0)1 the Intimate Structure of Crystals. 295 



are thus related cannot readily be arranged so as to give a stable 

 structure, which will satisfy the conditions of cubic symmetry. 



Let us then regard the two atoms, which form a pair, and which 

 we may speak of as the paired atoms, to be approximated to each 

 other as in fig. 2, and next let one such molecule be placed over 



FIG. 3. 



another similar one, but inverted, so that the paired atoms form the 

 corners of a square, and the unpaired atoms rest upon them imme- 

 diately over the centre of the square (fig. 3). The resulting figure is 

 that of an octahedron, and might be regarded as the crystalline 

 element from which other forma could be built up. Within certain 

 limits determined by the relative dimensions of the paired and un- 

 paired atoms, such a primititive octahedron might possess the 

 " regular " character, i.e., lines obtained by joining the centres of the 

 atoms, or by drawing common tangent planes to their surfaces taken 

 in threes, would be that of a regular octahedron. This would ob- 

 viously be the case if the atoms were all of equal size, but it might also 

 be if the unpaired atoms were larger than the paired atoms, but more 

 closely approximate. Yet such an octahedron could not by itself be 

 regarded as satisfying the requirements of cubic symmetry, for of the 

 three rectangular axes which may be imagined to be drawn from the 

 centre of the figure through the centres of the atoms, one, that which 

 passes through the unpaired atoms, differs in its properties from the 

 rest, inasmuch as it passes through two atoms of different kind to the 

 other four. 



It might be possible to uphold the view that jn a chance distribu- 

 tion of such octahedra as many might be found with their single axis 

 on one crystallographic axis as on another, but few crystallographers, 

 I presume, would be prepared to admit that the exigencies of cubic 

 symmetry could be so easily satisfied. 



It is possible, however, to arrange our octahedra into groups which 

 are completely symmetrical. In the case of regular octahedra, there 

 would appear to be but one way of doing this. We may imagine 

 three rectangular axes, the " tetragonal " axes of the cubic system : on 

 each of these a primitive octahedron may be supposed to be placed, 

 so that the axis passing through the unpaired atoms may coincide 

 with one of the semi-axes of the rectangular system; and the other 



