046 Scientific Proceedings, Royal Dublin Society. 
(B.) Formation of homogeneous assemblages when the balls, or 
mutually repellent centres, are of two kinds. 
We now come to the cases of homogeneous arrangement brought 
about by closest-packing in which the balls are of two kinds only, 
and in some of which they are not linked together to form groups 
of any kind, while in others they are so linked. 
In these and other cases in which more than one kind of ball 
is present, and provided the centres are unlinked, the nature of the 
arrangement produced will depend on the relative sizes of the 
balls of different kinds.’ 
For the sake of simplicity, let us first suppose that the ball 
centres are all confined to the same 
plane, but free to move in this plane. 
If they were all alike and indepen- 
dent, they would evidently pack closest 
in the triangular arrangement, in which 
each centre is equidistant from six 
nearest centres, and they would dis- 
play a less compact packing in the 
quadrilateral arrangement, in which 
each centre is equidistant from four 
nearest centres. 
‘But when two kinds of balls, one larger than the other, are 
present, the triangular arrangement referred to may not give 
close-packing at all, and the sizes may be so proportioned as to 
give closest-packing in the quadrilateral arrangement depicted 
in fig. 7; this packing being somewhat closer than would be 
of different compounds of a common constituent is very often the occasion of their 
possessing allied properties. 
It should be remembered, in connexion with the resemblance that has just been 
pointed out, that some. or indeed all, of the so-called elements may prove in the end to 
be compounds. Where this is the case the remarks made later respecting compounds 
will apply instead of what is said here as to the elements. 
1Tf elastic balls are used and the closest-packed assemblage is compressed (see 
p. 529), the arrangement will also, in nearly all cases, be influenced by the repulsions 
found subsisting between the different ball centres, these repulsions, at least such of them 
as have any modifying effect on the form of the assemblage, having to form a system 
in statical equilibrium. 
