December i6, 1915] 



NATURE 



42: 



is really too cumbersome and heavy for con- 



mient use. If chapters i. to vi. and chapter xi. 



formed one volume, with the steam tables as an 



ippendix, the other chapters would fit well into 



second volume. 



In conclusion, we offer our warm congratula- 

 js to the author. He has achieved a great 

 isk ; this book is a testimony to his powers as 

 original worker, and to the wide grasp he has 

 )btained of the whole field of work covered by 

 ''it. We would commend a careful study of the 

 book to those, only too numerous, detractors of 

 the work achieved by British men of science and 

 practical engineers. They will find ample testi- 

 mony that in this field of human activity the 

 British workers easily hold a foremost place. 



T. H. B. 



MA THEM A TIC A L TEX T-B O OKS. 



(1) Plane Geometry. By G. St. L. Carson and 

 Prof. D. E. Smith. Part i., pp. vi + 266. 

 Part ii., pp. vi + 259-482. (London and Boston : 

 Ginn and Co., 1914-15.) Price 2s. 6d. each 

 part. 



(2) Elements of Algebra. By G. St. L. Carson 

 and Prof. D. E. Smith. Part ii., pp. v + 538. 

 (London and Boston: Ginn and Co., 1915.) 

 Price 2S. 6d. 



(3) Contributions to the Founding of the Theory 

 of Transfinite Numbers. By G. Cantor. 

 Translated by P. E. B. Jourdain. Pp. ix + 211. 

 (Chicago and London : The Open Court Pub- 

 lishing Co., 1915.) Price 35. 6d. net. 



(4) A Text-book on Practical Mathematics for 

 Advanced Technical Students. By H. L. Mann, 

 Pp. xii+487. (London: Longmans, Green and 

 Co., 191 5.) Price ';^s. 6d. net. 



';) Descriptive Geometry. By H. W. Miller. 



},vd edition. Pp. 149. (New York : J. Wiley 



and Sons, Inc. ; London : Chapman and Hall, 



Ltd., 1915.) Price 65. 6d. net. 

 (i) A /r^^^^ attempts are now being made to 

 J.VX formulate a system of geometry suit- 

 able to the immature minds of schoolboys, which 

 will on one hand develop their reasoning facul- 

 ties by some kind of logical training, and on the 

 other by a suflficiency of practical work clarify 

 their ideas as to the concepts which form the 

 basis of the subject. 



It is unfortunately true that as yet no general 

 agreement has l:)een obtained, or any course de- 

 termined which is not open to formidable attacks 

 from one school of thought or another. Time 

 alone will bring about consensus of opinion in a 

 controversy that has raged since the time when 

 Lewis Carroll wrote his " Euclid and his Modern 

 NO. 2407, VOL. 96] 



Rivals " ; and educational opinion will gradually 

 solidify by the action of those teachers and writers 

 who are attempting to express the results of their 

 personal experience. 



If for no other reason, we hope that this 

 volume will receive the serious consideration it 

 merits; for it offers, not indeed a final, but cer- 

 tainly a valuable contribution to these issues. It 

 would be beyond the scope of this notice to ex- 

 amine in any detail the course followed ; and it 

 is detailed examination alone that justifies the 

 passing of any judgment. The authors have had 

 extensive experience in the matters of which they 

 write, and the views they have formed are the 

 product of a genuine knowledge of the needs and 

 capacities of junior students and of those psycho- 

 logical considerations to which educationists are 

 now attaching due limportance. 



(2) The first part of this text-book has already 

 been noticed in these columns ; the second part, 

 written on similar lines, carries the student as far 

 as progressions and the binomial theorem for a 

 positive integral index. We notice with regret 

 that the section on graphs includes the tracing of 

 the ellipse 4.\;2 + gy^ = 288 ; such work should, in 

 our opinion, be relegated to co-ordinate geometry 

 proper; we think also that examples on the 

 greatest term in a binomial expansion, although 

 sanctioned by tradition, might well be omitted 

 from the ordinary algebra course. But, except 

 for a few minor points such as these, the character 

 of the book appears to us excellent, and we shall 

 expect to see it hold its own in the strenuous com- 

 petition that every text-book on elementary algebra 

 has now to face. 



(3) This volume contains the two classical 

 memoirs on transfinite cardinal and ordinal 

 numbers which Prof. Cantor contributed to the 

 Mathematische Annalen in 1895 and 1897. They 

 are prefaced by a long introduction (more than 

 80 pages) by Mr. Jourdain, in which he traces 

 the growth of the theory of functions through the 

 nineteenth century, with special reference to the 

 work of Cantor and Weierstrass ; the concluding 

 pages of the book contain some notes on modern 

 developments. 



This introduction will undoubtedly prove of 

 great value to English students and teachers ; its 

 admirable summary of the progress of ideas will 

 smooth their pathway and assist and encourage 

 them to study that modern work to which the 

 author has himself already furnished substantial 

 contributions. 



(4) Although the first few chapters are devoted 

 to such algebra, trigonometry and geometry as 

 technical students are likely to require, the main 

 purpose of this book is to provide a suitable 



