378 



NATURE 



[May i8, 191 1 



(2) This is an abbreviated edition Of the "Public 

 School Arithmetic," by tlie «une authors. The 

 number of examples worJted out in detail has been 

 materiallv diminished on the ground that the average 

 boy is apt to r«ly too much on this forjn of assistance 

 and so avoids the necessity of thinking for himself. 

 This is, of course, a matter of opinion. It is not at 

 all an easy thinii: to train students to read for them- 

 selves; in general they are far too prone to rely on 

 oral help. In more advanced work, it is unquestion- 

 able that there is a real educational value in forcing 

 a bov to find out for himself the meaning of what 

 the text-book is explaining, provided only that the 

 book itself is a good one. Of course, progress is 

 made more slowly in these circumstances, but the 

 substance of what is read is more likely to be digested 

 owing to the increase of mental effort. It is, how- 

 ever, hard to decide at what stage this recourse to 

 books should be encouraged. The present volume 

 gives a very thorough account of all branches of the 

 subject. Indeed, in our opinion it contains far more 

 than it is desirable for the average boy to know. The 

 tiint' required for mastering its contents is so con- 

 •^id. r.il)le that it will leave small opportunity for pro- 

 ceeding to more fruitful work. But .so long as an 

 exhaustive study of the subject is required by examin- 

 ing bodies, it will be necessary for writers to meet 

 this demand. In this the present volume is eminently 

 successful. 



(3) and (4) In the opinion of the authors of this 

 treatise, which is issued in fwo volumes, the subjects 

 of algebra and geometry should be fused together 

 as far as possible. It is suggested that students are 

 more likely to realise the relations which subsist 

 between these two portions of elementary mathe- 

 iiiatics, if a single text-book is placed in their hands. 

 An ( x.-unination of the contents of the separate 

 volumes shows that algebra predominates in the first 

 and rreometry in the second ; but in each case it is 

 true to say that the correlation of the two subjects 

 is kept consistently in view. The first course includes 

 the elements of algebra u|) to simultaneous linear 

 equations, factors, and fractions, and the fundamental 

 ideas of geometry, viz., congruence, parallel. sm, and 

 similarity, with numerical illustrations and straight- 

 forward constructions. The principle of moments is 

 used to provide some interesting algebraic problems. 

 The advanced course contains a more systematic 

 account of formal geometry, iIk jnoperties of the 

 circle, theorems on areas and similar figures, the 

 investigation of regular polygons, and more difficult 

 constructions. With this is combined the general 

 solution of the quadratic, the algebraic theorv of 

 proportion, graphical algebra, and simple numerical 

 trigonometry restricted mainly to right-ruigled tri- 

 angles. Tlic nianipvilation which is expected frt>ni 

 the student is of ;i slmplo cliaracltr. This is prob- 

 ably the best plan for students of the age for which 

 this book is designed. But we doubt whether it is 

 equally desirable to exclude at the same time any- 

 thing which can be properlv called a rider. Numerical 

 work in geometry provides the most certain means of 

 elucidating now ideas, but unles< xh'-^ 



NO. 2168, VOL. 86] 



with a certain amount of theoretical work, the in- 

 trinsic value of the subject is sacrificed. The abilit\ 

 to solve a simple rider is the best index of the intel- 

 lectual growth of the student. 



(5) The title of this book »« an adequate descrip- 

 tion of its contents. It consists of about eieht 

 hundred examples, illustrating the theorems of 

 elementary plane and solid geometry, and it yieWs a 

 collection of questions which many will find a useful 

 supplement to formal treatises. 



OUR BOOK SHELF. 



Oniitologia Argi'tithta. Catdlogo sistemdlico y de- 



scriptivo de las Aves de la Jiepublica Argentina. 



By Dr. R. Dabbene. Tctne Primers. Pp. xiv-^ 



513. (Buenos Aires : .Museo Nacional, 1910.) 

 The object of the present work, of which tin 

 volume before us is only the first, is to provide, 

 as we learn from the preface, a systematic list of 

 all the genera and species of birds inhabiting -Argen- 

 tina, mainly from the point of view of their ge<j- 

 graphical distribution, for the use, chiefly, of students 

 of ornithology in the Republic. Most of the species 

 common to the neighbouring countries of Brazil. 

 Bolivia, Paraguay, and of the frontiers of Chili and 

 Uruguay are included, since it is highly probabl> 

 that the birds of these regions will be discovered in 

 the .Argentine when it is more fully explored. In- 

 cluded also are all the species inhabiting the archi- 

 pelagoes and islands lying off the shores, as well .-t^ 

 the lands extending southward to the Antarctic circle. 



The work is to contain three parts. The first deal> 

 with those anatomical characters of birds which ire 

 of dassificatory value. The second discusses th- 

 geographical distribution of the birds of the Republic, 

 with a list in systematic order of all its recent and 

 fossil species, and their assignation to the differenr 

 zones — shown on a coloured map— into which the 

 author divides the region. The final section, to be 

 dealt with in future volumes, will contain brief 

 diairnoses of the orders and families, &c.. of bird- 

 represented in the Argentine, with keys for differen- 

 tiating the species, which number 469, referable t(' 

 71 families. An extensive bibliography is appended 

 to each section. 



.Although Dr. Dabbene is largely indebted, with 

 due acknowledgment, for his morphological facts to 

 European investigators, and among English workers 

 especially to Huxley, Garrod. Forbes, Beddard, 

 Chalmers Mitchell, Garrod, and Newton — from whose 

 works most of his figures are derived, the volume 

 will be of very great value to students so disadvan- 

 tageouslv remote from the great European libraries 

 and books of reference, as are those domiciled in 

 .Argentina. The section devoted to geographical dis- 

 tribution brings concisely together the data under 

 this head, and will be appreciated by those elsewhere 

 interested in South .American ornitholoLfx . The 

 volume is provided with very full indice- 

 Pie Sameupftauzen (Bliitetipflanzcti, P/ud... ^,. .;.cu). 



Bv Prof. K. Wilhelm. Pp. xvi-(-isi. ^ (Wien 



and Leipzig : F. Deuticke, iqio.) 

 Thekf. can be no disagreement with the author's 

 opinion that the only satisfactory method of acquiring 

 a knowledge gi plant classification is to practise the 

 determination of unknown species with the aid of a 

 flora or other systematic compilation. It has been 

 Dr. Wilhelm 's object to supply a coinpilation suitable 

 for the use o^ foresters, agricultural, pharmaceutical, 

 and other technir.nl students. The chief essentials 

 'tpear to be a differentiation. 



