Bartow—A Mechanical Cause of Homogeneity of Crystals. 649 
if the arrangement of the balls and the linear dimensions are 
different. 
On the other hand, they will be capable of the kind of inter- 
calation referred to, if in a roughly intermingled collection of two 
different kinds of assemblage, where both are about to solidify, it 
is found that at boundaries between the different kinds very close 
packing indeed is attained when the two adjacent structures are 
similarly orientated. For if this is so a bounding plane-layer of 
the growing solid composed of the one assemblage is capable of 
receiving an accretion either of another layer of the same kind of 
assemblage, or of a suitable layer of the other assemblage. 
If two intercalated assemblages are so related as to be capable 
of subdivision into space-units' which are identically shaped or 
very nearly so, or indeed if the shape and size of an aggregate 
formed of a finite number of contiguous space-units of some kind 
of one assemblage are identical with the shape and size of an 
ageregate formed by the same or some other finite number of 
contiguous space-units of some kind in the other assemblage, it is 
evident that there may be extremely little disturbance of regu- 
larity at ad/ the boundaries between the two kinds. 
Tf, however, while accretion of one kind of assemblage on the 
other readily takes place over small portions of some of the bounding 
surfaces of the growing solid, the space-units are not congruent, and 
this will generally be the case, it is evident that the regularity at 
the boundaries between the different kinds will be merely an 
initial one, 7.e., found only at the points at which the accretion of 
one kind on the other makes a fresh start, and that, like the 
surfaces between the differently orientated individual assemblages 
of a mass solidified before the arranging sought to be accomplished 
_ by the principle of closest-packing is completed,” or the more or 
less irregular surfaces at which in most cases individual twin- 
assemblayes meet during the continuance of their growth, the boun- 
dary formed as two assemblages of different kinds grow side by 
side will be a surface of some kind where they meet unconformably. 
Nevertheless this want of congruence at some boundaries will be quite 
consistent with the property that all corresponding directions in the two 
1 See note 1, p. 586. 2 See p. 620. 3 See p. 623. 
