PRESIDENTIAL ADDRESS, 529 
Tasie I. 
Inorganic Substances, the Number of 
Atoms in the Molecule of which is 
respectively : Organic 
System Sub- 
Elements stances 
More 
2 3 (pe 5 than 5 | 
Per cent.| | 
Cubic . * . : . 50 | 685 | 42 5 | 12 5.8 2.5 
Hexagonal . . . . 35 | 19°5/] 11 3538 14°6 4:0 
Metragonal . 3. sll. 5 4:5 | 19 5 | 66 7 50 
Orthorhombic . s ae 3°0 | 23:5 | 50 36 273 34:0 
Monosymmetric . . . 5 4:5 3 5 6 37°3 475 
Anorthic 2 3 0 15 0 2 8 7:0 
Number of cases examined 
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 agreement 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 monoatomic element; many of the elements are, 
however, certainly polyatomic. Imagine, therefore, 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, exhibits the axial ratios, a:b : c=0-9958: 1: 0:9988, 
B=95° 46’; the relative dimensions in the three directions, a, b, and c, are 
almost the same as in the cubic system, and the angle between the directions 
a and c is B=95° 46’, instead of 90°. This substance has nearly the dimensions 
of a cubic crystal, and is obviously ‘ 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 
departure 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 modifications of carbon and phosphorus 
are cubic, whilst the black graphite is monosymmetric and the red phosphorus is 
orthorhombic in crystal form; this is in accordance with the general view that 
colour is the result of some particular kind .of molecular aggregation. 
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 as to the nature of the equilibrium which determines the 
arrangement of the atoms in a crystalline element is of too simple a character. 
In 1912 Laue showed that on passing a narrow pencil of X-rays through a crystal 
plate the emergent rays were capable of forming a regular, geometrical pattern of 
spots upon a photographic plate placed to receive the emergent beam; the pattern 
of spots thus produced was in agreement with the symmetry of the direction in 
the crystal plate in which the beam was passed. This discovery was developed 
and very considerably extended by Bragg, who was able to show that an X-ray 
