| 
A ? 
ii 
just fit into them. Hach large sphere will then be in contact with 
eight of the same size and twelve of the smaller size, and each — 
small sphere will be in contact with six of the larger spheres. 
Such an arrangement would appear to give closest-packing, for/y 
spheres of two sizes thus proportioned. 
The type of homogeneous structure is that marked 25a, in my 
list. The generic symmetry is that of class 9 in Sohncke’s list.” 
The two kinds of centres are present in the numerical proportions 
1:2. Hach kind formsa singular point system, the less numerous 
kind lying at the point of intersection of hexagonal and digonal 
axes and planes of symmetry, and the more numerous at the points 
of intersection of trigonal and digonal axes and planes of symmetry. 
004 Scientific Proceedings, Royal Dublin Society. 
Case of rhombohedrism. 
In the closest-packed arrangement of spheres of two different — 
radii, referred to on page 549, the centres of one set occupy the 
centres, and the centres of the other set, the angles of the cubes of © 
a cubic partitioning of space. Suppose now that we have two sets 
of spheres whose radii are nearly in the proportion requisite for 
this arrangement, but that the smaller are rather too small for the 
purpose. Closest-packing will then probably be attained in an — 
acute rhombohedral arrangement, in which each of the larger 
spheres is in contact with six of the same size and six of the smaller 
size, and each of the smaller spheres is in contact with six of the — 
larger ones, this arrangement being derived from the cubic one just 
referred to by a slight relative elongation of the assemblage in the 
direction of a cube diagonal and uniform contraction in directions — 
transverse to this. ; 
The type of homogeneous structure presented is that marked — 
52a, in my list. The generic symmetry is that of class 12 in — 
Sohncke’s list. The two kinds of centres are present in equal — 
numbers. Hach kind forms a singular point system, the centres 
all lying at the points of intersection of trigonal and digonal axes 
and on lines of intersection of planes of symmetry. 
ta a , et, 
oe rT ee ae 
1 Zeitschr. fiir Kryst., 23, p. 45. 2 Tbid., 20, p. 460. 
3 Zeitschr. fiir Kryst., 28, p. 47. 4 Ibid., 20, p. 461. 
