1910] on tlie Ohemkal Sifjnifi ranee of Crystal 8tructv,re. 825 



manner in which the parts of the structure are arranged ; this assump- 

 tion is that the structure is a geometrically " homogeneous " one, 

 that is, a structure the parts of which are uniformly repeated through- 

 out, corresponding points having a similar environment everywhere 

 within the edifice. The assumption of geometrical homogeneity as 

 the characteristic of crystalline solids leads at once to the great problem 

 solved by the crystallographers of the nineteenth century. This con- 

 sisted in the inquiry as to how many types of homogeneous arrange- 

 ment of points in space are possible, to the study of those types and 

 to their identification, in symmetry and other respects, with the known 

 systems into which crystalline solids fall. This work was commenced 

 by the German crystallographer Frankenheim in I80O, and completed 

 by the English geometrician Barlow in 1894. Briefly stated, the final 

 conclusion has been attained that 230 geometrically homogeneous 

 modes exist of distributing material, or points representing material 

 throughout space, and that these 2?>0 homogeneous types of structure, 

 the so-called homogeneous "point-systems," fall into the 32 types of 

 symmetry exhibited by crystalline solids. Models of a number of 

 homogeneous point systems illustrating some of these types are 

 exhibited. 



It is, however, obvious that the limitation of the possibilities of 

 solid crystalline arrangement to 230 types marks but one stage in the 

 determination of the nature of crystal structure, and throws no direct 

 light on the relation between crystal structure and chemical constitu- 

 tion. Although by the end of the nineteenth century we had learnt 

 that corresponding points of the units of crystalline structures form 

 homogeneous point-systems, the great problem still remained of 

 determining what are the entities which become homogeneously 

 arranged, for what reason they become so arranged, and in what way 

 the conclusions drawn by modern chemistry are reflected in crystal 

 structure. This problem was a legacy to the twentieth century, and 

 it now remains to indicate briefly the extent to which it has been 

 solved and the results of chemical importance which have accrued 

 during its investigation. 



The problem may be most easily visuahsed in connection with 

 some comparatively simple case, that, for instance, presented by the 

 crystaUine forms assumed by the elements themselves. It is gene- 

 rally admitted that an elementary substance consists of identical 

 atoms, each of which acts as a centre of operation of attractive and 

 repulsive forces. In a solid crystalline structure the atoms are 

 obviously not free to travel through the mass, each, if not indeed 

 fixed to a particular spot, being retained within a certain minute 

 domain ; each of these domains must be regarded as possessing a centre 

 which marks the mean position of the atom. 



The crystalline condition of an element may consequently be 

 defined as one of equilibrium between forces of attraction and repul- 

 sion emanating from or referable to a flock of points homogeneously 



