358 SCIENCE PROGRESS 



lead to interesting developments ; for instance it may happen 

 that a particular structure may be partitioned in different ways 

 so as to yield units of the same composition but differently con- 

 stituted ; and it may thus be possible from geometrical considera- 

 tions to gain an insight into such purely chemical phenomena 

 as that of isomeric change. 



The Interpretation of Valency 



By a logical development of this fundamental hypothesis of 

 crystal structure, the authors have come to some noteworthy 

 conclusions which, when they become generally understood, 

 cannot fail to influence the trend of modern thought. The most 

 important of these conclusions concerns that debatable question, 

 the nature of valency. From the consideration of the geometrical 

 properties of close-packed assemblages of spheres, the remarkable 

 deduction is made that valency is an expression of a volume 

 relationship. The particular geometrical properties from which 

 this deduction is made are those which relate to the conversion 

 of one assemblage, by substitution of certain of its parts, into a 

 related assemblage. Suppose that from any particular close- 

 packed assemblage spheres or sets of spheres of influence be 

 removed homogeneously so as to produce a number of cavities 

 and that these cavities be then similarly filled by other spheres or 

 sets of spheres of influence : then if the same density of packing 

 is to be preserved without remarshalling the assemblage, the 

 total volume of the sphere or spheres thus introduced into each 

 cavity must be about equal to that of the sphere or spheres re- 

 moved from that cavity. The bearing of this fact upon the 

 question of valency will become clear if a concrete example, 

 such as the derivation of triphenylamine from benzene, be con- 

 sidered. Without troubling for the present about the form of 

 the assemblage characteristic of crystalline benzene, suppose it 

 to be possible to form a cavity in that assemblage by removing 

 three adjoining hydrogen spheres, one from each of three ben- 

 zene units. It will be found that if a nitrogen sphere is to 

 be squeezed into such a cavity so that only a slight readjust- 

 ment is necessary to restore close-packing, the volume of the 

 nitrogen sphere must be equal to that of the three hydrogen 

 spheres or three times that of a single hydrogen sphere of 

 influence. The mind is led instantly to connect this circum- 

 stance with the fact that the valency of nitrogen is 3, that of 



