June 22, 1911] 



NATURE 



545 



specialised portion of the book is preceded by an 

 admirable review of the morphology of crystals and 

 the structure theories of Bravais, Wiener, Sohncke, 

 von Fedorow, and Schonflies (again we notice the 

 omission of a British name, that of Barlow). Such 

 a review is of special value, as it gives us the con- 

 sidered opinion of one who regards crystals essentially 

 from the physical and mechanical point of view, and 

 whose original investigations have brought him more 

 than usually in touch with the phenomena dependent 

 on the internal molecular and atomic arrangement of 

 crystals. The influence of such an experience and 

 of the character of this field of research is evident 

 in a most interesting manner throughout. As Prof. 

 Voigt so truly says : — 



" Die besonderer Bedeutung welche die Krystallform 

 fiir den Aufbau der Krystallphysik besitzt, liegt darin, 

 dass dieselbe eine einfachste und anschaulichste 

 physikalische Wirkung der Konstitution der Substanz 

 darstellt." 



The specialised portion of the book deals with pyro- 

 electricity, pyro-magnetism, thermal dilatation, elec- 

 trical and thermal conduction, thermo-electricity, di- 

 electric influence, ferromagnetism, elasticity and 

 internal friction, piezo-electricity and piezo-mag- 

 netism, and the effect upon them of change of tem- 

 perature, all being considered specially with reference 

 to crj'Stals, as organised and perfect solids. The 

 ground covered is thus very wide, and the practical 

 investigator is most grateful to Prof. Voigt for 

 placing within easy reach the theory and mathematics 

 or all these branches of the subject. If only a few 

 more practical hints as to the mode of carrying out 

 the experiments, and more and better illustrations of 

 the apparatus could have been given, the work would 

 have been well-nigh perfect. 



(2) This book does not profess to be a complete 

 treatise on crystallography, but embodies the earlier 

 lectures of the course in mineralogy given for some 

 years by the author at the Ecole Nationale des Mines 

 at Saint-Etienne, of which he is the director. Crys- 

 tallography is considered first of all as the necessary 

 introduction to the study of mineralogy by students 

 training for mining engineers, and is therefore limited 

 to those properties of crystals which are useful for 

 the identification of mineral species. Hence, many of 

 the less apparent physical properties of crystals are 

 passed over, and those which are considered are dealt 

 with from this limited point of view rather than for 

 their own intrinsic interest. Indeed the author almost 

 apologises for the necessity of treating even cursorily 

 the fundamentally important optical properties of 

 crystals. 



The above will have sufficiently indicated the severe 

 limitations of the book, and the narrow aspect from 

 which it is presented. Crystallography has suffered, 

 perhaps more than any other science, in the past from 

 such limitations, imposed by being relegated to a 

 corner in a course of mineralogy, which is itself fre- 

 quently merely taken as a subsidiary part of a course 

 in geology. There are strong indications that the 

 time has now arrived, however, when these limitations 

 should be swept away, and the fact boldly recognised 

 NO. 2173, VOL. 86] 



that the child has outgrown the parent, .and that 

 crystallography has become a wide and important 

 subject on its own account, embracing (i) crystal 

 morphology ; (2) the optics and other physical proper- 

 ties of organised solids; (3) mineralogy; and (4) the 

 crystallography of metals. Recent progress in the 

 subject has been so rapid, its importance has become 

 so palpably enhanced, that partial presentments of 

 the character of the book before us are entirely be- 

 hind the times, and no longer called for, except for 

 the convenience of a particular set of students who 

 may desire to have their professor's lectures before 

 them in print. 



While from the latter point of view it is possible 

 to say much that is good about the book, there are 

 some defects that cannot be ignored. The illustra- 

 tions of crystals, for instance, are obviously in many 

 cases inaccurately drawn, that is, not in clinographic 

 or any other projection correctly to their proper 

 elements, but are merely approximations of the nature 

 of ruled rough sketches; hence, lines which should 

 be parallel are often conspicuously not so. Also while 

 one is glad to see a greater tendency than in other 

 French books on this subject to employ the simple 

 and scientific symbols of Miller for the crystal faces 

 and forms, the advantages of which are fully admitted 

 by the author, the notation of Levy is still given as 

 well in conformity with French usage, although the 

 probable confusion to the mind of the student would 

 appear to dictate its abandonment as an unnecessan.' 

 complication, especially considering the limited time 

 available for the cn,'stallographic part of the curri- 

 culum of these students. 



A further limitation is the marked tendency to base 

 the whole crystal morphology exclusively on the laws 

 of Haiiv as expanded by Mallard, and on the space- 

 lattices of Bravais. Now it will be clear from the fol- 

 lowing review of Prof. Sommerfeldt's book how great 

 is the importance of the space-lattice ; but this bocJc goes 

 to the other extreme in stopping short at this work 

 of the French savants. The only work on homo- 

 geneous structures referred to beyond it is that of 

 Schonflies, and this, moreover, is only dealt with 

 briefly as an afterthought in an appendix, and appar- 

 ently largely as a development of the mathematical 

 work of Jordan. No mention could be found of the 

 work of Sohncke, von Fedorow, or Barlow, in de- 

 veloping the 230 types of homogeneous structures pos- 

 sible to crystals. 



Curiously enough, the part of the book most diffi- 

 dently presented, the optical, is the most readable 

 and interesting, and is marked with originality of dis- 

 tinct value. Indeed, this section leaves the reader 

 with the wish that it had been extended, as the author 

 appears to be on specially familiar and congenial 

 ground. 



(3) This is a suggestive little book, the main object 

 of which appears to be to present a simplification of 

 the mode of regarding the homogeneous structure of 

 rrystals as a complicated point-system of the character 

 indicated by Sohncke. Its essence is that the space- 

 lattice (Raumgittcr) is considered as the basis of the 

 structure. The method is to drop the idea of essen- 



