Bartow—A Mechanical Cause of Homogeneity of Crystals. 545 
to one another without producing a hollowness of the grouping, 
@.e., the distance between the opposite centres of a group is then 
far greater than that separating nearest centres; and hollowness 
of the grouping seems inconsistent with close-packing, so that it 
would seem that the centres, where more than six go to form a 
single group, must occupy positions with respect to the structure 
which are not identical with one another. When this is the case 
our task is similar to the one before us when we come to deal with 
cases of balls of more than one kind. 
Enough has been said to show that, in the case of similar ball 
centres linked together in various ways, compact packing and 
homogeneousness of arrangement commonly go together, and we 
may regard the following proposition as established. 
Closest-packing produces, under the given conditions, a great variety 
of homogeneous arrangements of balls of a single size, when these balls 
are fitted together to form symmetrical groups consisting of two, three, 
four, or six balls, and the balls which form a group interpenetrate. The 
nature of the arrangement is in each case determined by the 
relation which subsists between the distance apart of adjacent 
centres of the same group and the distance between the nearest 
centres of different groups. 
The strict parallel as to general symmetry obtaining be- 
tween the various homogeneous closest-packed arrangements of 
centres of one kind, some of which have just been traced, and the 
various crystal forms of the elements is obvious, the linking 
together of two or more of the centres to form a group being 
paralleled by the supposed linking together of two or more 
similar atoms to form a molecule.’ 
1Jt has sometimes been suggested that when atoms, whether of the same or 
different kinds, combine to form a molecule, the individuality of the atoms is lost, 
much in the same way that the individuality of a number of superposed movements of 
any kind is lost, and not separately discernible in the resultant movement. 
The objection to this view is that, in the case of a chemical combination, we can 
always, by analysis, recover the same identical combining atoms from the combination, 
while in the case of combined movements the identity of the component movements is 
completely lost, so that we can no more say that the resultant movement contains the 
movements whose combination produced it, than that it contains any other of the infinite 
number of conceivable groups of movements which would have this same resultant. 
And this objection is supported by the evidence we have that the presence in a number 
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