394 BELL SYSTEM TECHNICAL JOURNAL 



and it was no longer necessary to lay down an "either . . .or" 

 alternative. It was conceivable that in spite of all the evidence that 

 a stream of negative electricity through a vacuum consists of particles, 

 yet in some ways it might act as though it consisted of waves. In 

 1925 Elsasser did remark that such a stream might be diffracted by a 

 crystal; for the wave-lengths which de Broglie had assigned to 

 electrons, moving with such speeds as are customary in technical 

 vacuum tubes, were again of that order of magnitude 10~^ cm., which 

 had suggested to Laue that X-rays might be diffracted by crystals. 

 Early in 1927 Davisson and Germer looked for the diffraction-pattern 

 of negative electricity with a crystal of nickel, as Friedrich and 

 Knipping nearly fifteen years before had looked for that of electro- 

 magnetic radiation with a crystal of zincblende. The techniques 

 were very different, and for a time there was confusion due to the 

 refraction of the electron-waves in the crystalline substance; but 

 even at the start they found a pattern very like that which was 

 predicted, and when the influence of refraction was understood, the 

 discrepancies were cleared away. So they proved that negative 

 electricity is partly of the nature of waves, and initiated the spectro- 

 scopy of electrons; and in examining how the diffraction-pattern was 

 affected by films of gas on the surface of the crystal, Davisson and 

 Germer were the first to perform a crystal analysis by electron-waves. 



The accepted model for an ideal crystal — accepted now these last 

 two hundred years — is an array of objects or particles much too small 

 to be seen, all exactly alike, all oriented exactly alike, and spread out 

 in three-dimensional space with perfect regularity of arrangement. 

 These particles are marshalled in ranks and files like soldiers on parade, 

 except that the parade is in three dimensions instead of two, as if on 

 every floor of some colossal building a regiment were drawn up. 

 Were the arrangement only in two dimensions, I could find numberless 

 other examples — the pattern of printed wallpaper, a chessboard, the 

 meshes of a handkerchief, the array of jacks on a telephone switch- 

 board, the sections or the townships into which mid-western prairie 

 country is divided, the unvaried multitude of windows on the walls of 

 many a skyscraper. But in three dimensions the only similes which 

 present themselves are a honeycomb, and cannonballs piled in a heap 

 such as are set around old war memorials, and the girders of a steel- 

 frame building as we see them before the walls cover them over. All 

 these pictures fall very far short of suggesting the millions upon 

 millions of particles which are conceived to constitute even the smallest 

 of visible crystals, or their continual trembling in thermal agitation. 



The particles are said to be arranged upon a lattice. The lattice is 



