626 Scientific Proceedings, Royal Dublin Society. 
the projections of points lying at different distances from the 1 
plane of the diagram are differently indicated. 
The result of this compound shearing, accompanied. by an 
appropriate linear shrinkage or expansion of the mass, is therefore 
to produce an interpenetrant twinning in the cubic symmetry, the 
portions marked a being similarly orientated and indeed con- 
tinuous in arrangement, but having the opposite orientation to 
those marked (3, which are also similarly orientated and continuous — 
in structure among themselves. 
The kind of twinning thus reached is atone exhibited by 
fluor-spar, and by galena. 
In all cases, at least two shears in different directions, opposite 
or otherwise as the case may be, will be needed to accomplish 
twinning by dimorphous change in the way just explained. If 
there are but two shears there will be only one separating surface, 
and the twin assemblages formed will not be interpenetrant. 
The arrangement of parts prevailing in two adjoining blocks 
which shear in different directions may, after the shearing has 
taken place, bear an identically-similar relation to the surface 
separating the blocks, or they may bear an enantiomorphously- 
similar relation, in which they will generally be symmetrical or 
mirror-twins. In the latter case the two arrangements will be 
enantiomorphous wnless they are identical with their own mirror- 
images. 
Mirror-twin tetragonal crystals of copper pyrites furnish an 
example of twinning in which the two individuals bear only 
an enantiomorphously similar relation to the separating plane, 
although they themselves are identical and not mere enantio- 
morphs.? 
Multiple twinning. 
Interpenetrant twinning originated in the way just indicated, 
may be described as a method of multiple twinning in which the 
identity of orientatation of the parts of alternate individuals of the 
twin system causes these alternate individuals to function collec- 
tively as a single individual, thus making it possible to regard the 
1 See L. Fletcher ‘‘On twins of copper pyrites.” London, Edin., and Dublin 
Philosophical Mag., Series 5, vol. xiv., p. 276. 
Seat 
