BarLtow—A Wechanical Cause of Homogeneity of Crystals. 661 
plane of symmetry, and the axial angle is 593°. The isomorphous 
mixture of the two salts, however, invariably show the same 
cleavage and optic axial plane as the ammonium salt; a mixture 
containing 88°7 per cent. of the thallium salt was, moreover, 
obtained, in which the optic axial angle was found to be 48° 31’, 
being thus completely identical with that of the pure ammonium 
salt. 
A resemblance of a lower order than isomorphism is con- 
ceivable between assemblages which have some constituents the 
same and similarly arranged or grouped in both. For although 
the congruence may not be adequate to produce equality of all 
corresponding angles or any intercalation, the arrangement may 
be so far alike in both as to come under the same type of symmetry 
and to have some axial lengths in one equal to some in the other. 
An illustration will, perhaps, make this plainer :—Suppose that 
an assemblage, when closest-packed, is found with its unit-groups 
arranged in rhombic symmetry in parallel layers in such a way 
that when it is partitioned symmetrically in the simplest manner 
possible, the cells are right-rhombic prisms, each containing a 
unit-group. 
And suppose that a second assemblage is composed of unit- 
groups, each of which consists of the same constituents arranged 
in the same manner as in the first-named groups, and in addition to 
these some other constituents ; the portion of a group which is the 
same forming the larger part of it, and the additional constituents 
being placed at opposite ends of the group. 
It is then conceivable that the second assemblage when closest- 
packed will also be capable of symmetrical partitioning into cells 
which are right-rhombic prisms, and that the only difference 
between the partitioning of the first and that of the second assem- 
blage will be that the prismatic cells of the latter will be rather 
longer than those of the former, the cross sections being identical. 
In such a case there will be aremarkable morphotropic relation- 
ship between the assemblages, for two out of the three axial 
directions will furnish the same values in both, and so consequently 
will the zone containing these two directions. 
1 See Wyrouboft’s researches in Zeitchr. f. Kryst, 13, p. 648; also Pope’s transla- 
tion of Fock’s ‘‘ Introduction to Chemical Crystallography,” p. 138. 
