1929 L-DE BROGLIE Since it is scarcely possible to use electrons other than such that have under gone a voltage drop of at least some tens of volts, you will see that the wave- length i predicted by theory is at most of the order of 10"cm, i.e. of the order of the Angstrom unit. It is also the order of magnitude of X-ray wave- Since the wavelength of the electron waves is of the order of that of X rays, it must be expected that crystals can cause diffraction of these waves completely analogous to the Laue phenomenon. Allow me to refresh your memories what is the Laue phenomenon. A natural crystal such as rock salt, for example, contains nodes composed of the atoms of the substances making up the crystal and which are regularly spaced at distances of the order of ar Angstrom. These nodes act as diffusion centres for the waves and if the crystal is impinged upon by a wave, the wavelength of which is also of the order of an Angstrom, the waves diffracted by the various nodes are in phase agreement in certain well-defined directions and in these directions the total diffracted intensity is a pronounced maximum. The arrangement of these diffraction maxima is given by the nowadays well-known mathematical heory developed by von Laue and Bragg which defines the position of the maxima as a function of the spacing of the nodes in the crystal and of the wavelength of the incident wave. For X-rays this theory has been admirably confirmed by von Laue, Friedrich, and Knipping and thereafter the diffrac- tion of X-rays in crystals has become a commonplace experience. The ac curate measurement of X-ray wavelengths is based on this diffraction: is there any need to remind this in the country where Siegbahn and co-workers are continuing their fine work? For X-rays the phenomenon of diffraction by crystals was a natural con- sequence of the idea that X-rays are waves analogous to light and differ from it only by having a smaller wavelength. For electrons nothing similar could be foreseen as long as the electron was regarded as a simple small corpuscle However if the electron is assumed to be associated with a wave and the density of an electron cloud is measured by the intensity of the associated wave,then a phenomenon analogous to the Laue phenomenon ought to be expected for electrons. The electron wave will actually be diffracted in tensely in the directions which can be calculated by means of the Laue-Bragg theory from the wavelength 2=ly/mD, which corresponds to the known velocity v of the electrons impinging on the crystal. Since, according to our general principle, the intensity of the diffracted wave is a measure of the density of the cloud of diffracted electrons, we must expect to find a great254 1929 L-DE BROGLIE Since it is scarcely possible to use electrons other than such that have under￾gone a voltage drop of at least some tens of volts, you will see that the wave￾length l predicted by theory is at most of the order of 10-8 cm, i.e. of the order of the Ångström unit. It is also the order of magnitude of X-ray wave￾lengths. Since the wavelength of the electron waves is of the order of that of X￾rays, it must be expected that crystals can cause diffraction of these waves completely analogous to the Laue phenomenon. Allow me to refresh your memories what is the Laue phenomenon. A natural crystal such as rock salt, for example, contains nodes composed of the atoms of the substances making up the crystal and which are regularly spaced at distances of the order of an Ångström. These nodes act as diffusion centres for the waves and if the crystal is impinged upon by a wave, the wavelength of which is also of the order of an Ångström, the waves diffracted by the various nodes are in phase agreement in certain well-defined directions and in these directions the total diffracted intensity is a pronounced maximum. The arrangement of these diffraction maxima is given by the nowadays well-known mathematical theory developed by von Laue and Bragg which defines the position of the maxima as a function of the spacing of the nodes in the crystal and of the wavelength of the incident wave. For X-rays this theory has been admirably confirmed by von Laue, Friedrich, and Knipping and thereafter the diffrac￾tion of X-rays in crystals has become a commonplace experience. The ac￾curate measurement of X-ray wavelengths is based on this diffraction: is there any need to remind this in the country where Siegbahn and co-workers are continuing their fine work? For X-rays the phenomenon of diffraction by crystals was a natural con￾sequence of the idea that X-rays are waves analogous to light and differ from it only by having a smaller wavelength. For electrons nothing similar could be foreseen as long as the electron was regarded as a simple small corpuscle. However, if the electron is assumed to be associated with a wave and the density of an electron cloud is measured by the intensity of the associated wave, then a phenomenon analogous to the Laue phenomenon ought to be expected for electrons. The electron wave will actually be diffracted in￾tensely in the directions which can be calculated by means of the Laue-Bragg theory from the wavelength l = h/mv, which corresponds to the known velocity v of the electrons impinging on the crystal. Since, according to our general principle, the intensity of the diffracted wave is a measure of the density of the cloud of diffracted electrons, we must expect to find a great