PROF. W. H. BRAGG ON X-RAYS AND CRYSTAL STRUCTURE. 267 



spectrum of intensity 34. Here, again, the intensities are very nearly proportional to 

 the amounts of the masses concerned. 



Assuming that these cases illustrate a general principle, let us apply it to a case 

 where spacings differ as well as plane composition. Consider the various orders of 

 the (100) spectra, The first order corresponds to a spacing 3 02 A.U. and is due to 

 CaCO planes only ; the remaining oxygen planes are regularly spaced at an interval 

 0'151 A.U. and contrihute nothing to the first order spectrum. The second order 

 spectrum is due to CaCO planes with the O planes in opposition. The third order is 

 due to CaCO planes only, and the fourth to CaCO and O planes acting in conjunction. 

 Thus the effective masses are in the ratio 68 : 36 : 68 : 100. The normal rate of 

 decline is about 100 : 20 : 7 : 3. When these two causes of variation of intensity are 

 superimposed we. obtain the series 68x100 : 36x20 : 68x7 : 100x3, which may be 

 expressed as 149 : 16 : 10'5 : 6'6, the first being put equal to 149 for the sake of easy 

 comparison with the experimental figures. It will be seen that, on the whole, there 

 is a good agreement. The third order does not compare very well ; but the 

 explanation of the small second and large fourth, as compared with a normal series 

 of spectra, is very clear. 



It may be pointed out that the (211), (100), and (110) planes must have exactly 

 similar spacings and distributions of weight no matter what value we adopt for x/d. 

 This is obvious when we consider that they all intersect the (ill) planes in successive 

 lines such as nm, ore, pq of fig. 15, their inclinations to the (ill) planes being the 

 only variables. In the figure the plane nopqcrn is a (ill) plane, nfiam a (100) plane, 



ngbm a (llO) plane, and EoCe a (211) plane. The last contains the axis and is 

 perpendicular to the (ill) planes. * 



Now if we compare the intensities of the higher orders of these planes, we find 

 they are not quite alike. For instance, 149 : 18 : 15 is not the same as 61 : 6 '4 : 2'8. 



The differences are accounted for in part at least by the effects of temperature 

 which always affect the higher orders more than the lower. The normal decline of 

 100 : 20 : 7 : 3 is only a rough average for a moderate spacing; if the spacing is 

 small and the spectra are consequently found at higher angles, their decline in 

 intensity is more marked. We should expect the (110) spectra to fall off more 

 quickly than the (100) spectra, although the two sets of planes are exactly similar. 



Probably, however, there are other minor causes at work ; we shall presently come 

 to a suggestion of one at least. The point is that putting aside these small, but real 

 and perhaps important discrepancies, we do succeed in accounting very satisfactorily 

 for the large differences in the intensities of the different orders. Perhaps this is 

 best seen from fig. 16. Here all the intensities are grouped together in one diagram ; 

 the crosses indicating the amounts as transferred from fig. 14. In each case 

 the intensity has also been divided by the fraction of the molecule which contributes 

 to it. For instance, we divide 149 by 68, 18 by 36 in the (100) series ; the first 34 



