138 PHYSICS OF THE ELECTRON 



ties 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 possi- 

 bility. 



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 law T s of electrostatics and of electro- 

 dynamics. We know that the distribution of electric charges and 

 electric fields in a system of electrified bodies is always such that the 

 electrostatic energy W e , 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 W m local- 

 ized 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 4^ times the intensities of the currents in- 

 closed by the line. 



If displacements are possible, the conductors maintained at con- 

 stant 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 max- 

 imum. In all cases of maxima and minima, an infinitely small mod- 

 ification 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 neces- 

 sarily at the same time the two kinds of fields, we seek to find how, 



