. 
562 Scientific Proceedings, Royal Dublin Society. 
Over these gaps place equal spheres of greater size, and over 
the points midway between them a second set of equal spheres 
smaller than those over the gaps, the size of the spheres in the 
two sets being such that their centres lie in the same plane 
and that they are in contact. ; 
On the second layer thus formed place a third layer similar 
to the first and vertically over it, and then a fourth similar to 
the second in like manner, and so on. 
In such an assemblage each smaller sphere is in contact 
with five of the same size, two of the medium size and two of 
the large size; each medium-. 
_ sized sphere is in contact with pa a Ee 
six small and three large ; each 
large sphere with twelve small Ja 
and six medium-sized.1 The 
type of homogeneous structure 
presented is numbered 23a, in 
my list.” The genericsymmetry 
is that of class 11 in Sohncke’s 
list of Krystallklassen. The 
three kinds of centres are pre- 
sent in the proportions 1 : 2: 6. 
All the centres occupy singular 
points, those of one of the two 
less numerous kinds lying on hexagonal axes, those of the other 
on trigonal axes, and all in planes of symmetry. 
Case of pyramidal hemihedrism of the tetragonal system. 
Arrange a plane layer of spheres in close square order, but 
with gaps asshown in fig. 16. Over these gaps, and also over the 
; 
4 
4 
a 
points midway between them, place other spheres in contact with — 
those first placed of such radii that their centres all lie in the same 
plane, and that they touch one another. 
On the second layer thus formed, place a third layer similar to 
the first and vertically over it, and then a fourth similar to the 
second in like manner, and so on. 
1 See note 5, p. 551. 2 Zeitschr. fiir Kryst., 23, p. 45. 
