BarLtow—A Mechanical Cause of Homogeneity of Crystals. 621 
the arranging for closest-packing. Or, if the change of state be 
sudden, some differently-orientated portions which are unable in the time 
to get similarly-orientated, may find themselves able to fall into some 
relative orientation which, though i does not give such close-packing 
as the same-ways orientation would do, comes but little short of it. 
Very symmetrical fitting together of differently-orientated 
identical assemblages, such as might furnish cases of the kind last 
referred to, can often be obtained if a single homogeneous assem- , 
blage be divided by a principal plane, ¢.e., a plane which intersects 
a great number of contiguous similar ball centres, or one which 
lies evenly between two successive similar planes which do so; and 
the half of the asscmblage on one side of the plane be turned 
through 180° about an axis occupying a certain position perpen- 
dicular to the latter. Or in cases where the symmetry of the 
plane of centres taken alone is such that it has a digonal axis 
which lies within it, the rotation may be made about this axis, but 
in this case duplicates of the same half of the assemblage dif- 
ferently orientated will be fitted together, and not the two halves. 
of the same individual assemblage differently orientated. 
The differently orientated fragments of an assemblage which 
are thus combined may be of the same or of different size. 
It wili be characteristic of twinning caused in this way that 
the phenomenon will be promoted by any condition which hinders 
the mutual adjustment requisite for the production of homogeneity, 
its occurrence will be fortuitous, and it will be done away with as 
the conditions are made more favourable to the unchecked operation 
of the principle of closest-packing. 
Crystals furnish types of aggregation corresponding to all the 
cases mentioned; indeed most crystals that appear to be single 
individuals are built up of more or less numerous distinct crystals 
which are not quite parallel in orientation to one another, though 
continuous in their substance and in optical contact. The symme- 
trical union of differently orientated individual crystals of the same. 
kind which is known as ¢winning furnishes parallels to the case last 
named. 
Only those cases of crystal twinning can, however, be claimed 
as resemblances to the accidental twinning of identical homo- 
geneous assemblages above referred to, in which no repetitions or 
