188 On the Arrangement of Atoms in Crystals. 



case for sulphur, selenium, tellurium, iodine, arsenic, anti- 

 mony, bismuth. 



15. In order to obtain a more complete knowledge o£ the 

 distances between atoms which hold electrons in common, 

 the examination of salts such as the nitrates, chlorates, 

 bromates, sulphates, and selenates would be desirable. The 

 investigation of these salts presents some difficulty, since their 

 crystalline forms are complex. The symmetry of the crystal 

 is of less assistance in determining; the arrangement of the 

 atoms than it is for the simple crystals, as it is of a much 

 lower type. It is hoped that the empirical relations formu- 

 lated in this paper will help in this investigation. The 

 conception of the atoms as a set of spheres ot: appropriate 

 diameters packed tightly together limits the number of 

 possible arrangements and aids in deciding the correct 

 disposition of the atoms. The scheme may be of assistance 

 in analysing the structure of crystals such as quartz*, 

 sulphur*, and the alkaline sulphates t, crystals for which the 

 dimensions of the lattice are known, but which have so far 

 proved too complicated for complete analysis. 



Summary . 



1. An examination of the distances between neighbouring" 

 atoms in a crystal leads to an empirical relation determining 

 these distances. The distance between the centres of two 

 atoms may be expressed as the sum of two constants charac- 

 teristic of the atoms. The arrangement of the atoms in a 

 crystalline structure may therefore be pictured as that of an 

 assemblage of spheres of appropriate diameters, each sphere 

 being held in place by contact with its neighbours. 



2. This empirical law is summarized by the curve of 

 fig. 3, where the constants for a number of: elements, arranged 

 in the order of their atomic numbers, are plotted. The 

 curve is periodic and resembles Lothar Meyer's curve of 

 Atomic Volumes. Each atom occupies a constant space 

 in any crystalline structure of which it forms part. The 

 space occupied by the alkaline metals and alkaline earths 

 is greatest, that occupied by the electronegative elements 

 least. 



3. The accuracy of the relation is discussed. Variations 

 of the order of 10 per cent, between the calculated and 

 observed distances occur, so that the law is only approxi- 

 mately true. Nevertheless, it is of considerable assistance- 



* W. H. Bragg, Proc. Roy. Soc. A. vol. Ixxxix. (Jan. 1914). 

 t Ogg and Hopwood, Phil. Mag. [6] xxxii. p. 518 (1916). 



