we only have _n_ - _p_ relations, generally linear, between our _n_ parameters and their derivatives. To simplify the enunciation, suppose that the sum of the work of the external forces is null, as well as that of the quantities of heat given off to the outside. Then the signification of our principle will be: _There is a combination of these n - p relations whose first member is an exact differential_; and then this differential vanishing in virtue of our _n_ - _p_ relations, its integral is a constant and this integral is called energy.