Page:Proceedings of the Royal Society of London Vol 69.djvu/313

Rh 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