Bartow—A Mechanical Cause of Homogeneity of Crystals. 551 
homogeneous structure to which such an assemblage belongs is that 
_ numbered 7b; in my list... The generic symmetry is that of class 
30 in Sohncke’s list.*, The two kinds of balls are, as in the last 
_ ease, present in equal numerical proportions ; each kind of centre 
forms a singular point-system, all centres lying on trigonal axes, 
and also in planes of symmetry. All the balls are operative.® 
There is an important difference between this case of closest- 
packing, and the cases for two kinds of balls previously given. In 
_ the latter no kind of partitioning of the structure into unit groups 
of balls is possible which is not arbitrary, and, owing to its incom- 
patibility with the coincidence-movements (Deckbewegungen), pro- 
ductive of a lowering of the type of symmetry. In the present 
case, partitioning into groups of the form A,, By, can take place 
without lowering the type.‘ 
Case of gyrohedral hemthedrism of the cubie system. 
Again, the radii of two different sets of spheres may be so pro- 
portioned that the closest-packed mixed’ 
arrangement is of the following kind :— 
Partition space with maximum regu- 
larity into similar plane-walled cells, 
whose centres are at the centres and angles 
of a cubical partitioning of space; these 
cells will be octahedra truncated by cubes 
in such a way as to reduce the octahedron 
faces to regular hexagons (fig. 11). 
Join three alternate angles of each of the hexagonal interfaces, 
selecting the angles symmetrically, and bisect the lines thus drawn. 
There are two ways of doing this (a and 4, fig. 11, in which only 
the bisecting points are shown). 
At the points of bisection of one set thus obtained, place the 
centres of spheres whose diameter is such that they touch one 
Fig. 11. 
1 Zeitschr. fiir. Kryst., 23, p. 52. 2 Zeitschr. fiir Kryst., 20, p. 467. 
3 See p. 547. 
4 See Mineralogical Magazine, vol. xi., p. 130. Comp. post, p. 587. 
5 Some sort of linking will most likely be requisite for this kind of packing to 
obtain; the massing of each set by itse/f in closest-packing will probably demand less 
space than any mixture of the two kinds of the nature here described. 
