156 



NATURE 



[December to, 1908 



SCHOOL ARITHMETICS. 

 (i) A School Arithmetic. With Answers. By H. S. 

 Hall and F. H. Stevens. Pp. xi!i+475 + xxxi.\. 

 (London : Macmillan and Co., Ltd., 1908.) Price 

 with answers, 45. 6d., without answers, 35. 6d. 



(2) A Modern Arithmetic, 7vith Graphic and Practical 

 Exercises. By H. Sydney Jones. Pp. xiv+598. 

 (London : Macmillan and Co., Ltd., 1908.) Price, 

 with or without answers, 4^. 6d. 



(3) Advanced Arithmetic and Elementary Algebra and 

 Mensuration. A Text-book for Secondary Schools 

 and Students preparing for Public Examinations. 

 By P. Goyen. Pp. xii-l-435. (London : Macmillan 

 and Co., Ltd., 1908.) Price 3:?. 6d. 



(4) Elementary Mensuration. By W. M. Baker and 

 A. A. Bourne. Pp. vi4-i44. (London: George 

 Bell and Sons, igo8.) Price is. 6d. 



(5) Practical Arithmetic and Mensuration. By Frank 

 Castle. Pp. viii-l-249. (London : Macmillan and 

 Co., Ltd., 1908.) Price 25. 



nPHE widespread attention that has been given 

 J- during the last decade to the study of elemen- 

 tary mathematics has had a most salutary effect on 

 the teaching of arithmetic, as is evidenced by the 

 improved text-books that are now available and illus- 

 trated by the five books under review. The claims 

 of science, the laboratory, and the workshop are 

 coming to be adequately recognised, and commercial 

 arithmetic is not allowed unduly to dominate the 

 course. Moreover, some amount of experimental and 

 quantitative work is done in connection with the sub- 

 ject, and associated more or less closely with decimal 

 measurements, mensuration, approximate methods of 

 computation, and perhaps with the use of tables of 

 logarithms and even of sines and cosines. Again, 

 algebraical notions and graphical processes are natur- 

 ally and inevitably much in evidence. Altogether the 

 treatment is on broader lines, the examples are drawn 

 from a wider region, and arc in much closer contact 

 with common every-day experiences. 



(i) The book by Messrs. Hall and Stevens fully 

 realises the high expectations with which it has been 

 awaited, and will immediately rank as one of the 

 best text-books on the subject. Every modern de- 

 velopment of value is embodied in its pages, and the 

 whole is arranged with the thoroughness and skill 

 which is always a feature of any work undertaken 

 by the experienced authors. The book is divided into 

 two parts, which may be obtained either separately 

 or together, and with or without answers. The first 

 part gives the fundamental principles and processes 

 with which every youth should become familiar, very 

 special attention being given to orderly arrangement 

 of work and the cultivation of habits of rapid and 

 accurate computation. The second part is somewhat 

 more technical, and allows opportunity for discrimina- 

 tion according to the class of pupil. Where all is so 

 good it is unnecessary to particularise. The explana- 

 tions and proofs are always sufficient, clear, and con- 

 cise; the well graduated examples are abundant, and 

 range over a wide field of interest; the production 

 of the book is a fine example of the printer's art; 

 and from every point of view this arithmetic is of 

 NO. 2041, VOL. 79] 



almost unrivalled excellence, and must soon be widely 

 used in our schools. 



(2) The title chosen by Mr. Jones for his book is 

 most appropriate, for as regards originality of treat- 

 ment and as leading the way in the reform this 

 arithmetic is second to none, while at the same time 

 the whole ground is covered in a thoroughly efficient 

 manner. The author exhibits a charming faculty for 

 selecting examples from new and unexplored sources, 

 thereby adding greatly to the interest and diversity 

 of the work, ^'ariety is otherwise obtained by ar- 

 ranging the sets of exercises respectively as oral, 

 mental, graphic, practical, general, revision exercises, 

 and typical examination papers. The graphical and 

 practical examples, comprising drawing, measuring, 

 weighing, &c., using simple apparatus, are especially 

 valuable, forming a systematic and most desirable 

 course in quantitative experimental work. The chapter 

 on logarithms includes the use of the slide-rule. The 

 chapters on mensuration, statistics and averages, 

 stocks, shares, and bills of exchange are particularlv 

 good. Teachers will find part i. of the book sufiicient 

 for the Oxford and Cambridge local and similar 

 examinations in arithmetic, and this, with part ii., 

 will meet all the requirements of otlier examinations 

 such as those of the Army and the Civil Service. The 

 general get-up of the book is most attractive. 

 Teachers and students alike will welcome this notable 

 arithmetic, and it should be extensively adopted. 



(3) The author of this work is an inspector of 

 schools in New Zealand, and its appearance is an 

 indication that our colonies are in touch with modern 

 developments in the teaching of elementary mathe- 

 matics. The book proceeds on lines very similar to 

 those just noticed ; algebraical symbols are in con- 

 tinuous use from the start ; the algebra extends to 

 quadratic equations and the progressions, and the 

 mensuration is carried as far as problems on the 

 simpler geometrical solids. The subject is well pre- 

 sented and is quite up to date, and the student is pro- 

 vided with a large number of good and varied 

 examples. 



(4) The major portion of this book, including a 

 chapter on contracted arithmetic, deals with the pro- 

 perties, construction, and mensuration of plane 

 figures, with an application to surveying. The 

 later chapters relate to the simple geometrical 

 solids and the annulus. Proofs of the for- 

 mulae are given, though those for the surface and 

 volume of an annulus are not altogether convincing. 

 The general treatment is very elementary and simple ; 

 it does not include any mention of the prismoidal 

 formulae. Many sets of examples and revision papers 

 are provided, the answers being collected at the end 

 of the volume. 



(5) The " Practical .Arithmetic " by Mr. Castle is 

 primarily intended for students of technical classes 

 and evening schools, where, in making actual 

 measurements in the laboratory, the pupil sees the 

 necessity for and becomes acquainted with the 

 more important arithmetical processes, including 

 approximations and contracted methods. Thus 

 theoretical study is subordinated to practical work, 

 and the knowledge of principles is acquired largely 



