Bartow—A Mechanical Cause of Homogeneity of Crystals. 589 
Take next a case in which the ball centres, while all of one 
kind, are similarly linked to one another to form groups of three. 
Manifestly for each of the three centres of a group to be similarly 
placed with respect to the remaining centres of the same group, 
they must lie at the three angles of an equilateral triangle. 
Suppose— 
(a) That the distances between the three centres linked together 
to form a group are small as compared with the distances between 
the nearest centres in different groups when equilibrium is 
reached. 
As in the corresponding case of groups containing two balls, 
very close packing will be attained if the arrangement of the 
groups is that of the sphere centres in figs. 1 and 2, but 
this would not appear in general to be 
the closest-packing possible if we take 
the shape of the groups into conside- 
ration, 7.e., unless the distance between 
the centres of a group is so small as to 
make the shape of the group quite in- 
operative. It would seem that the 
closest-packing possible is attained 
when the disposition of the groups ap- 
proximates to the one referred to on p. 
534 (and see fig. 3), and the orientation 
of the groups is such that the arrangement of the ball centres is 
that of a system 52 of Sohncke,' whose generating point lies 
on one of the digonal axes which intersects trigonal axes near 
to one of the latter, and on a line of intersection of planes of 
symmetry. ‘The structure presented is of the type marked 24a, 
in my list ;? and the generic system displayed by sucha system is 
the holohedral symmetry of class 9 in Sohncke’s list of Krystall- 
klassen.* The nature of the arrangement is shown in fig. 5, in 
which each group is seen to consist of three interpenetrating spheres 
which are in contact with the spheres of adjoining groups. The 
1 See ‘“‘Entwickelung &c.”’, p.115. Compare Zeitschr. fiir Kryst., 23, pp. 23 and 25. 
2 See Zeitschr. fiir Kryst., 23, p. 45. The ‘‘doppeltes System’’ is No. 87a of 
Fedorow, Zeitschr. fiir Kryst., 24, viii., Taf. vi. 
3 Zeitschr. fiir Kryst., 20, p. 460. 
