BarLtow—A Mechanical Cause of Homogeneity of Crystals. 577 
filling space as symmetrically as possible; thus experiencing a 
change from the asymmetric to the regular system.’ 
As an example of a change such as would come under the 
second head may be given that of an assemblage consisting of two 
kinds of balls present in the proportions 1:2 from the gyrohedral 
hemihedrism of the cubic system described on page 551, to the 
holohedrism of the hexagonal system described on page 553. 
Changes belonging to division 1 may, it is evident, take place 
in solidified assemblages without doing violence to the ties above 
defined which constitute their solidity, but it is hard to conceive of 
changes belonging to division 2 as occurring in a solidified homo- 
geneous assemblage without causing the destruction of these ties ; 
unless indeed the redistribution be of a trivial character. 
The changes comprised in division 1 can be subdivided into 
two classes. 
(a) Comprising all those in which the change on passing the 
critical point takes place smoothly, 7. e., not per saltum. 
(6) Comprising all cases in which on passing the critical point 
the assemblage is suddenly found out of equlibrium, and makes a 
change of form per saltwm to reach equilibrium in the new type of 
arrangement. 
The following will illustrate the nature of a change of class a. 
Suppose that we have a stack of spheres of two sizes such as 
is described on page 547, the larger spheres having the closest- 
packed arrangement of figs. 1 & 2, and the smaller spheres just 
fitting into the largest interstices left between these. 
If now, keeping the size of the smaller spheres the same,’ the 
size of the larger spheres be gradually diminished to a slight 
extent, so that they can no longer have as many contacts with one 
another, the stack will, it would appear, continue to be as close- 
packed as possible ¢f the separation of the larger spheres takes place 
in planes drawn through the sphere centres perpendicular to some one 
of the cube diagonals of the space partitioning, and the remaining 
contacts between these larger spheres be preserved intact. 
1 This instance is given merely to show the kind of change meant, not as one 
likely to be realized. 
2 As the effect under consideration depends on a relative change of size, this comes 
to the same thing as changing the size of both kinds. ae 
2 
