5o6 



NATURE 



[January 6, 191 6 



between the works and the research laboratories 

 of the universities. He also deals with the 

 prospects of the new dye company, and suggests 

 certain lines along which this enterprise might 

 develop to the best advantage. G. T. M. 



SCHOOL MATHEMATICS. 

 (i) A First Book of Arithmetic. By S. Lister. 

 Pp. vii + 258. (London: Macmillan and Co., 

 Ltd., 1915.) Price i5. 6d. 



(2) Elementary Algebra: First Year Course. By 

 F. Cajori and L. R. Odell. Pp. vii + 206. 

 (New York : The Macmillan Co. ; London : 

 Macmillan and Co., Ltd., 1915.) Price 35. net. 



(3) Revision Papers in Algebra. By W. G. 

 Borchardt. Pp. vi + 152 + Answers. (London: 

 Messrs. Rivingtons, 1915.) Price 2s. 



(4) Tables for Converting Shillings, Pence, and 

 Farthings into Seven Places of Decimals of a 

 Pound; and for the Reconversion of Decimals. 

 Pp. 6. (London: C. and E. Layton, n.d.) 

 Price 15. net. 



(5) The Rapid Reckoning Chart. By Dr. E. E. 

 Fournier d'Albe. (London : Educational 

 Supply Association, Ltd.) Price 3d. net. 



(i) 'TPHE decimal fraction is the central point 

 X of modern arithmetic. This is realised 

 by Mr. Lister, who begins his book with the 

 graphical abacus. The explanation of its use for 

 integers leads up very simply to its use for decimal 

 fractions. All other aids are also pressed into the 

 service, such as the use of metric measurements, 

 expression of a decimal in words as so many 

 tenths and hundredths, and the actual measure- 

 ment of lengths by a suitably divided ruler. It 

 is, in fact, difficult to see how the dullest boy 

 can fail to grasp the idea as presented by Mr. 

 Lister. 



We are pleased to see a book on arithmetic 

 compressed within little more than 200 pages, but 

 rather regret the suggestion contained in the title 

 "A First Book of Arithmetic" that further books 

 on the subject must be used. The title may, 

 however, be nothing more than a concession to' 

 custom. Similar concessions are seen in the very 

 elaborate tables of money and measures and in 

 the conversion between different systems of 

 measures. Such concessions are not ■ only par- 

 donable ; they are necessary if -a book is to suc- 

 ceed. We wish the book all success; it is the 

 best we have seen for a long time. 



(2) This book on elementary algebra is pleasing 

 in several ways. It contains historical notes on 

 the development of algebraic notation, including 

 the remarkably clever notation in use among the 

 Egyptians nearly four thousand years ago. There 

 NO. 2410, VOL. 96] 



are also portraits of famous mathematicians, with 

 historical notes. The type is pleasant to the eye 

 and eminently legible, and the general get up of 

 the book attains the usual high American 

 standard. Graphs are suitably introduced by a 

 temperature curve and a graph of the price of 

 coal ; and the treatment of the multiplication of 

 negative quantities is the best we have seen. 

 Yet, when we come to the essence of an 

 algebra, the problem, we find all the old unnatural 

 riddles and never a hint of a problem that is real 

 or connected with daily life ; and this in a book 

 to which a famous American professor lends his 

 name. When we consider the advance that has 

 been made in England we are tempted to thank 

 God that we are not as other nations are, and to 

 derive more pleasure in this way than from all 

 the merits of the book. 



(3) With the ink upon our pen still wet from 

 our Pharisaical boast, we turn to the "Revision 

 Papers in Algebra " and find ourselves liable to 

 the question, "Wherein is this book better than 

 the other? " It is true that this book also con- 

 tains no natural problems. The natural problem 

 belongs chiefly to the beginnings of the subject, 

 and the student who carries his studies on to 

 indices, surds, binomial theorems, and manipula- 

 tion must not expect them. The questions before 

 us are fully as good as he has any right to expect. 

 His proper course is to study the calculus instead, 

 or, if he is too weak a mathematician for that, 

 to drop the subject of mathematics. Meantime 

 examiners require this stuff, schools teach it, the 

 pupil must know it, and Mr. Borchardt meets 

 their needs admirably. 



(4) The calculating machine arrived some time 

 ago, and some of the results of its arrival begin 

 to emerge. The imperial system of weights and 

 measures does not fit the calculating machine. 

 The machine will not (without assistance) tell you 

 the price of 3 tons 7 cwt. 30 lb. of copper at 

 60Z. 175. 4d. a ton. So far as pure money calcula- 

 tions are concerned, the necessary assistance is 

 provided by the tables we have before us for ex- 

 pressing any sum of money as the decimal of a 

 pound sterling and vice versa, an excellent and 

 well-printed table of four pages. The sum of 

 money prepared by this table is put into the 

 machine, and the result provided by the machine 

 is restored by the table to its usual form. In some 

 happy future we shall decimalise our money once 

 for all by Act of Parliament. Until then these 

 tables by Messrs. Layton have great value as a 

 labour-saving device. 



(5) Dr. Fournier d'Albe's ingenious chart is a 

 graphical computer which will perform various 

 operations up to the extraction of the cube root. 



