of it which we know, that is to say, by the electric and magnetic fields, which it is possible to arrive at, as I have already remarked, without admitting at any time the laws of dynamics, the ideas of mass and force under their ordinary form. We will find this last to be a derived and secondary idea.
V. Electromagnetic Dynamics
(24) Change of Point of View. It seems thus much more natural to reverse the conception of Maxwell and to consider the analogy which he has pointed out between the equations of electromagnetism and those of dynamics under Lagrange's form as justifying much more the possibility of an electromagnetic representation of the principles and ideas of ordinary, material mechanics, than the inverse possibility.
It is necessary then for us to solve our second problem, that of the dynamics of the electron, of its motion in a given external field, without having recourse to the principles of mechanics, by purely electromagnetic considerations.
Hertz's equations, which permit a solution of the first problem, are here not sufficient, and we have need of a more general principle, which assumes not the motion of the electrons given, but that determines it.
(25) The Law of Stationary Energy. We will use this principle under a form indicated by Larmor, and which we can look upon as a generalization of the known laws of electrostatics and of electrodynamics. We know that the distribution of electric charges and electric fields in a system of electrified bodies is always such that the electrostatic energy We, contained in the medium modified by the field, is a minimum. The analogous principle holds for the magnetic field produced by currents of given intensities. The energy Wm localized in the magnetic field is less for the real distribution of it than for all other distributions satisfying the condition that the integral around a closed line is equal to 4π times the intensities of the currents inclosed by the line.
If displacements are possible, the conductors maintained at constant potential are in stable equilibrium if the electrostatic energy is a maximum, and the currents of given intensities are likewise in stable equilibrium if the energy of their magnetic field is a maximum. In all cases of maxima and minima, an infinitely small modification of the system from the configuration of equilibrium produces a zero variation in the energy: it is stationary.
(26) General Principle. When, instead of remaining permanent, the state of the system is variable, and if there are represented necessarily at the same time the two kinds of fields, we seek to find how,
