MOLECULAR ARCHITECTURE 705 



numbers recurring. The dimensions of the alternative rhom- 

 bohedral marshalHng are not known ; but on theoretical grounds 

 the z value should be slightly less than 2780. In the pseudo- 

 cubic mode of packing the spheres, on the other hand, we may 

 look for pseudo-cubic symmetry, that is to say, two or all 

 three equivalence parameters may be approximately equal. 

 Under these circumstances the axial directions would be so 

 chosen that the usual z value could not appear. Further, the 

 ratio X \y in rhombohedral crystalline benzene would be 

 o"866o : I ; and finally the ratios 0'8i65 : i or r4i4 : i might 

 appear in compounds possessing pseudo-cubic marshalling. 



The Crystalline Structure of Benzene Derivatives 



It has been shown how relationships are to be recognised 

 between benzene and its crystalline derivatives. Many different 

 types of benzene substitution products have already been 

 examined crystallographically from the point of view of the new 

 theory and many remarkable results have been obtained from 

 the study of equivalence parameters. In some of these com- 

 pounds the hexagonal benzene marshalling, in some the pseudo- 

 cubic marshalling, is traceable ; in many cases one of the 

 equivalence parameters is approximately 2780, the z parameter 

 of benzene ; other compounds show the rhombohedral mar- 

 shalling and have one parameter slightly less than 2780, i.e. 

 corresponding with the z value characteristic of the (unknown) 

 second alternative benzene assemblage. 



Before proceeding to discuss the results which have been 

 obtained, it will be as well to mention one or two difficulties 

 which stand in the way when we wish to compare the crystal 

 constants of different substances. In any crystallographic 

 system except the cubic, the observer has a certain range of 

 choice of axial ratios, the particular axial ratios deduced depend- 

 ing upon the indices ascribed to particular faces appearing on 

 the crystal. The lower the type of symmetry the greater is 

 this freedom of choice, until in the monosymmetric system the 

 interaxial angle yS becomes a matter of choice and in the anorthic 

 system all three axes are chosen arbitrarily. Now suppose 

 that on an orthorhombic crystal, for instance, two forms m and 

 n occur either of which may be designated {m}, that is to 



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