680 Scientific Proceedings, Royal Dublin Society. 
details of the action of these assemblages when combining may be 
given, and a few further resemblances pointed out before quitting 
this part of the subject. 
It has been stated above that two assemblages will ultimately 
combine in the proportions in which they pack closest; this refers 
to the completed process, there may, and indeed generally will be 
transitional combinations, some of them homogeneous, and which, 
as compared with the constituent assemblages unmixed, produce 
increased closeness of packing, but not the closest possible. 
Suppose, for example, to take a very simple case, that a set of 
unlinked balls A, mixed with a set of unlinked balls B, pack 
closest when they are homogeneously arranged in a certain way 
which employs the two kinds in the numerical proportions 1: 2. 
It is then evident that other homogeneous arrangements of the 
balls are possible into which they enter in equal proportions, and 
that one of these may, while it doesnot give such close-packing as 
that of the arrangement just referred to, give closer-packing than 
is attained by the balls when unmixed. Also that during the 
process of intermixing to produce the closest-packed arrangement, 
the balls may here and there fall into this less closely-packed 
arrangement. And although if its attainment anywhere is not 
accompanied by a change of state which stereotypes it, such an 
arrangement will prove but a temporary one, 7 will be made per- 
manent if a change of state fixes it as it is here and there produced. 
Any hindrance to the achievement of the closest-packing 
possible, such, for example, as a scanty but widely disseminated 
supply of some of the materials, will be likely to favour the pro- 
duction of this less closely-packed combination.” 
_The closest-packed arrangement will be appropriately called 
saturated, and transitional combinations unsaturated,’ the properties 
expressed by these terms being closely paralleled by the properties 
of chemical atoms thus named, both in cases of chemical synthesis, 
and also in those of diffusion. 
1 This is somewhat analogous to the accidental twinning above referred to. See 
p- 620. 
2 The method of production of a second combination from the same constituents 
which is here described must not be confounded with that based on change of conditions. 
(Comp. pp. 575 and 678.) 3 Comp. p. 607. 
