694 SCIENCE PROGRESS 



arrangement of the sphere-centres in the assemblage traceable 

 to the existence of small inequalities between the distances 

 separating nearest sphere-centres. The united result of these 

 two factors is a degradation of symmetry and whilst it is 

 found possible under the new conditions to obtain cubic or 

 hexagonal symmetry as in an assemblage of uniform spheres, 

 the symmetry is of a somewhat lower order. The degradation 

 of the symmetry of the assemblage finds expression in the 

 disappearance of certain of the elements of symmetry which 

 characterise the cubic and hexagonal closest-packed assemblages 

 of equal spheres. These latter are said to present holohedral 

 cubic or hexagonal symmetry ; the suppression of elements of 

 symmetry referred to leads to the production of the so-called 

 hemihedral and tetartohedral types of cubic and hexagonal 

 symmetry. 



Now let us look at the facts. A large number of binary 

 compounds such as oxides and sulphides of bivalent elements 

 and chlorides, bromides and iodides of univalent elements 

 have been examined crystallographically and almost without 

 exception these are found to crystallise in hemihedral cubic 

 or hexagonal forms. Further in the case of binary substances 

 crystallising in the hexagonal system, as in the case of elements 

 presenting this type of symmetry, the axial ratio a : c approxi- 

 mates to I : I "6330 or I :o'8i65. 



How near the actual observed value of a:c approaches to 

 the theoretical value is well shown in the following table : 



Compound. a : c (observed). a : c (ideal). 



Beryllium Oxide, BeO . . . . i : r6305 i : i"6330 



Zinc Oxide, ZnO i : i'6o77 ,, 



Zinc Sulphide, ZnS . . . . I : 0-8175 i = 0-8165 



Cadmium Sulphide, CdS . . . i : 0-8109 >» 



Silver Iodide, Agl I : 0-8196 ,, 



The compounds in this table are practically the only binary 

 hexagonal compounds known. The great majority of binary 

 substances are cubic, very few crystallising in other systems. 

 Among these last may be mentioned tetragonal mercurous 

 chloride and iodide (if these be given the double formulae 

 HgjCla and Hg2l2 they are not strictly binary, as in such 

 compounds the mercury atomic sphere of influence may have 

 a valency volume = 2) ; orthorhombic litharge, PbO; mono- 

 symmetric mercuric oxide, HgO and a fevv^ more. 



