170 BELL SYSTEM TECHNICAL JOURNAL 



Again, one may pour a stream of electrons against a crystal or an 

 optical ruled grating, after having measured the speed of the electrons 

 in one of the well-known ways depending ultimately on the deflection 

 of such a beam in known electric and magnetic fields.^ The mass 

 of the electrons being known, one knows also their momentum. Now 

 the crystal or the grating, whichever it may be, forms from the primary 

 beam a diffraction-pattern of new beams. Well! the formation of a 

 diffraction-pattern is the primary reason for saying that light is wave- 

 like, and it gives the primary way of measuring wave-length of light. 

 One is equally obliged to admit that a stream of free negative elec- 

 tricity is wavelike, and to accept the value for its wave-length which 

 the diffraction-pattern gives. Again it turns out that the wave-length 

 is equal to the quotient of h by the momentum of the electrons. 



It may be objected that in all of those experiments, the corpuscles 

 were observed in a vacuum. Compton measured X-rays before and 

 after scattering, but during the measurements they were in vacuum 

 or at any rate in air. Davisson and Germer, Thomson and Rupp, 

 observed electrons returning through the same evacuated space as 

 they had crossed on their way to the diffracting lattice. One might 

 emphasize that all these savants compared momenta and wave-lengths 

 for different beams in the same medium instead of comparing them for 

 the same beam in different media. The distinction is certainly worth 

 noticing; but happily there are experiments which bear directly on 

 refraction. Davisson and Germer measured, not precisely the 

 refraction of an electron-stream passing from vacuum into nickel, but 

 a minor perturbation of the diffraction-pattern which is due to that 

 refraction. We will analyze their result, for nothing shows more 

 clearly the relations — or lack of relation, the reader may think — 

 between speed of waves, speed of corpuscles and measured speed of 

 stream. 



Davisson and Germer came to values of the index of refraction 

 (sin 0/sin d') which were greater than unity — which corresponded 

 therefore to a bending of the stream towards the normal, as it passed 

 from vacuum into nickel — which therefore signified that the speed of 

 the waves is not so great in nickel as in air. 



On the other hand, it is known that when an individual electron 

 passes from vacuum into a metal, its kinetic energy and its velocity 

 increase as it goes through the surface. We have in fact the situation 

 described in the corpuscle-theory picture of refraction, a few pages 

 back. Return to equations (4) and (5), and consider a corpuscle for 



^ The experiments of Davisson and Germer, of G. P. Thomson, and of Rupp (cf. 

 the eighteenth article of this series). 



