WAVE NATURE OF ELECTRON 251 since W is constant in a constant field. It follows that Fermats and maupe tuis principles are each a translation of the other and the possible trajectories of the corpuscle are identical to the possible rays of its wave These concepts lead to an interpretation of the conditions of stability in- troduced by the quantum theory. Actually, if we consider a closed trajectory C in a constant field, it is very natural to assume that the phase of the asso ciated wave must be a uniform function along this trajectory. Hence we may write ∫=∫ d integer This is precisely Plancks condition of stability for periodic atomic motions The conditions of quantum stability thus emerge as analogous to resonance phenomena and the appearance of integers becomes as natural here as in the theory of vibrating cords and plates The general formulae which establish the parallelism between waves corpuscles may be applied to corpuscles of light on the assumption that the rest mass mo is infinitely small. Actually, if for a given value of energy W, mo is made to tend towards zero, u and V are both found to tend towards c and at the limit the two fundamental formulae are obtained on which Einstein had based his light-quantum theory W=hy Such are the main ideas which I developed in my initial studies. They showed clearly that it was possible to establish a correspondence between waves and orpuscles such that the laws of mechanics correspond to the laws of geomet- rical optics. In the wave theory, however, as you will know, geometrical and particularly when interference and diffraction phenomena are involved, it is quite inadequate. This prompted the thought that classical mechanics is also only an approximation relative to a vaster wave mechanics. I stated as much almost at the outset of my studies, ie. "A new mechanics must be developed which is to classical mechanics what wave optics is to geomet- ical optics". This new mechanics has since been developed, thanks mainlyWAVE NATURE OF ELECTRON 251 since W is constant in a constant field. It follows that Fermat’s and Mauper￾tuis’ principles are each a translation of the other and the possible trajectories of the corpuscle are identical to the possible rays of its wave. These concepts lead to an interpretation of the conditions of stability in￾troduced by the quantum theory. Actually, if we consider a closed trajectory C in a constant field, it is very natural to assume that the phase of the asso￾ciated wave must be a uniform function along this trajectory. Hence we may write : This is precisely Planck’s condition of stability for periodic atomic motions. The conditions of quantum stability thus emerge as analogous to resonance phenomena and the appearance of integers becomes as natural here as in the theory of vibrating cords and plates. The general formulae which establish the parallelism between waves and corpuscles may be applied to corpuscles of light on the assumption that here the rest mass m. is infinitely small. Actually, if for a given value of the energy W, m. is made to tend towards zero, v and V are both found to tend towards c and at the limit the two fundamental formulae are obtained on which Einstein had based his light-quantum theory Such are the main ideas which I developed in my initial studies. They showed clearly that it was possible to establish a correspondence between waves and corpuscles such that the laws of mechanics correspond to the laws of geomet￾rical optics. In the wave theory, however, as you will know, geometrical optics is only an approximation: this approximation has its limits of validity and particularly when interference and diffraction phenomena are involved, it is quite inadequate. This prompted the thought that classical mechanics is also only an approximation relative to a vaster wave mechanics. I stated as much almost at the outset of my studies, i.e. "A new mechanics must be developed which is to classical mechanics what wave optics is to geomet￾rical optics". This new mechanics has since been developed, thanks mainly