January 23, 1896] 



NA TURE 



267 



The necessities of these different classes of students 

 had carefully to be borne in mind in writing the book, 

 and consequently a work of somewhat peculiar character 

 has been compiled. We think it undesirable that the 

 aim of an author should be quite so far-reaching. The 

 extensiveness is bound to detract from the value of the 

 work for any particular class. As regards the matter 

 actually in the volume, it is more elementary in character 

 than that of Prof. Macalister's little book, though occupy- 

 ing about double the space. A redeeming feature of the 

 work is the illustrations, which are judiciously chosen 

 and very well executed. J. S. Edkins. 



OUR BOOK SHELF. 

 Practical Plane and Solid Geotnetry. By Joseph 



Harrison, M.I.M.E., A.M.I.C.E., and G. A. Baxandall. 



Pp. vi 4- 183. (London : Macmillan and Co., 1895.) 

 Practical geometry is taught primarily as an aid to 

 systematic, accurate and rapid delineation of concrete 

 objects, and, in most cases, it forms part of the student's 

 work very early in his scientific or technical training. 



In the organised science school the subject is taken 

 contemporaneously with the first or first two books of 

 Euclid ; while the student in a technical school almost 

 invariably goes through his elementary course of practical 

 geometry before he arrives on the other side of the pons 

 asinorum. This seems to be hardly logical, for the 

 more important problems in practical plane geometry to 

 be found in elementary text-books depend on proposi- 

 tions in Euclid's third and sixth books ; and the early 

 problems in solid geometry are based on theorems in 

 the eleventh book ; but in the majority of technical 

 classes it is in the nature of things that practical 

 geometry must be taught where Euclid's sixth and 

 eleventh books are practically sealed. It is imperative 

 that every student should be satisfied with the foundation 

 upon which his future work is to be built ; and the truth 

 of theorems, which have such general application as that 

 of similar triangles, must be made apparent at the outset ; 

 and with beginners, this can best be done experimentally. 

 It is rarely that the author of a text-book is bold enough 

 to advocate the experimental demonstration of the truth 

 of a law in geometry, though that is almost the only 

 method in many other branches of science. 



In the little work before us, Messrs. Harrison and 

 !5axandall have so far deviated from the beaten track 

 lis to get through a good deal of their work without 

 some of the usual cumbrous and, to beginners, un- 

 intelligible definitions ; and have added, in the form of 

 an appendix, some theorems and definitions that may be 

 found useful in a second reading. Some new problems 

 have been introduced in the first and second chapters, 

 which are devoted to plane geometry and graphic 

 arithmetic respectively. The authors have wisely con- 

 densed the whole of the former into one chap'ter ; and 

 though one may be considered pedantic for saying so, 

 there are still left in some problems that can hardly be 

 called by the first word of the title-page. It is with 

 great satisfaction that we notice the absence of any 

 attempt to introduce statics with the graphic arithmetic. 

 Too much can hardly be said in favour of graphic statics 

 in its proper place ; but when taught without any 

 reference to the laws of equilibrium, it is not only 

 useless but harmful. , 



The student is gradually led on to the study of solid 

 geometry by a series of well-chosen diagrams and 

 figures, and becomes well-grounded in the orthogonal 

 projection of solids before he approaches the usual 

 oblique line and plane problems. The figures in the 

 text are bold, clear, plentiful and well-lettered ; and this 



NO. 1369. VOL. 53] 



is a feature which, if lost sight of, causes much incon- 

 venience and annoyance. 



Altogether this is a work which is very carefully com- 

 piled, and from which a student can extract for himself 

 a great deal of information without outside assistance. 

 A Treatise on Hydraulics. By Prof. Henry T. Bovey. 



Pp. viii 4- 336. (New York : John Wiley and Sons. 



London : Chapman and Hall, 1895.) 

 The contents of this book formed the subject-matter of 

 a series of lectures on hydraulics, delivered by the author 

 at McGill University, Montreal ; and though chiefly in- 

 tended for students, it will doubtless prove valuable for 

 reference to hydraulic engineers. The book deals with 

 the experimental theory of the motion of water, its flow 

 in pipes and open channels, and its practical application 

 to hydraulic motors. The subject is divided into seven 

 chapters, treating successively of flow through orifices 

 and over weirs, fluid friction, flow in pipes, flow of water 

 in open channels, methods of gauging, impact, and 

 hydraulic motors and centrifugal pumps. The matter is, 

 for the most part, treated mathematically ; and the book 

 will be mainly useful to persons who have studied mathe- 

 matics ; whilst numerous examples are appended at the 

 end of most of the chapters, together with their answers, 

 which will give students facility in working out hydraulic 

 problems, and enable them to acquire a more thorough 

 grasp of the principles enunciated. One hundred and 

 ninety-six simple diagrams and drawings serve to illus- 

 trate and elucidate the text ; and the book, being clearly 

 and concisely written, will enable the intelligent reader, 

 with some knowledge of mathematics, to obtain a deeper 

 insight into the theory of hydraulics, and the principles of 

 its application to practical purposes. The short chapter 

 on gauging the velocity of flow in open channels, de- 

 scribes briefly and practically the different instruments 

 used for the purpose ; whilst the long final chapter, on 

 hydraulic motors, explains, with the aid of formulas, the 

 principles involved in the hydraulic ram, pressure- 

 engines, the accumulator, hydraulic brakes, the various 

 forms of water-wheels and turbines, and centrifugal 

 pumps. 

 The Scientific Foundations of Analytical Chemistry. By 



Wilhelm Ostwald, Ph.D. Translated by George 



McGowan, Ph.D. (London: Macmillan, 1895.) 

 The peculiarly interesting character of this book has 

 already been pointed out in the review of the German 

 edition (see NATURE, vol. li. p. 482), and Dr. McGowan's 

 translation now places its doctrines within the reach of 

 English readers. 



The only alteration made by the author upon the 

 original edition, is the introduction of a portion of a 

 chapter on the theory of electrolytic methods of analysis. 

 This includes an account of the mode in which the 

 processes of oxidation and reduction occurring in voltaic 

 cells, and the order in which metals separate from a 

 mixture of electrolytes under the influence of a definite 

 external electromotive force, can be correlated with the 

 potential differences given by the metals and the electro- 

 lytes used. J. W. R. 

 Elementary Algebra. By J. W. Welsford, M.A., and 



C. H. P. Mayo, M.A. Pp. xiii + 407. (London : 



Longmans, Green, and Co., 1895.) 

 Since, in its early stages, algebra is a generalisation of 

 arithmetic, the authors give a short account of some of 

 the processes of arithmetic, as an introduction to their 

 subject. The book differs in character and arrangement 

 from most text-books on algebra : for instance, the 

 radical sign is explained at the same time as the positive 

 integral index ; factors are freely used ; a table of 

 logarithms is introduced ; and oral exercises are given. 

 There are about four thousand examples to test the 

 student's knowledge, and impress the book-work upon 

 his memory. 



