402 BELL SYSTEM TECHNICAL JOURNAL 



This allusion to parallel slits in a screen will simplify the next steps. 

 It is well known that when to a pair of parallel slits, new ones just 

 like them are added at equal intervals one after the other, the fringes 

 are not displaced. The bright fringes shrink, the dark ones widen, 

 but their central lines remain unshifted. As more and more slits are 

 added, as more and more lines are ruled on a metal surface to constitute 

 a grating, the dark fringes encroach steadily on the bright ones, and 

 it becomes easier to locate the central lines of these latter with precision. 

 As they grow narrower, they brighten, the energy which was lavished 

 over a wide angular range being gathered into a small one as it is 

 progressively Increased by the addition of new slits or rulings. So 

 there Is a double gain. In the limit, nothing remains but the central 

 lines, and these are brilliant. And In the limit, these lines are still 

 located where the formula derived for only two slits predicted that 

 the maxima of brightness should be found. 



Now in the same way, when to a pair of like and likewise-oriented 

 atom-groups additional such groups are added so as to form an evenly 

 spaced row, the annular fringes on the wall of the ensphering bulb 

 are not changed in location but in distinctness. The bright fringes 

 contract into brighter rings, the dark ones broaden Into (relatively) 

 dark bands. The multitude of the atoms sharpens the diffraction-pattern. 

 In the limit, the bright rings are very sharp and brilliant, and they 

 are still located at exactly the angles predicted by equation (3) derived 

 for two atom-groups only. Remember however that a ring may not 

 be equally bright all around Its circuit. It is only an enhancement 

 of the scattering-pattern of the individual atom-group; and this in 

 general will vary from one point to another. 



So much for the single row or file of groups of atoms! We must 

 now pass to two dimensions, and predict the diffraction by a plane 

 in which groups are arranged in a network. In the plane, rows of 

 atoms lie side by side at equal spaclngs. We might start with one 

 of the rows, and estimate how Its diffraction-pattern Is amplified 

 by the cooperation of a second and then a third and a fourth and 

 eventually an infinite number of added rows laid parallel with it at 

 equal intervals. Owing to this equality of intervals and the new 

 periodicity which it entails, the diffraction-rings of the pattern of the 

 individual rows will be amplified not uniformly, but only at certain 

 points; precisely as owing to the equal intervals between the atom- 

 groups of the single row these amplified the pattern of the individual 

 group not uniformly, but only over certain rings. However we can 

 reach this result in another way, by considering three atom-groups 

 forming a triangle, as formerly we considered two forming a pair. 



