Bartow—A Mechanical Cause of Homogeneity of Crystals. 587 
caused by the balls of the same group being drawn rather nearer 
together, much as they are in the assemblage of paired balls of 
type 5, described on page 538. The two balls of a group are not, 
however, necessarily placed similarly, as in the last-named case, 
although balls of one kind lie very nearly at the cube centres, 
those of the other kind very nearly at the cube angles of the space 
partitioning employed to generate the system. 
The result will be an assemblage of type 2, displaying the 
symmetry of class 32 in Sohncke’s list,’ the positions of centres of 
both kinds being singular points lying on the trigonal axes, but 
the spaces between the different points on such an axis being not | 
all equal but alternately equal. 
It is clear that the existence of the links must be postulated in 
order to get the balls arranged, as suggested, in the symmetry of 
type 2, and therefore that we have not shown by the foregoing 
how such groups can be produced, but only how they can be 
arranged. Their production may be effected by the symmetrical 
breaking-up of complicated assemblages into simpler ones in an 
endless variety of ways.’ 
2. Groups similar to one another of the composition A, B, may 
form an assemblage of type 7b,, and may be obtained from a certain 
assemblage of this type. 
Thus if an assemblage consisting of two kinds of balls present 
in equal numbers arranged in the tetrahedral hemihedry of the 
cubic system described on page 550 have its adjacent balls all 
linked together, this assemblage can, by asymmetrical breaking of 
the links, be divided into identical grouplets, each consisting of a 
tetrahedrally arranged group of four larger balls, to which are 
linked four of the smaller balls, these also having a tetrahedral 
arrangement, and the two regular tetrahedra formed by joining 
the balls of each set being oppositely orientated. All the four 
balls of each kind are therefore similarly placed in the grouplet. 
3. Groups similar to one another of the composition A, B, 
may form an assemblage of type 62a,, and may be obtained from 
a certain assemblage of this type. 
Thus if an assemblage consisting of two kinds of balls present 
1 See Zeitschr. f. Kryst., 20, p. 467. 2 See p. 682. 
