to study of the Structure of Crystals. 131 



of atoms must correspond with some space group and 

 may be thought of as resulting from the regular arrange- 

 ment in space of a large number of small groupings of 

 atoms, all alike in size and shape. These small groupings, 

 which we shall call for convenience "crystal molecules," 

 can be built up by the superposition of several sets of 

 equivalent points, which, then, repeat themselves 

 according to some one of the fourteen space lattices. 

 For instance, consider the compound AB. If the atom 



Fig. 1. — The monoclinic point group C-^^ (holohedry). P (a; ?/ 2;) , P ^[x y z), 

 F ^ ^ (x y z), and F ^ ^ ^ {x y z) are equivalent points. 



A occurs at the point (xyz) it must also appear at each 

 one of the other n-1 equivalent points of that group. The 

 atoms of B must occupy other n points in space, one of 

 which will be (x^ y^ z^. Either of these groups of equi- 

 valent points, when repeated according to a suitable lat- 

 tice, would form a space group ; taken together, these 

 groups of equivalent points define a crystal molecule. 

 Such crystal molecules, when placed at the points of a 

 lattice, yield a structure which represents the positions of 

 the atoms in a crystal. 



There is a slightly different and, for the determination 

 of crystal structure, perhaps more usable way of looking 



