MOLECULAR ARCHITECTURE 699 



homogeneously into similarly constituted units having the com- 

 position CsHg. These units must have such a constitution that 

 they conform precisely to the known chemical properties of 

 benzene. This last point, of course, is most important. Among 

 such chemical properties must be noted the possibility of 

 forming but one mono- substitution product of benzene, three 

 isomeric di- substitution products, etc. Also it should be noted 

 that benzene derivatives do not exist in enantiomorphic forms. 



Benzene crystallises in the holohedral orthorhombic system, 

 having the axial ratios « :/^ :c = o"89i : i : 0799 (Groth). If the 

 equivalence parameters of benzene be calculated, according to 

 the method already given, from these axial ratios, they are found 

 to be xiy.z = 3'ioi : 3*480 : 2780, the valency volume being 30. 

 These three numbers represent three translations mutually at 



Fig. I. 



right angles in the crystalline structure of benzene. Hence any 

 assemblage of spheres derived to represent crystalline benzene 

 must exhibit holohedral orthorhombic symmetry and at the 

 same time must possess three translations at right angles cor- 

 responding in dimensions to the above equivalence parameters. 



Such are the data with which the problem has to be solved. 

 The solution at which Barlow and Pope have arrived in the 

 paper referred to is as follows. Six spheres of volume 4 are 

 placed so that their centres lie at the apices of a regular octa- 

 hedron. Six spheres each of volume i are then placed in 

 six of the eight similar hollows lying round the octahedral 

 group in such a manner that the two unoccupied hollows are 

 diametrically opposed. Up to the present then we have a 

 structure (see fig. i) representing the complex CeHe and it 

 remains to pack a number of these together in homogeneous 

 close-packed arrangement to arrive at the structure corre- 

 sponding in symmetry and dimensions to crystalline benzene. 

 A method of packing in harmony with the data is arrived at 

 as follows : 



