684 
NATURE 
_ [Aucust 27, 1914 
the observed axial ratios of forsterite and prolectite. 
All the values referred to are given in Table III., 
and it will be obvious that the agreement between 
the calculated and the observed equivalence parameters 
is very close; as this agreement could not occur with- 
out the operation of the law of valency volumes, 
which was deduced from entirely different data, strong 
confirmation of the accuracy of the law is provided. 
Tasce III. 
Minerals W Axial Ratios Equivalent Parameters | 2/W 
G3 RUNG (2 25 y Zz 
Chondrodite... 34 | 1708630: 1 : 3°14472 | 2°3367 2°1510 6°7644 | 0'19895 
Humite +» 48 | r'o802t : 1 2 4°40334 | 2°3343 271610 9°5155 | 0719824 
Clinchumite... 62 | 1°08028 : t : 5°05883 | 2°3354 2°1646 12°2491 | 0°19756 
Prolectite : | 
observed 20 | 10803 : 1: 178862 2°3130 2°1414 4°0385 | 0°19977 
Prolectite : 
calculated 20 | 1°0818 :1:1°8618 | 2°3365 2'1589 4°0211 | 0°19968 
Forsterite : 
observed 14 | 0°9296 :1:1°r714 | 2°3426 21778 2°7442 | 019601 
Forsterite: 
calculated 14 | o’9240 :1 1°174r | 2°3365 21589 2°7433 | 0°19585 
The several illustrations of the operation of the law 
of valency volumes have been quoted in detail for the 
purpose of showing how difficult it is to avoid the 
conclusion that this deduction represents some physical 
reality. It may be traced in connection with quantita- 
tive data of other kinds; during the last few years 
it has been very successfully applied by Le Bas to the 
interpretation of the molecular volumes of liquid sub- 
stances. 
From what kas been already said it will be seen 
that the great problem as to the relation between crystal 
structure and chemical constitution, of which the solu- 
tion seems imminent, is a stereochemical one; as- 
semblages must be built up in accordance with the 
principle of homogeneity and in some form of close- 
packing, in which each component atom of a chemical 
molecule is represented as the sole occupant of some 
specific solid area. The properties of these assem- 
blages must also be in agreement with the crystallo- 
graphic measurements and the X-ray photographs 
yielded by the substances represented. 
A brief indication may be given of what has been 
already effected in this connection. The normal 
paraffin hydrocarbons of the general composition 
C,Hon+2 consist of a chain of the composition 
(CH,),, to each end of which one hydrogen atom is 
attached; in accordance with the principles already 
indicated, a close-packed assemblage of the empirical 
composition CH, can be constructed from carbon and 
hydrogen spheres of the respective volumes 4 and 1, of 
such a nature that it can be divided by planes into 
blocks, each made up of strings of tne composition 
(OO) On M@la KOH. St eho > CH. At each 
plane of cleavage of the assemblage hydrogen spheres 
can be inserted in appropriate numbers so that close- 
packing is restored when the cleavage faces are 
brought together again; the assemblage will then 
have the composition H . (CH,).,, . H, and may be 
geometrically partitioned into units each representing 
one molecular complex of a normal paraffin. It is 
noteworthy that these units exhibit the configurations 
indicated by the van ’t Hoff-Le Bel conception for the 
normal paraffins. Other assemblages can be con- 
structed which represent in a similar manner the 
secondary and tertiary paraffins, and all these assem- 
blages are of one particular geometrical type, that 
which corresponds to the chemical behaviour charac- 
teristic of the paraffins. In these assemblages replace- 
NO: 2230, 37Ol-"a3] 
el 
ments may be effected so as to introduce new geo- 
metrical features of arrangement corresponding to the 
presence in the molecule of an ethylenic or an acety- 
lenic bond, and thus other classes of hydrocarbons 
can be represented in accordance with the conception 
of close-packing; the process can be extended to the 
polymethylene and aromatic hydrocarbons and to their 
substitution derivatives, and throughout a close corre- 
spondence is observed between the numbers of iso- 
merides possible, with their constitutions and con- 
figurations, and the experimental facts. 
Many considerations indicate the fruitfulness of the 
mode of regarding organic substances just briefly 
sketched; one may be more particularly specified. An 
assemblage representative of benzene has been sug- 
gested which accords with the crystalline form and 
chemical properties of the hydrocarbon, and can be 
geometrically partitioned inte units, each representing 
a single molecule. The equivalence parameters of the 
substance are 
x: V3 2S=370n 2 2-480)"2-9e0. 
The dimension y is twice the diameter of a carbon 
sphere, and that of z slightly less than the sum of 
the diameters of a carbon and a hydrogen sphere. 
Now a dimension approximating closely to the z value 
for benzene can be found amongst the equivalence 
parameters of large numbers of arcmatic compounds, 
indicating that in these crystalline substances the ben- 
zene complexes are stacked one upon the other so as 
to preserve the z dimension, but that the columns so 
formed are pushed apart in the derivatives to an 
extent sufficient to admit of the entrance, in close- 
packing, of the substituting radicles. A few cases 
of this kind were quoted by Barlow and myself, and 
many others were discovered by Jerusalem;° quite 
recently the subject has been subjected to a very 
thorough quantitative examination by Armstrong, Col- 
gate, and Rodd.’ The exhaustive nature of the ex- 
perimental work of these latter authors and the care 
with which their conclusions are drawn leave little 
room for doubt as to the accuracy of their main con- 
tention, namely, that the crystallographic method 
affords material from which the stereochemical con- 
figurations of aromatic substances can be deduced. 
If cystallography is to be used as a tool in the ser- 
vice of stereochemistry in anything like the way which 
has been briefly sketched in this address, a number 
of important results should accrue. We have seen 
that in the structure assigned to rock-salt, each sodium 
atom is identically related to six chlorine atoms; only 
when the crystal is disintegrated by solution in water 
does the necessity arise for a choice to be made, the 
sodium atom then selecting one particular chlorine 
atom as a mate. Even then the sodium chloride 
molecule present in solution appears to spend the 
greater part of its time in dissociation, namely, in the 
act of changing its partner. There is thus in the 
theory of crystal structure something which bears a 
superficial relationship to electrolytic dissociation, and 
the further study of this aspect of the subject may be 
fruitful. 
Again, the solid crystalline structures which we have 
attempted to build up present, as one essential feature, 
the property that they can be partitioned geometrically 
into unit cells, each composed of one molecule of the 
substance; thus, the rock-salt structure can be parti- 
tioned into cells each representing the molecule NaCl. 
In this instance, the partitioning can be performed 
6 Trans. Chem. Soc., 1909, 95, 1275. 
7 Trans. Chem. Soc., 1910, 97, 1578; Proc. Roy. Soc., A, 1912, 87, 2043 
19 13, 89, 29253 1914, Qo, 111. 
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