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602 Scientific Proceedings, Royal Dublin Society. 
present in the assemblage; in other cases it will be closer if both | 
are present. * 
To give two simple illustrations. 
If a number of similar groups have their outside ball-centres — 
so arranged as to form either regular 12-point groups or 24-point 
groups,’ and we form a close-packed homogeneous assemblage in 
which the centre-points of the groups lie at the centres of a number 
of cubes filling space, the groups will fit into one another better if 
they are all identical than they will if some are of one hand, some 
of the other hand. 
If, however, we form a close-packed homogeneous assemblage 
by placing groups whose outside ball-centres form 24-point 
groups, with their centres at the centres and angles of the cubes of 
the space-partitioning, the packing will be closer when half of the 
groups are of one hand, half of the other hand symmetrically 
distributed, than it will be if all are identical. 
We see, therefore, that the principle of closest-packing will in 
some cases, under some conditions, make assemblages which are 
composed of similar groups of two enantiomorphous kinds split up 
to form separate assemblages of each kind of group, while under 
other conditions it. will cause the two enantiomorphous kinds to 
intermix when two assemblages each consisting of one kind alone are 
brought in contact. And both effects may come about in a great 
variety of ways, and with almost all conceivable kinds of asymme- 
trie groupings, and the same assemblage may under one set of 
conditions display the one effect, and under another set of condi- 
tions display the other effect. 
Further, one or the other of these effects will often be presented 
when more than one kind of group is present, and, indeed, it is 
conceivable that the presence of an additional kind of ball or 
complex of balls in an assemblage may cause it to exhibit one of 
the properties referred to instead of the other. 
The effects just mentioned are exactly paralleled in the 
behaviour of some chemical compounds. Thus, van ’t Hoff says :— 
“ The separation of the two isomers, endowed with rotation-proper- 
1 See Sohncke’s ‘‘ Entwickelung einer Theorie &c.,’’ pp. 156 and 166, or Zeitschr. 
fiir Kryst. 27, p. 451. To produce the most striking effect the ball-centres should lie 
well away from the symmetry-planes of the system of axes. 
