170 Prof. W. L. Bragg on the 



on the other hand, may be anywhere along these axes, pro- 

 vided they all occupy similar positions, and yet be in accord- 

 ance with the symmetry. The determination of their positions 

 must be made by a quantitative examination of the diffraction 

 of the X rays by the structure, since the parameter which 

 fixes their positions may have any value between certain 

 limits. The oxygen atom in the series of carbonates iso- 

 morphous with calcite has similarly an indeterminate posi- 

 tion depending on the value of a certain parameter. In the 

 case of the ruby, A1 2 3 , two parameters are necessary to 

 define the crystal structure ; in quartz, Si0 2 , four parameters 

 must be determined. The difficulty of analysing a crystal 

 structure by the X rays is greatly increased by the necessity 

 for defining these parameters, and it is this which has limited 

 the types of crystals which have so far been fully worked 

 out to the simpler forms where these parameters are few 

 in number. 



The first part of this paper deals with certain empirical 

 relations, which hold between the distances separating atoms 

 from their nearest neighbours in the simpler crystalline 

 structures, and which the author has found to be of service 

 in the analysis of complex crystal forms. In the latter part 

 of the paper the physical significance of these relations will 

 be discussed, particularly in relation to the theories of atomic 

 structure proposed by Lewis * and Langmuirf . 



2. These relations may be expressed in a simple manner 

 by regarding the atoms in a crystal as an assemblage of 

 spheres packed tightly together, the centres of the spheres 

 coinciding with those of the atoms. Each sphere is held in 

 place by touching several neighbours. It will be shown that, 

 within certain limits, it is possible to assign to the sphere 

 representing an atom of any element a constant diameter 

 characteristic of that element. The distance between the 

 centres of two neighbouring atoms may be expressed as the 

 sum of two constants, represented by the radii of the corre- 

 sponding spheres. The molecular volume of a compound is 

 in general very far from being equal to the sum of the mole- 

 cular volumes of the elements composing it. On the other 

 hand, if the distances between the atoms are considered, it 

 will be shown that an additive law holds with considerable 

 accuracy. The apparent variations in the contribution of any 

 particular element to the molecular volume of compounds of 

 which it forms a constituent are to be explained by differences 



* G. N. Lewis, Journ. Amer. Chem. Soc. xxxviii. p. 762 (1916). 

 f I. Langmuir, Journ. Amer. Chem. Soc. xli. p. 868 (1919). 



