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Prof. W. J. Sollas. 



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. 

 A^ r e may speak of it as Case II. 



