NATURE 



261 



THURSDAY, JUNE 6, 1918. 



SYMMETRY IN NATURE. 

 Lectures on ihc Principle of Symmetry and its 

 Applications in All Natural Sciences. By Prof. 

 l'\ M. Jaeger. Pp. xii+333. (Amsterdam: 

 "Elsevier" Publishing' Co., 1917.) 



rHIS is a book of unusual character, written 

 by a Dutchman, Dr. F. M. Jaeger, professor 

 of inorganic and physical chemistry at the Uni- 

 versity of Groningen, Holland, who is personally 

 known to many English and American men of 

 science from his visits to this country and the 

 United States, and who .is not only a chemist, but 

 also, what is infinitely rarer, an accomplished 

 crystallographer. Although published" in Amster- 

 dam, it is written in the Elnglish language, and 

 dedicated to an Englishman, the president of the 



[ Chemical Society, Prof. W. J. Pope. 



I These alone are reasons why a welcome should 



^ be given to the book ; but its own merits are also 

 adequate to deserve it. The author is well known 

 for his researches on enantiomorphism and optical 

 activity, for his crystallographic investigation of 

 the hexagonal ethyl sulphates of the rare earths 

 iid other substances, and most recently for a 

 -cries of beautiful photographs of Laue X-radio- 

 grams taken with the crystals of a considerable 

 number of important substances. Prof. Jaeger is 

 obviously a great admirer of the work of Prof. 

 Pope, for which the latter received the Longstaff 

 medal of the Chemical Society, on the relation 

 between the crystal form of optically active sub- 

 stances and their chemical nature, on the true 

 character of a racemic substance as a molecular 

 compound of the two optically active antipodes, and 

 of a pseudo-racemic substance as an intimate, ex- 

 ceedingly fine, alternating repetition of the two 

 \arieties, and his work generally in confirming 

 Pasteur's law. 



The most important section of the book, its 

 latter half, is devoted to an excellent summary of 

 these investigations and those of other workers 

 in this domain, together with their relation to 

 the theories of van't HofF and Le Bel concerning 

 the asymmetric carbon atom, and to the further 

 work of Pope and Kipping on the asymmetric 

 atoms of nitrogen, sulphur, selenium, tin, silicon, 

 and phosphorus. Practically everything that is 

 surely grounded in chemical crystallography is 

 tlustered around tJie two subjects of enantio- 

 morphism and isomorphism, and it is the former 

 only that is dealt with in this book, the latter 



\ Jieing scarcely touched, which is somewhat of a 

 disappointment. 



In yet another aspect, however, the book is 

 remarkable. It deals with the principle of sym- 

 metry, applied so generally as to include the 

 animal and vegetable kingdoms as well as crystals. 

 < )ne of the happiest features is the excellent photo- 

 raphic figures of highly symmetrical living 

 *)l)jects, such as radiolaria, Circoporus octdhedrus , 

 <'ircorhegma dodecahedra, Circogonia icosahedra, 

 NO. 2536, VOL. 101 ] 



pollen seeds, fruits, and especially flowers. 

 Indeed, the amount of ground covered is well- 

 nigh bewildering. The first four chapters deal 

 with the nature, aesthetic value, and laws of sym- 

 metry ; with the deduction of symmetry character 

 as a mathematical problem ; with mirror-image 

 repetition by reflection and inversion ; with the 

 derivation of the possible types of symmetry by 

 the method of groups of movements ; and with the 

 applications to the morphology of crystals, plants, 

 and animals. 



Chap. vi. is omnivorous, for it deals with the 

 systems of crystal symmetry, the derivation of 

 the 230 types of homogeneous crystal structures 

 and of the thirty-two classes into which they fall, 

 including the fourteen Bravais space-lattices, the 

 j sixty-five regular point-systems of Sohncke, and 

 I the methods of Schonflies, Federov, and Barlow 

 ' for deriving the rest of the 230 types by use of 

 mirror-image repetition ; with the space-lattice in 

 relation to Hauy's law; with the Barlow -Pope 

 valency volume theory ; with the diffraction and 

 reflection of X-rays by the planes of atoms in 

 crystals, and the X-ray analytical methods of 

 Laue and Bragg; with the existence or otherwise 

 of chemical molecules in crystals; with Werner's 

 co-ordination theory ; and in conclusion with 

 phyllotaxis, the symmetrically spiral arrange- 

 ment of the leaves of plants. It is, however, in 

 the latter part of the book, and especially in the 

 two chapters on Pasteur's law, that the author 

 is at his best. He concludes with some valuable 

 suggestions for further research, especially as 

 regards the premier problem of bio-chemistry, the 

 asymmetric synthesis of organic molecules. 



It is interesting that Prof. Jaeger does not 

 commit himself to a definite opinion concerning 

 the Barlow-Pope valency volume theory, although 

 he points out that the X-ray work has not afforded 

 any support to the theory, and he clearly per- 

 ceives the futility of tampering with *axial ratios. 

 As regards the persistence of the molecule in the 

 crystal, one is glad to see that the author agrees 

 that geometricians have gone too far in deleting 

 the molecule as an entity in the solid crystal, for 

 he rightly points out that although the crystal 

 structure is essentially one of atoms, still the 

 molecule remains in position, and unless its entity 

 be. admitted, all kinds of difficulty arise as to 

 valency, interatomic forces, enantiomorphism of 

 the chemical molecule, effect of solution, and so 

 forth, all of which are insoluble on the purely 

 atomic assumption. 



As above mentioned, isomorphism is not dealt 

 with, doubtless because the symmetry remains the 

 same in all isomorphous substances. Consequently 

 the law of progression with atomic number, of 

 the crystal angles, elements, and physical con- 

 stants, in such series as the rhombic sulphates 

 and selenates of the alkalis and the mono- 

 clinic double sulphates and selenates contain- 

 ing 6H;0, now so thoroughly established 

 and so perfectly explained by Mdseley's law 

 connecting the atomic number with the com- 

 plexity of the atom, is not referred to. Yet in the 



