AUGUST 27, 1914| 
capital means the abolition of effort; but as in the 
body the power of independent growth of the parts 
is limited and subordinated to the whole, similarly in 
the community we may limit the powers of capital, 
preserving so much inequality of privilege as corre- 
sponds with physiological fact. 
At every turn the student of political science is con- 
fronted with problems that demand biological know- 
ledge for their solution. Most obviously is this true 
in regard to education, the criminal law, and all 
those numerous branches of policy and administration 
which are directly concerned with the physiological 
capacities of mankind. Assumptions as to what can 
be done and what cannot be done to modify indi- 
viduals and races have continually to be made, and the 
basis of fact on which such decisions are founded 
can be drawn only from biological study. i 
A knowledge of the facts of nature is not yet 
deemed an essential part of the mental equipment of 
politicians ;-but as the priest, who began in other ages 
as medicine-man, has been obliged to abandon the 
medical parts of his practice, so will the future be- 
hold the schoolmaster, the magistrate, the lawyer, 
and ultimately the statesman, compelled to share with 
the naturalist those functions which are concerned 
with the physiology of race. 
SECTIONS? 
CHEMISTRY. 
OPENING ADDRESS BY PROF. WILLIAM J. Pope, M.A., 
LL.D., F.R.S., PRESIDENT OF THE SECTION. 
(Concluded from p. 649.) 
THE two assemblages can now be described in a 
quantitative manner by stating the symmetry and also 
the relative dimensions of each. The cubic assem- 
blage exhibits symmetry identical with that of the 
cube or the regular octahedron, a symmetry charac- 
teristic of so-called holohedral cubic crystals; the 
relative dimensions in different directions are defined 
by the symmetry. The assemblage can, in fact, be 
referred to three axes parallel to the edges of a cube, 
and as these directions are obviously similar in a 
cube, their ratios are of the form, a:b:c=1:1:1. 
This expression indicates that if the assemblage, sup- 
posed indefinitely extended through space, is moved 
by a unit distance in either of the three rectangular 
directions, a, b, and c, the effect, as examined from 
any ee is as if the assemblage had not been moved 
at all. 
The symmetry of the hexagonal assemblage is 
identical with that of a hexagonal prism or of a 
double hexagonal] pyramid, and is that characteristic 
of the so-called holohedral, hexagonal, crystalline 
system; the relative dimensions are no longer defined 
entirely by the symmetry, and are conveniently stated 
as the ratio of the diameter, a, of the prism or pyra- 
mid, to the height, c, of the pyramid. The ratio, 
a:c, for the assemblage of spheres under discussion 
can be calculated; it assumes two forms, correspond- 
ing to two modes of selecting alternative principal 
diameters of the prism as unit. The alternative 
ratios are: a :c =1 : 1-6330 Or @:c=1: 1-4142. 
This somewhat lengthy theoretical discussion has 
now reached a stage at which it can be applied to the 
observed facts; the accompanying table (Table I.) 
states the mode in which crystalline substances of 
different degrees of molecular complexity distribute 
themselves amongst the various crystal systems. Of 
the elements which have been crystallographically 
examined, 50 per cent. are cubic, whilst a further 35 
per cent. are hexagonal; and consideration of the 
data for these latter shows that they exhibit approxi- 
NO. 2339, VOL. 93] 
NAT ORE 
6051 
mately the axial ratios characteristic of the hexagonal 
closest-packed assemblage; thus magnesium shows 
a:c=1:1-6242, and arsenic the ratio a: c=1-4025. 
TaBe I. 
Inorganic substances, the num- 
ber of atoms in the molecule of 
which is re: pectively : Organic 
System. Sub- 
Elements stances 
More 
2 3 4 5 | thans 
Per cen’. 
Cubic 50 68°5 42 5 ete 5 nSh ees 
Hexagonal 35 LOSSe eI 35 138) (414 Oy 4a 
Tetragonal ae 5 47-5 | 19 See Ken || pf 50 
Orthorhombi: ... 5 37Q)| 23'°5;| 50:| 935) 27acieda 
Monosymmetric 5 4e5b 3 § || Szegeeares 
Anorthic He fe) fo) 155 | Oalu ee: 5 70 
No. of cases ex- 
amined for each 
vertical column 140 67 | 63 20 | 50 | 673. | 585 
Whilst the crystal structure of some 85 per cent. of 
the crystalline elements seems to be in general agree- 
ment with the simple assumption of equilibrium which 
has been made, the divergence presented by about 15 
per cent. of the elements still awaits explanation. The 
previous discussion applies to the theoretically simple 
case of a monatomic element; many of the elements 
are, however, certainly polyatomic. Imagine, there- 
fore, that in the crystal structure, agreeing with the 
cubic or hexagonal arrangement just described, the 
similar atoms are grouped to form complex molecules, 
each containing two or more atoms; the geometrical 
effect of this grouping, if any, should be, first, to 
degrade the symmetry of the structure, and, secondly, 
to slightly alter its relative dimensions. It would 
therefore be expected that if the elements which are 
neither cubic nor hexagonal owe their departure from 
those systems to molecular aggregation, the crystal 
dimensions should approximate closely to those of the 
two ideal assemblages; this is, indeed, found to be 
the case. Monosymmetric sulphur, for instance, ex- 
hibits the axial ratios, a:b: c=0-9958: 1 : 0-9988, 
B=95° 46’; the relative dimensions in the three direc- 
tions a, b, and c, are almost the same as in the cubic 
system, and the angle between the directions a and ¢ 
is B=95° 46’, instead of g0°. ‘This substance has 
nearly the dimensions of a cubic crystal, and is obvi- 
ously ‘pseudo-cubic’’; the same is true of all other 
elements which depart from true cubic or hexagonal 
symmetry. 
The crystalline forms presented by the elements are 
consequently in accordance with the assumption that 
the crystal structures are equilibrium arrangements 
of the component atoms of the two kinds described. 
It is also indicated that aggregation of the atoms to 
form molecular complexes is responsible for the depar- 
ture from simple cubic or hexagonal symmetry; in 
this connection it is interesting to note that the 
strongly coloured elements depart most widely from 
these two systems. Thus, the colourless modifica- 
tions of carbon and phosphorus are cubic, whilst the 
black graphite is monosymmetric and the red phos- 
phorus is orthorhombic in crystal form; this is in 
accordance with the general view that colour is the 
result of some particular kind of molecular aggrega- 
tion. 
Although so much general correspondence of a 
quantitative character is to be observed between the 
observed facts and the anticipations developed from 
the equilibrium assumption, it has become evident 
during the last year or two that the conception formed 
