i6S' 



NATURE 



[December 8, 1910 



(6) There is little that differentiates this from the 

 other numerous text-books on arithmetic which have 

 appeared during the last few years. The supply of 

 examples for oral and written purposes is plentiful, 

 and a large number of test papers are provided. 

 Although it is probable that those who use this 

 book will find it thoroughly satisfactory, yet we do 

 not consider that it marks any real advance on other 

 recent publications of a similar nature. 



(7) The present work is far more than a mere re- 

 vision of Hall and Knight's " Elementary Algebra." 

 Although some of the features of this book, first pub- 

 lished twenty-five years ag'o, have been retained, yet 

 the organic changes in method of late years demand 

 alterations so considerable that the volume before us 

 is to all intents and purposes a new book. It is 

 marked throughout by the same clearness of style and 

 thoroughness of treatment which characterised the 

 author's earlier work. Graphical methods are em- 

 ploved, but it is satisfactory to note that they have 

 been kept within reasonable limits. The tendency to 

 allow it to expand into an elementary course of 

 analytical geometry is a fatal error, for it overlooks 

 the fact that the student is not sufficiently mature at 

 that stage to be able to appreciate the significance of 

 the theoretical aspect of the subject. We hope that 

 this book will be widely used, for it is both sound and 

 comprehensive. Part i. carries the reader as far as 

 simultaneous quadratics. We understand that part ii. 

 is to be published very shortly. 



(8) It has often been pointed out that one significant 

 feature of the influence of examining bodies on the 

 educational curriculum is the tendency to standardise 

 into distinct types, and to collect under separate head- 

 ings, applications of general principles which the 

 student should be so educated as to work out for him- 

 self, when required to do so. The old-fashioned text- 

 books on arithmetic bear emphatic witness to this de- 

 plorable result ; and it is of some importance to con- 

 sider whether works on algebra are not similarly 

 affected. This is not the place, however, to develop 

 this theme ; but in England it is satisfactory 

 to note that the principles which have actuated those 

 educational bodies which are responsible for the leav- 

 ing certificate and Army qualifying- examinations do 

 much to minimise a very real danger. The author of 

 the present volume attempts to meet the sitaution by 

 focussing attention on the central facts and encourag- 

 ing the reader to make the requisite applications for 

 himself. By avoiding multiplication of detail, he is 

 able to cover a wider range and prepare the student 

 for more advanced work, in a shorter time than would 

 otherwise be possible, without any sacrifice of prin- 

 ciple. The explanatory matter is both full and clear, 

 and there are many useful hints, particularly in con- 

 nection with the solution of problems. We are, how- 

 ever, inclined to regret that the method of undeter- 

 mined coefficients is omitted, and that the chapter on 

 the binomial theorem is not prefaced by some quite 

 •short account of permutations and combinations, 

 treated numerically. There is at the end of the book 

 a useful collection of more than a thousand examples 

 for revision purposes, which are rather harder than 



NO. 2145, VOL. 85] 



those given in the text. The author has done his work 

 well, and his book deserves a good reception. 



(9) There is much that is novel in the plan of thi~ 

 book. Broadly speaking, there are two types of text- 

 books. In one the subject is presented in as simple 

 and elementary a fashion as possible, with no attempt 

 at investigating the fundamental axioms and principk - 

 on which the theory is based, and in the other a sub- 

 stantial knowledge of the actual analytical results i- 

 assumed and attention is concentrated on the formal 

 concepts. Both of these are beneficial, when properI\ 

 used. In the study of elliptic functions, for example, 

 it is customary to approach the subject by considering 

 such cases of integration which do not lead to an\ 

 known elementary function; but when the student ha- 

 acquired a knowledge of the general results, it is ver\ 

 valuable to start again and take as the base the theor\ 

 of a doubly-periodic function.' Prof. Picken has sei 

 himself the task of compiling a book for those who 

 are actually starting trigonometry during their univer- 

 sity course. His contention is that such students will 

 have attained a maturity of mind which will be fulh 

 capable of appreciating the theoretical principles of 

 this subject, and his object is therefore to supplement 

 the ordinary school treatises which refer almost exclu- 

 sively to numerical applications. We have little doubt 

 that the class of students the author has in view will 

 materially benefit by his work, which, although brief- 

 is both lucid and scholarlv. 



OUR BOOK SHELF. 



Milch und Molkereiprodiikte, ihre Eigenschaftcu, 

 Zusamtnensetziing und Gezt'innung. By Dr. Paul 

 Sommerfeld. Pp. 140. (Leipzig : Quelle and Meyer,. 

 1910.) Price 1.25 marks. 



This little book forms one of a series entitled "Wissen- 

 schaft und Bildung," the object of which is to pre- 

 sent the intelligent reader with brief accounts of par- 

 ticular subjects. It is rather more technical than 

 our own popular books of the same size would be, 

 and naturallv it lacks the completeness of a mono- 

 graph. But it would prove distinctly useful for a large 

 class of readers, including students and lecturers at 

 agricultural colleges, and farmers who take more 

 than a conimercial interest in their work. It seems, 

 indeed, to be a verv useful method of dealing with a 

 complex subject like agriculture. 



The first chapter describes the constituents of milk, 

 giving a clear and concise account of the protein, 

 carbohydrates, fats, and mineral matter present, and- 

 then follows a section on the characteristics of milk 

 from various animals. In discussing human milk 

 some interesting statistics are given that show 

 how difficult it is to supply any artificial food to- 

 infants that shall take the place of the mother's milk. 

 In Berlin during iqo^ the total number of infants 

 dving under twelve months of age was 10,170. The 

 method of feeding 7738 of these was known ; 7064 

 had been fed on cow's milk and onlv 674 on human 

 milk. The figures for other years are similar. 



The chapter devoted to the bacteriology of milk i? 

 subdivided into three portions, dealing respectively 

 with fermentation organisms, with organisms produc- 

 ing: disease in man, and with organisms producing 

 taints or defects in milk, such as ropiness. As all 

 this is compressed into less than twenty pages the 

 treatment is necessarilv verv brief. 



