PKOF. W. H. BRAGG ON X-KAYS AND CRYSTAL STRUCTURE. 



271 



effective centres is increased in the same proportion. We suppose the same number 

 of corrugations to be acting in each case. 



This is practically the very condition of the comparisons we made in certain cases of 

 calcite. 



So also if we compare figs. 18 and 20, where the amplitudes are the same but the 



C 



Fig. 20. 



spacings are narrower, we may expect the intensities to be proportional to the 

 spacings, when the number of corrugations is the same, because the number of 

 effective centres varies in that proportion. 



Suppose that the density, or the number of the effective centres, in various strata 

 of an atom perpendicular to a given direction is given by the curve in fig. 21, where 

 QOP is drawn in the given direction, and MN represents the stratum density at the 

 distance ON from the centre. 



Consider a crystal formed of atoms of one kind, arranged in regularly spaced 

 planes, which all contain the same number of atoms to the unit of area. One atom 

 from each plane will suffice to represent that plane. If, therefore, the density 

 distributions of atoms from the different planes are represented by the curves 

 QCP, Q'C'P', &c. (fig. 22), the periodic density of the whole crystal is represented by 



Fig. 22. 



the upper wavy curve formed by adding together the curves of the separate atoms. 

 The distance from crest to crest is what we have called d, the spacing. 



Suppose this curve were known and a harmonic analysis made of it. We should 

 obtain a series of harmonic terms having periods d, d/2, d/3, .... 



2 N 2 



