140 MOLECULAR GROUPING 



a crystalline polyhedron follows the law usually known as 

 the ' law of rational indices/ 



This law states that any possible plane in a crystal can 

 be determined by means of four planes, no three of which 

 are parallel: in what way is best shown in Fig. 28 

 by drawing three of the planes about the point o, viz. 

 XOY, YOZ, zox, and the fourth as ABC. The position of a fifth 

 plane, say A'B'O', is conditioned by the fact that the ratio 

 of the so-called indices 



OA' OB' oc' 



OA ' OB oc 



can only be given by whole numbers, such as 

 mm: p say 2:3: 5 



or can only be rational. 



In describing a crystalline form therefore, it is sufficient 

 to give the angles made by a suitable group of four planes : 



ZOY = a, ZOX = /3, YOX = y, 



as axial angles, and the ratio 



OA : OB : oc = a : b : c 



as axial distances, so that the whole crystal is defined by 

 means of five elements. 



2. Attempt at Explanation of the Geometrical Law by 

 Arrangement of Molecule Centres (Frankeiiheim, Bravais). 



A very simple conception, probable also on other grounds 

 to be explained later, gives a plausible meaning to the 

 above geometrical law. This consists in the assumption of 

 a regular arrangement of the crystalline centres, such that 

 they are alike and parallel throughout the crystal. As 

 previously the position of four non-parallel planes sufficed 

 for the entire structure, so here the position of four 

 molecule centres, j, 2, 3, 4 (Fig. 29), not lying on one plane. 

 The axial angles then correspond to the angles between 



