122 



NATURE 



[June 21, 1917 



technical subject is enhanced by the inclusion of 

 a portrait of one only connected politically as an 

 organiser with the industry. If any technical 

 book is good, a portrait of a celebrity will not 

 help its usefulness or sale; if bad, no one will 

 want it because of the frontispiece. Technical 

 literature might well be exempt from such 

 embellishments. 



" THOUGHT-SUBJECTS/' 



(i) The Supervision of Arithmetic. By W. A. 

 jessup and L. D. Coffman. Pp. vii + 225. (New 

 York : The Macmillan Co. ; London : Mac- 

 millan and Co., Ltd., 1916.) Price 5s. net. 



(2) Second-Year Mathematics for Secondary 

 Schools. By Ernst R. Breslich. Second edi- 

 tion. Pp. XX + 348. (Chicago, 111. : University 

 of Chicago Press ; Cambridge : At the Uni- 

 versity Press, 1916.) Price 45. net. 



(3) Elementary Dynamics of the Particle and 

 Rigid Body. By Prof. R. J. A. Barnard. Pp. 

 vi + 374. (London: Macmillan and Co., Ltd., 

 1916.) Price 6s. 



(i) A CONSIDERABLE amount of elaborate 

 ■^~*- investigation has gone to the making of 

 "The Supervision of Arithmetic." It might very 

 well have been analysed and the results presented 

 in a small pamphlet. It is not clear why the 

 book has been imported into this country. It can 

 be of no earthly interest or value to the English 

 teacher to know in detail a mass of information 

 such as "the distribution of cities according to 

 per cent, time, exclusive of recesses and opening 

 exercises, devoted to arithmetic." The tables 

 appear to be the kind of thing to which in Ameri- 

 can educational courses a diploma is awarded. 

 If this be the case, it seems that pretentious 

 theses for a master's degree may be compiled 

 without any real thinking being done. 



We are likewise at a loss to conjecture for 

 whose benefit the tables are compiled, seeing that 

 elaborate explanations are attached to so many 

 that carry on the face of them their meaning. It 

 is not always easy to see the object of some of 

 the investigations — e.g. what is the point in a 

 table showing the order of teaching the multipli- 

 cation table in cities according to their popula- 

 tion? No doubt we are stupid an^ old-fashioned, 

 but we feel a pricking in our thumbs when we see 

 certain tables which to the mind of the compilers 

 seem to decide "whether the books are arithme- 

 tics or something else." It is only fair to add 

 that they have a haunting suspicion that their 

 task may seem "foolish." Be that as it may, 

 they reach a limit (? superior or inferior) when 

 they present us with tables showing from five 

 elementary arithmetics the words that begin with 

 ^"s" and with "w," respectively (they say, "be- 

 ginning with 5 and w "), and when they tell us 

 that 94 proper names are used 342 times, " Ella 

 and Kate 6 times each, Helen 8, Henry 9, Carl 

 12, Fred and James 16 each, Frank 24, Mary 27, 



NO. 2486, VOL. 99] 



and John 40. There are in the same pages 224 

 words beginning with c, and these words are used 

 a total of 1403 times." To the being of dim and 

 bounded faculties this seems table-making gone 

 astray. It makes us tired. 



Though there is much that is interesting and 

 much that is useful, the ideals do not always 

 seem to us to be wholesome. "Translated into 

 words, the table means that in June the graduate 

 of a grammar school [whatever that may mean] 

 should be able to work correctly in eight minutes 

 twelve examples like that under Test 1. [adding 

 nine rows of three figures], in four minutes 

 twelve examples like Test ii. [subtracting two 

 rows of ten figures]," in six minutes twelve 

 sums like 4179 x 36, in eight minutes twelve sums 

 like 61,707-^67, and so on. If the aim is to turn 

 out cheap calculators for business men, we can 

 understand how this will appeal to the commercial 

 instinct, but what a cast-iron ideal for the 

 "graduate of a grammar school," and at what a 

 cost will it be reached ! 



All this apparatus of statistical stuff appears to 

 be for the benefit of arithmetic "supervisors." 

 Quis custodiet custodes? Already the note of 

 revolt has been sounded. We observe that in the 

 last number of L'Enseignement mathematique 

 Prof. D. E. Smith delivers his soul on this point : 

 " Unfortunately, our courses on education are so 

 often concerned with measurements of pupils' 

 accomplishment, with statistical curves, and with 

 ephemeral theories based upon limited observa- 

 tions, that teachers of such thought-subjects as 

 mathematics are generally suspicious of their 

 value." We are not in the least surprised. 



(2) "The material as arranged in this course 

 opens to the student a broader, richer, more 

 useful, and therefore more alluring field of ideas, 

 and lays a more stable foundation for future 

 work, than does any separate treatment. A 

 great saving of the students' time is effected by 

 developing arithmetic, algebra, geometry, and 

 trigonometry side by side." The first of these 

 statements contains a large claim, but we can 

 say without hesitation that Mr. Breslich's volume 

 is deserving of careful consideration by the 

 teacher of elementary mathematics as a part of 

 general culture. It is conceived on sound lines, 

 and if there are many minor points that invite 

 criticism — Quot homines, tot sententiae — the one 

 fact emerges that at the end of a second year the 

 student who has mastered these pages will be 

 in possession of a verj' satisfactory body of 

 mathematical equipment, and will be fully aware 

 of its practical value in everyday life. His 

 thoughts will be able to play freely, up to a certain 

 point, in three dimensions ; he will have acquired 

 something more than a vague idea of the nature 

 of a proof; he will have the feeling that he has 

 assisted in the building up of something definite, 

 and full of meaning, with the aid of tools in the 

 use of which he will see every reason of interest 

 and utilitv for endeavouring to become more 

 expert. His interest in the great mathematicians 



