NA rURE 



593 



THURSDAY, AUGUST 24, 1905. 



SCHOOL MA r HEMATICS. 

 Easy Craphs. By H. S. Hall, M.A. Pp. vii + 64. 

 (London: .M.'u-niillan and ("o., Ltd., 1905.) Price 



IS. 



The RiuUnu-iits oj Pnuticil .\rathcniatics. By A. 



Con-terdinc, M..\., ,ind .\. Barnes, M.A. Pp. 



xv+i^j. (Londoti : |ohn NFurrav, 11)05.) Price 



2S. 6ii. 

 Elementary Praciica! Matlicmalics. By H. A. .Stern, 



NL.\., and W. H. Tophani. Pp. viii + 1 10 + viii. 



(London: George Bell and Sons.) 

 1 Fir.':t .ilgcbra. By \V. M. Baker, M..\., and A. A. 



Bourne, M.A. Pp. x+176 + xxxv. (London: George 



Bell and .Sons, 1905.) Price 2.?. 

 .Mgebraical Grounding. By D. E. Shorlo, M..\. 



Pp. 46. (London : Rivington, 1905.) Price is. net. 

 Exiunptcs in Algebra. By Charles M. Clay. Pp. 



\ii+^72. (New York: The Macniillan Co.; Lon- 

 don: Macniill.an and Co.. Ltd., U)o5.) Price .\s. 



net. 

 Gennielrieal Conies. By G. W". Caunl, M..\., and 



C. M. Jessop, M..\. Pp. vi + So. (London; Edward 



.\rnold.) Price is. 6rf. 



THE. lillle book on " Easy flraphs," by Mr. 

 H. S. H.all, is the result of ripe experi- 

 ence, and is intended to lead the beginner by 

 very easy stages and show liim all the points that 

 require special attention in squared paper work and 

 the lessons to be learnt therefrom. Great attention 

 is paid to the suitable choice of scales and the proper 

 figuring of the diagrams. Linear graphs with in- 

 ferences and applications occupy fully half the book, 

 the latter half relating to algebraical equations and 

 graphs of the second degree with one or two cubics. 

 The numerous examples are Interesting and sugges- 

 tive, and all the answers are given at the end. We 

 agree with the author in deprecating the undue em- 

 ployment of graphs, especially as the field in which 

 they may be legitimately used is sufficiently extensive. 

 The book will be deservedly popular. 



The "Rudiments of Practical Mathematics," by 

 Messrs. Consterdine and Barnes, is a very excellent 

 treatise, intended more particularly for students above 

 twelve years of age who are preparing for industrial 

 pursuits. The heuristic method is in the main fol- 

 lowed, and the material for exercises is largely drawn 

 from the students' own measurements, suitable ob- 

 jects of a simple kind being provided for this purpose, 

 with appliances for measuring lengths, areas, 

 volumes, weights, and times. Thus every rule and 

 process is definitely associated with some direct quan- 

 titative application, and the subject assumes a real 

 and living interest and cannot fail to be assimilated. 

 The subject-matter is purposely confined to that which 

 is in daily use in industrial occupations, so that there 

 is time for this to be dealt with in a very thorough 

 manner. In this volume arithmetic, algebra, and 

 geometry are so interwoven that any attempt at 

 separation would appear quite unnatural. Thus when 

 ;ui important principle, say that of proportion, is 

 NO. 1869, VOL 72] 



under review it can be studied and developed with 

 the completeness which its importance demands, 

 arithmetically, algebraically, and geometrically. 

 Students are taught the use of logarithms, and also 

 sufficient trigonometry to enable them to solve right- 

 angled triangles; they use compasses and setsquares, 

 draw simple plans and elevations, and make dimen- 

 sioned free-hand sketches in pictorial or other pro- 

 jection, and they are introduced to the notion of a 

 vector bv means of displacement and velocity dia- 

 gr.ims. In some places there may be an insufficient 

 number of examples for the purposes of drill, but 

 .iltogether the subject is admirably developed and pre- 

 sented; the book is well adapted to its purpose, and 

 its wide adoption would have a very beneficial effect. 



The " Elementary Practical Mathematics," by 

 Messrs. Stern and Topham, is a preliminary volume 

 comprising the first nine chapters of a more complete 

 text-book on which the authors are engaged. It re- 

 lates to physical measurement with exercises based 

 thereon, including the measurements of length, 

 angles, mass, area, volume, specific gravity, with the 

 practical calibration of certain glass vessels. The 

 two first chapters deal with contracted arithmetical 

 processes and squared paper work, but otherwise a 

 knowledge of " theoretical " mathematics is assumed. 

 The work is intended as a first course for the junior 

 forms of schools, and especially for boys preparing 

 for army examinations. The apparatus is fairly com- 

 prehensive, and the experiments are well described. 

 The book will be very useful to those arranging a 

 course in an important branch of practical mathe- 

 matics. 



The "First Algebra," by Messrs. Baker and 

 Bourne, is adapted from the first part of the authors' 

 larger work, and, proceeding in the customary order, 

 carries the subject up to quadratic equations and 

 fractional and negative indices. Arithmetical and 

 graphical illustrations are freely introduced, and a 

 special feature of the work is its very easv gradua- 

 tion and the large number of examples, some oral, 

 provided at every stage, so that students using the 

 book properly cannot fail to obtain a full knowledge 

 of the subject. The answers are completely given, and 

 themselves extend to thirty-five pages. The book 

 gives an admirable first course in algebra. 



Mr. Shorto's " Algebraical Grounding " is a col- 

 lection of the definitions, axioms, law-s, rules, and 

 proofs belonging to the subject, without examples, 

 and arranged in logical sequence. It is intended 

 as a summary of the oral teaching usually imparted, 

 and could well be used in conjunction with a collec- 

 tion of examples. It includes logarithms, the pro- 

 gressions, and the binomial theorem. 



The collection of eight thousand " Examples in 

 Algebra," by Mr. Clay, has been accumulating for 

 the last twenty vears, during which time the author 

 has been engag'ed in teaching the subject in America, 

 and has found that the examples provided in the 

 ordinary text-books are deficient in both quantity and 

 variety, and not regularly graded. The teacher will 

 here find examples in superabundance, increasing in 

 difficultv by almost insensible steps from the simpler 



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