AUGUST 20, 1914] 
NALORE 
649 
indicates the way to the discovery of fresh facts. 
The assumption is that each atom in a crystalline 
structure acts as a centre of operation of two opposing 
forces: (a) a repellent force, attributable to the kinetic 
energy of the atom, and (b) an attractive force, both 
forces, like gravity, being governed by some inverse 
distance law. Such an assumption forms an essential 
part of the classical work of Clerk Maxwell and van 
der Waals on the kinetic theory of gases and liquids. 
Its application to solid crystalline substances, where 
it must be applied in conjunction with the principle 
ef structural homogeneity, was made by Barlow and 
myself in 1906. 
The operation of the assumption just stated 
readily visualised by considering the simplest possible 
case, that, namely, of a crystalline element each mole- 
cule of which consists of but one atom and in which 
all the atoms are similar. Consideration of this kind 
of case shows that the set of identically similar centres 
is 
of attracting and opposing forces will be in equili- 
brium when one particular simple condition is 
fulfilled; the condition is that, with a given density 
of packing of the centres, the distance separating 
nearest centres is a maximum. Two homogeneous 
arrangements of points fulfil this condition, and these 
exhibit the symmetry of the cubic and the hexagonal 
crystalline systems. 
Since the nature of the two arrangements of points 
is not easily realised by mere inspection, the systems 
must be presented in some alternative form for the 
purpose of more clearly demonstrating their pro- 
perties; this is done conveniently by imagining each 
point in either arrangement to swell as a sphere until 
contact is made with the neighbouring points. The 
two arrangements then become those shown in Figs. 
rt and 2, and are distinguished as the cubic and the 
hexagonal closest-packed assemblages of equal 
spheres; they differ from all other homogeneous 
arrangements in presenting maximum closeness of 
packing of the component spheres. The equilibrium 
condition previously remarked—that, with a given 
NO. 8, VOL. 93] 
233 
density of distribution of the force centres in space, 
| the distance separating nearest centres is a maximum 
—is revealed in the assemblages of spheres as the 
| condition that the spheres are arranged with the maxi- 
mum closeness of packing. 
A further step is yet necessary. Each point in the 
arrangements considered is regarded as the mean 
centre of an atom of the crystalline element, but the 
assumption originally made states nothing about the 
magnitude of the atom itself; it is therefore convenient 
to regard the whcle of the available space as filled by 
the atoms, without interstices. This is conveniently 
done by imagining tangent planes drawn at each 
contact of sphere with sphere, so partitioning the 
available space into plane-sided polyhedra, each of 
which may be described as the domain of one com- 
ponent atom. The twelve-sided polyhedra thus derived 
from the cubic and the hexagonal assemblages repre- 
Fic. 2. 
sent the solid areas throughout which each atom 
exercises a predominant influence in establishing the 
equilibrium arrangement. 
(To be continued.) 
NOTES. 
A Reuter telegram states that the New Zealand 
meeting of the British Association has been cancelled, 
and that the members will return home after visiting 
Brisbane and Melbourne. 
record the death, at 
A. J. Jukes-Browne, 
WE deeply regret to have to 
Torquay, on August 14, of Mr. 
ES Res: 
TuHeE death is reported, in his sixty-fourth year, of 
Dr. Franklin W. Hooper, director since 1889 of the 
Brooklyn Institute of Arts and Sciences. He had 
previcusly been professor of natura] science at 
Adelphi College, Brooklyn. He was the organiser of 
