The values of the distances at any instant depend upon their initial values, upon those of their first derivatives and also upon something else. What is this _something else_? If we will not admit that this may be simply one of the second derivatives, we have only the choice of hypotheses. Either it may be supposed, as is ordinarily done, that this something else is the absolute orientation of the universe in space, or the rapidity with which this orientation varies; and this supposition may be correct; it is certainly the most convenient solution for geometry; it is not the most satisfactory for the philosopher, because this orientation does not exist. Or it may be supposed that this something else is the position or the velocity of some invisible body; this has been done by certain persons who have even called it the body alpha, although we are doomed never to know anything of this body but its name. This is an artifice entirely analogous to that of which I spoke at the end of the paragraph devoted to my reflections on the principle of inertia. But, after all, the difficulty is artificial. Provided the future indications of our instruments can depend only on the indications they have given us or would have given us formerly, this is all that is necessary. Now as to this we may rest easy. CHAPTER VIII ENERGY AND THERMODYNAMICS ENERGETICS.--The difficulties inherent in the classic mechanics have led certain minds to prefer a new system they call _energetics_. Energetics took its rise as an outcome of the discovery of the principle of the conservation of energy. Helmholtz gave it its final form. It begins by defining two quantities which play the fundamental rôle in this theory. They are _kinetic energy_, or _vis viva_, and _potential energy_. All the changes which bodies in nature can undergo are regulated by two experimental laws: 1º The sum of kinetic energy and potential energy is constant. This is the principle of the conservation of energy. 2º If a system of bodies is at _A_ at the time t_{0} and at _B_ at the time t_{1}, it always goes from the first situation to the second in such a way that the _mean_ value of the difference between the two sorts of energy, in the interval of time which separates the two epochs t_{0} and t_{1}, may be as small as possible. This is Hamilton's principle, which is one of the forms of the principle of least action. The energetic theory has the following advantages over the classic theory: 1º It is less incomplete; that is to say, Hamilton's principle and that of the conservation of energy teach us more than the fundamental principles of the classic theory, and exclude certain motions not realized in nature and which would be compatible with the classic theory: 2º It saves us the hypothesis of atoms, which it was almost impossible to avoid with the classic theory. But it raises in its turn new difficulties: