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



were only rough, and the mode of interpretation was not very certain. Nevertheless 

 it was possible to say that x/d (see fig. 15) was about 0'30. 



The measurements here shown are much more complete and accurate. They 

 indicate that the value of x/d should be put a little lower, say 0'25 to 0'27. Perhaps 

 this appears most clearly from the (ill) planes. These are of somewhat peculiar 

 structxire, as shown in fig. 14. Whatever may be the value of x/d, planes of 

 calcium and of CO alternate with each other ; but oxygen planes interleave them. 

 If x/d = 0'25 they bisect the distances between the Ca and CO planes. This would 

 account for the strength of the fourth order spectrum (21). The smallness of the 

 second order (100) also is in accordance with this view. There can be little doubt 

 that the atoms are very nearly a quarter of the way from one carbon atom to the 

 next. The figure shows the arrangement of atoms in the planes on this supposition. 



Now it is remarkable that in two cases we have different sets of planes with the 

 same or at least commensurable spacings. The second order (ill) occurs at almost 



exactly the same angle as the first (211). Tins enables us to compare the effects of 



differing arrangements of atoms apart from the effect of differing angles of reflection. 



The first order (ill) is due to the full spacing of the (ill) planes, viz., 2'83 A.U. ; 



o 



but the second order is due to half this spacing, viz., 1'41 A.U. In the former the 

 Ca and the C() 3 in each molecule are in opposition, in the second in concurrence. 

 The whole weight of every CaCO 3 unit (40 + 12 + 48 100) is thrown into the scale 

 in the formation of the latter spectrum. Its intensity is 58. 



The first order (211) is due to the same spacing. In this case the planes may be 



o 



divided into two groups : first, a set of CaCO planes with a spacing 1'44 A.U. ; and, 

 secondly, a set of O planes with a regular spacing of 0'72 A.U. The latter have no 



effect at all at the point where the first (211) spectrum occurs. The whole intensity 

 of the latter, viz., 38, is due to the CaCO in each molecule, that is, to a weight of 68 

 out of the 100. The intensities of the two spectra are proportional to the weights 

 contributing to them for 68/100 = 0'68 and 38/58 = 0'66. 



It is to be observed that the conditions for this comparison are excellent ; the 

 angles of reflection are the same, so that there is no need to consider anything that 

 depends on this angle. Also the number of molecules swept over by the X-rays is 

 the same in each case. The only difference is that in one case the whole molecule is 

 in action, in the other, part of it. 



A second opportunity of comparison occurs in the (ill) and (110) spectra. The 

 first order spectrum of the latter is due to the CaCO in each molecule, as in the 







(211) case, and to a spacing 1'90 A.U. ; its intensity is 61. The second spectrum of 

 the (ill) is due to the same spacing. The Ca and CO planes may be considered to 

 act together, with the O planes in opposition. The mass 68 is acting against the 

 mass 32 ; the balance 36 may be considered as the origin of the second (ill) 



