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634 Scientific Proceedings, Royal Dublin Society. . 
which fit up together as described can undergo linear distortions 
and compensating shearing in the way above explained without 
separating one from another at their planes of contact. 
Consequently if the given assemblage is subjected to a change 
of conditions of such a nature that on reaching a critical point the 
cubic symmetry ceases to give closest-packing, and some arrange- 
ment which would be obtained by means of compound distortions 
whose components are related as just prescribed, becomes the 
closest-packed arrangement, and if, further, the change can occur 
more easily if there isa minimum of alteration of the external 
shape, then a passage from one dimorphous form to the other will 
take place in segments in the way indicated without rupture or strain. 
There will however, be some alteration of the dimensions in 
directions radiating from the centre, and in the case supposed, in 
which linear expansions are combined with appropriate shearing, 
the plane surfaces of the original tetrahedron will be raised up at 
their middles so as to be converted into triangular pyramids. And 
if the change of form be but slight, the faces of these pyramids 
will be very slightly inclined to the tetrahedron face from which 
they originated, and will therefore be what are called in crystals 
vicinal faces. 
The result of the combined distortions will be to convert the 
cubic symmetry into monoclinic symmetry. 
If in the case just supposed planes are drawn through the 
tetrahedron edges so as to form a cube, the cube-faces after the 
distortion will be found each to consist of two planes inclined 
at a re-entrant angle of nearly 180°, the angle edge running along 
one of the face diagonals. 
As to other ways, besides the one just given, in which an 
assemblage in cubic symmetry of the tetrahedral or of some other 
class, can be transformed to a lower symmetry without strain or 
rupture and with but slight alteration of its parts:—Instead of 
the regular tetrahedron we can employ some other regular polyhe- 
dron possessed of the requisite cubic symmetry, and the faces of 
which are regular polygons whose sides are all similarly related to 
the structure of the assemblage. 
Thus we can make use of a cube or of a rhombic-dodecahedron 
placed in a symmetrical manner in the assemblage. 
