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metrical function of direction. Also it may depend on the side of 

 the group on which the primary waves impinge, or, in better words, 

 on the direction whence they come. Of course, in any particular 

 case, it might turn out to be a symmetrical function of direction, or 

 it might be the same function whichever the side of the atom which 

 the primary waves encounter; but we should not rely in advance on 

 either of these simplicities. I must qualify this statement somewhat: 

 the crystallographers have their ways of learning more or less (and 

 sometimes a good deal) about the symmetry of the atom-group, and 

 thus foretelling certain aspects of its diffraction-pattern. Moreover 

 in many cases it is possible to make in advance a good estimate of the 

 absolute intensity of the scattered waves. It will do no harm to 

 remember these encouraging facts; nevertheless it will be best for us 

 to keep our ideas fluid by supposing an atom-group of absolute 

 asymmetry, the scattering-pattern of which is one of the ultimate 

 objects of the quest. 



Fig. 4 — Illustrating diffraction by a single file of atom-groups. 



I must state with all emphasis that whatever may be foretold or 

 measured in the scattering-pattern for electromagnetic waves (X-rays) 

 need not always be valid in the scattering-pattern for electron-waves. 



Consider now the amplification which ensues when other atom- 

 groups are added to the first one, to form with it an evenly-spaced row. 



Denote by a the distance between corresponding points in adjacent 

 groups (Fig. 4). Suppose the primary waves to emanate from a 

 point P, while the observation of the scattered intensity is made at a 

 point Q (on the wall of the bulb, to continue the picture). In practice 

 the distance a is so submicroscopically small, that P and Q are practi- 

 cally infinitely far away; yet it is easiest to begin by thinking of them 

 as nearby, and passing to the limit. Designate then by Ri, Ro the 



