Bartow—A Mechanical Cause of Homogeneity of Crystals. 628 
then, consistently with the above two factors, quite arbitrarily 
take any continuous form. 
If any irregularity or modification of the rate of growth is 
caused at any surface of one individual by the proximity of a 
surface or surfaces of another individual, or by any other means, 
it is evident that the conformation of the separating surface will be 
thereby affected. 
Further, although the principle of closest-packing may be 
expected to fit the two nuclei of a twin assemblage together in a 
very symmetrical manner at the outset, it does not follow that 
after coalescence has once commenced, there will be any specially 
symmetrical fitting together of the growing individuals at the 
separating surface ; for the relative situations and rates of growth 
being, as has just been said, the only factors determining the locus 
of the separating surface, no latitude is left for the principle of 
closest-packing to produce symmetrical fitting together of the 
growing individuals. 
As a direct consequence of this it may be concluded that the 
locality of the separating surface must commonly be a place where 
symmetry is disturbed and which is not therefore very favourable 
to symmetrical growth, and to compare with this there is the fact 
that although single crystals never exhibit re-entrant angles, 
the occurrence of these angles between distinct crystals which are 
juxtaposed, whether as twins or otherwise, is extremely common. 
Twinning caused by dimorphous change. 
Tf the conditions of equilibrium of an assemblage undergo a 
dimorphous change which causes it to cease to find equilibrium in 
one kind of homogeneous arrangement and to approximate towards 
some other as the closest-packed arrangement,’ the rearrangement 
of the parts which takes place will, unless a very radical one indeed, 
be facilitated by some uniform distortion of the assemblage as a 
whole. And this distortion may consist of one or more linear 
shrinkages or expansions of the assemblage as a whole, or of some 
simple shear which slides its layers on one another, or of some 
combination of these simple methods of modifying form without 
1 Comp. p. 575. 
SCIEN. PROC. R.D.S., VOL. VII., PART VI. 27, 
