632 Scientific Proceedings, Royal Dublin Society. 
Thus suppose that in a case of multiple twinning,’ the solid j 
angles at which the twinning blocks fit together are unaffected by — 
the dimorphous change, so that the alteration takes. place without 
rupture or strain ; then it is evident that the change will be perfectly 
reversible and that a fluctuation of the conditions to and fro past 
a certain critical point may produce any number of oscillations 
from one dimorphous symmetry to the other without causing 
confusion. And we shall see immediately that there need be 
but very trifling alteration in the external form when the 
change takes place. 
Further, in the ideal case thus put, the reversibility will 
still hold good ifthe mass is a growing one, the junctions formed 
between growing individuals after the dimorphous change has taken 
place being as symmetrically constituted as those produced at the | 
time of this change. 
But if the solid angles between the blocks are not absolutely 
unaffected by the dimorphous change, some strain or rupture 
being involved in the continuance of the twinning blocks in their 
original relative situations, we see that, although so long as there 
is no accretion after the change has taken. place reversibility will 
still be possible if the strain or shifting is but very slight, 7 
growth takes place, the added portions, however slight the strain, 
will come together more or less unconformably at their boundaries. 
And that the less symmetrical character of the newly-formed 
junctions as compared with those produced at the time of the 
dimorphous change which owe their constitution to the higher 
symmetry of the original form, will be a hindrance to any reversal 
of the dimorphous change after it has once taken place. 
With reference to the change of external form, slight or other- 
wise, involved by a dimorphous change which leaves the solid- 
angles at which the twinning-blocks fit together entirely or almost 
entirely unaffected, we note that in cases where all the twinning- 
blocks meet in a single point—as they will, for instance, where the 
change is from a cubic symmetry—if the change involves but slight 
distortion, a single face or plane-direction in one symmetry may 
be transformed in the other into a set of pyramid faces inclined at 
1 See above, p. 626. 
