NATURE 



193 



THURSDAY, JULY 2, 1891. 



CR YSTALLOGRAPHY. 



Elements of Crystallography for Students of Chemistry, 

 Physics., and Mineralogy. By George Huntingdon 

 Williams, Ph.D., Associate Professor in the Johns 

 Hopkins University. Second Edition, Revised, pp. 

 246, with 383 Woodcuts and 2 Plates. (London : 

 Macmillan and Co., 1890.) 



THE position which crystallography ought to occupy 

 in a scheme of scientific education is far from being 

 generally recognized. Every day the importance of this 

 branch of science, not only to the mineralogist and geo- 

 logist, but also to the physicist and chemist, is becoming 

 more deeply felt ; and fyet, as a general rule, the sys- 

 tematic study of crystallography is left quite unprovided 

 for in our schools and Universities. 



If we take any standard treatise on physics, we shall 

 find that the subject of the measurement and calculation 

 of crystal forms is almost, if not entirely ignored ; and 

 though it is, of course, absolutely impossible to discuss 

 optical and other physical phenomena without reference 

 to the wonderfully suggestive relations which exist 

 between the properties resulting from internal molecular 

 structures, and the crystalline forms which are the *' out- 

 ward and visible sign " of such molecular structure, yet 

 the references are usually vague and, not unfrequently, 

 misleading. In confirmation of this statement, it may be 

 mentioned that in a very widely-used treatise on physics 

 — one that has passed through many editions in this and 

 other countries — there is a hopeless confusion between 

 the terms " hemihedrism " and " hemimorphism" in the 

 account which is given of the remarkable phenomena of 

 pyro-electricity. 



Nor, as a rule, have chemists dealt more adequately 

 with the subject of crystallography than their brethren 

 the physicists. In many chemical treatises we find such 

 terms as pyramidal, prismatic, octahedral, rhomboidal, 

 &c., employed so loosely as not to give the student the 

 faintest idea of the real symmetry of the forms which are 

 referred to. This neglect of crystallography by chemists 

 is seen to be the more serious when we remember two 

 important circumstances— first, that crystallization is 

 often the only means which chemists possess of isolating 

 and readily distinguishing many bodies ; and secondly, 

 that new substances are being continually formed by the 

 chemist, the study of some of which may throw new and 

 important light upon crystallographic principles. 



Mr. Fletcher, in a very suggestive address to the 

 Mineralogical Society, has justly remarked : — 



" Hitherto, at least, the chemists of this country have 

 been too content, either to leave the crystalline forms of 

 their artificial products undetermined, or to impose the 

 task of their determination on the already sufficiently 

 occupied mineralogist. It seems obvious that in a satis- 

 factory system of education every chemist should be 

 taught how to measure and describe the crystalline 

 characters of the products which it is his fate to ca JJinto 

 existence. ... A knowledge of the elements of crystallo- 

 graphy, including the mechanics of crystal-measurement, 

 ought to be made a sine qud non for a degree in chemistry 

 at every University." 



NO. 1 131, VOL. 44] 



The consequence of this neglect of crystallography by 

 physicists and chemists has been that the teaching of 

 crystallography has fallen almost entirely into the hands 

 of mineralogists and geologists. But there is no more 

 reason why every book on mineralogy should commence 

 with a crystallographic treatise, than that it should in- 

 clude dissertations on refraction or articles on chemical 

 analysis. " Crystallography should be taught as a special 

 subject," and the student who, after his training in physics 

 and chemistry, takes up the subject of mineralogy, ought 

 to know at least as much of the measurement and sym- 

 metry of crystal forms, as he does of the effects of various 

 media on different kinds of radiant energy, or the re- 

 actions of the several bases and acids. 



It would be easy to show that, much as mineralogists 

 have done for the study of crystallography, the latter 

 science would have been developed more logically, and 

 perhaps more rapidly, if the illustrations of the pheno- 

 mena of crystallization had not been so exclusively 

 sought among natural products. We find not a few 

 examples in the terminology of the science of the effects 

 of this one-sided growth of crystallography. 



Crystallography is based upon purely mathematical 

 considerations, and the study of the principles of crystal- 

 measurement, the discussion of crystal-symmetry, and 

 the calculation of fundamental forms, ought clearly to 

 be one of the first branches of applied mathematics to 

 be taken up by the student of physics ; thus the study of 

 crystallography should certainly precede that of physical 

 optics. If this course were followed, the student of 

 chemistry and mineralogy would come to the teachers of 

 those sciences with such an amount of preliminary in- 

 formation as would enable him to profit by their 

 instructions. 



In the work now before us. Dr. Williams fully recog- 

 nizes the importance of the principles for which we have 

 been contending, and has endeavoured to supply English- 

 speaking students with a short and clear treatise on the 

 principles of crystallographic science. It is certainly 

 remarkable that the countrymen of Wollaston, Whewell, 

 and Miller should have had to wait so long for a work of 

 this character ; though every student of the subject must 

 gratefully remember the aid afforded by the admirable 

 little primer prepared some years ago by Mr. Gurney, 

 and published by the Society for Promoting Christian 

 Knowledge. 



Of Dr. Williams's qualifications for undertaking a work 

 of this kind it is unnecessary to speak. His numerous 

 original researches afford abundant evidence of his devo- 

 tion to crystallographic study, and in the preparation of 

 the work he has had the advice and assistance of 

 one of the first crystallographers of the United States, 

 Prof. S. L. Penfield, of New Haven. 



In order to keep the work within the smallest possible 

 limits, it has been restricted to geometrical crystallo- 

 graphy, but otherwise the work has been modelled upon 

 the same lines as Groth's standard work, " Physikalische 

 Krystallographie." The plates and very numerous wood- 

 cuts afford the greatest possible aid to the reader, and 

 the typography leaves nothing to be desired. In looking 

 through this revised edition, we are struck with the 

 almost entire absence of those typographical errors that 

 so easily creep into a work of this kind, and which, 



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