542 Scientific Proceedings, Royal Dublin Society. 
close-packed stack of equal cubes (that of a kubisches centrirtes 
Raumgitter), and the arrangement of the ball centres is that of a 
system 56 of Sohncke (Type 10 in my list), whose generating point 
hes on a trigonal axis near to, but not at, a cube centre. Such a 
structure is of the type marked 10b, in my list.* The generic 
symmetry displayed is tetrahedral hemihedrism, being that of 
class 30 in Sohncke’s list. 
Suppose finally— 
(C.) That the distance between two of the ball centres forming 
a tetrahedral group is almost as great as the distance separating 
the nearest centres in different groups. 
The arrangement of the centres can now approximate very 
closely to that of the sphere centres of figs. 1 and 2. This is accom- 
plished if the centre points of the groups form a cubic space-lattice, 
and the arrangement of the centres is that of a system 54 of 
Sohncke (type 7 in my list) whose generating point lies on a 
trigonal axis at a distance rather less than d/4 from a cube centre 
where d is the diameter of a cube of the space-partitioning which 
I have employed to generate this system. (If the distance were 
exactly d/4 the particles would have the closest-packed arrangement 
shown in figs. land 2). The structure obtained is of the type num- 
bered 7b; in my list.* The generic symmetry, as in the last case, is 
tetrahedral hemihedrism, being that of Sohncke’s class 80. ‘There 
is, however, another arrangement of the tetrahedral groups of balls 
which gives equally close-packing with that just described. For 
a closest-packed cubic assemblage of spheres can be partitioned 
into tetrahedral groups in two different ways, 7.e., (a) one of the 
form just described in which the system, after partitioning, pre-— 
sents the type of symmetry No. 7b:, and (d) one in which each 
triplet of spheres forming a face of a tetrahedral group is fitted 
into a triplet of an adjoining tetrahedral group. ‘The arrange- 
ment of the ball centres, when the groups are placed in this 
way, is that of a system 63 of Sohncke whose generating point 
lies on a trigonal axis at a distance rather less than d/4 from a 
1 Entwickelung &c.”, p. 157. Comp. Zeitschr. f. Kryst., 23, p. 20. 
2 Zeitschr. f. Kryst., 23, p. 62. 
3 Tbid., 20, p. 467. + Zeitschr. f. Kryst., 23, p. 52. 
