136 



causal relations between chemical and crystallographical arrangement 

 and between the forces which determine the configuration of atoms 

 in space, in connection with those governing the structural arrange- 

 ment of the crystallonomical units. 



16. A highly suggestive theory concerning the problem men- 

 tioned, was developed in 1916 by Barlow and Pope 1 ). It represents 

 a happy completion of Barlow's views on homogeneous configu- 

 rations and the most closely packing of spheres by the aid of a new 

 fundamental hypothesis about the relation between the valency of an 

 atom and the space it occupies in such homogeneous assemblages. 

 The domain of each chemical atom is a distinct portion of space, 

 which it occupies by virtue of an influence exerted uniformly in every 

 direction. These spheres of influence are now supposed to have a 

 volume which in every compound is nearly proportional to the valency 

 of the atom, the factor of proportionality being the same for all atoms 

 of the same crystallised substance ; and according to the authors, a 

 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 occasionally by definite rotations too. 



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 



i) W. Barlow and W. J. Pope, Journ. Chem. Soc. London 89.1675. (1906); 

 G. Le Bas, ibid. 91. 112. (1907); W. Barlow and W. J. Pope, Journ. Chem. 

 Soc. 91. 1150. (1907); 93. 1528. (1908); F. M. Jaeger, Zeits. f. Kryst. 44. 61. 

 (1907); W. Barlow and W. J. Pope, Journ. Chem. Soc. 97. 2308. (1910); W. 

 Barlow, Miner. Mag. 17. 314. (1916); cf. also: W. Barlow, Zeits. f. Kryst. 29. 

 433. (1889); cf. also the work of A. E. H. Tutton: Isomorphism and Crystal- 

 structure, (1913). 



