558 BELL SYSTEM TECHNICAL JOURNAL 



rangement as the atoms in the crystal of silver. Four atoms only are 

 required to fix a simple crystal arrangement; the chlorine atoms in 

 CCI4 occupy the corners of a regular tetrahedron, and this figure 

 determines the face centered cubic arrangement. The chlorine atoms, 

 to which nearly the whole of the scattering is due, may thus be properly 

 thought of as forming exceedingly small crystals of this structure; the 

 vapor is thus a crystal aggregate similar to that of polycrystalline silver. 

 The marked differences between the two patterns are due to the dis- 

 parity in the number of atoms forming the individual crystals in the 

 two cases. The number in the chlorine crystals — four each — is the 

 smallest possible, and the "resolving power" of the crystal, regarded 

 as an optical instrument, is in consequence the least possible. The 

 form of the pattern for CCI4 accords with the tetrahedral arrangement 

 of the chlorine atoms; the scale of the pattern with the calculated 

 wave-length of the electrons fixes the length of the tetrahedron edge. 



The purpose of this report is accomplished with the description of 

 these few representative experiments which reveal and demonstrate — 

 so far as demonstration is possible — a wave aspect of electrons in 

 conformity with de Broglie's conception. The experiments do not 

 tell us in what medium, if any, the waves occur, with what speed they 

 are propagated, whether they are longitudinal or transverse and cap- 

 able of polarization — they tell us merely that when electrons reach an 

 element of space from a given source simultaneously over different 

 paths the resultant intensity (the number of electrons traversing the 

 element per unit time, as we think of it) is not the arithmetic sum of 

 various scalar contributions as we naturally expect it to be, but is 

 given instead by the square of the sum of contributions which are vec- 

 tor quantities — in precisely the manner with w*hich we are familiar in 

 optics. We must make the addition as if we were dealing with super- 

 posed trains of waves — with due regard for phase as well as amplitude. 

 This kind of addition is characteristic of trains of waves. When we 

 find quantities which add together in this particular way we concludie 

 that the quantities are, in fact, trains of waves; this is our reason for 

 regarding light and X-rays as wave phenomena and it is our reason 

 also for so regarding electrons. 



Having demonstrated the convenience, if not indeed the necessity, 

 of regarding electrons in certain circumstances as waves rather than 

 as particles, we enquire naturally if these waves are refracted on passing 

 from one medium to another like the waves of light and X-rays, and 

 whether or not they are polarizable. We rather expect to find that 

 they do exhibit refraction, for if the wave-length of a beam of electrons 

 in vacuo is given by X = (150/Fj^ " we expect that on passing into a 



