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145 



MASKEL YNE'S CRYSTALLOGRAPHY. 

 Crystalloj^raplty, a Trea/isc on the Morphology of 

 Crystals. By N. Stor>-.Maskclync, M.A., K.R.S., 

 Professor of Mineralogy, Oxford. 521 pp. and xii. pp., 

 398 figures, 8 plates, 8vo. (Clarendon Press, 1895.) 



\rTEK wandering in the desert for considerably more 

 than forty years, the English student of crystallo- 

 graphy is at length brought within sight of the promised 

 land ; it is true that guides have been offered to him 

 m the interval, but they have spoken in strange tongues, 

 and have sometimes been mere dust-clouds of unneces- 

 sary formula' and notations, calculated rather to bewilder 

 than to lead. 



The long-expected treatise of Prof Maskclync will be 

 found to fully justify the anticipations with which it has 

 been awaited ; those who desire to study crystals and 

 crystallogiaphy arc no longer confronted by the want of 

 an authoritative handbook, and need no longer lose them- 

 selves among the works of foreign authors. The English 

 books hitherto available are few in number. The re- 

 markable "Treatise"' and "Tract" of the late Prof 

 Miller established, in the most rigid manner, a mathe- 

 matical basis for the science, and must always remain 

 standard works — masterpieces of precision. These two 

 books contain, in a few pages, all that is essential ; but 

 being condensed into a bald sequence of theorems, they 

 appeal almost exclusively to the mathematician. Mr. 

 Gurney's little introduction to the subject, and the text- 

 book of the late Prof V,. H. Williams, are excellent 

 stimulants to the beginner, but will not suffice for the 

 more advanced student ; the present work supplies most 

 completely what was wanted. 



It is easy to state what is required from the practical 

 point of view in a text-book on the morphology of crystals : 

 the learner desires to know what are the forms of 

 crystals, and how the)' differ from other figures ; he must 

 be told how they are determined and described, and for 

 educational purposes it is especially important that the 

 geometrical relations should be established by simple 

 methods of proof from intelligible principles. 



.■Ml this the present \olumc satisfactorily accomplishes. 

 .■\ crystal is considered to be, for morphological purposes, 

 a complex of planes which obey a simple geometrical 

 law — that known as the law of rational indices, and the 

 early part of the book is consequently devoted to the 

 investigation of such a complex, and shows, further, how- 

 it is denoted and represented ; this involves a series of 

 propositions relating to axes and indices, to stereographic 

 projection, and to the relations of zones. The idea of 

 symmetry superimposed on such a geometrical complex 

 is considered in the two following chapters, and the six 

 systems, having thus been established, are considered in 

 detail in cha|)ter vii. 



.\llhnugh this treatise will certainlj- not prove attrac- 

 tive to readers who are totally unfamiliar with mathe- 

 matical methods and conceptions, yet it succeeds in 

 giving simple and elegant proofs (many of them new) 

 of all the necessary theorems without introducing^ any 

 advanced mathematics. .-Xt the same time the book is 

 NO. 1 33-, VOL 52J 



far from being a geometrical study. The eighth and 

 ninth chapters, comprising more than one hundred pages, 

 are devoted to the practical methods emjjioyed in the 

 goniometrical measurement and calculation of angles, and 

 to the manner in which crystals are depicted by projec- 

 tions and perspective drawings ; further, each crystalline 

 type is represented by copious examples from minerals 

 and chemical products, and frequent references will be 

 found to the bearing of certain physical investigations 

 upon the points discussed. .Such a complete treatment, 

 for example, as is here given of the twinning of diamond, 

 quartz, and felspar is infinitely more satisfactory than 

 the meagre sketch usually found in text-books, whether 

 of crystallograph)- or mineralog\'. 



But the book contains far more than is indicated 

 above ; it is, at least so far as regards certain aspects 

 of the subject, a really philosophic treatise, of which 

 the originality and peculiar interest will be best ap- 

 preciated by a reader who refers to the discussion of 

 crystalloid symmetry contained in the fifth and si.xth 

 chapters. Here the nomenclature is to a large extent 

 new, although some of the terms have become familiar 

 in Mr. Crurney's little book, where they are mentioned 

 as due to Prof Maskelyne. Many of them are invaluable 

 aids to precision ; haplo- and diplo-hedral, meta- and 

 anti-strophic, holo- and hemi-systematic, for example, 

 are terms which avoid much circumlocution, introduce 

 clear conceptions, and once used can scarcely be dis- 

 pensed with. 



The chapters dealing with symmetry must ha\c been 

 familiar to Prof Maskelyne's pupils many years ago, at 

 a time when the importance of this subject was by no 

 means recognised ; to him is undoubtedly due the credit 

 of first in this country directing to crystal symmetry the 

 consideration which it deserves, which, moreover, it failed 

 to receive in the methods of Miller. In the present book 

 symmetry is of cardinal importance : the systems are 

 deduced from a discussion of the possible forms which 

 inay be assumed by the systematic triangle, i.e. the 

 triangle formed by the intersection of a sphere with 

 three adjacent planes of symmetry ; the mcro-symmetrical 

 divisions of the systems are then considered as resulting 

 from the possible " presence or absence of certain faces 

 consequent upon the abeyance of the actual symmetrical 

 character of planes which are otherwise potentially planes 

 of symmetiy " ; in other words, the symmetry of the 

 system is regarded as a complete type latent in the 

 hemihcdral and tetartohedral crystals, and exercising 

 a symmetrical influence by virtue of the axes of symmetry, 

 which arc themselves the result of dormant jjlanes of 

 symmetiy. 



Now in recent years new methods of treating crystallo- 

 graphy, also mainly from the point of view of symmetry, 

 have been developed in other countries ; to avoid criti- 

 cising the present treatise in the light of the newer 

 teaching, would be to shirk a responsibility obviously 

 imposed upon a conscientious review. 



One method frames a theory of crystal structure which 

 shall accord with the observed homogeneity of crystals, 

 finds in how many ways such structures may be sym- 

 metrical, and so deduces the systems ; such is the course 

 pursued in Mallard's magnificent treatise upon the basis 

 of Bravais' theory of structure, and a similar method 



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