Bartow—A Mechanical Cause of Homogeneity of Crystals. 633 
very large angles to one another, and when the alteration is very 
trifling indeed, the existence of these slightly-inclined planes 
(vicinal planes' of the mineralogist) and some slight discrepancies 
in the angular values may be the only morphological evidence 
presented of the dimorphous change having taken place. 
A reference to particular cases, accompanied by comparisons 
with corresponding phenomena displayed by crystals, will, it is 
hoped, make these matters clearer. 
For example:—An assemblage which has tetrahedral cubic 
symmetry can, byan appropriate dimorphous change, be transformed 
to monoclinic symmetry, with but slight alteration of arrangement 
and in a manner compatible with the preservation of the general 
features of the tetrahedral form, in the following manner. 
Somewhere in the assemblage draw a regular tetrahedron with 
its principal axes coincident with trigonal axes of the assemblage.” 
Join the angular points of the tetrahedron with its centre, thus 
outlining a partitioning of it into four blocks each of which is a 
right triangular pyramid, the vertices of the four pyramids coming 
together at the centre of the tetrahedron. 
If now each of these four triangular pyramids experiences a 
similar uniform linear distortion, say an expansion, in the direction 
of its perpendicular, it is evident that the four vertices can no 
longer fit up together. 
But if each of the four pyramids be divided into three equal 
segments by planes perpendicular to its base drawn through the 
slant edges, and each of the twelve similar segments thus obtained 
be subjected to an appropriate simple shear which slides on one 
another planes of centres which are vertical to the pyramid base 
and parallel to the side of this base which bounds the segment, 
the alteration of the solid angles at the tetrahedron centre caused by the 
linear distortion can be exactly compensated by these shears and reduced 
to sero. 
Therefore twelve segments or blocks of a tetrahedral assemblage 
1 Tt is not suggested that this may be the origin of all vicinal planes, but only of 
those occurring in cases of the kind here referred to. 
2 For this to be possible, the assemblage must be of one of the types in which the 
trigonal axes intersect one another. A slightly modified method must be pursued in 
the cases of the less regular types. 
