340 



NATURE 



[February 9, 1905 



treatment on the physical properties of metals. The 

 phase rule, which is briefly explained, could be given 

 a practical application by referring to the nature of 

 alloys, particularly in the case of carbon-iron mixtures. 

 As is the case with all the works published by the 

 well known firm of Ulrico Hoepli, the printing and 

 reproduction of the illustrations leave nothing to be 

 desired. It is, however, a pity that so many proper 

 names are wrongly spelt ; thus Graham is uniformly 

 spelt Grahm, and Van der Waals T'nn der ]'aals. 

 More than ten misprints of other names are observ- 

 able. W. A. D. 



A NEW CRYSTALLOGRAPHY. 

 Grundzuge der KrisfaUographie. Bv Prof. C. M. 

 Viola. Pp. iv + 38g. (Leipzig: W. Engelmann, 

 1904.) Price II marks; bound, 12 marks. 

 ' I ^HE opinion is rapidly gaining ground that the 

 ■i- theory of crystallography based on the laws of 

 rational indices and symmetry no longer suffices 

 without modification for the classification and descrip- 

 tion of crystals. It is recognised on the one hand that 

 isomorphism of kindred substances shows itself (as in 

 the Humite group of minerals) more in similarity of 

 crystalline habit and angles than in identity of optical 

 and geometrical symmetry, and on the other hand 

 that vicinal faces with high indices may play an 

 important part in the economy of crystals. Prof. Viola 

 is evidently of opinion that the old methods cannot be 

 adapted to meet the situation, and his book is as 

 revolutionary as it well could be. Crystals are here 

 divided into 7 sygonies, 10 fundamental forms, and 

 29 harmonies; symmetry is but a particular case of 

 harmony; twins are two similar crystals with two 

 predominant elements in common ; the number of 

 space-lattices is reduced to 10, and of space-groups 

 to 156. The basis of classification is descriptive, not 

 geometrical ; blende, felspar, and garnet belong to the 

 same fundamental form, chalcopyrite and tetrahedrite 

 to the same harmony. 



If the author had merely attacked the existing theory 

 and advocated a classification expressing the results of 

 direct observation alone, independent of any hypothesis, 

 he might have had some success. Unfortunately, he 

 has tried to build up a mathematical theorv of his 

 own, with disastrous results. The average shape of 

 all crystals of a substance grown under approximately 

 the same conditions is its " habit "; the average shape 

 of all habits is its "fundamental form." The rate 

 of growth in any direction is proportional to the 

 " cohesion " in that direction (measured, apparently, 

 by the force needed to break a rod of the substance 

 the length of which lies in the given direction), and 

 cleavage takes place perpendicular to the lines in which 

 minima of cohesion are well marked. It follows that 

 the fundamental form has always a centre of 

 symmetry. These assumptions are hardly justified by 

 the cleavage and usual habit of many crystals, e.g. 

 fluorite and tetrahedrite, but the mathematical develop- 

 ment of these hypotheses is, if possible, still more un- 

 fortunate than the premises themselves. It is argued 

 (p. 14, cf. Fig. 20) that if two faces grow outwards 

 with velocities c, and Cj, (i) their intersection moves 

 NO. I 84 1, VOL. 71] 



with the velocity c^, compounded of Cj and c,, (2) there- 

 fore the face perpendicular to c, grows with velocity 

 '^3> (3) C3 is a maximum or a minimum when c, and c, 

 are minima. Of these statements (i) and (3) are un- 

 true, and (2) absolutely unproven. Thus the funda- 

 mental principles on which nearly the whole of the 

 book is based are w-rong. Much of the reasoning is 

 of the same fallacious nature, or is, at best, only an 

 appeal to probability ; but one more example must 

 suffice. 



The author sets himself (p. 251) the impossible task 

 of proving that a symmetry-axis of a homogeneous 

 medium is 2-al, 3-al, 4-al, or 6-al without employing 

 either the law of rational indices or a molecular struc- 

 ture. He accomplishes this by assuming that if the 

 medium is brought to self-coincidence by a rotation 

 through an angle 27 about an axis C, it cannot be 

 brought to self-coincidence by a rotation about C 

 through any angle less than 27. 



Prof. Viola apparently considers the space-lattice as 

 only a convenient geometrical expression of the 

 physical properties of a crystal, not as corresponding 

 to any reality of cr)'stal-structure. It is true that he 

 proves (by assuming that the densities of the molecule 

 and of the crystal as a whole are equal, see pp. 280, 

 335) that the unit of crystalline structure must be the 

 same as the chemical molecule ; but on pp. 322 and 334 

 he uses arguments which would prove the existence 

 of an infinite number of such units in a finite volume. 



Crystallographers owe a debt of gratitude to the 

 author for his clear and complete lists of references to 

 the literature of the various subjects with which he 

 deals ; the historical notes are also very valuable. The 

 chapters on the two-circle goniometer and the stereo- 

 graphic projection contain much that is interesting 

 and not in the usual text-books. The appearance of 

 the book is attractive, but there is a large number of 

 misprints, some of which quite obscure the author's 

 meaning. Harold Hilton. 



OUR BOOK SHELF. 



The Arris and Gale Lectures on the Neurology of 

 Vision. By J. Herbert Parsons, B.S., D.Sc, 

 F.R.C.S. Pp. 70. (London: Hodder and 

 Stoughton, 1904.) Price 2^. 6d. net. 

 The two lectures delivered by Mr. Parsons in the 

 spring of last year before the Royal College of 

 Surgeons deal with some points on the neurology of 

 the eye which are of extreme interest. The first 

 lecture has for its subject the course of the afferent 

 impulses from the retina to the central ner\'ous system, 

 and their final distribution in the cerebral cortex. 

 Since the delivery of tlicse lectures there have been 

 several important contributions to this latter subject. 

 The case of Dr. Beevor and Dr. Collier, reported in 

 the summer number of Brain, seems to go conclusively 

 against the more restricted visual area for which 

 Henschen argues. In this case, despite the fact that 

 the lingual lobe, the depths of the calcarine fissure, and 

 the lower cuneal lobe were all affected, the restriction 

 of the field of vision was simply quadrantic. The 

 truth seems to be that the limits of the visual cortical 

 area correspond to the limits of the layer of Gennari. 

 and that this varies markedly in its relations to thi 

 surface in different cases. 

 The second lecture deals with an equally important 



