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This article is taken from the manuscript prepared by the author for his address at the joint meeting of Section B of the American Association for the Advancement of Science and the American Physical Society on December 28, 1927, at Nashville, Tennessee. An account of this work giving fuller experimental details is given by Davisson and Germer in the December, 1927, issue of the Physical Review. These experiments are fundamental to some of the newer theories in physics. Until they were performed, it could be said that all experimental facts about the electron could be explained by regarding it as a particle of negative electricity. It now appears that in some way a “wave-length” is connected with the electron's behavior. The work thus shows an interesting contrast with the discovery of A. H. Compton that a ray of light (a light pulse) suffers a change of wave-length upon impact with an electron, the change of wave-length corresponding exactly to the momentum gained by the electron. Until Compton's work, all the known facts about light could be explained by thinking of light as a wave motion. The Compton effect seems to prove the existence of particles of light. Physics is thus faced with a double duality. Compton showed that light is in some sense both a wave motion and a stream of particles. Davisson and Germer have now shown that a beam of electrons is in some sense both a stream of particles and a wave motion. At the same time, theoretical advances have been made which seem to pave the way for an understanding of this curious situation. A general account of these new developments was given by K. K. Darrow in his series “Contemporary Advances in Physics” in the Bell System Technical Journal for October, 1927. Some remarks on the relation of the Davisson and Germer experiments to the new mechanics were given in this article, p. 692 et seq. — Editor.