578 Scientific Proceedings, Royal Dublin Society. 
Now the relative arrangement of the sphere-centres thus 
reached is produced by a uniform contraction of the cubical arrange-— 
ment in one of the four directions of the cube diagonals, the 
arrangement reached being therefore a rhombohedral one. The 
change experienced takes place smoothly without any discontinuance 
of equilibrium, and it is therefore of the kind marked a. 
To illustrate the nature of a dimorphous change of the class 
marked 6. Suppose that in the stack of spheres of two sizes 
which has become rhombohedral in the way just explained the 
ratio between the radii of the larger and smaller spheres con- 
tinues to fall in value, and passes the point at which the equilibrium 
arrangement becomes again a cubic one, viz. that described on page 549 
(and see fig. 9). 
Now during all the previous change in the ratio of the radii up 
to this point the contacts between the larger spheres in the 
equilibrium arrangement have continued of the same nature, but 
directly this point, at which the arrangement a second time becomes cubie, 
ts passed, these contacts become broken, and it would appear that 
almost immediately after passing this point, for closest-packing to 
obtain, the larger spheres must approach one another in planes at 
right angles to one of the directions of the trigonal axes of the 
system till they come in contact in these planes. This involves a 
sudden uniform contraction of the system in all directions at right 
angles to such an axis and a uniform expansion in the direction of 
the axis. 
The changes of division 2 must, it is evident, be per saltum. 
If an assemblage passes two critical points in succession at each 
of which the existing type of equilibrium-arrangement is exchanged 
for a different type in one of the ways above described, we have 
trimorphism ; if three such critical points are passed, tetramor- 
phism. 
Turning now to the experimental facts we find that these are 
closely akin to the conclusions reached above. In the first place 
there is the fact that a mere dimensional change of a crystal which 
does not amount to dimorphism, ¢.g., an alteration of bulk caused 
by change of temperature, is different in different directions except 
in cases of crystals belonging to the regular system. And, just 
such a relation between form and dimensional change will be found 
