334 TRANSACTIONS OF SECTION B. 
replacements may be effected so as to introduce new geometrical features of 
arrangement corresponding to the presence in the molecule of an ethylenic or 
an acetylenic 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 correspondence is observed between the 
numbers of isomerides possible, with their constitutions and configurations, 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 suggested which accords with 
the crystalline form and chemical properties of the hydrocarbon, and can be 
geometrically partitioned into units, each representing a single molecule. The 
equivalence parameters of the substance are 
w:y: z=3°101 : 3-480: 2°780. 
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 aromatic compounds, 
indicating that in these crystalline substances the benzene 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, Colgate, and Rodd.’ The exhaustive 
nature of the experimental 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 contention, namely, that the crystallographic method affords 
material from which the stereochemical configurations of aromatic substances 
can be deduced. 
If crystallography is to be used as a tool in the service 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 partitioned into cells each representing the 
molecule NaCl. In this instance, the partitioning can be performed in a variety 
of ways corresponding to the allocation of one particular sodium atom to 
either of six chlorine atoms; the alternative modes of partitioning lead to the 
production of molecular units of identical configuration. In many cases, how- | 
ever, alternative methods of geometrically partitioning the assemblage represent- 
ing the crystalline structure do not yield units of the same configuration; thus, 
the assemblage representing phloroglucinol can be geometrically partitioned in 
two distinct ways. Each of these gives a unit of the composition C,H,O,, but 
the configuration of the unit of the one partitioning corresponds to the chemical 
structure of the 1: 3 : 5-trihydroxybenzene, 
C(OH) . CH 
Ho? \sc(OH) 
. \c(OH) : CH 
6 Trans. Chem. Soc., 1909, 95, 1275. 
7 Trans. Chem. Soc., 1910, 97, 1578; Proc. Roy. Soc., A, 1912, 87, 204; 1913, 89, 
292; 1914, 90, 111. 
