BarLtow—A Mechanical Cause of Homogeneity of Crystals. 625 
arrangement involved by the necessity for closest-packing may be 
accomplished by a simple shear which slides layers of the com- 
plexes that are vertical to the plane of the diagram on one another 
in a uniform manner, taken in conjunction with a simple linear 
expansion or contraction of the assemblage as a whole. 
For if the direction of the projection of the shear be indicated 
by the line AB, and each of the layers of particles referred to be 
moved vertically to the plane of the diagram upon the layer next 
to it a distance e where X is the vertical distance between succeed- 
ing horizontal layers in the original disposition, we obtain a 
Fig. 17. Fig. 18. 
rhombohedral arrangement. And this rhombohedral arrangement 
can by appropriate shrinkage or expansion in the direction of the 
principal axis be so distorted that the points shall come to lie 
either — 
1. At the centres of half the eubes of a system of cubes filling 
space symmetrically chosen. 
2. At the centres of all the cubes. 
3. At the centres and solid angles of all such cubes. 
Now, if the change of external form involved by the shear is 
opposed by some restraining influence, it may be easier, in place of 
a single shear, for six simultaneous similar shears to take place in 
such a way that the plane layer of points represented by fig. 17, 
becomes the six slant faces of a six-sided pyramid. The symmetry 
of the arrangement thus reached is indicated by fig. 18, in which 
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