May 17, 1900J 



NATURE 



53 



that arithmetic should be so often confounded with 

 the vulgar art of logistic — the necessary, but ignoble, 

 reckonings of the exchange and the market-place. Even 

 those who are aware of the distinction often fall into 

 another error, which is almost equally pernicious. To 

 most of them scientific arithmetic means the " Theory of 

 Numbers," a term which they vaguely associate with an 

 unknown, mysterious branch of mathematics with which 

 only a few eccentric specialists have any concern. 



The facts of the case are very different. It is true, of 

 course, that the exact and logical foundation of the very 

 rudiments of arithmetic has required the efforts of a 

 series of the greatest intellects ; that in order to follow its 

 numerous ramifications, and appreciate its relation to 

 other parts of analysis, demands a large amount of ability 

 and perseverance ; and that many of its truths have, as 

 yet, only been proved by elaborate, one may even say 

 artificial, methods ; while other theorems, almost certainly 

 true, still baffle all attempts at demonstration. But, in 

 spite of all this, it may be asserted that arithmetic re- 

 quires less apparatus and less preliminary training than 

 any other branch of mathematics ; and that, whether as 

 a recreation or as a field for research, it amply rewards a 

 very moderate degree of application. 



It is not without reason, therefore, that Prof Cahen 

 addresses himself deliberately toamateur mathematicians ; 

 and, in fact, anyone gifted with common sense, unspoiled 

 by a vicious course of school instruction, ought to profit 

 by his lucid and entertaining pages. In six chapters he 

 deals in sufficient detail, and with appropriate numerical 

 illustration (a most important point), with the elementary 

 definitions and laws of operation, with linear and quadratic 

 congruences, and with the elementary theory of binary 

 quadratic forms. After this come a series of notes, 

 ranging from scales of notation to an outline of the 

 properties of Gauss's complex integers and their nearest 

 allies ; and, finally, a very useful set of tables, which 

 afford the reader material for those applications to par- 

 ticular cases, without which the general theory cannot 

 possibly be mastered. 



The appearance of this work, as well as of others with 

 a similar object in view (for instance, M. J. Tannery's 

 excellent " Legons d'Arithmetique "), encourages the hope 

 that some improvement may be effected in the teaching 

 of arithmetic in schools, and that a sound knowledge of 

 its first principles may cease to be the monopoly of a 

 very small minority of University graduates. It is, un- 

 fortunately, true that a very large proportion of class- 

 books, both in arithmetic and in algebra, contain half- 

 informed, misleading attempts at expounding theory 

 which are really worse than the old-fashioned bundles of 

 " Rules " ; and unless these are replaced by something 

 better, the efforts of reformers will have the lamentable 

 result of producing a state of things worse than the old 

 routine : a mere jargon of pseudo science, a barbarous 

 patchwork of sham " Principles." 



M. Cahen's work will be found of interest, not only by 

 the amateur in search of recreation, but by intelligent 

 teachers and arithmeticians of every degree of proficiency ; 

 while the professed devotees of the science will look with 

 pleased anticipation for the more extended work on the 

 same subject which the author appears to be preparing. 



G. B. M. 

 NO. IS94. VOL. 62 1 



OUR BOOK SHELF. 



Atlas of Urinary Sediments, with special reference to 



their Clinical Significance. By Ur. Hermann Riedel. 



Translated by F. C. Moore, M.Sc, M.D. Victoria. 



Edited and Annotated by Sheridan Delepine, M.B., 



CM. Edinburgh, B.Sc. Pp. viii -f- in, and 36 plates. 



(London : C. Griffin and Co., Ltd., 1899.) 

 Thf: work before us, as is evident from its title, is an 

 atlas, and will be of interest rather on account of its 

 plates, which are very beautiful, than of its letterpress ; 

 this latter, however, which is situated at the end of the 

 book, covers more than a hundred pages, and is provided 

 with a bibliography and an index of authors and subjects. 

 The text is sub-divided into an introduction and two 

 parts. The introduction deals with methods of collection 

 and examination, &c. Part i. is devoted to unorganised, 

 Part ii. to organised sediments. The editor has added 

 considerably to the original text, his remarks being indi- 

 cated by parentheses : he occasionally differs with Dr. 

 Riedel concerning fact. The large additions to the text 

 made by the editor have rather altered the character of 

 the work, and have probably increased the sphere of its 

 usefulness. 



Under organised seditnents bacteria are considered. 

 A useful chapter is to be found at the end concerning the 

 making of permanent specimens of urinary sediments. 



The book should be of value to urinologists, and the 

 plates certainly to physicians in general. The thanks of 

 the profession are due to the translator and the editor 

 for making the work available to English readers, and 

 amplifying its contents 



Dante. By Edmund G. Gardner, M.A. "The Temple 



Primers." Pp. vi+159. (Dent, 1900.) 

 A VERV admirable book, by the author of Dante's "Ten 

 Heavens." Dante was a master of the science of his 

 time, and Mr. Gardner has shown that he has not only 

 carefully studied the " Divina Commedia" from the point 

 of view of literature, but has taken pains to carefully 

 annotate all the references to the then systema tnundi 

 on which so much of the action of the poem depends. 

 Diagrams and explanations are given at the end of the 

 book, which will be found most useful by the student. 



The Farmstead. By Prof J. P. Roberts, Director of the 

 College of Agriculture, Cornell University. Pp. vi-l-350. 

 (New York : The Macmillan Company. London : 

 Macmillan and Co., Ltd., 1900.) 

 This is a very readable compendium of suggestions in 

 regard to providing a beautiful, economical, and healthy 

 rural home. Although written for American farmers, it 

 contains much that is of interest to all who are con- 

 cerned with a country life, and few will peruse the book 

 without gleaning some useful hints. There are special 

 chapters on house-furnishing, decoration, and sanitation 

 by Prof. Mary Roberts Smith, who writes pleasantly on 

 the lighter sides of a farmer's life. A strong case is 

 made out for the educational opportunities of the farm, 

 which are shown to be ample enough to satisfy the most 

 exacting advocate of Nature Study. W. S. 



Object Lessons in Botany from Forest., Field, Wayside 



and Garden. Book ii., for Standards iii., iv. and v. 



By Edward Snelgrove, B.A. Pp. xviii-t-297. (London: 



Jarrold and Sons.) 



This is a meritorious little book, and ought to well 

 serve its purpose of inculcating habits of accurate and 

 precise observation in the young pupils for whom it is 

 designed. Although we notice a few slips here and there, 

 they are not serious ones, and are quite eclipsed by the 

 excellent character of the book as a whole. The author 

 is convinced, as he says in the preface, of the value of 

 elementary botany in the education of children, and we 

 think his book justifies his contention. 



