218 BELL SYSTEM TECHNICAL JOURNAL 



standard methods of optics are at once available for calculating the 

 wave-lengths of electrons of various speeds. We do not hesitate to 

 make these calculations, nor do we hesitate to attach physical 

 significance to the results. 



The experiments by which these phenomena are revealed have been 

 made by Dr. Germer and myself in New York, by Thomson and 

 Reid in Scotland, by Rupp in Germany, by Rose in England, by 

 Nishikawa and Kikuchi in Japan, and by Szczeniewski in France. 

 The subject is being actively cultivated at present, and there may be 

 still other experiments of which I have not yet heard. I do not 

 propose to give a detailed description of any of the investigations. 

 The type of result and the methods of treating the data are so exactly 

 those of optics — including, of course, X-rays as one of its branches — 

 that the details would hardly interest you. I shall have something 

 to say later on about the general nature of the results, but to begin 

 with I shall attempt a brief account of certain theoretical speculations 

 in which these results were more or less definitely anticipated. 



It is a remarkable circumstance, and one that attests to the excep- 

 tional insight and daring of Louis de Broglie, that these newly dis- 

 covered properties of the electron were suspected, and a definite 

 hypothesis concerning them was formulated, two or more years 

 before any of the experiments I have mentioned had been performed; 

 even the exact relation between the speed and wave-length of the 

 electron was accurately predicted. It is true that Einstein had at an 

 even earlier date made use of the idea that an assemblage of gas 

 molecules may for certain theoretical purposes be regarded as equiva- 

 lent to a system of standing waves, but de Broglie seems first to have 

 seen clearly that the duality of wave and corpuscular properties to 

 which we are becoming reconciled in the phenomena of light might 

 be characteristic also of electrons and material particles in general. 



If light and X-rays behave in certain circumstances as if they are 

 particles, why should there not be circumstances in which particles 

 behave as waves? This question was suggested to de Broglie, not by 

 any idea of the general fitness of things nor by any sense of symmetry 

 in the universe, but by the realization, which he shared with others, 

 that the laws of classical mechanics had been so amended in the Bohr 

 atom model as to have become all but non-existent. It was generally 

 felt that the Bohr atom had become too artificial to be acceptable, 

 and that the real trouble arose from an unwarranted extrapolation of 

 classical mechanics to systems of atomic size. 



To understand the hypothesis on which de Broglie hoped to build 

 a new model of the atom it will be necessary to have clearly in mind 



