And then a question presents itself: among all these quantities measured experimentally, which shall we choose to represent the parameters _q_? Which shall we prefer to regard as the derivatives of these parameters? This choice remains arbitrary to a very large extent; but, for a mechanical explanation to be possible, it suffices if we can make the choice in such a way as to accord with the principle of least action. And then Maxwell asked himself whether he could make this choice and that of the two energies _T_ and _U_, in such a way that the electrical phenomena would satisfy this principle. Experiment shows us that the energy of an electromagnetic field is decomposed into two parts, the electrostatic energy and the electrodynamic energy. Maxwell observed that if we regard the first as representing the potential energy _U_, the second as representing the kinetic energy _T_; if, moreover, the electrostatic charges of the conductors are considered as parameters _q_ and the intensities of the currents as the derivatives of other parameters _q_; under these conditions, I say, Maxwell observed that the electric phenomena satisfy the principle of least action. Thenceforth he was certain of the possibility of a mechanical explanation. If he had explained this idea at the beginning of his book instead of relegating it to an obscure part of the second volume, it would not have escaped the majority of readers. If, then, a phenomenon admits of a complete mechanical explanation, it will admit of an infinity of others, that will render an account equally well of all the particulars revealed by experiment. And this is confirmed by the history of every branch of physics; in optics, for instance, Fresnel believed vibration to be perpendicular to the plane of polarization; Neumann regarded it as parallel to this plane. An 'experimentum crucis' has long been sought which would enable us to decide between these two theories, but it has not been found. In the same way, without leaving the domain of electricity, we may ascertain that the theory of two fluids and that of the single fluid both account in a fashion equally satisfactory for all the observed laws of electrostatics. All these facts are easily explicable, thanks to the properties of the equations of Lagrange which I have just recalled. It is easy now to comprehend what is Maxwell's fundamental idea. To demonstrate the possibility of a mechanical explanation of electricity, we need not preoccupy ourselves with finding this explanation itself; it suffices us to know the expression of the two functions _T_ and _U_, which are the two parts of energy, to form with these two functions the equations of Lagrange and then to compare these equations with the experimental laws.