Barlow —A Mechanical Cause of Homogeneity of Crystals. 637 
of the shifting, if it occurs, will evidently much depend on 
what surfaces of weakness are present in the structure, 7. e., 
what cleavage planes, gliding planes dependent on cleavage 
planes, &c.? : 
Suppose, for example, that a cubic structure undergoes a dimor- 
phous change which divides it into six individuals of square- 
pyramidal form, each of which experiences an expansion along its 
perpendicular. Then, if the individuals are to remain in contact as 
before, and the dimorphous change does not produce the precise 
shearing requisite to neutralize the change of the solid angles of 
the individuals that fit up together which is produced by the 
expansion,” there will have to be some shifting of parts along lines 
of weakness. 
If now planes parallel to the cube faces are not planes of 
weakness, but planes parallel to dodecahedron faces are, and no 
others, we must look for such a shifting along the latter directions 
as will, on the whole, be practically equivalent geometrically to. 
the balance of the shearing, which has by some means to be made 
up in order to exactly compensate the effect of the expansion at the 
solid angles. 
Now the resultant of two equal similar shears perpendicular to 
a cube face, having the directions respectively of two dodecahedral 
faces inclined to one another at 90°, is a single shear also perpen- 
dicular to the cube face and having the direction of a second cube: 
face. The shifting in the case supposed will therefore largely 
consist of a number of movements along every two dodecahedral 
plane directions thus related, the amount of movement in each 
being somewhere about the same. 
As already remarked, if the shifting in a case of this kind is 
inconsiderable, it is conceivable that it may not prevent reversi- 
bility of the dimorphous change, so long as no accretion has taken’ 
place since the change. 7 
If the general movement is small, and shifting can easily take 
place, but little strain may be set up, and the relations between 
the parts may be but little altered by the change, and thus but 
little removed from those appropriate to the higher symmetry. 
1 As to how gliding planes may be connected with cleavage planes, see p. 645. 
2 Comp. p. 633. 
