42 



NATURE 



[September 20, 1917 



schools and colleges before entering upon a busi- 

 ness career." 



Such is the claim put forward by Messrs. Palmer 

 and Stephenson in their preface. But there is a 

 very large other class of pupil for whom it is 

 growing daily more and more necessary to study 

 books of this kind. We refer to the great army 

 of students who do not receive a thorough com- 

 mercial training in our modern schools and who 

 do not contemplate entering upon a business 

 career. 



The game of keeping boys and girls shut up 

 in stuffy rooms memorising things that will be of 

 no use whatever to them in actual life, simply 

 in order that they may score marks by copying 

 them out in an examination-room, has been car- 

 ried too far in the past, and we hope that one 

 effect of the war will be to consign to the rubbish 

 heap a large proportion of the waste luxuries of 

 our present academic educational systems, and to 

 replace them by subjects better calculated to de- 

 velop national efficiency. A sound and thorough 

 training in the principles of business and finance 

 should not be the monopoly of a privileged class 

 of pupils who enter special courses, but should 

 be made available, and indeed compulsory, for 

 every boy and girl who attends a secondary 

 school, and may then go on to the university. 



The present book contains exactly the kind of 

 arithmetic which is required by everyone who 

 hopes to earn money or to invest it and receive 

 the interest, and who is compelled to pay rates 

 and taxes. Everything is of the most practical 

 nature possible. There are, in the two parts, six- 

 teen facsimile illustrations of such things as 

 cheques, stock and share certificates, poor-rate 

 demands, receipts and the like, and the only thing 

 wanted to make the collection complete is an 

 income-tax form, which is what probably gives 

 the average citizen more trouble than all the rest 

 put together. But the subject-matter is by no 

 means limited to questions of finance. Element- 

 ary mensuration is treated in great detail and 

 applied to doors and windows, dust-bins, flower 

 borders, bookcases, radiators, and other articles. 

 Contracted multiplication and division are well 

 done, although we regret that the authors do not 

 explain how far the processes may be carried with 

 approximate data. The authors also make every 

 effort to introduce into the examples statistics 

 relating to the trade and commerce of the British 

 Empire. Moreover, the book is written in an 

 interesting and stimulating style. Even at the 

 very beginning we have a brief account of the 

 methods of counting and numeration of early his- 

 tory and of savage tribes. It almost makes one 

 wishone were a modern- child, so that one could 

 be educated on such a book instead of on the old 

 useless drudgery of algebra and Latin and Greek 

 genders. 



When the book goes into a new edition we 

 should ask the authors carefully to consider 

 whether it would not be useful to introduce sec- 

 tions dealing with logarithms and the slide rules. 

 There is unfortunately a widespread superstition 

 among mathematical ignoramuses that it is neces- 

 NO. 2499, VOL. 100] 



sary to repeat some nonsense about indices to 

 every pupil before teaching him the simple rule 

 that to multiply two numbers together you simply 

 have to add their logarithms, but, judging from 

 the present book, Messrs. Palmer and Stephenson 

 appear quite capable of making the subject in- 

 dependent of this silly prejudice. 



The insistence on rough checks in arithmetical 

 work is very important, especially in view of the 

 tendency among examination candidates to throw 

 away 100 marks which they might have saved by 

 checking one question in order to scrimmage five 

 marks by starting another. The task of gather- 

 ing together such enlightening collections of ex- 

 amples as are here found must have been very 

 laborious, and we are surprised not to find Govern- 

 ment examinations enumerated among the sources 

 from which they are drawn. 



(2) All science students, and, indeed, most other 

 people, require some kind of training in the 

 meaning, use, formulation, evaluation, and inter- 

 pretation of algebraic formulae, and their inverse 

 uses involving the solution of equations. This is 

 not the same thing as the addition, subtraction, 

 multiplication, and division of the collections of 

 dry bones hitherto described as "algebra," for 

 the victims of that kind of drudgery often say 

 they never knew these things had any use or 

 meaning. A very fair introduction to what is re- 

 quired may be obtained by taking Mr. Clapham's 

 "Arithmetic for Engineers " and turning to chaps, 

 iii., iv. , and v., which deal respectively with 

 "Symbols and their Uses," "Simple Equations," 

 and "Transposition of Formulae." Here, then, is 

 another instance in which class-distinctions require 

 to be broken down, and the mathematical instruc- 

 tion drawn up for engineering students thrown 

 open to the rank and file of the pupils of our 

 schools and colleges. For nearly twenty years the 

 writer of this review has persistently advocated 

 that algebra should be taught through the use of 

 formulae, such as area = length x breadth, the con- 

 verse use or inversion of the formula leading to 

 the problem of solution of equations, as when the 

 area and breadth are given and the length is the 

 unknown quantity. Although such a method is 

 contemplated in a recent syllabus issued by the 

 Civil Service Commission, Mr. Clapham is the 

 first, or nearly the first, writer to develop this 

 very simple and obvious method consistently. His 

 method of treatment should even suffice to dispel 

 the doubts which a beginner might experience as to 

 the sanity of the mathematicians who use ah to 

 denote the result of multiplying, instead of adding, 

 a and h. Not only is the notation carefully ex- 

 plained, but multiplication and . division formulae 

 take precedence, both in the text and examples, 

 over those involving addition and subtraction, and 

 the practical illustrations show that in dealing 

 with concrete quantities brevity is often of more 

 use in writing products than sums. 



The two previous chapters deal with "Vulgar 

 Fractions " and " Decimal Fractions " respec- 

 tively. Here, again, we are glad to see insist- 

 ence placed on rough checks and approximations, 

 but at the same time the author, by his objection 



