On the Intimate Structure of Cryxf.lx. 



297 



The two cases we have described are extremes between which a 

 whole series of intermediate stages may exist. It may be observed, 

 however, that gyrohedral hemihedry is associated with all these inter- 

 mediate stages, and that none but the extreme cases afford complete 

 holohedry. 



FIG. 5. 



The configuration in the intermediate forms is dependent first on the 

 relative dimensions of the two kinds of atoms, second on the distance 

 between the unpaired atoms and the correlated distance between the 

 paired atoms, and third on the amount of twist or rotation which 

 must be" given to the primitive octahedra to bring the paired atoms of 

 adjacent octahedra into contact. 



If the parameters on the axis of the unpaired atoms be shorter than 

 those on the axes of the paired atoms, the first case is impossible, 

 because when the unpaired atoms near the origin are in contact, the 

 paired atoms would not have room to take up the position described 

 in Case I, and would either have to part company with the unpaired 

 atoms, or the square figure which they form would have to rotate 

 about the rectangular axis on which its centre lies, till its diagonal 

 when projected on a plane containing this axis and one of the others 

 has the same length as the parameters of the unpaired atoms, i.e., till 

 the supposed octahedra project into principal sections of a regular 

 octahedron. 



To bring the various figures which may result from the different 

 grouping of primitive octahedra to the test offered by a study of 

 molecular volumes, it becomes necessary to devise a mode of parti- 

 tioning space within the crystalline edifice in such a manner as to assign 

 to each molecule its appropriate share. .Let planes be drawn parallel 

 to any two of the rectangular axes through the centre of each primi- 

 tive octahedron, these planes will intersect to form a cube (fig. 6, c.c.), 

 within which will be contained six molecules of the crystal, i.e., six 



