The last part of energetics must be consecrated to the study of the general principles of this science. These principles are two in number, the principle of the _conservation of energy_, or Mayer’s principle, and the principle of the transformation of energy, or Carnot’s principle. The doctrine of energy thus reduces to two fundamental laws the multitude of laws, often known as “general,” to which natural science is subject. § 7. THE PRINCIPLE OF THE CONSERVATION OF ENERGY. In all that precedes, the principle of conservation has intervened at every step. In fact, the very idea of energy is connected with the existence of this principle. We first discover the idea in the work of the philosophical mathematicians who established the foundations of mechanics:—Newton, Leibniz, d’Alembert, and Helmholtz; or of inductive physicists such as Lord Kelvin. Its experimental proof, sketched by Marc Seguin and R. Mayer, is due to Colding and Joule. _It is Independent of the Kinetic Theory._—Mayer’s law states that energy is indestructible; that all phenomenality is nothing but a transformation of energy from one form to another, and that this transformation takes place either at equal values, or rather, at a certain rate of equivalence. This is what takes place when thermal energy is transformed into mechanical energy (equivalent 425). This rate of equivalence is fixed by the researches of physicists for each category of energy. It will be noticed that this law and this theory of energy, which is always presented by authors of elementary books as a consequence of the kinetic theory, is quite independent of it. In the preceding lines we have not even mentioned its name. We have not assumed that all phenomena are movements or transformations of movements, whether sensible or vibratory; we have not affirmed that what was passing from one phenomenal determination to another was the _vis viva_ of the motion, as is the case in the impact of elastic bodies. No doubt the kinetic theory affords us a very striking image of these truths which are independent of it; but it may be false: and the theory of energy which assumes the minimum of possible hypotheses would yet be true. _It contains a great many other Principles._—The principle of the conservation of energy contains a large number of the most general principles of science. It may be shown without much difficulty that, for example, it contains the principle of the inertia of matter, laid down by Galileo and Descartes; that of the equality of action and reaction, due to Newton; and even that of the conservation of matter, or rather of mass, due to Lavoisier. And finally, it contains the experimental law of equivalence connected with the name of the English physicist Joule, from which may be derived the Law of Hess and the principle of the initial and final states which we owe to Berthelot.