76 



NA TURE 



\May 24, 1888 



too, is to be congratulated on its good fortune in having 

 as an occupant of the Chemical Chair in its University, 

 one who has shown himself so successful in attaining 

 practical, while not losing sight of the scientific, results 

 of his researches. 



OUR BOOK SHELF. 



Elementary Chemistry. By William S. Furneaux, 

 F.R.G.S., Science Demonstrator, London School 

 Board. (London: Longmans, Green, and Co., 1888.) 



The main object of this little work is to assist young 

 students intending to sit for the chemistry examination of 

 the Science and Art Department in the new alternative 

 elementary stage. It appears to be, in fact, an illustrated 

 expansion of the detailed syllabus published by the 

 Department in their Directory. 



The want of such a work has possibly been felt by 

 many teachers of this "alternative'' or "natural" 

 chemistry, which appears to be rapidly becoming more and 

 more popular with young beginners. There is something 

 truly fascinating in learning these mysteries of common 

 things, and, what is still more important, the knowledge 

 gained has its practical applications in every-day life. 

 In order to afford teachers some idea of the methods 

 recommended of performing the class experiments them- 

 selves, the Department have caused to be placed in the 

 western galleries of the South Kensington Museum a 

 complete set of apparatus, as simple and inexpensive as 

 is compatible with the object in view, arranged under the 

 personal direction of the examiners, to illustrate the 

 method of performing each of the experiments indicated 

 in the syllabus. It is to be hoped, therefore, that all who 

 are interested in the teaching of the alternative elementary 

 stage of chemistry, an1 who can conveniently do so, will 

 avail themselves of this opportunity of comparing the 

 experimental methods there recommended with those 

 which they themselves have previously adopted. One 

 cannot help thinking that many of the methods illustrated 

 by Mr. Furneaux are much too complicated, and it is to 

 be regretted that his book was in the press before the 

 completion of the collection in the western galleries, 

 which was accomplished about two months ago. 



The majority of the theoretical explanations leave little 

 to be desired. The ideas of the author, however, as to 

 the nature of the Bunsen flame appear scarcely to accord 

 with more recent investigations, the effect of mixture with 

 an inert gas being entirely overlooked. A. E. T. 



Companion to the Weekly Problem Papers. By the Rev. 

 John Milne, M.A. (London : Macmillan and Co 

 1888.) 



The title of this work gives no adequate idea of its 

 contents. It consists of some 340 pages, which, if about 

 60 pages be excepted, are devoted entirely to geometry. 

 Besides the author, several other mathematicians are 

 contributors, viz. Mr. R. F. Davis, Prof. Genese, Rev. T. 

 C. Simmons, and Mr. E. M. Langley. 



The object of the book seems to be to give prominence 

 to what is here designated " The Modern Geometry of 

 the Triangle." This is seen to consist of a group of 

 pretty theorems which arise from a consideration of the 

 " Brocard points " and the " Lemoine point " of a triangle. 

 The successive chapters bear the titles, " Antiparallels, 

 lsogonals, and Inverse Points," " The Brocard Points and 

 Brocard Ellipse," " The Lemoine Point and Triplicate 

 Ratio Circle," " The Brocard Circle and First Brocard 

 Triangle," "The Tucker Circles," "The Cosine and 

 Taylor Circles," " The Co-Symmedian and Co-Brocardal 

 Triangles," and " Miscellaneous Theorems and Construc- 

 tions." They comprise a good and almost complete 

 account of the present knowledge of these subjects. 



On p. 180 there is a re'sumJ of the bibliography, 

 which has evidently been carefully compiled by the knot 

 of enthusiasts in this country who have followed in the 

 footsteps of M. Le noine M. Brocard, M. Vigarie', Prof 

 Neuberg, M. Catalan, and others. To these investigators 

 on the Continent most of the results here given were 

 known prior to 1881 ; they were subsequently arrived at 

 independently by mathematicians in England who were 

 unacquainted with the work already accomplished, in the 

 same field of research, abroad. In fact, in the resume', 

 discoveries, and rediscoveries, and rediscoveries of re- 

 discoveries succeed one another in bewildering fashion. 

 The reasons which have led to the nomenclature in 

 certain cases are difficult to fathom. We find, for 

 instance, a circle associated with the name of one mathe- 

 matician, when, admittedly, the same circle had been 

 examined by a Continental investigator some years 

 previously, whose name, if name be necessary, it ought 

 to bear. 



The algebraic portions comprehend sections on 

 "Theory of Maximum and Minimum," "Theory of 

 Elimination," " Summation of Series," " Binomial Series," 

 and "Algebraical and Trigonometrical Identities." 



The book will be chiefly useful to those who take an 

 interest in recent triangular geometry ; it will enable them 

 to refer to original sources in Continental mathematical 

 publications, and to follow further developments in English 

 magazines. They will also find collected here most of 

 the leading propositions given in a form which is without 

 doubt both judicious and attractive. 



Elementary Hydrostatics, with Numerous Examples 

 and University Papers. By S. B. Mukerjee, M.A. 

 (Calcutta: Thacker, Spink, and Co., 1888.) 

 THE compiler of this handy little work is Assistant Pro- 

 fessor of Mathematics in the Lahore College, who, having 

 been, as is the wont of his order, unable to select from 

 the nu nerous text-books in existence one which seemed 

 fully to meet the wants of his classes, has culled his ele- 

 gant extracts from them, and so got what he wanted. 

 This proceeding is a good one for his pupils, and saves 

 them the trouble and expense of purchasing and reading 

 many text-books. The selection is well made, and the 

 compiler suitably acknowledges his indebtedness to the 

 English writers (especially to Dr. Besant's classical work). 

 The subjects handled are definitions and first principles, 

 density and specific gravity, equilibrium of fluids, total 

 pressures and resultant pressures on immersed surfaces, 

 floating bodies, on air and gases, determination of 

 specific gravities, and the application of hydrostatical 

 principles in the construction of instruments and ma- 

 chines. Then follow several papers of problems set in the 

 Calcutta University Examinations from i860 to 1884; and 

 the book closes with an appendix of formulae to be re- 

 membered, and another appendix which gives a short 

 history of the growth of the principles of hydrostatics, 

 taken for the most part from Whewell's " History of the 

 Inductive Sciences." In the body of the work are given 

 numerous illustrative examples, many of which have been 

 carefully worked out. Putting on one side the manufac- 

 ture of the book — and herein, perhaps, Mr. Mukerjee is 

 only more honest in making known his indebtedness than 

 many are in the writing of tect-books— we can congratu- 

 late the students on having such a good work in their 

 hands, and can indorse the favourable opinion expressed 

 upon it by Prof. T. C Lewis, Principal of the College. 



Arithmetic for Beginners: a School Class-book of 

 Commercial Arithmetic. By the Rev. J. B. Lock, M.A. 

 (London : Macmillan and Co., 1888.) 

 It is not necessary to report upon this little book at any 

 length. It is founded upon the author's larger work, but 

 modifications as to arrangement and treatment of some 

 of the subjects and as to the examples have been intro- 

 duced. Then, with an eye to the requirements of the 



