434 



NATURE 



[September io, 1903 



books, the second contains a chapter on the chemical 

 properties, more especially with regard to the problem 

 of the classification of species; the third contains 

 several articles which have not previously found their 

 way into text-books of mineralogy (pp. 228-41); they 

 relate to the crystalline form and physical properties of 

 "solid solutions," and are especially useful in the 

 discussion of the felspars ; the fourth contains a chapter 

 -on the determination of minerals, and affords many 

 useful and practical hints suggested by a long ex- 

 perience. 



The first book is by far the longest, and is itself 

 divided into two nearly equal sections; the first {98 

 pages) deals with the geometrical properties of crystals, 

 the second (81 pages) with their physical properties. 

 It may be objected that it is impossible to give to the 

 student, within the compass of 98 pages, an adequate 

 idea of the theory of crystallography, but it must be 

 remembered that, in a work on mineralogy, minute 

 crystallographic detail would be out of place; such 

 detail is already given to the student in the special 

 treatises of Prof. Maskelyne ("The Morphology of 

 Crystals "), of Prof. Lewis (" A Treatise on Crystallo- 

 graphy "), and of Mr. Hilton (" Mathematical Crystal- 

 lography and the Theory of Groups of Movements "). 

 What the mineralogical student requires is a brief 

 sketch of the whole subject to enable him to grasp the 

 general bearings ; this the author has given, and it is 

 all that should be expected from him. It may be 

 mentioned that the author has sought to bring about 

 uniformity of nomenclature of the thirtj'-two classes 

 -of symmetry by coming to an understanding with Prof. 

 E. S. Dana, the editor of the well-known " System of 

 Mineralogy"; but notwithstanding their agreement 

 we find it difficult to reconcile ourselves to a nomen- 

 clature which compels one to say that a crystal of 

 cinnabar (HgS) belongs to the quartz class; the 

 systematic nomenclature suggested on p. 280 seems 

 more full of. promise. Attention may be directed to 

 the form of student's goniometer, as improved by the 

 author, which is figured on p. loi, and also to the 

 convenient goniometer designed by him for fixing on 

 the stage of a microscope (p. 178). 



The chapters treating of the optical properties (70 

 pages) will probably be the most generally appreci- 

 ated by students, owing to the great use made of these 

 properties in the determination of the mineral con- 

 stituents of rock-sections by means of the polarising 

 microscope. It gives to the student a sufificiently 

 precise sketch of the subject without entering into 

 mathematical discussions, and proves once more that 

 it is possible to give to the student an idea of the 

 optical characters of biaxial crystals without any un- 

 satisfactory hypothesis as. to optical elasticity and its 

 variability with crystallographic direction. 



Part ii., which gives a description of the more im- 

 portant mineral species, is subdivided merely into 

 sections dealing with the various mineral groups. It 

 differs from other works of a similar kind in that it is 

 in great part readable, instead of being a minera- 

 logical dictionary. The readable part and the 

 dictionary part are kept quite distinct from each other, 

 both in position and in the size of type. Further, there 

 NO. 1767, VOL. 68] 



is no attempt to give long lists of localities ; these are 

 left to be sought for in the books of mere reference ; 

 the author is satisfied, and doubtless the student will 

 be satisfied, with descriptions of specimens from the 

 more noteworthy localities, and with accounts of the 

 more important modes of occurrence, and of these we 

 think the author has made a judicious selection. As 

 for the readable portion, it is full of interesting and 

 valuable information. 



The author has a simple and pleasant style which 

 attracts the reader, occasionally relieving the technic-^ 

 ality with a touch of the driest humour, as, for in- 

 stance, when he finds it convenient (p. 350) to treat 

 dihydric oxide as a member of an anhydrous series. 



The English student of. crystallography and miner- 

 alogy is to-day in a happy position as compared with 

 his forerunners ; his path is continually made more 

 and more easy by the publication of excellent text- 

 books ; but there will long remain sufficient inherent 

 difficulty to prevent these subjects of study from losing 

 their educational value, and, as regards research, the 

 recent discovery of radium in the long-known mineral 

 pitchblende shows that the statement made by the 

 alchemist several centuries ago is still true — " a man 

 may consume his whole life in the study of a single 

 mineral without arriving at the knowledge of all its 

 qualities." 



SCHOOL MATHEMATICS. 

 A Junior Geometry. By Noel S. Lydon. Pp. vi+171. 



(London : Methuen and Co., 1903.) Price 25, 

 Technical Arithmetic and Geometry. By C. T. Millis, 



M.I.M.E. Pp. xiv + 254. (London: Methuen and 



Co., 1903.) Price 3s. 6d. 

 The Modern Arithmetic for Advanced Grades. Wood- 

 ward Series. By Archibald Murray (Harvard). Pp. 



464. (St. Louis : Woodward and Tiernan Printing 



Co., n.d.) 

 The Junior Arithmetic, being an Adaptation of the 



Tutorial Arithmetic, suitable for Junior Classes. 



By R. H. Chope, B.A. Pp. viii + 363. (London: 



W. B. Clive, 1903.) Price 25. 6d. 



MR. LYDON 'S book, which is meant for young 

 pupils, has many good points and a few bad 

 ones. Like many other very recent books on geo- 

 metry, it ignores Euclid's order, method, and 

 language. In this way it appeals more readily to the 

 understanding of the pupil than the orthodox Euclidean 

 works do; but the definition "a straight line is one 

 which lies ' evenly ' between its extreme points," and 

 the words " notice that the line you have ruled lies 

 evenly between its extreme points A and B," show a 

 strong conservatism. The pupil will indeed be cle\a>r 

 if he can give a clear indication of the thing which 

 he notices. The use of the terms vertical and hori- 

 zojital in the following manner must be very strongly 

 condemned : — 



"When a straight line is drawn upright on th^ 

 paper it is called a vertical line, when drawn in a 

 slanting direction it is called an oblique line, and when 

 drawn level on the paper it is called a horizontal line." 



Early teaching of this kind is responsible for the 

 flagrant misuse of the terms vertical and horizontal 



