L 
Including the departure from strict homogeneity just referred — 
to, we have now dealt with four distinct ways in which assemblages 
may fail in homogeneity and yet exhibit a related orientation and 
symmetry of their parts, such as are found in crystals. They 
are :— 
1. A want of uniformity in the arrangement of the inoperative 
constituents which does not extend to the operative ones, the latter, 
when taken alone, displaying homogeneity of arrangement.’ 
2. A bending or twisting of thin assemblages whose parts are 
so related that they pack closer when thus curved than they do 
when homogeneously placed.? 
3. A more or less irregular intercalation of two different con- 
gruent or partially congruent assemblages, in which, however, one 
or both preserve the same orientation of corresponding parts.° 
4. A lack of symmetry in the unit-groups composing an 
assemblage which is not sufficient to prevent them from perform- 
ing the same functions as would the more symmetrically-shaped 
groups which they nearly resemble. ‘To make the assemblage 
perfectly homogeneous it would, therefore, merely be requisite to 
correct these slight departures from regularity without changing 
the rest of the structure. The positions of the defects with respect 
to the group-centres present a haphazard variety within the limits 
prescribed by the arrangement of the perfect portions of the 
assemblage. 
The intercalation of differently-constituted fragments of 
homogeneous assemblages in the ways above described will, 
obviously, be likely in many cases to modify the effect of change 
of conditions. Thus it is obvious that if, under change of tem- 
perature, one constituent does not change its bulk at the same rate 
as the other, a condition of strain must be looked for in the mixture 
which is not found in either constituent taken alone, and that the 
effects of this strain will, so far as the qualities of the constituents 
are concerned, be anomalous and not to be accounted for by any 
addition or subtraction of their individual properties. 
To compare with this we may mention the observation of 
Brauns that while pure crystals of alum, lead nitrate, and barium 
664 Scientific Proceedings, Royal Dublin Society. 
1 See p. 548. 2 See p. 568. 3 See p. 649. 
