068 Scientific Proceedings, Royal Dublin Society. 
conditions is such that every part of the surface of the growing sole 
experiences on the whole the like conditions. 
If, however, the change is not sufficiently slow to give this 
uniformity of conditions in a fluid assemblage at different points — 
of the boundary of a solidified portion of it, some departure from 
uniformity of accretion is to be looked for. 
This will especially be so if the fluid assemblage which is of the 
same composition as the mass already solidified is more or less 
fragmentary and interspersed among portions of differently- 
constituted fluid assemblages which are not partaking in the 
solidifying change. For although in this case the place of maximum 
tranquillity, 7.e., the surface of the growing solid, will still be the 
place of growth, the relative rute of growth at different parts of this 
surface will be regulated chiefly by the relative distribution or — 
supply of the material for growth, and the supply of material — 
being different at different places the growth will be irregular 
As irregular growth thus caused is, however, a matter which : 
does not come within the scope of our investigation, this interesting 
topic must be dismissed with the remark that Lehmann’s investiga- 
tion of the nature and causes of the growth of skeleton crystals — 
seems to the author to be entirely satisfactory.2 This remark 
is intended, however, to apply only to the cases of irregular 
growth in which the structure is congruent—to skeleton crystals 
but not to bent or branched crystals. As we shall see immediately, 
closest-packing is capable of producing bent and branched assem- 
blages which are very nearly homogeneous, although it is of course 
impossible for them to be quite so. 
Impaired Homogeneity—Bent and Branched Crystals. 
We have hitherto in these pages regarded mixed assemblages — 
of balls which are subjected to a process of closest-packing as 
forming two great divisions—division 1, to which this section is — 
especially devoted, comprising all those in which closest-packing 
is attained in a homogeneous arrangement, and division 2 those — 
1 Compare ante, note 1, p. 566. 
20. Lehmann “ Ueber das Wachstum der Krystalle.’’ Zeitschr. fir Kryst., 1, 
p. 453, especially page 471. 
