This example will suffice to make my thought understood; I could cite many others. Thus who would suspect, in reading the pages devoted to magnetic rotary polarization, that there is an identity between optical and magnetic phenomena? One must not then flatter himself that he can avoid all contradiction; to that it is necessary to be resigned. In fact, two contradictory theories, provided one does not mingle them, and if one does not seek in them the basis of things, may both be useful instruments of research; and perhaps the reading of Maxwell would be less suggestive if he had not opened up to us so many new and divergent paths. The fundamental idea, however, is thus a little obscured. So far is this the case that in the majority of popularized versions it is the only point completely left aside. I feel, then, that the better to make its importance stand out, I ought to explain in what this fundamental idea consists. But for that a short digression is necessary. THE MECHANICAL EXPLANATION OF PHYSICAL PHENOMENA.--There is in every physical phenomenon a certain number of parameters which experiment reaches directly and allows us to measure. I shall call these the parameters _q_. Observation then teaches us the laws of the variations of these parameters; and these laws can generally be put in the form of differential equations, which connect the parameters _q_ with the time. What is it necessary to do to give a mechanical interpretation of such a phenomenon? One will try to explain it either by the motions of ordinary matter, or by those of one or more hypothetical fluids. These fluids will be considered as formed of a very great number of isolated molecules _m_. When shall we say, then, that we have a complete mechanical explanation of the phenomenon? It will be, on the one hand, when we know the differential equations satisfied by the coordinates of these hypothetical molecules _m_, equations which, moreover, must conform to the principles of dynamics; and, on the other hand, when we know the relations that define the coordinates of the molecules _m_ as functions of the parameters _q_ accessible to experiment. These equations, as I have said, must conform to the principles of dynamics, and, in particular, to the principle of the conservation of energy and the principle of least action. The first of these two principles teaches us that the total energy is constant and that this energy is divided into two parts: 1º The kinetic energy, or _vis viva_, which depends on the masses of the hypothetical molecules _m_, and their velocities, and which I shall call _T_. 2º The potential energy, which depends only on the coordinates of these molecules and which I shall call _U_. It is the _sum_ of the two energies _T_ and _U_ which is constant.