564 Scientific Proceedings, Royal Dublin Society. 
been shown. by the author’ to possess the generic symmetry of one 
or other of the thirty-two classes of crystal-symmetry. 
In most of the instances of symmetrical arrangement above 
traced it is not easy to determine with certainty whether we have 
arrived at a system which can give stable equilibrium or not, but 
there is a high probability that in very many cases stable equili- 
brium is attainable in the arrangement described without any 
linking being premised, if certain appropriate relations between 
the repulsions be chosen. In any case we have established the 
following proposition :— 
That assemblages belonging to all of the thirty-two classes of erystal- 
line symmetry result from closest-packing of balls of different sizes, when 
the relations between the different radu take the widest possible range 
of variety, and cases of packing together of spheres formed into groups 
in the way premised are included, as well as the cases in which the 
spheres are unlinked. 
This proposition has, as has just been intimated, been established 
from a consideration of comparatively simple cases; the employ- 
ment of more complicated assemblages would lead to the same 
conclusions.” 
An examination of some results corresponding to the facts of 
stereo-chemistry which is undertaken later* will show that in some 
of these more complicated assemblages the centres of the same kind 
occupy enantiomorphously-similar, as well as identically-similar, 
positions, like the points of a Fedorow-Schonflies ‘‘doppeltes 
System.’ 
The spread of symmetrical arrangement in an assemblage. Crystal 
growth. Bent and branched crystals. 
If a process of close-packing, due to the interaction of its parts, 
is the agency by which an assemblage becomes arranged symme- 
trically, it is evident that the solidification, 7. e., complete linking 
up of the parts which produces a rigid homogeneous assemblage, 
is not strictly concurrent with, but subsequent in time to, the arrang- 
1 Zeitschr. fiir Kryst., 23, p. 1. 2 See note 1, p. 533. 
3 See pp. 582 e¢ seg. - 4 Zeitschr: fiir Kryst., 23, p. 41. 
