96 



NATURE 



[JuLv 21, 192. 



The experiments just described, however, show that 

 minute traces of formaldehyde are by no means 

 poisonous, but actually enhance photosynthetic 

 activity in a remarkable degree. The intermediate 

 stages of transformation from formaldehyde to 

 carbohydrate are likely to be rapid ; there would 

 therefore be no accumulation of formaldehyde to a 

 poisonous degree. 



At first sight it is inconceivable that infinitesimal 

 traces of certain chemical substances could have such 

 a potent influence on life-activity. There is, however, 

 no doubt of the reality of the phenomenon. 



J. C. BosE. 



Bose Institute, Calcutta. 



Molecular and Crystal Symmetry. 



I GATHER from Messrs. Shearer and Astbury's 

 reply (Nature, June 2; p. 740) to my former letter 

 to Nature (May 12, p. 632) that my mention of 

 a paper by Fedorov has unhappily diverted their 

 attention from the main issue. As any attempt to 

 disentangle numerous side issues would only take 

 up valuable space, I propose to confine my remarks 

 to the few points connected with recent X-ray 

 developments. 



In attempting to show that I was in error in 

 supposing that nothing can be said about the 

 symmetry of the molecule until the position of every 

 atom in it is determined, Shearer and Astbury 

 invoke the X-ray evidence of benzoic acid ; but it 

 will be found on examination that their proof rests 

 on an assumption that if two crystal molecules are 

 symmetrically disposed with regard to a structural 

 plane the molecular symmetry is thereby limited. 

 My own view is that the molecular symmetry remains 

 untouched, and that the actual X-ray results can 

 be equally harmonised with any type of molecular 

 symmetry, provided the molecules be orientated in 

 a general way, i.e. so that no molecular plane or axis 

 of symmetry be parallel to any structural plane or 

 axis. What is, indeed, wanted is an experimental 

 proof that a structural plane beset with molecules, 

 individually symmetrical but facing the plane 

 asymmetrically, is distinguishable from a plane 

 studded with asymmetric molecules ; but as such 

 an experiment is unrealisable, I do not see how the 

 symmetry of an individual molecule can be deduced 

 without first determining the positions of every 

 atom in the structure. Further, I fail to see how 

 Messrs. Shearer and Astbury can take a different 

 view, for if the molecular symmetry of a complex 

 organic compound can be deduced from X-ray 

 measurements, what object was there in advancing 

 Shearer's rule ? If it were really feasible, it would 

 surely be better to solve the intimate structural 

 details of benzoic acid by the method of experiment 

 than by a process of speculation. 



The only other subject I need refer to is that of 

 tartaric acid. It now appears that my previous 

 conjecture, that Astbury's crystal molecule is axially 

 symmetrical, was erroneous, and that this substance 

 is really in formal agreement with Shearer's rule. 

 I may, however, point out that I was formerly 

 particularly adverse to drawing any definite con- 

 clusion from such a complicated structure, a position 

 which I see no reason to modify. In this connexion 

 it is pertinent to add that evidence from simple 

 compounds is already coming in. Dickinson'^ recent 

 investigation of tin tetraiodide reveals 8 chemical 

 molecules, each of a symmetry number 6, to the 

 unit of structure ; and as the symmetry number is 

 generally held to be 24 (and not 48) the rule is corre- 

 spondingly infringed. 



NO. 2803, VOL. I I 2] 



In conclusion, it may be useful to add a word .^. 

 explanation on the part played by Shearer's rule in 

 X-ray investigations of organic compounds. In tiie 

 typical case of benzoic acid classical methods of 

 crystallography allow of the determination of tlie 

 symmetry and also of the relative edge-lengtlis 

 the unit of structure. Building on this foundat; 

 the X-ray method goes further by determining 1 

 mass associated with this unit, its absolute dimensio 

 and therefore volume, and, somewhat approximately, 

 the relative positions of the centres of gravity of its 

 constituent molecules. This represents a great 

 advance to the crystallographer, but scarcely so to 

 the chemist unless such molecular centres can be 

 expanded into bodies of definite shape and atomic 

 configuration. Now as volume determines neither 

 external shape nor internal structure the problem is 

 obviously one of great complexity, and X-ray results 

 cannot usefully be applied to its solution on account 

 of the enormous number of variables concerned in 

 cr>'stals of low symmetry and complex chemical 

 composition ; consequently, more general but less 

 direct aids have to be relied on. 



One method of bridging the gap is to adopt the 

 hypothesis that atomic radii are approximately 

 constant in crystals, whereby a radius determined 

 from an element or simple inorganic compound can 

 be carried over to a complicated organic compound. 

 By such means spheres of appropriate sizes can be 

 packed together in a tentative way so as to fill 

 variously shaped cells of the correct volume, but 

 there is obviously still much scope for varieties of 

 arrangement and some further limiting principle is 

 needed. That actually favoured at the present 

 moment is Shearer's rule that a crystal makes the 

 utmost use of the symmetry of its component 

 molecules, or, alternatively stated, that the moleculeo" 

 symmetry is deducible as being the crystal symmetry 

 divided by the number of molecules involved in 

 the unit of structure. Since such a rule generally 

 leads to low molecular symmetries (i.e. those which 

 are practically consistent with any given arrange- 

 ment), it is somewhat difficult to see how it can serve 

 to limit the number of structural solutions. It can, 

 however, be employed in a more superficial way, 

 since the creation of an upper limit to molecular 

 symmetry serves to rule out any stereochemical 

 formulae of still higher symmetry. Thus, it has 

 been suggested that the Kekule and Clans formulae 

 for benzene must be abandoned in favour of the 

 Dewar formula, at any rate in the crystal. 



Such results are obviously worthy of attention 

 in so far as Shearer's rule is true. The present 

 position is that the rule is a postulate and so also 

 are the results that flow from it, ranging from the 

 disposition of electrons in a crystal molecule of 

 alumina to that of the atoms in any complex organic 

 compound. T. V. Barker. 



University Museum, Oxford, 

 June 16. 



Stirling's Theorem. 



Mr. H. E. Soper, in Nature of May 5, p. 601, gives 

 Stirling's Theorem in the form 



r- (n^\y^^ 



( _ 1 ^_ , 7 , \ 



^^""P- ^ 24(«-f-i)288o(« + !)'«■*' • • • /• 

 This form suggests that a first approximation of 



the form ^2"- a ) 



might be made exceed- 



ingly accurate by choosing a in a suitable way. 



