646 Scientific Proceedings, Royal Dublin Society. 
Partition space into equal similar obtuse rhombohedra by ‘ 
drawing three sets of parallel planes in an appropriate manner. 
At the points of bisection of all the rhombohedron edges place 4 
eentres of equal spheres whose magnitude is such that they touch — 
one another. 
With their centres at all the rhombohedron angles place a 
second set of equal spheres of such a radius as to touch the spheres 
first placed. ; 
Finally, with their centres at all the rhombohedron centres 
place a third set of equal spheres which are also of such a radius 
as to touch the spheres first placed. 
The spheres at the rhombohedron angles are then each in 
contact with six spheres; those at the rhombohedron edges, and 
those at the centres are each also in contact with six. 
If we regard such an assemblage as made up of layers of balls 
lying in planes parallel to the rhombo- 
hedron faces it is seen that it has the 
property referred to above, and is 
capable of distortion to a rhombic 
form, a face of the rhombohedron be- 
coming the base of the rhombic prism. 
The kind of movement is diagram- 
matically indicated in fig. 19, the 
shifted portions of each layer being 
supposed kept in contact with the un- 
shifted portions of the same layer at one end during the shear. 
This condition involves a slight temporary separation or widening 
of the distance between the layers, at least in the neighbourhood 
of the separating surface of the twins formed. 
The type of homogeneous structure presented is that numbered 
52a, in my list... The generic symmetry is that of Class 12 in 
Sohncke’s list.” The three kinds of balls are present in the 
numerical proportions 1 : 1:3. 
The resemblances to the details of the case of the artificial 
twinning of Iceland spar are here very close, the atoms composing 
this substance having indeed the numerical proportions referred 
Hig. 19. 
1 Zeitschr. fiir. Kryst., 23, p. 47. 2 Tbid., 20, p. 461. 
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