7o6 SCIENCE PROGRESS 



say, we assume that any face of the crystal form if produced 

 will intercept each axis at its own axial length from the centre. 

 Now if m be made {m}, n becomes {121} and the ratios 

 a : b and c : b have a certain value. But we might equally well 

 have called n {in}, in which case w would be {212} and the 

 values of the two ratios a : b and c : b would become just 

 double what they were before. 



If we are to compare the dimensions of the crystal structures 

 of different bodies, it is obvious that we must make certain 

 that the dimensions compared are really comparable. The 

 dimensions we compare are those given by the equivalence 

 parameters and these are calculated from the axial ratios. The 

 axial ratios must therefore be comparable and in order to make 

 them so it frequently becomes necessary to modify the values 

 given by different observers by multiplying them by some 

 simple whole number or fraction. Some objection has been 

 raised to this treatment of axial ratios but from what has been 

 said it will be obvious that some such treatment must sometimes 

 be resorted to. 



In the case of monosymmetric crystals the choice of the 

 ^ angle offers some difficulty. It is found, however, that most 

 benzene derivatives may be regarded as in some manner 

 derived from orthorhombic benzene, viz. from the first or third 

 form of benzene assemblage, one right angle being destroyed 

 through a shear ; it is usual to chose the angle which is nearest 

 to 90° on the zone parallel to the axis of symmetry for the 

 interaxial angle. When this rule is followed the results obtained 

 are generally satisfactory. At present, however, little can be 

 done with anorthic crystals. 



The simplest derivatives of benzene are those in which one 

 or more hydrogen atoms have been displaced by other uni- 

 valent atoms, e.g. atoms of halogen elements. In accordance 

 with the principles already put forward halogen derivatives of 

 benzene possess the same valency volume as benzene itself; 

 hence they should exhibit a crystal structure almost identical 

 with that of the parent substance. This is indeed found to 

 be the case. Hexachloro- and hexabromo-benzene exhibit 

 rhombic symmetry, whilst several other halogen-substituted 

 benzenes exhibit rhombohedral symmetry. The following 

 table shows the equivalence parameters of a number of these 

 substances : 



