a 
BarLtow—A Mechanical Cause of Homogeneity of Crystals. 635 
As before, we shall join the angular points with the centre of 
the figure and have linear distortions perpendicular to the poly- 
hedron faces compensated by appropriate shearing of the segments 
which are obtained by drawing planes perpendicular to these faces 
through their angles. 
In all such cases it is not difficult to see that the polyhedron 
faces will be elevated or depressed at their middles by the combined 
effects of the distortions so as to be converted into pyramids whose 
vertices point outwards or inwards as the case may be, and if the 
distortion be trifling the faces of the pyramids will be but slightly 
inclined to the direction of the face from which they were derived. 
We have said that if the shearing exactly compensates the 
linear distortion so far as the effect on the solid angles of the 
blocks or segments which fit together at the centre of the polyhe- 
dron is concerned, there will be no rupture or strain at the 
surfaces of contact between these twinning blocks. If, however, 
the compensation is not very exact we may expect evidence of 
more or less disorganisation of the parts of the assemblage, such 
as small rifts, or strains, or traces of shear; although at the 
same time the general change of form may take place in a 
fairly symmetrical manner. This, as we shall see immediately, 
is important. 
If any operations, analogous to those just traced, take place 
in nature we must expect that in all cases where the alteration 
in arrangement brought about by the dimorphous change is very 
slight, the boundaries of the twinning-blocks will only roughly 
approximate to the situations in which they would be found in 
an ideal case where the conditions are supposed perfectly uni- 
form at all morphologically-similar points. 
In the ideal cases, where no strain and very little deforma- 
tion are caused by the passage from the higher to the lower 
symmetry, it may well be that so little change in the arrange- 
ment and interaction of the parts takes place that there is little 
or no perceptible departure in the lower symmetry from the optical 
properties of the original higher symmetry, e.g., in the case of a 
cubic crystal changing to a group of monoclinic individuals, no 
appreciable departure from isotropism in the latter. Where this 
is so there may be nothing but the presence of the vicinal faces to 
