Bartow—A Mechanical Cause of Homogeneity of Crystals. 535: 
in Fedorow’s list;1 it has the generic symmetry of class 9 in 
Sohncke’s list of ieretallle deen: g 
As a and 0 are just as closely packed, one as the ens it would 
seem, at first sight, that in every case where the centres are of a 
single kind, one of these arrangements is as available as the other. 
But this can hardly be the case, for it is conceivable that the 
initial disposition of the centres may by some means, perhaps 
fortuitously, be nearer to the one arrangement than to the other 
in some given case; and if this is so, the assemblage will pass more 
easily to the arrangement to which it thus already approximates, 
and on reaching it can experience no disposition to adopt the other. 
And further, a fortuitous arrangement ts, in some respects, nearer to 
form (a) than to form (b). For, in a, the planes most thickly set 
with ball centres have four different directions, viz., those per- 
-pendicular to the cube diagonals, while in 6 they have but 
one such plane direction. And if we suppose that, starting with 
a fortuitous arrangement, the first step towards closest-packing 
is the production of a large number of aggregations in which 
closest-packing prevails, but which are variously orientated, it is 
obvious that the passage to a continuous closest-packed arrange- 
ment which absorbs all these, will partly consist in reducing the 
number of the different orientations of the groups, and that, as 
the movements requisite to reduce them to four will be less, on the 
whole, than would be requisite to bring them to a single common 
orientation, the cubic arrangement marked a will generally be 
easier to reach than the hexagonal one marked 0.° 
If, as in the last case, the balls are all similar, but are aggregated 
to form a number of similar groups in which each ball is similarly 
linked to the remaining balls of its group, the conditions obviously 
become much more complex, and it is easily seen that the closest- 
packed arrangement will but rarely be of the type just named.* 
1 Zeitschr. fiir Kryst., 24, p. 236. 2 Tbhid., 20, p. 460. 
3 The argument is perhaps easier to follow if we think of the balls as shaken close 
together in a bag. 
4 Tf the reader desires to study the simpler cases of arrangement before he addresses 
himself to the more complex, he should pass on at once to the cases in which the 
balls are of two kinds. (See p. 546). 
