694 BELL SYSTEM TECHNICAL JOURNAL 



This coincidence makes one wonder whether, if a stream of such 

 electrons were projected against a crystal such as is used for diffracting 

 X-rays, there would be a semblance of diffraction. Nothing yet said 

 about the waves leads inevitably to such an inference. On the con- 

 trary, it might well be argued that we have no greater justification 

 for expecting to observe them in the ordinary world of space and 

 time than for expecting the x and the y of an algebraic equation to 

 come to life before our eyes. It might forcibly be pointed out that 

 while in this instance and the instance of the hydrogen atom the 

 "waves" are defined in ordinary space, there are other instances — 

 supplied for instance by rotators — in which the wave-equation is 

 formally similar to (195) and the theory quite as effective, and yet 

 the alleged "waves" exist only in the configuration-space and indeed 

 in non-Euclidean configuration-space, which is much the same as 

 saying that they do not exist at all. Nevertheless it appears that 

 there is indeed a diffraction of electrons by crystals, and that the 

 wave-length indicated by the diffraction-angles is in accordance with 

 the value given by de Broglie! The first evidence for this amazing 

 and portentous effect will be narrated by its discoverers Davisson and 

 Germer in the following issue of this Journal.^® 



Notice that the speed of the associated wave-train is not the same 

 as that of the flying particle; it is -yjE/lm, that of the particle is 

 ^^lEjm. It is, however, the wave-length of the wave-train which is 

 measured by the diffraction-experiments; not the speed, and not the 

 frequency. This is important; for it is the wave-length which is 

 exempt from the consequences of the essential uncertainty in the 

 value of E. In classical mechanics, energy-differences alone are 

 definite, but the absolute values of the "energy" of a system are not 

 defined; the definition of energy involves an arbitrary additive con- 

 stant. If now we were to add an arbitrary constant to the kinetic 

 energy of the free electron, and call E the sum of the two, we should 

 alter the frequency and alter the speed assigned to the wave-train; 

 but we should not alter the wave-length, for the wave-length is strictly 

 equal to hl^i2m{E — V) with V standing for the potential energy of 

 the free electron, and the added constant would enter into V and 

 vanish by subtraction. Returning to the preceding sections of this 



-"Consult meanwhile their note in Nature, 119, pp. 558-560; 1927. The predic- 

 tion was first published by VV. Elsasser {Naturwiss., 13, p. 711; 1925). For addi- 

 tional intimations of evidence for undulatory qualities in matter cf. G. P. Thomson, 

 A. Reid {Nature, 119. p. 890; 1927); T. H. Johnson, Nature, 120, p. 191 (1927); E. 

 G. Dymond, Phys. Rev. (2), 29, pp. 433-441 (1927). Schroedinger's elegant treat- 

 ment of the Compton effect is based upon the conception of electrons as wave-trains 

 {Ann. d. Phys., 82, pp. 257-264; 1927); for a more elaborate treatment of Compton 

 effect cf. W. Gordon {ZS.f. Phys., 40, pp. 117-133). 



