What now does the principle of least action tell us? It tells us that to pass from the initial position occupied at the instant t_{0} to the final position occupied at the instant t_{1}, the system must take such a path that, in the interval of time that elapses between the two instants t_{0} and t_{1}, the average value of 'the action' (that is to say, of the _difference_ between the two energies _T_ and _U_) shall be as small as possible. If the two functions _T_ and _U_ are known, this principle suffices to determine the equations of motion. Among all the possible ways of passing from one position to another, there is evidently one for which the average value of the action is less than for any other. There is, moreover, only one; and it results from this that the principle of least action suffices to determine the path followed and consequently the equations of motion. Thus we obtain what are called the equations of Lagrange. In these equations, the independent variables are the coordinates of the hypothetical molecules _m_; but I now suppose that one takes as variables the parameters _q_ directly accessible to experiment. The two parts of the energy must then be expressed as functions of the parameters _q_ and of their derivatives. They will evidently appear under this form to the experimenter. The latter will naturally try to define the potential and the kinetic energy by the aid of quantities that he can directly observe.[6] [6] We add that _U_ will depend only on the parameters _q_, that _T_ will depend on the parameters _q_ and their derivatives with respect to the time and will be a homogeneous polynomial of the second degree with respect to these derivatives. That granted, the system will always go from one position to another by a path such that the average action shall be a minimum. It matters little that _T_ and _U_ are now expressed by the aid of the parameters _q_ and their derivatives; it matters little that it is also by means of these parameters that we define the initial and final positions; the principle of least action remains always true. Now here again, of all the paths that lead from one position to another, there is one for which the average action is a minimum, and there is only one. The principle of least action suffices, then, to determine the differential equations which define the variations of the parameters _q_. The equations thus obtained are another form of the equations of Lagrange. To form these equations we need to know neither the relations that connect the parameters _q_ with the coordinates of the hypothetical molecules, nor the masses of these molecules, nor the expression of _U_ as a function of the coordinates of these molecules.