1929 L DE BROGLIE For him the wave will thus have a frequency: √r-B2 and will propagate in the direction of the x-axis at the phase velocity: By the elimination of B between the two preceding formulae the following elation can readily be derived which defines the refractive index of the vacuum n for the waves considered A <<group velocity>> corresponds to this <claw of dispersion>>. You will be aware that the group velocity is the velocity of the resultant amplitude of a group of waves of very close frequencies. Lord Rayleigh showed that this velocity u satisfies equation I a(nm) Here U=v, that is to say that the group velocity of the waves in the system ryxt is equal to the velocity of the corpuscle in this system. This relation is of very great importance for the development of the theory The corpuscle is thus defined in the system ryzt by the frequenc e phase velocity V of its associated wave. To establish the parallelism of which we have spoken, we must seek to link these parameters to the me. chanical parameters, energy and quantity of motion. Since the proportion- ality between energy and frequency is one of the most characteristic relations of the quantum theory, and since, moreover, the frequency and the energy transform in the same way when the Galilean reference system is changed, we may simply write nergy=h x frequency, or W=hu248 1929 L.DE BROGLI E For him the wave will thus have a frequency: and will propagate in the direction of the x-axis at the phase velocity: By the elimination of b between the two preceding formulae the following relation can readily be derived which defines the refractive index of the vacuum n for the waves considered: J 2 fi-= p2- V2 A <<group velocity>> corresponds to this <<law of dispersion>>. You will be aware that the group velocity is the velocity of the resultant amplitude of a group of waves of very close frequencies. Lord Rayleigh showed that this velocity U satisfies equation : I -=-- a (4 U &J Here U = v, that is to say that the group velocity of the waves in the system xyxt is equal to the velocity of the corpuscle in this system. This relation is of very great importance for the development of the theory. The corpuscle is thus defined in the system xyzt by the frequency v and the phase velocity V of its associated wave. To establish the parallelism of which we have spoken, we must seek to link these parameters to the me￾chanical parameters, energy and quantity of motion. Since the proportion￾ality between energy and frequency is one of the most characteristic relations of the quantum theory, and since, moreover, the frequency and the energy transform in the same way when the Galilean reference system is changed, we may simply write energy = h x frequency, or W = h v