404 BELL SYSTEM TECHNICAL JOURNAL 



In these equations n and n' stand for integers but they need not 

 stand simultaneously for the same integer. In all directions for which 

 6 and Q' satisfy equations (3) and (4), there will be maximum amplifi- 

 cation of the diffraction-pattern of any atom-group by its pair of 

 neighbors. 



Now equation (3), with various integer values 0, 1, 2, • • •, substi- 

 tuted for n one after the other, described a system of rings on the 

 wall of the bulb — parallel rings like latitude-circles, with the poles at 

 the points where the bulb is intersected by the line drawn through its 

 centre parallel to AB. Likewise equation (4), with various integer 

 values for n' , describes a system of rings oblique to the first, having 

 its poles at the points where the diameter drawn parallel to AC 



Fig. 6 — Diffraction pattern of electron-waves attributed to the array of atom- 

 groups in the superficial plane of a mica crystal. (S. Kikuchi; Japanese Journal of 

 Physics.) 



through the centre of the bulb reaches the wall. There are inter- 

 sections between the rings of the two systems, and these intersections 

 are the points — the discrete, the finitely numerous points — where the 

 diffraction-pattern of the atom-group is most greatly amplified. So 

 long as there are but three of the groups, these points are merely the 

 centres of broad, hazy, bright (of course, in practice, utterly invisibly 

 dim) blotches. But when to the three groups we add enormously 

 many others to form the extensive two-dimensional network of which 

 a section is depicted in Fig. 5, interference eats away the edges of 

 these patches and enhances their centres, and in the limit nothing 

 remains of the diftraction-pattern except brilliant dots at the inter- 

 sections of the rings. 



The next and last step follows immediately. The crystal is built 



