628 Scientific Proceedings, Royal Dublin Society. 
Further, if the alteration is from a higher to a lower _ 
symmetry, and commences at the outer boundaries of the mass, — 
i.e., at the place where any trifling local movements are, in one 
direction, quite unfettered, the shape of the mass may have some - 
influence in determining from how many centres the change shall 
simultaneously originate; and thus, if the form of the mass he 
symmetrical, the number of differently-orientated sections in which 
the lower symmetry presents itself may bear a definite relation to 
the number of different orientations of similar parts found in the 
higher symmetry. At the same time any very slight discrepancies 
in the conditions at different corresponding points of the mass will 
suffice to prevent the growth about different origins from pro- 
ceeding at the same rate, and will cause the boundaries ultimately 
determined by the relative progress of the metamorphosis spreading 
from different neighbouring origins, to present much irregularity. 
It will be seen that a change of a solid assemblage of the kind 
just described, if it involve no dislocation, will be reversible, t.e., if 
after undergoing the change the conditions alter appropriately, 
the mass will revert to the original symmetry, and be capable of 
oscillating to and fro from one type of symmetry to the other. Very - 
slight variations in the successive changes will, however, suffice to 
alter the precise situation of the boundaries of the sections from 
time to time as the lower type of symmetry recurs. 
Moreover, for reversibility to be possible there must be no 
accretion to the assemblage after passing from the higher symmetry, 
that is unless the change be accomplished with absolute freedom 
from strain. Tor unless this ideal condition is realized, the grow- 
ing portions of adjoining individuals will come together unsym- 
metrically, é.e., the space-lattices formed by their singular points 
will not make one continuous system; and in this respect the 
newly-formed compound assemblage will differ from the old, and 
be incapable of passing as a whole to the higher symmetry. 
If there be accretion after the change, and consequent deterio- 
ration of the symmetrical relation at the newly-formed boundaries, 
we must not look for reversibility, but in other respects there may 
be no prominent properties to enable us to distinguish this from a 
case in which reversibility is possible. 
In connection with these conclusions two facts with regard to 
