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taken of anonymous communications.) 
Molecular and Crystal Symmetry. 
THE relation between the symmetry of a crystal 
and that of the component molecules has been recently 
discussed by G. Shearer (Proc. Phys. Soc., 1923, vol. 
35, p- 81), who, unknowingly following the same train 
of thought, has arrived at the conclusion, previously 
stated by Fedorov (Zeits. Kryst., 1912, vol. 52, p. 22), 
that a crystal obeys what may be termed a principle 
of conservation of symmetry. Thus, if ” be the 
“symmetry number” of the structural unit or 
parallelepipedal brick (the number of identical or 
enantiomorphously related asymmetric parts into 
which it is subdivisible), # the number of molecules 
it contains, and » the symmetry number of each 
molecule, then n/m=p, or alternatively pm=n, 
i.e. the symmetry of the individual molecules multi- 
plied by their number gives the symmetry of the 
crystal. If the formula be correct no symmetry is 
dissipated, the whole of the molecular symmetry 
being taken up by the crystal. Now, so far as 
Fedorov was concerned, the matter was purely 
speculative, for the X-ray method had only just 
been discovered and its exact meaning was still 
obscure, but Shearer has gone a step further by 
collecting X-ray data in support of the principle 
(or ‘‘ Shearer’s rules’’), with the result that it has 
been provisionally adopted by Sir W. H. Bragg 
(Journ. Chem. Soc., 1922, vol. 121, p. 2766) as a 
working hypothesis in the interpretation pf X-ray 
measurements. As I think the various considerations 
advanced by Shearer are inconclusive, and are already 
leading to very questionable conclusions concerning 
the stereochemical formule of certain aromatic 
compounds, I would here submit the Fedorov-Shearer 
principle to a brief discussion. 
It is self-evident that any real vindication of the 
principle involves a knowledge of all the three terms 
p, m, and v of the formula. Now the last two quanti- 
ties are relatively easily determined, but the molecular 
symmetry # is a much more difficult matter, for it 
implies a determination with a tolerable degree of 
accuracy of the position of every atom in the structure, 
and as such difficulties have not yet been overcome 
in the case of such complicated compounds as the 
benzene, naphthalene, and anthracene derivatives 
investigated by Sir W. H. Bragg, it is evident that the 
field for testing the principle is very restricted. As 
a matter of fact, the evidence adduced by Shearer is 
very scanty, consisting as it does of the demonstration 
that in no known case is m>n, followed by the state- 
ment that if certain values of p be allowed, then all 
the crystals can be brought into line with the prin- 
ciple. It must be noted that there is no experimental 
evidence in favour of these special p-values (which 
are, then, really postulated), and that most of them 
are not what one would expect from chemical know- 
ledge (unless, of course, the molecular configuration 
in the crystal has not the same symmetry as it has 
in solution). Thus, crystal molecules of a- and 
8-naphthol, resorcin, benzoic, salicylic, and phthalic 
acids are all held to be asymmetric, from which it is 
to be inferred that the crystals contain two kinds of 
molecules in the manner of racemic acid. Then, 
NO. 2793, VOL. 111] 
NATURE 

[May 12, 1923 7 
4 
again, naphthalene is held to have no plane of 
symmetry, and so on. ee 
There is, however, one organic compound for which — 
all the three terms p, m, and » have been reasonably 
well established, namely, the erdinary tartaric acid 
recently investigated by W. T. Astbury (Proc. Roy. 
Soc., 1923, vol. 102, p. 506). This is apparently held 
to conform with the principle, but as I do not’ agree 
with Messrs. Shearer and Astbury that the molecule 
is asymmetric, the case calls for a brief examination. 
The acid has long been known to have the formula ~ 

HO OH 
~ 
H—c#—_*C_H 
HO,C7 \co,H 
in which the two carbon atoms marked out by 
asterisks are the so-called asymmetric carbon atoms, — 
i.e. atoms surrounded by four different groups in an 
asymmetric tetrahedral manner (the four groups” 
being in each case H, OH, CO,H, and CHOH . CO,H). 
If a three-dimensional model be constructed according 
to the above scheme, it will be found to take three 
forms, depending on the way in which the duplicated 
groups H, OH, CO.H are arranged about the main 
stem, C* *C. One form is identical with its 
mirror-image (Pasteur’s meso acid); the other two 
are non-identical mirror-images of each other (enantio- 
morphous) and represent the ordinary dextro acid of 
commerce and Pasteur’s rare /aevo acid respectively. 
It is the d-acid that is under examination, but the 
same will hold for the /-acid. If we inspect the model 
for symmetry we shall find a twofold (digonal) axis — 
somewhere or other in the plane normal to the central 
stem, no matter how we may have previously affected 
the relative positions of the two ends by rotating 
one against the other (about the main stem). It 
may be added, parenthetically, that Astbury arbi- 
trarily limits his discussion of the stereochemical 
model to six such positions, but in every case the 
molecular configuration of tartaric acid in the liquid 
or dissolved condition is not asymmetric (as generally 
described). ti 
With regard to the state of the molecule in the 
crystal; a study of Astbury’s paper leads me to the 
conclusion that the molecule is still symmetrical. 
The statement that “ one-half of the ordinary tartaric 
molecule behaves exactly like the other half and is 
indistinguishable from it’’; the pains that seem to — 
have been taken to preserve this parity in allocating - 

the various atoms within the structure ; and, finally, 4 
the evidence of the numerous figures, all go far to — 
counteract the impression created by Astbury’s use — 
of the term “‘ asymmetric molecule.’’ It seems as 
if the unobtrusive molecular twofold axis (normal to 
Astbury’s ‘“‘ dumb-bell axis ’’) has been overlooked. 
If this is so, then the state of affairs in a crystal 
of tartaric acid can be described as follows. The 
structure is not simply built up of a single space- 
lattice arrangement, with the molecular axes uniting 
to create the symmetry axis of the crystal, but is 
constructed of a pair of molecular lattices, mutually 
interpenetrating, the office of the second being to 
restore the symmetry lost by a refusal of the crystal 
to recognise molecular symmetry. As all the mole- 
cular symmetry is wasted, the Fedorov - Shearer 
principle is infringed to the utmost possible limit. 
The above exhausts the material at present avail- 
able for any practical discussion of the symmetry 
principle; for the numerous inorganic crystals 
reviewed by Shearer are evidently not put forward 
as proofs, but rather as contingent illustrations of 
the way in which the principle serves to limit the 

