650 _ Scientific Proceedings, Royal Dublin Society. 
kinds of assemblages display similar orientation. There will, no 
doubt, in such a case be some mutual local accommodation of the 
arrangements of the parts of the assemblages where the two kinds — 
meet, but this will not be likely to disturb parallelism of the 
contact layers. 
Not only isomorphous assemblages but also assemblages dis- 
playing less similarity, provided they contain similar planes of — 
centres which will fit sufficiently well together to pack very 
closely, may become intercalated in a more or less symmetrical 
manner if the conditions of solidification are favourable, but we 
see that with a less correspondence of parts than is requisite for 
isomorphism the symmetry, except in cases of slight admixture, 
will be greatly deteriorated, and probably in few cases will there 
be uniformity of orientation of all the distinct fragments of the 
same kind of assemblage throughout any considerable space.+ 
For two assemblages to be absolutely isomorphous as a con- 
sequence of partial identity of composition,” it is not necessary for 
their like parts to behave identically under the same exernal con- 
ditions, the corresponding balls need not be precisely the same, it 
is only necessary that the operative statical system of interacting 
parts in the one assemblage, or some symmetrical system equivalent. 
to it, shall bear the same proportions as those in the other assem- 
blage do, so as to make corresponding angles the same in the two 
equilibrium arrangements. ‘This is a much less specialized con- 
dition for isomorphism than the one stated first. 
It is important to notice that the equality of corresponding 
angles just referred to may be associated with the exhibition of 
different types of symmetry. For this will be the case if in two 
assemblages in which the distances in three principal directions 
between the principal singular points’ bear the same ratios in . 
1There may, however, occasionally be enclosure of a large number of isolated 
fragments, and perhaps of a continuous mass, of the one assemblage within a con- 
tinuous mass of the other assemblage throughout which uniformity of oricntation 
prevails. Compare note 1, p. 631. 
2 Cases of isomorphism may arise from fortuitous relationship between the different 
sets of principal or singu.ar points found in different assemblages, but these, which we 
necessarily be of very infrequent occurrence, will not be considered here. 
3 See note 1, p. 627. 
eS 
