Bartow—A Mechanical Cause of Homogeneity of Crystals. 663 
_ formation of an assemblage which treats this slight deformity as non- 
eaistent. 
To make this plainer by means of an example :—Suppose that 
a linked group has cubic symmetry, except that out of twenty-four 
outermost balls but twenty-two or twenty-three are similar and 
similarly situated, dissimilar balls making up the twenty-four 
and occupying places which are symmetrically situated, or nearly 
so; it is then conceivable that the closest-packing of a number 
of groups of this description may be one which disregards the 
slight irregularity and puts the groups together with their 
centres at the points of a cubic lattice, and with their pre- 
dominating symmetrically arranged balls forming, as far as they 
go, a system in cubic symmetry. 
In a case of this kind the positions of the irregularities will not 
be symmetrically distributed; in other words the groups, when 
the deformities are taken into account, will be found variously 
orientated and the assemblage will not be strictly—v. e., mathema- 
tically—homogeneous, although, owing to the average effect of the 
deformities being the same in corresponding directions, the general 
symmetry will not be appreciably impaired. 
Large groups will be more particularly liable to function as 
though of a higher symmetry than they actually possess in the 
way just described. 
To compare with this we have the observation frequently made 
with reference to carbon compounds and their derivatives, that the 
higher the symmetry of the parent substance the less is the change 
in crystalline form caused by substitution. Thus the cubic form 
of ammonium alum is unaffected by the entrance of a methyl 
group in place of an atom of ammoniacal hydrogen, whilst such a 
substitution in an orthorhombic or monosymmetric compound 
would lead to a considerable alteration in crystalline form. If 
the parent substance contains several equivalent hydrogen atoms, 
it not infrequently happens that the symmetry of the system is 
decreased by substitution for one of these atoms; but that, as 
several or all of the hydrogen atoms are displaced, the products 
again crystallize in the same system as the parent substance.’ 
1 See Pope’s translation of Fock’s ‘‘ Chemische Krystallographie,’’ p. 181. 
