iv Proceedings. {^October i^th, igoy. 



hexagonal elements exhibit axial ratios approximating to one or 

 other of these values. The fact that so large a proportion (85 

 per cent.) of the elements crystallise in either the cubic or the 

 hexagonal system is therefore closely paralleled by the fact that 

 their crystal structures can be graphically represented by homo- 

 geneous closest-packed assemblages of equal spheres in accord- 

 ance with the authors' previous work. 



It is shown that the crystalline forms affected by elements 

 crystallising in systems of lower symmetry than the cubic and 

 hexagonal can be derived by slight distortion from one or other 

 of the two closest-packed assemblages above mentioned ; the 

 requisite distortion may result from molecular aggregation or 

 from some other cause. 



Most of the crystalline binary compounds consist of two 

 elements of the same valency, and, in accordance with the 

 authors' previous conclusions, atoms of the same valency must 

 be represented in the crystalline edifice by spheres of approxi- 

 mately the same size. The reason is thus derived for the fact 

 that most binary compounds crystallise in either the cubic (68'5 

 per cent.) or the hexagonal (i9"5 per cent.) system. Homo- 

 geneous assemblages have, therefore, been constructed from 

 spheres of two kinds, but of approximately equal size, which 

 represent the crystalline structures of cubic and hexagonal com- 

 pounds, such as Agl, KI, CaO, &c. ; it is shown that the pro- 

 perties of these structures correspond very closely with those 

 observed upon the crystalline materials. The dimorphism of 

 silver iodide is elucidated by the simple manner in which the 

 cubic closest-packed assemblage can be converted into that of 

 hexagonal symmetry. A close agreement exists between the 

 calculated axial ratios stated above for the hexagonal assemblage, 

 and those observed upon the hexagonal binary compounds. 



The crystalline structure appropriate to such substances as 

 rubidium tri-iodide, Rblg, thallic iodide, TIT^, &c., is derived in 

 a similar manner to the above, and it is shown that close agree- 

 ment occurs between the derived and observed crystal forms. 

 By the study of such crystalline substances it can be shown that 



