October 6, 1923] 



NA TURE 



505 



case is not analogous to racemic acid, for there is no 

 enantiomorphism of the grossly material nuclei or 

 inner swarms of electrons. 



It need scarcely be added that the optically active 

 sodium chlorate (or bromate) follows the above 

 scheme and is in agreement with recent X-ray atomic 

 lodels. The instantaneous racemisation on dis- 

 )lution may well be attributed to the delicate nature 

 a purely electronic type of enantiomorphism. 

 The above suggestions are possibly open to the 

 ejection that they are too elusive to be put to an 

 cperimental test. This leads me to suggest material 

 )r future investigation, which may help towards a 

 lecision. The rhombohedral dithionates of calcium, 

 rontium, and lead are usually quoted as having 

 tour molecules of water of crystallisation, thus, 

 JPbSjOg, 4H2O. If this is really true, it would seem 

 J to follow that the crystal unit must contain six, if not 

 'twelve or even twenty-four, molecules of the salt, and 

 that no successful elucidation is to be expected with 

 present-day X-ray technique. But a rhombohedral 

 crystal with four instead of three or six molecules of 

 water almost amounts to a contradiction in terms, 

 and the early analyses of these salts (ignition to an 

 anhydrous sulphate) are perhaps not conclusive. A 

 particularly simple crystal structure is consistent with 

 a hexahydrated salt ; in fact any eventual proof of a 

 four-unit cell would determine the water content as 

 securely as a chemical analysis. It is therefore con- 

 ceivable that the structure is modelled on the calcite 

 pattern (four molecules to the Bragg unit) according 

 to the following scheme : 



[eHjOJPb^ 



O3S- -SO3 . . . [6H20]Pb^ 



and that we shall have an X - ray pseudo-sym- 

 metry, the atomic assemblage appearing to have the 

 symmetry of calcite, while the crystal structure has 

 the symmetry of quartz (the crystals are optically 

 active, but not the solution). The rhombohedral 

 (or hexagonal ?) anhydrous potassium salt may, 

 perhaps, follow similar lines, but the crystallography 

 is somewhat obscure. 



No good purpose would be served by following out 

 the consequences of a deformation of the RO3 group 

 into lower systems of crystallisation. Nor need the 

 case of an RO4 group be discussed, as it does not seem 

 to offer any likelihood of pseudo-symmetry. 



As previously indicated there is no such possibility 

 of pseudo-symmetry as the above, when no atom, ion, 

 or molecule occupies a specialised position in the 

 structure. None is therefore to be expected in any of 

 the 420 optically active structures previously men- 

 tioned. In theory, then, we have here another 

 possible way of testing the above suggestions, but 

 practical considerations, unfortunately, rule out any 

 likelihood that the X-ray analyst will be able to 

 determine any kind of symmetry in such complicated 

 compounds in the present generation. In Astbury's 

 recent investigation of tartaric acid the symmetry 

 had, perforce, to be assumed. 



The only other possibility that has occurred to me 

 is that the arrangement of the internal electrons (as 

 opposed to the chemical electrons) may affect crystal 

 symmetry ; but as it is difficult to see how this could 

 have any physico-chemical manifestation at the 

 crystal surface, it has not been further examined. 



In conclusion, it will be realised that the work on 

 sal-ammoniac may represent a turning point in the 

 liistory of the X-ray method, for no matter whether 

 X-ray symmetry be held to be a pseudo-symmetry or a 

 rue symmetry, the practical consequences are the 

 ame. As emphasised by Wyckoff, the X-ray analyst 

 must henceforth look upon crystal symmetry with 

 suspicion, and not be led astray at the outset of his 



NO. 2814, VOL. I 1 2] 



interpretation. Unfortunately, this leaves him in the 

 air so far as symmetry is concerned, and implies a re- 

 vision of many past models. The symmetry of calcite, 

 for example, from the X-ray point of view is not 

 necessarily the symmetry of Hauy. To the crystallo- 

 grapher it will remain so, until such time as new 

 evidence shall demand a lower symmetry. 



The following summary may be useful. Each 

 crystal has a definite symmetry — that of a structure 

 of a physico-chemical order of complexity. At the 

 present time the only way to determine this symmetry 

 is to study the surface or make use of such a generalisa- 

 tion as the Pasteur principle, which has established 

 itself on a permanent foundation. Any higher sym- 

 metries are pseudo-symmetries, and have their origin 

 in a suppression of certain determinants. A notable 

 example is X-ray symmetry, for it is compulsorily 

 based on an atomic conception of crystal structure, 

 and not on the molecular basis demanded by a wealth 

 of chemical facts. An attempt is made to bridge the 

 gulf between X-ray symmetry and crystal symmetry, 

 but it is felt that the real solution is not yet in sight, 

 owing mainly to the lack of a general chemical method 

 of investigating crystal structure in situ. 



T. V. Barker. 



University Museum, Oxford, 

 September 8. 



Some Curious Numerical Relations. 



In the course of a series of computations it was 

 noticed that the ratio of the numerical values of the 

 following pairs of quantities is in each case an integral 

 power of ten. This curious relation is so surprisingly 

 exact that it seems worthy of record : 



(A/27r)'' = i-o88o6 X 10-" erg'' sec.^ 

 g'/Ko = 1-08804 ^ 10-** erg cm. es. 



e =4-774 X lo"" es. 

 hjk =4-777 X lo"" sec. deg. 



mo =8-9991 X lo"''^ gm. 

 c* = 8-9916 X 10"" cm.* sec.-* 



^1 =5-30507 X 10-* cm. 

 «/mo =5-30500 X 10^' es. gm.-^ 



The symbol es has been used to denote the electro- 

 static unit of charge, r^ the radius of the first Bohr ring 

 in hydrogen, Kq the dielectric constant of a vacuum, 

 k the gas constant per molecule ; the other symbols 

 have their usual significance. The values that served 

 as the basis of the computation were those just given 

 for e, e/nio, and c, and the following : h, 6-554 ^ lo"" 

 erg sec. ; the faraday, 2-89365 x 10" es. per equivalent ; 

 the volume of one gram-molecule of ideal gas at 0° C. 

 and one standard atmosphere, 22411-5 cm." per 

 mole ; and 0° C, 273-1° K. 



N. Ernest Dorsey. 

 1410 H Street, N.W., 

 Washington, D.C. 



Lichens and their Action on the Glass and 

 Leadings of Church Windows. 



I HAVE read with great interest the paper by Dr. 

 Ethel Mellor in Nature of August 25 and I should 

 like to refer to one or two points. 



The paper gives the general impression that the 

 decay of ancient stained glass is produced by the 

 action of lichens. This has frequently been suggested, 

 but surely the reverse is the case — the decay of the 



O 2 



