140 



crystalline structure must be regarded as a most closely packed, homo- 

 geneous assemblage of the spheres of influence of the component atoms. 



The whole assemblage of atoms, most closely packed in the way 

 described, is of course homogeneously partitionable into exactly 

 similar cells which all contain a single chemical molecule. 



It will be clear that each point in every cell corresponds to a 

 homologous point in any other cell, and that these homologous 

 points of the same kind will represent a space-lattice characterised 

 by definite translations, and also occasionally by definite rotations. 



The unit-cell containing the single molecule, and built up by 

 spheres of atomic influence, has therefore in the whole assemblage 

 a similar function as the "repeat" had in our "patterns" formerly 

 discussed. The homogeneous, periodical nature of the whole structure 

 makes the partitioning into "molecular cells" to some extent arbi- 

 trary from a theoretical point of view, just as was previously pointed 

 out when we spoke of the significance of the conception of "molecule" 

 in the crystalline state. 



If a sphere be taken from the whole complex and replaced by 

 another, the total solid volume of the replacing and replaced spheres 

 must be almost the same. Thus the cavity produced by three hydrogen- 

 atoms may be nearly filled up by one trivalent nitrogen-atom, etc. 



It must here be remarked that the proportionality of the volume 

 of the influence-spheres and the valencies of the respective atoms, 

 is only an approximate one. This follows among other things from 

 the fact that the isomorphous substitution of K by Rb, or by Cs, 

 does not lead to identical crystal-forms, and also from the fact that 

 the univalent Li-, or Afa-atoms do not replace those of K, Rb, Cs, 

 isomorphously. From this the possibility of a slight shifting of these 

 spheres in most closely packing after such substitutions, and, as a 

 consequence of this, a change of symmetry, may be conceivable. 



17. The theory just described in outlines, has been applied 

 by both the authors in a very ingenious way to explain a number 

 of peculiarities and phenomena observed in crystals. For these 

 applications we must refer the reader here to the series of publications 

 mentioned in the preceding paragraph. It cannot be denied that 

 there often appears some arbitrariness with respect to the way in 

 which these assemblages are brought into agreement with the crys- 

 tallographical data at hand, especially with respect to the selection 

 of the "multiples of the axial ratios" as calculated from direct mea- 

 surements. This is the same criticism which has often been actually 



