560 Scientific Proceedings, Royal Dublin Society. 
One out of every three centres of each kind lies in a plane of 
symmetry, and the centres thus distinguished, therefore, form two 
singular point-systems. The axes are parallel to the plane of the 
diagram and horizontal; the planes of symmetry are perpendicu- 
lar to the plane of the diagram through vertical lines. 
A. second ease of holohedrism of the monochiic system. 
If in a stack of spheres arranged for holohedrism of the hexago- 
nal system in the way described on p. 553, the smaller spheres are 
just too small to fill the cavities containing them, the grouping 
referred to will not give closest-packing, but if the system be canted 
over slightly, and the spacing of the spheres in the layers be very 
slightly modified in an appropriate manner, an arrangement which 
is probably a closest-packed arrangement can be obtained which 
is an example of holohedrism of the monoclinic system. The type 
of homogeneous structure is that marked 64a, in my list.1 The 
generic symmetry is that of class 3 in Sohncke’s list of Krystall- 
klassen ; the two kinds are present in the numerical proportions 1: 2. 
Centres of the same kind do not all occupy similar positions in the 
structure. 
C. Formation of homogeneous assemblages when the balls are of three 
kinds. 
Case of tetartohedrism of the cubic system. 
Partition all space into equal cubes. 
Place similar tetrahedral grouplets, each consisting of four 
equal spheres in contact with each other, so that their centres 
occupy the centres of the cubes. ; 
Similarly place tetrahedral grouplets composed of spheres of 
another size at all the cube angles. 
Finally place tetrahedral grouplets composed of spheres of a 
third size at all the middle points of the cube edges.” 
Tf all the grouplets are similarly orientated, and their axes have 
the four directions of the cube diagonals, sizes can be selected for 
the three sets of spheres which will give very close packing in the 
1 Zeitschr. fir Kryst., 23, p. 48. 
2 Or at all the middle points of the cube faces, the latter having the same situa- 
tions relatively to the cube centres as the middle points of the cube edges have 
relatively to the cube angles. 
