NATURE 



73 



THURSDAY, MAY 22, 1879 



MILNE'S CRYSTALLOGRAPHY 



Notes on Crystallography and Crystallophysics. By 

 John Milne, F.G.S. (London: Trubner and Co., 

 1879.) 



THAT two little treatises should have appeared, written 

 at so near a date the one to the other as Mr. Gurney's 

 and Mr. Milne's introductory tracts on crystallography, 

 shows that there is at least some want at last beginning 

 to be felt for the means of studying that important but 

 somewhat neglected science. 



And it is suggestive of some singular reflections that 

 one of these little treatises should come from Japan 

 written by one of that teaching body at Yedo, of which 

 Prof. Perry is a distinguished member. 



Is there a demand springing up among the subjects of 

 the Mikado for branches of knowledge which have hardly 

 obtained a footing in institutions in which scientific train- 

 ing is given in Great Britain ? Or is it that the Japanese 

 have enticed to their colleges Englishmen who are so far 

 ahead of their colleagues at home, that they are less tram- 

 melled by routine, and endeavour in the instruction they 

 give to the youth of Japan to work out a more complete 

 and comprehensive curriculum for the student of chemical 

 science and physics than is recognised at home ? What- 

 ever be the cause, we have, in Mr. Milne's little treatise 

 as we had before in Mr. Gurney's, an attempt to supply 

 an educational want. We must award to Mr. Milne all 

 the credit which is his due for the intention this attempt 

 involves, and for his courage in undertaking it, with what 

 was apparently a small and inadequate equipment either 

 in previous study or in the literary material necessary for 

 making his treatise thorough and worthy of the purpose 

 that suggested it. The book is concise and its form 

 fairly well planned ; and if our praise cannot be extended 

 to the execution of that plan the circumstances under 

 which the little volume has been produced have to be 

 considered in extenuation of the dispraise. But in criti- 

 cising it, it is essential to consider its seventy pages solely 

 on their merits. Like Mr. Gumey, Mr. Milne follows 

 Prof. Miller's system of crystallographic notation, and 

 endeavours to make clear the simplicity and elegance of 

 that system. His first line, however, in explanation of 

 the system, the sixth line of his Introduction, is, to say the 

 least, infelicitous. " In this (Miller's) system," he says, 

 " the symbols of a face consist of three whole numbers, 

 each of which invariably refer to the same axes ; " a 

 sentence in which are compendiously represented the 

 faults of the book, faults due partly to inaccuracy of 

 mathematical conception, and partly to a mode of em- 

 ploying the English language, for which perhaps some 

 excuse is to be found in a long residence in Yedo, but 

 which surely one of the three home-editors, Mr. T. Davies, 

 Mr. H. Woodward, and Prof. Morris, might have taken 

 the liberty of correcting. 



What Mr. Milne intended to convey in the above un- 



grammatical sentence was, of course, that the symbol for 



a plane is constituted by three whole numbers termed 



indices, which may include one or two zeros ; the par- 



VoL. XX. — No. 499 



ticular axis to which an index has reference being given 

 by the position of the index in the symbol. If Mr. 

 Milne would, for instance, consider the application of 

 his statement to the symbols for the faces y, /, &c., 

 .of the crystal of cuprite, which he discusses on p. 27, 

 and where by the by he makes the blunder in his 

 result of putting (015) for (051), he would find that 

 his statement amounts to the assertion that these two 

 last symbols are identical, an assertion that would re- 

 duce the system of Miller to all the ineptitude of that 

 of Naumann. 



In deducing on p. 16 the symbol of a zone from 

 the symbols of the planes belonging to it the author 

 proceeds on the tacit assumption that he has rectan- 

 gular axes to deal with, thus leaving unexplained the 

 case of crystals belonging to systems referred to oblique 

 axes ; and these form a large majority of the known 

 crystals. 



In his mode of treating the problem by algebraic geo- 

 metry in the last paragraphs on p. 17 he is certainly not 

 to be congratulated. 



It is from this p. 17 that one begins to find the hope- 

 lessness of this little book fulfilling, in its present crude 

 form, the purpose its author proposes for it; that, namely, 

 of making the simple system of F. Neumann and Miller 

 intelligible either to the student slenderly equipped with 

 mathematical knowledge, or to the votary, too often the 

 partizan of the system of K. Naumann. 



For it is evident that Mr. Milne has been unfortunate 

 in his English editors. Mr. T. Davies, a gentleman 

 universally esteemed for his personal character as well as 

 for a very complete familiarity with minerals and rocks, 

 obtained by the daily handling and scrutiny of them 

 during twenty years of service in the British Museum, 

 undertook, it seems, to pass through the press the little 

 book of which copies lithographed by a Japanese native 

 had been sent home to him and to others by Mr. Milne. 

 If Mr. T. Davies had enlisted the aid of some one who 

 possessed a rudimentary knowledge of algebra and plane 

 trigonometry he might have saved Mr. Milne's little book 

 from being useless. Then probably 00 - 01 ; 00 — 10 ; 

 1 1 — 00 would have been written o X o - o X i, &c., and 

 would have been intelligible, and such a misprint as that 

 on p. 21, " .', (112) being {sic) the indices of the plane at 

 J_ J to [ill] and [no]," might have been avoided. Of 

 course a plane X'' to [ni] and [iioj is (1 10) or (110) and 

 not (112) ; but Mr. Milne meant to write the two zones as 

 [ill] and [1 10]. Misprints of this serious kind are very 

 numerous ; other instances are {loh) for {loh), {org) for 

 {or^), or {p - s) for o,r{p - s) on p. 22 ; \Wvw for 

 UVIV on p. 24 ; [312] twice for [312] on p. 26 ; the fre- 

 quent omission of brackets where they are necessary : for 

 instance, a'^kr - Iq instead of c^{kr - Iq) on p. 17; and 

 these are the sort of errors which puzzle a student who is 

 not a fair mathematician, precisely the student for whom 

 the book is meant, since any one possessed of a httle 

 mathematical knowledge would naturally prefer to have 

 recourse to Miller' s Tract on Crystallography, a book of 

 the existence of which Mr. Milne seems to be unaware, to 

 judge from a note on p. 34. In a treatise on a science 

 which presents to the student novel forms of notation the 

 want of even the most elementary acquaintance vrith 

 algebra that has allowed the introduction into the type, of 



