Forty years have passed since the mechanical explanation of the universe reached its definite and perfect form. It dominates physics under the name of the _theory of kinetic energy_. The minds of men in our own time are so strongly impregnated with this idea that most scientists of ordinary culture get no glimpse of the world of phenomena but by means of this conception. And yet it is only an hypothesis. But it is so simple, so intuitive, and appears to be so thoroughly verified by experiment, that we have ceased to recognize its arbitrary and unnecessarily contingent character. Many physicists from this standpoint consider the kinetic theory as an imperishable monument. However, as in the case of H. Poincaré, the most eminent physicists and mathematicians are not the dupes of this system; and without failing to recognize the immense services which it has rendered to science, they are perfectly well aware that it is only a system, and that there may be other systems. Certain among them, such as Ostwald, Mach, and Duhem, believe that the monument is showing signs of decay, and at present the theory is opposed by another theory—namely, the theory of _energy_. The theory of _energy_ is usually considered and presented as a consequence of the kinetic theory; but it is perfectly independent of it, and it is, in fact, without relying on the kinetic theory, without assuming the unity of physical forces, which are combined in molecular mechanics, that we shall expound the general system. This is not the point at issue for the moment. It is not a question of deciding the reality or the merit of this or that mechanical explanation; it is a question of something more general, because upon it depends the _idea of matter_. It is a question of knowing if there are any explanations other than mechanical. The illustrious English physicist, Lord Kelvin, does not seem willing to admit this. “I am never satisfied,” he said, in his _Molecular Mechanics_, “until I have made a mechanical model of the object. If I can make this model, I understand; if I cannot, I do not understand.” This tendency of so vigorous a mind to be content only with mechanical explanations, has been that of the majority of scientific men up to the present day, and from it has arisen the scientific idea of matter. What is matter, in fact, to the student of mechanics? It is mass. All mechanics is constructed of masses and forces. Laplace said: “The mass of a body is the sum of its material points.” To Poisson, mass is the quantity of matter of which a body is composed. Matter is therefore confused with mass. Now, mass is the characteristic of the motion of a body under the action of a given force; it defines obedience or resistance to the causes of motion; it is the _mechanical parameter_; it is the co-efficient proper to every mobile body; it is the first _invariant_ of which a conception has been established by science.