624 Scientific Proceedings, Royal Dublin Society. 
materially affecting relative distribution of parts. This will espe- ) 
cially be the case when the change is from one system of sym- — 
metry to another. If, for example, an assemblage passes from 
cubic to rhombohedral symmetry, much, if not all, of the conse- 
quent rearrangement will, in general, be most readily effected by 
a uniform distortion of the mass which alters the angles of the 
cubical space-lattice so as to convert it into a rhombohedral one. 
And if redistribution of the parts is hindered by the partial solidi- 
fication of the mass, the predominance of this general distortion 
in the arranging process will be the more pronounced. 
Now if in the case of an assemblage which is thus changing its 
form as a consequence of change in the conditions of equilibrium, 
the external and other conditions render it easier for the assem- 
blage to effect the alteration of form in sections whose directions of 
expansion and contraction are not the same, rather than as one undivided 
individual, sections or blocks differing in orientation will be pro- 
duced, and, as the principle of closest-packing will require as 
great an economy of space as possible to be practised, these sec- 
tions or blocks will be very symmetrically related to one another: 
in other words, a twinned assemblage will be produced. And the 
condition which makes it easier for the change to take this shape 
may be restraint of alteration of form arising from the situation 
of the assemblage within or in contact with solidified masses of 
some sort, either of the same or of some different composition. 
To make this clearer, let us take the following simple example : 
Suppose that, under certain external conditions, a number of 
similar complexes of balls are found when closest-packed to be 
arranged with their centre-points at the centres of the prisms of 
a system of identical hexagonal prisms with plane ends symme- 
trically fitted together to fill space, all the group centres lying 
therefore directly over one another in the arrangement shown 
in fig. 17. 
If now the conditions change so that the complexes when 
arranged as just described are no longer in equilibrium, but attain 
equilibrium in a simple cubic arrangement,’ the alteration im the 
1 This necessitates the form of a single complex being compatible with cubic 
symmetry. 
