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586 Scientific Proceedings, Royal Dublin Society. ] 
The centre of a unit group is not necessarily the centre of a 
geometrical space-unit? of the assemblage in which it occurs ;? it 
may be the centre of an aggregate consisting of two or more of 
such units taken together. Some of its ball-centres may lie upon 
axes of rotation, and thus bear a similar relation to two or more of 
these units. ‘The number of space-units which can be comprised 
in a unit-group is, however, very limited, for it is evident that in 
ascertaining the situations of the space-units composing such a 
group, 20 coincidence movements (Deckbewegungen) of the assemblage 
ave admissible which shift the centre point of the unit-group, since 
these would not bring the group to coincidence (Deckung) with 
itself.* 
The following are some possible simple ways in which unit- 
groups may be formed by partitioning homongeneous assemblages. 
into units of one kind only, or conversely, in which similar unit- 
groups may be fitted together to form homogeneous assemblages :— 
1. Groups similar to one another of the composition A B, 7. e., 
each composed of two different balls of given kinds, may form an 
assemblage of type 2. 
_ Thus in an assemblage consisting of a number of similar 
groups, each composed of two balls of different kinds, let the link 
uniting the two centres be of such a nature that when equilibrium 
is arrived at the distance separating the centres in a group is but 
little less than the distance separating dissimilar centres in ad- 
jacent groups. Further, let the relations between the balls be 
very nearly that prevailing in the assemblage of type 7a, de- 
scribed on page 549. 
The arrangement of the centres for closest-packing will then, 
very approximately, be that prevailing in the last-named assem- 
blage, a slight departure from this arrangement being, however, 
1 A geometrical space-unit of a homogeneous structure is any continuous portion 
' of space which encloses every kind of point or position from which it can be viewed or 
considered, and but one of each kind.’ Comp. “ Zeitschrift fiir Krystallographie,’’ 23, 
p. 37. 
2 Comp. Zeitschr. f. Kyrst. 23, pp. 37-38, and 59, Taf. ii, figs. 18, 16, 17, 18. 
3 The hypothesis that crystal molecules are large composite units made up of a great 
number of smaller units, i.e., of chemical molecules, is not, therefore, consistent with 
the geometrical necessities of symmetrical partitioning. 
4 See Zeitschr. f. Kryst., 23, p. 10. 
