ELECTRONS AND QUANTA 223 



governing the directions of beams, which in the case of X-rays is 

 negHgible, is in experiments with low-speed electrons marked and 

 important. 



Fortunately, we are not prevented by this complication from arriving 

 at perfectly definite values of wave-lengths from observations on the 

 Laue type of electron diffraction, and these wave-lengths turn out 

 to be in acceptable agreement with the values of h/mv, as predicted 

 by de Broglie. 



Further evidence of electron refraction is contained in the obser- 

 vations we have made on the electron analogue of the Bragg X-ray 

 reflection beam. And from the data of these experiments we have 

 constructed a dispersion curve for nickel which displays some of the 

 features to be expected from certain theoretical considerations. In 

 conjunction with these measurements we have made additional 

 determinations of electron wave-lengths, and these agree within one 

 per cent or less with the values calculated from de Broglie's formula. 



In the similar experiments made by Szczeniewski and by Rose, 

 no certain evidence of electron refraction has been found. This may 

 be due to some important difference in regard to refraction between 

 bismuth and aluminium, the crystals employed in their experiments, 

 and nickel, the crystal upon which our measurements were made. 

 On the other hand Rupp has found evidence of refraction for a number 

 of metals in measurements which he has made on the diffraction of 

 low-speed electrons by crystal aggregates. 



Electron diffraction differs from X-ray diffraction also in the matter 

 of resolution. The X-ray beams are ordinarily extremely sharp 

 because of the very great number of elements comprised in the 

 diffracting lattice. Much broader beams are met with in electron 

 diffraction — particularly in the diffraction of low-speed electrons — and 

 occurrences of the beams are much less critical in wave-length. These 

 characteristics are explained by the slight penetration of the electrons 

 — and therefore of the electron waves — into the cr>^stal; the effective 

 number of scattering centers is small and the resolving power of the 

 grating is correspondingly low. 



The diffraction of electrons by crystal aggregates has been studied 

 in Aberdeen by G. P. Thomson, who first observed this phenomenon, 

 and by Rupp in Gottingen. Thomson has worked with thin poly- 

 crystalline foils of various metals and with high-speed electrons for 

 which the refractive indices are practically unity. The results which 

 he has obtained are in perfect agreement with those obtained in the 

 corresponding experiments with X-rays — electrons of a given wave- 

 length form exactly the same series of diffraction rings as would be 

 formed by X-rays of the same wave-length. 



