Page:Proceedings of the Royal Society of London Vol 69.djvu/312

296 two axes, passing through the paired atoms, lie opposite and parallel to the other two axes of the rectangular system, i.e., to those on which the octahedra are not situate. If now the octahedra be pushed towards each other till they meet a form will result such as is shown in plan in fig. 4. It will be observed that this configuration is stable, for

FIG. 4.

six of the unpaired atoms are in contact about the origin, the paired atoms are in contact with the unpaired and with each other, and further the paired atoms of adjacent octahedra touch each other in twos at each corner of the square figure which they form. This arrangement, in its unmodified form, does not appear to be a common one, but it is probably presented by fluorspar ; we may term it for reference, Case I.

A second arrangement may be conceived as the result of rotating each of the primitive octahedra of the preceding form through an angle of 45 around the axis on which they lie ; the side, and not the diagonal, of the square figure formed by the paired atoms will then lie parallel and opposite to the remaining rectangular axes (fig. 5 (>)). In this case if the primitive elements were regular octahedra, the paired atoms of adjacent octahedra would no longer touch, and the system would be unstable. Contact, however, may be brought about by pushing the unpaired atoms which lie away from the origin closer towards those which lie near it ; this will bring about a divergence of the paired atoms of each octahedron from each other, and an approxi- mation to their neighbours, till the latter are touched. With the establishment of contact stability is ensured, for although the paired atoms of each octahedron are no longer in contact with each other, they are supported on both sides by the unpaired atoms. I am unable to give an instance of this arrangement as occurring in fact. We may speak of it as Case II.