2/0 



NATURE 



[November 7, 1912 



grouped together. The supply of riders, par- 

 ticularly in connection with angle properties of 

 the circle, seems rather inadequate. We are glad 

 to see that limit methods of proof are employed 

 lor the fundamental tangent properties. 



(4) There are several novel features in this text- 

 book. It is divided into thirty-five sections, each 

 of which professes to contain the material for one 

 lesson ; but we are inclined to think some of these 

 sections will occupy four or five hours if an 

 adequate amount of time is assigned to rider 

 work. The theorems are not numbered, and no 

 references to previous propositions are given in 

 the proofs; a conversational method is employed 

 which for beginners possesses obvious advantages, 

 and the order of the theorems differs from that 

 usually followed. The scope of the work includes 

 the first three books of Euclid, the properties of 

 similar figures, and the fundamental propositions 

 of solid geometry. We are of opinion that the 

 character of the book will render it more useful 

 to the teacher than to the student. 



(5) In order to meet the wishes of those teachers 

 who prefer to take all book-work orally, the 

 authors have now issued in a separate form the 

 exercises contained in their "School Arithmetic." 

 The work is published in two parts, the first of 

 which deals with fractions, decimals, factors, 

 compound quantities, and unitary method. Both 

 in quality and variety the collection of examples 

 is admirable. 



(6) Many teachers will be glad to hear that the 

 solutions of the exercises in Godfrey and Siddons's 

 " Solid Geometry " have now been published. 

 Where we have tested them we have found that 

 they are set out very clearly. Mr. Beaven has 

 avoided the temptation to which in such cases 

 writers often succumb of allowing a desire for 

 brevity to obscure lucidity of expression. The 

 figures which illustrate the solutions of the 

 problems on plan and elevation are drawn with 

 great care, and tlie methods emplo\'ed are fully 

 explained. 



(7) This is in no sense a text-book on hydro- 

 dynamics. .A few formula? are quoted from 

 various mathematical treatises, but no proofs are 

 given. The purpose of the author is to introduce 

 the student to the ideas of the subject, and to 

 point out the rather arbitrary conditions under 

 which, in the present state of knowledge, the 

 mathematician is compelled to work. We do not 

 think that the novice will find the contents of this 

 volume at all easy to understand and coordinate 

 with his other scientific reading. The number of 

 quotations from many different authorities and 

 the variety of topics alluded to may well tend to 

 confuse those who have little previous knowledge 



NO. 2245, VOL. 90] 



of the subject. In the hands of a skilled lecturer I 

 we think the material of this book and the lines I 

 of thought indicated would interest and stimulate 

 a class of students of ordinary ability. The 

 character of the work leads us to believe that the 

 author's purpose would be achieved with a real 

 measure of success by oral methods. 



(8) The authors of this treatise have succeeded 

 in producing a work wholly unlike any other text- 

 book on the subject with which we are acquainted. 

 They take as their motto a pregnant sentence from 

 Tannery's " Lecons d'alg^bre et d 'analyse " : — 

 "J'ai horreur d'un enseignement qui n'est pas 

 toujours sincere ; le respect de la veritd est la . 

 premiere le(;on morale, sinon la seule, qu'on | 

 puisse tirer de 1 'etude des sciences." Their con- 

 tention is that the average schoolboy is fully 

 capable of realising the fundamental ideas upon 

 which the science of algebra and, in fact, all 

 analysis is based, and that a powerful educative 

 instrument is discarded if no attempt is made to 

 discuss the base-principles of the subject. They 

 regard rigour in fundamentals as important as 

 variety in application, and the power to understand 

 the meaning of a process as more valuable than 

 the ability to apply it. 



With these ideas in the abstract few people will 

 disagree, but the majority of teachers hold that 

 work of this character must be reserved for 

 specialists. They consider that the mental calibre 

 of the ordinary schoolboy, and the limited time 

 at his disposal, are scarcely adequate to permit of 

 the high standard required by the authors of this 

 work. Great things can, of course, be done by 

 an enthusiastic and able teacher ; and we have no 

 doubt at all that Mr. Barnard obtains excellent 

 results at Rugby by following the lines here indi- 

 cated. Hut we question whether the ordinary 

 teacher could be expected to meet with success. 

 We have not the space to comment in any detail 

 on the contents of this volume, but we would urge 

 teachers to procure a copy and study it for them- 

 selves. They will find in it much thrit is highly 

 suggestive, and will gather from it a number of 

 new ideas. It is in every respect a remarkable 

 work. 



(9) By the direction of the Board of Trinity 

 College, Dublin, a new edition of Dr. Salmon's 

 treatise on analytic geometry of three dimensions 

 has been prepared. The editor has retained the 

 substance of what appeared in the fourth edition, 

 but has brought it into line with more recent work 

 by inserting a number of new sections ; the list 

 of references has also been supplemented. Among 

 the additions that have been made we note some 

 excellent plates showing models of the various 

 species of quadrics, a paragraph on Fiedler's pro- 



