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conditions originally assumed is too simple. It will be seen, however, that 
the Bragg results furnish a proof of one part of the assumption made concerning 
equilibrium, namely, that each component atom operates separately; the dis- 
cussion of the properties of crystals on the assumption that the crystal structure 
may be regarded as built up of similar mass-points, due to the mathematical 
physicists of the last century, therefore requires to be reopened. ‘Thus, the 
Bragg structure of rock-salt is represented by dividing space into equal cubes by 
three sets of parallel planes and replacing the cube corners encountered along the 
directions of the cube edges by chlorine and sodium atoms alternately; each 
chlorine atom then has six sodium atoms as its nearest and equally distant neigh- 
bours. With which of the‘latter the one chlorine atom is associated to form a 
molecule of sodium chloride is not apparent from the nature of the crystal 
structure. 
Time need not be now occupied with the further discussion of the crystalline 
structure of simple substances; until the discovery of the X-ray effects thus 
briefly described, no direct method of determining those structures was available, 
and, in view of the paucity of the experimental data, only the possibilities of 
arrangement could be considered in the light of the Barlow-Pope mode of treat- 
ment. It will, however, be useful to review some of the results which accrue 
from this latter method of regarding the problem of crystal structure in general. 
Taking the general standpoint, which is also in accordance with the Bragg 
results, that each component atom of a crystalline structure has a separate 
spacial existence, and premising that the atomic domains are close-packed in the 
assemblage in accordance with some particular type of equilibrium law, it 
becomes obvious that crystalline structure presents a volume problem. The law 
arrived at after a careful investigation of the subject—the so-called law of 
valency volumes—states that in a crystalline structure, the component atoms 
occupy domains approximately proportional in volume to the numbers represent- 
ing the fundamental valencies of the elements concerned; the student of the 
subject of molecular volumes will hardly accept this conclusion without con- 
vincing evidence of its correctness—it indicates, for instance, that in crystalline 
potassium sulphate, if the atomic volume of potassium is taken as unity, those of 
sulphur and oxygen each have the value two. Many different lines of crystal- 
lographic argument converge, however, to this law, and, if the latter is in the 
end found to be incorrect, it at least represents something fundamental which still 
awaits enunciation in a more generally acceptable form. A few illustrative 
instances may be quoted. 
If valency be a volume property, the relation should be revealed in the 
compositions of chemical substances, especially those of composite character. 
The sum of the valencies in potassium sulphate, K,SO,, is 12, and in ammonium 
sulphate, (NH,),SO,, 24, just twice the number; the two substances are so closely 
related that they crystallise together to form ‘solid solutions’ (isomorphous 
mixtures). Similarly, in the alums, such as K,SO,+A1,(SO,),+24H,0, the 
valencies are 12+36+96; the sum of the valencies of the water present, 96, is 
just twice that, 48, of those exhibited by the metallic sulphates. Similar 
curious numerical relationships occur in each of the well-defined series of double 
salts. 
Again, if the valency volume law hold for two substances of different crystal- 
line form, such as orthorhombic rubidium nitrate, RbNO,, and rhombohedral 
sodium nitrate, NaNO,, the metal, the nitrogen and the oxygen in each com- 
pound should have the respective atomic volumes, 1, 3, and 2. As the sub- 
stances differ in density the absolute values of the atomic volumes of nitrogen and 
oxygen will differ in the two substances as examined at the same temperature; 
the ratios of the atomic volumes in either compound should, however, be as 
stated. Considering this conclusion in conjunction with the fact that these 
crystalline compounds represent symmetrically constructed assemblages, it would 
seem that the relative dimensions of the one crystal structure should be traceable 
in those of the other. Orthorhombic rubidium nitrate exhibits the axial ratios, 
a:b :c=1:7336:1:0°7106, three rectangular co-ordinates, a, b, and c, being 
used as the directions of reference; rhombohedral sodium nitrate exhibits 
@:c=1: 0°8276, the co-ordinates being three axes, a, making angles of 120° in 
one plane, and a fourth axis ¢, perpendicular to a. On converting the axial 
