October 21, 1915] 



NATURE 



199 



mcntary scientific facts, generally illustrated by 

 ri fcrence to phenomena which may fairly be ex- 

 pected to have come under the notice of an average 

 \outh, and by a few simple experiments, which 

 the student is intended to repeat; the second part 

 of each chapter indicates the application of the 

 xientific facts thus inculcated to some portion of 

 the miner's experience in the pit. Like all books 

 that set out to teach only such portions of a 

 s( ience as find direct application in any particular 

 iuanch of technology, this work deliberately 

 sacrifices the educational value of science in order 

 to arrive more rapidly and more easily at the 

 results derived from the acquisition of scientific 

 facts. It is undoubtedly a very good thing that a 

 coal-miner should be thoroughly familiar with the 

 fact that a combustible material intimately mixed 

 with air forms an explosive mixture, but the 

 acquisition of any number of such fragments of 

 knowledge, however valuable in themselves, does 

 not provide the mental training that is obtained 

 b\ the systematic study of any branch of science. 

 Such a book as the one under discussion should 

 not therefore be regarded as an adequate sub- 

 stitute for scientific education, but at best as an 

 introduction and an incentive to further and more 

 regular study of the sciences involved. It is a 

 book that may fairly be recommended to the 

 higher classes of an elementary school in a coal- 

 mining district, with the hope that it may give 

 tlte lads a desire to pursue their scientific studies 

 finther in evening continuation schools, where 

 tlicy would take a regular course of easy chem- 

 istry or physics, or both. 



The work upon the whole is well done ; the 

 main pitfalls in such a book lie in the direction 

 of slipshod statements on the one hand and over- 

 elaboration on the other. As an example of the 

 former we may quote the statement on page ii8 

 that hydrogen "is a colourless gas, violently ex- 

 plosive," and of the latter the attempt to teach 

 the molecular structure of gases on page 2. The 

 authors have, however, generally succeeded in 

 sieering their course fairly between either extreme, 

 <i!id the result is a book which should, as already 

 said, be quite useful to beginners, and will 

 1( ave them very little indeed to unlearn when they 

 1)( gin to advance further in their scientific studies. 



MA THEM A TICAL SCHOOL-BOOKS. 



(i) Arithmetic. Parts I., H., and HI., complete 



-.vith Answers. By C. Godfrey and E. A. Price. 



(Cambridge : At the University 



Price 45. ; without answers, 



Pp. xiii + 467. 

 Press, 1915.) 

 35. 6d. 

 (2) Pendlebury's 

 Si 



New Concrete Arithmetic, 

 th Year. By C. Pendlebury and H. Leather. 

 NO. 2399, VOL. 96] 



Pp. 80. (London : G. Bell and Sons, Ltd.) 

 Price 6d. 



(3) Plane Trigonometry. By H. Leslie Reed. Pp. 

 xiii + 290 + xvi. (London: G. Bell and Sons, 

 Ltd., 191 5.) Price 35. 6d. 



(4) Statics. Part //.' By F. C. Fawdry. Pp. 

 1^9-305 + viii. (London: G. Bell and Sons, 

 Ltd., 1915.) Price 2s. 



(5) Numerical Examples in Physics. By H. S. 

 Jones. Pp. xii + 332. (London: G. Bell and 

 Sons, Ltd.., 1915.) Price 35. 6d. 



(6) Exercises in Laboratory Mathematics. By 

 A. W. Lucy. Pp. 245. (Oxford: At the 

 Clarendon Press, 1915.) Price 3s. 6d. 



THE ideal text-book of arithmetic still remains 

 to be written, and the time has not yet 

 come when the ideal book would be a financial 

 success. It will equip the boy or girl with the 

 knowledge of the subject necessary for his other 

 studies and his after-life. It will drop some 

 branches which have in the past had usefulness 

 but are now useless, and it will refrain from deal- 

 ing with problems the subject-matter of which is 

 outside a boy's experience and unintelligible to 

 him, even if the calculation involved is simple once 

 the subject-matter is understood. The ideal book 

 with our present imperial system of weights and 

 measures will easily be comprised within a hun- 

 dred pages, and when the imperial system is 

 dropped and the metric system becomes general 

 the length will be further reduced. 



The discussion of prime factors, greatest com- 

 mon measure, and least common multiple leads up 

 to the extraction of square and cube roots, the 

 reduction of fractions to their lowest terms, the 

 addition of fractions, and the simplification of 

 complicated expressions. Now the final conveni- 

 ent form for any fraction (except the very sim- 

 plest) is the decimal form, and instead of reduc- 

 ing a fraction to its lowest terms we turn it 

 straight away into a decimal. For the addition of 

 fractions, in place of the vulgar method with all 

 the labour of common denominators, we convert 

 each fraction to a decimal (to as many significant 

 figures as we need), and then add. Complicated 

 expressions rarely turn up in natural problems; 

 they are in the main the invention of examiners and 

 text-book writers. Very little time, therefore, 

 need .be spent upon prime factors, greatest com- 

 mon measure, and least common multiple, and 

 these will occupy little space in the ideal text- 

 book. 



" Stocks and shares " should also be omitted. 

 The arithmetic is of the simplest. The trouble is 

 partly in the difficulty of the subject-matter, partly 

 in the unfamiliarity of the subject-matter, and 

 partly in the unsuitable nomenclature, so poor 



