October 16th, ipo6.] Proceedings. ix 



facts soft indiarubber balls are used, and the assemblages built 

 up from them are compressed until the interstitial space is 

 practically eliminated. This compression does not materially 

 alter the relative dimensions of a close-packed assemblage of 

 elastic spheres as measured between the sphere centres ; the 

 equilibrium of the mutual interactions of the elastic deformable 

 spheres of the artificial system represents an equilibrium between 

 attraction and repulsion such as has been usually postulated by 

 molecular physicists. The definite magnitude of sphere used in 

 the case of a given element does not represent the absolute 

 atomic volume of the latter. It stands for the relative atomic 

 volume as compared with the atomic volumes of other elements 

 present in the same compound ; this relative volume is found to 

 be almost constant throughout series of allied compounds. 



The development of the above conception of molecular con- 

 stitution leads to the conclusion that in a crystalline structure 

 the component spheres of atomic influence form a homogeneous 

 and close-packed arrangement, that is, a homogeneous arrange- 

 ment in which, if hard undeformable spheres are employed, the 

 maximum number of contacts and the minimum proportion of 

 interstitial space occurs. Further, it is found that in homo- 

 geneous close-packed assemblages of the elastic spheres of various 

 sizes, one particular kind of component sphere may be homo- 

 geneously replaced throughout the assemblage by other spheres, 

 the total volume of which is equal to that of the displaced 

 spheres in such a way that close-packing is re-established by the 

 occurrence of a slight shear or distortion of the assemblage. It 

 thus appears that the volumes of the spheres of influence of the 

 atoms composing a molecule are approximately directly propor- 

 tional to the chemical valencies of the component atoms. 



It therefore follows that if, in a series of chemically related 

 crystalline substances, the axial ratios, a : b : c, and the inter- 

 axial angles, o, /3 and y, have been suitably selected, the relative 

 molecular dimensions, x \y : z, or the "equivalent parameters," 

 are simple functions of the crystallographic dimensions and the 

 sum of the valencies of the atoms composing the molecules. 



