460 



NATURE 



[Sept. 12, 1^89 



DE LAP PA RENT'S ''MINERALOGY." 



Coiirs de Mineralogle. Par A, de Lapparent. 2me edi- 

 tion. (Paris : F. Savy, 1890.) 



IX years have elapsed since our announcement in 



s 



Nature of the appearance of this book, and now 

 the call for a second edition indicates the continually 

 increasing popularity of the work, not only in France, 

 but especially abroad, where more than half of the first 

 edition has been sold. This popularity must be ascribed 

 mainly to the fact that M. de Lapparent's " Cours de 

 Mineralogie" was the first educational work in which the 

 crystallographic theories of Bravais and Mallard were 

 expounded as a system, and constituted, one may say, the 

 basis of his lectures. 



Now that these theories are continually obtaining 

 a more favourable reception, it mast be recognized 

 that their diffusion has been largely effected by the 

 present " Cours de Mineralogie," owing mainly to the 

 remarkable power of exposition possessed by M. de Lap- 

 parent, of which he gave us a new proof when he pub- 

 lished his lectures on mineralogy in 1884. The same 

 quality is eminently conspicuous in this edition ; but 

 let us hasten to remark that the present is in reality 

 a new work, which contains nearly 100 pages more than 

 the first edition and a large number of new figures. A 

 glance is sufficient to show that the author has not been 

 content with revision, but has entirely reconstructed the 

 book. He has so developed the optical portion that the 

 volume becomes a sufficient introduction to the study of 

 petrography, this chapter now containing a description of 

 the refractometer, the quarter-wave-length mica, and 

 Bertrand's plate ; attention may also be directed to the 

 paragraph on complex molecules (p. 22), and to the de- 

 monstration of the terq uaternary system (p. 55) ; he has, 

 moreover, grouped in a series of chapters, which con- 

 stitute a homogeneous and strikingly uniform treatise on 

 the subject, the elegant theories of Mallard upon twinning, 

 isomorphism, and polymorphism. The description of 

 species has been considerably increased, especially by the 

 extended account of the rock-forming minerals ; and the 

 characters in microscopic sections of the minerals which 

 are most important in lithology are illustrated by figures 

 selected from the best authorities. In his own words, the 

 author, taught by experience and knowing how necessary 

 it is that numbers should be verified, has revised all the 

 crystallographic data ; he has given for each species the 

 corresponding axial ratios after imposing upon himself 

 the task of verifying by trigonometrical calculation the 

 agreement of these ratios with the fundamental angles ; 

 and he has selected from the latest and best publications 

 the optical data, such as double refraction, dispersion, 

 principal indices of refraction, and the numbers which 

 indicate the positions of the optic axes and bisectrices. 



Finally the index has been subjected to careful revision, 

 and has been augmented by 200 names which represent 

 the progress of descriptive mineralogy during the last 

 six years. Since, moreover, the chapter on calculation 

 has been developed and contains all the formulee in 

 common use, the practical value of the book has been 

 largely increased, and it should satisfy every requirement 

 of the University student ; it will prove of special service 

 to geologists occupied with the study of rocks, the class 



of readers whom the author appears to have continually 

 had in his mind in the composition of a treatise in which 

 the geological bias is discernible both in the classification 

 adopted, and in the manner in which the description of 

 the rock-forming minerals has been developed. 



In a word, this work not only affords a good general 

 idea of all that constitutes modern mineralogy, but is also 

 a useful introduction to the study of lithology. 



We are convinced that the book, written with the 

 remarkable lucidity and elegance which characterize the 

 works of M. de Lapparent, is destined to occupy the 

 same position in the study of mineralogy which in 

 geology has been held by the same author's " Traitd de 

 Geologie." A. F. Renard. 



OUR BOOK SHELF. 



Key to Higher Algebra. By H. S. Hall, M.A., and S. R- 

 Knight, B.A. (London: Macmillan and Co., 1889.) 



This work forms a key to the higher algebra, and con- 

 tains solutions fully worked out of nearly all the examples. 

 More than one solution of a problem is given in some 

 cases, and throughout the book repeated feferences are 

 made to the text and illustrative examples of the algebra. 

 The volume will prove most useful to teachers, and we 

 strongly recommend it to students who are beginning the 

 study of algebra without the aid of a teacher, for, by first of 

 all trying to work out the exampl es without the key, they 

 may learn much by a careful and judicious use of the 

 solutions afterwards. 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents . Neither can he undertake 

 to return, or to correspond with the writers of rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications. ^ 



On the Use of the Word Antiparallel. 



So much of the " recent geometry of the triangle " is 

 connected with the properties of " antiparallels," that it is a 

 matter of some interest to geometers to ascertain when they 

 came to be recognized as worthy of a distinctive name, and when 

 the name now in use was first applied. The following extracts 

 afford two early instances, and seem to imply that the term " anti- 

 parallel " had, at the dates given, been some time in existence. 



On p. 220 of Mutton's Miscellanea Mathemadca (1775) 

 occurs the following lemma by the Rev. Mr. Wildbore : — 



" If two lines FB, EC be antiparallel, and through their 

 extremities two right lines be drawn meeting each other in A, 

 it will be as AB^ : AE^ - AB^ : : AB^ - AF- : FE^ - BC- " ; 



and the demonstration begins as follows : — 



" The <; at B being by the nature of antiparallel lines the 

 supplement of that at E, and F of C, a circle may, by Eucl. III. 

 22, be drawn through those four points." 



After the lemma occurs this " Scholium " : — 



"The reader may from hence correct an error in 'Clark's 

 Dictionary' under the word antiparallels, where it is said that 

 the sides AE, AC are cut reciprocally proportional by the 

 line FB ; that is, AF : FE : : BC : AB, which is evidently 

 wrong. " 



