MOLECULAR ARCHITECTURE 359 



hydrogen being unity. And the conclusion at which Pope and 

 Barlow have arrived from considerations such as the above is 

 that, in any given crystal structure, the volumes of the spheres 

 of atomic influence of which the structure consists are approxi- 

 mately proportional to the fundamental valencies of the atoms 

 composing the molecule. For instance in the structure appro- 

 priate to triphenylamine, if the volume of each hydrogen sphere 

 be taken as unity, each carbon sphere has a volume 4 and each 

 nitrogen sphere a volume 3. Note the expression " fundamental 

 valencies," for it has never yet been found necessary, in the 

 numerous cases studied, to ascribe to the sphere of influence of 

 any atom a different volume from that expressed by its funda- 

 mental valency. The volume of a nitrogen sphere appears 

 always to be three times that of the sphere of a monovalent 

 atom, even in the ammonium compounds, in which the element 

 is usually considered to be pentavalent. 



This new conception of valency has an important bearing 

 upon the prevalent ideas, due to Kopp, of atomic and molecular 

 volumes. It was Kopp's belief that each element had its own 

 specific and constant atomic volume and that once these atomic 

 volumes were determined, any molecular volume could be 

 calculated b}^ summing up the volumes of the atoms contained 

 in the molecule. His results are, however, not compatible with 

 the new idea of the proportionality of valency and atomic 

 volume, as a single example will show. It has been demon- 

 strated by Barlow and Pope that benzene and paradibrom- 

 benzene have in the crystalline form almost identical spatial 

 arrangements ; and on the new hypothesis this is only to be 

 expected, since in p-dibrombenzene the spheres of atomic 

 influence of hydrogen and bromine will occupy equal volumes, 

 one-fourth that of a carbon sphere, just as in benzene each 

 hydrogen atomic sphere occupies one-fourth the volume of a 

 carbon sphere. This being so, the substitution of hydrogen by 

 bromine need not be accompanied by any profound change in 

 crystalline form. But Kopp ascribed to hydrogen and bromine 

 atomic volumes equal to 5*5 and 27-8 respectively; and if these 

 figures express the truth, it would be expected that substitution 

 of hydrogen by bromine should produce considerable distortion 

 in the crystalline assemblage of benzene. The fact that no 

 appreciable distortion is observed is evidence in favour of the 

 new doctrine. 



