a 
Bartow—A Mechanical Cause of Homogeneity of Crystals. 571 
join the centres of balls that touch in a thin assemblage lie in a 
parallel to the surface of the assemblage, we cannot have spherical 
bending of several layers, because this kind of distortion would 
involve material differences in the lengths of corresponding lines 
found in different layers. Such a situation of these lines does not, 
however, preclude cylindrical bending, provided their direction is 
that of the axis of the cylinder, for when this is the case their 
lengths will be unaltered by the distortion. 
It is not necessary, or indeed generally possible, that the 
curving of an assemblage shall present precisely the same degrees 
of symmetry as would be presented by the assemblage if undistorted, 
even when the modification of the latter by the limitation imposed 
on its extent is taken into account. Thus it is conceivable that 
the holomorphism of a thin assemblage may be impaired by a 
curvature which is concave towards one end of a holomorphic 
axis, and therefore convex towards the other end. For although 
symmetry will require that such a change shall be equally possible 
in either of the two opposite directions, its occurrence in the one 
direction in any part of the assemblage may preclude its occur- 
rence in the other in any other part of the same assemblage. 
Similarly a torsional twist experienced by an assemblage of small 
extent which is identical with its own mirror-image, may deprive 
it of the latter property, although the determination of the direc- 
tion of the twist—whether it shall be right-handed or left-handed, 
_ will depend on accident, or at least on external circumstances. 
A few words next with regard to the growth or increase of 
curved assemblages. 
The curvature of succeeding uniform layers of a curved assem- 
blage being necessarily different, it is evident that if a particular 
curvature gives closest-packing, and a very thin assemblage con- 
sisting of a very few layers and having this particular curvature 
be formed and solidified, layers added congruently to either face of 
such a nucleus will be unable to take up the closest-packed 
arrangement, those on the convex side having their dimensions 
along the surface rather too large, and therefore the distance 
between succeeding layers rather too small, and those on the 
concave side experiencing an unfavourable condition just the 
opposite of this. 
