VIU 



Supplement to ''Nature," May 3, 1906 



the " youthful " characteristics of the Burmese. 

 While the former " adapt " Occidental civilisation, 

 however, the Burmese can only " adopt " it, with the 

 result that it seems to denationalise them. 



The interesting chapter on women, who play so 

 large a part in Burma, being the equals of men 

 legally and socially, suggests another interesting 

 comparison (which Mr. Hall seems to miss) with the 

 French nation. The Burmese law of inheritance (that 

 is the Buddhist law that a man may make no dis- 

 posal of his goods after death) resembles the French 

 system of dividing the property between the children. 

 The result in both countries is to limit individual 

 ambitions and to raise the legal status of women, 

 who become co-partners with their husbands in all 

 business affairs and are often much the better horse. 



That this book is rather suggestive than con- 

 clusive is one of its charms, and no one who cares 

 for the mysterious and vanishing East should fail to 

 read this study of a people at school. 



Archibald R. Coloi'houn. 



ELEMENTARY MATHEMATICS. 

 (i) Easy Mathematics of All Kinds. Vol. i. Chiefly 

 Arithmetic. By Sir Oliver Lodge, F.R.S. Pp. xv + 

 436. (London: Macmillan and Co., Ltd., 1905.) 

 Price 45. 6d. 



(2) Arithmetic for Schools and Colleges. By John 

 .Alison and John B. Clark. Pp. viii + 471 +xlvii. 

 (Edinburgh and London : Oliver and Boyd, 1905.) 

 Price 45. 



(3) Elementary Trigonometry. By H. S. Hall and 

 S. R. Knight. Fourth edition, revised and enlarged. 

 Pp. xv + 415. (London: Macmillan and Co., Ltd., 

 1905.) Price 4i. 6d. 



(4) Engineering Mathematics, Simply Explained. By 

 H. H. Harrison. Pp. 165. (London : Percival 

 Marshall and Co.) Price 15. 6d. net. 



(i) /^NE of the reasons which induced a busy 

 ^-^ scientific man like Sir Oliver Lodge to write 

 a book on easy mathematics is thus given by the 

 author in the preface : — 



" The mathematical ignorance of the average edu- 

 cated person has always been complete and shameless, 

 and recently I have become so impressed with the 

 unedifying character of much of the arithmetical 

 teaching to which ordinary children are liable to be 

 exposed that I have ceased to wonder at the wide- 

 spread ignorance, and have felt compelled to try and 

 take some step towards supplying a remedy." 



No teacher of arithmetic or elementary mathematics 

 can afford to be without this most suggestive book, 

 in which the results of much thought and a wide 

 experience are presented in a deeply fascinating style, 

 and untrammelled by conventional or artificial restric- 

 tions. The first four chapters give suggestions for 

 teaching very young children the operations of 

 counting and the simple rules of arithmetic. The 

 appeal is made through their games and any concrete 

 things in which they are likely to have an interest, 

 and vulgar and decimal fractions and negative quan- 

 tities seem to present no difiiculties. The writer is 

 emphatic in his declaration that the whole subject of 

 NO- 1905. \OL. 74] 



mathematics is essentially experimental and should 

 be developed on an e.xperimental basis. Concrete 

 quantities are quite early dealt with like abstract 

 numbers, and multiplied and divided freely, e.g. 

 60 miles/ 1 hour is the speed of an express train. 

 The author advises that units should, where suit- 

 able, be inserted in the numerator and denominator 

 of a fraction, and cancelled like ordinary numbers, m 

 order to emphasise the dimensions of the quantities 

 under consideration. 



But it is impossible in a short article to give any 

 adequate account of the book, treating as it does, to 

 mention only a few things, of the decimalisation of 

 money, indices, logarithms, incommensurables and 

 discontinuity, approximations, progressions, means 

 and averages, differentiation, &c., with interesting 

 historical references and digressions, the whole being 

 continuously illustrated and illuminated by applica- 

 tions drawn from the wide domain of natural science, 

 of which the author has so extensive a knowledge. 



(2) The arithmetic bv Messrs. Alison and Clark is 

 a very complete treatise, written mainly on conven- 

 tional lines, and devoting a large portion of its space 

 to commercial aspects of the subject. But the authors 

 do not forget that the physical laboratory has also 

 claims on their attention, and they give many good 

 exercises in physics and mechanics, using four-figure 

 tables of logarithms, and approximate methods of 

 computation in appropriate cases. The authors arc 

 very partial to abstract reasoning, and general pro- 

 positions seem to us to be introduced and deductions 

 established somewhat prematurely, before the boy 

 can have the concrete and experimental knowledge 

 requisite to understand the matter. Thus in chapter 

 vi., immediately after the completion of the four 

 simple rules, the laws of the operations for the symbols 

 are fully discussed ; but it is wisely hinted that this 

 chapter may be skipped on a first reading. 



The text-book is intended for use in both schools 

 and colleges. It is profusely supplied with examples 

 of varying grades of difficulty. The answers collected 

 at the end of the volume themselves occupy forty- 

 seven pages of closely printed matter. The book is 

 very suitable for advanced pupils and for prospective 

 teachers, but beginners would require guidance as lo 

 what parts to omit. 



(3) The new edition of Messrs. Hall and Knight's 

 " Elementary Trigonometry " has been revised and 

 enlarged by the introduction and use of four-figure 

 tables of logarithms and antilogarithms of numbers, 

 and of natural and logarithmic functions of angles, 

 also by examples of the graphing of trigonometrical 

 functions, and the insertion of additional examples 

 of a practical nature. A first course is specially out- 

 lined which, by omitting some of the more advanced 

 formulae, allows numerical computations by four-figure 

 tables to be reached at a comparatively early stage, 

 and most teachers will no doubt follow this plan. 



The revision has brought the fourth edition up to 

 modern requirements, and little more need be said 

 about a book the great merits of which are so gener- 

 ally recognised. In defining the ratios and establishing 

 the fundamental formula for angles of any magni- 



