Dec. ii, 1884] 



NA TURE 



123 



popular matter, recalling to their minds some of the 

 scenes in connection with their own captures, or serving 

 as a stimulant for future expeditions. But after all it is 

 the plates that will be most frequently consulted. Of 

 these there are seventy-seven, mostly crowded with figures, 

 and including a few of transformations. Without the 

 recent adaptation of chromo-lithography, in a superior 

 form, to natural history subjects, the publication of such 

 a work as this (at the price) would have been impossible. 

 The author estimates that there are more than Soo 

 figures on these plates. It is impossible here to criticise 

 them seriatim. Those subjects that appear the most dif- 

 ficult are often the best (perhaps more detail in the way 

 of " stones " was used on them), and we are much pleased 

 with the Hesperidce, which, easy as they may look at 

 first sight, must prove very troublesome of application. 

 The "Blues" and "Coppers" [LyccBtiidcB) are fair, but 

 naturally fail in effect where metallic colours are neces- 

 sary. The worst, to our mind, are those of the Satyridce 

 (of which our " meadow-brown " is a familiar example), 

 and yet they look the easiest : we think here there is 

 evidence of trying to make too many species, with vary- 

 ing shades of practically the same colour, accommodate 

 themselves to one " stone." The size is rather too large 

 for a book to be used as a travelling companion, but we 

 think it is rather intended for home study. Paper and 

 type are very good (the former almost unnecessarily so). 

 There is not much to find fault with in the way of un- 

 corrected errors. This is satisfactory, because careless 

 correction is the crying evil of the present day, even in 

 works claiming a much higher scientific position than 

 does this, and often shows up the amount of know- 

 ledge possessed by writers of the authors and works 

 they quote. But such glaring errors as the following 

 should not have escaped correction : — Page 47, " Illus- 

 Mag." for " Illiger's Mag." ; p. 61 (and elsewhere), " Wein " 

 for " Wien " ; p. 153, " Sellmann's " for " Silliman's " ; 

 p. 3S0, " Thurnberg " for " Thunberg " ; and, as a crowning 

 morsel, p. 379, " Aumer Kungen " for " Anmerkungen." 

 In notices of some of the recent additions from Central 

 Asia, the author uses indiscriminately (sometimes on the 

 same page) " Samarcand" and" Maracand" as localities ; 

 we thought it was generally understood that the latter is 

 only the ancient name of the former. 



We have hitherto dealt with this work from a popular 

 point of view. But there is also the scientific side of the 

 question. The book will be of service as collectively 

 giving good descriptions and figures of all known Euro- 

 pean species brought down to date, and thus avert the 

 necessity of search through a multitude of scattered pub- 

 lications ; and in this it will be useful to other than 

 English readers. 



On the title-page the author adopts a super-title — 

 " Rhopalocera Europae." This we think a pity in a 

 work otherwise entirely in the English language. 



R. McLachlan 



ELEMENTARY MA THEM A TICS 

 Lehrbuch der Elementaren Mathetnatik. V. Schlegel. 



Pp. 712. (Wolfenbuttel, 1878-1880.) 

 "\ T J E have not had the good fortune to meet with this 

 » > work, but having now before us an elaborate 

 notice of it by M. Hoviel in the Bulletin des Sciences 



Mathematiques et Astronomiques, December, 1882 (pp. 

 301-313), we have thought that a few passages from the 

 notice would be acceptable to some of our readers, and 

 lead them to a personal examination of the original 

 treatise. 



The writer's opening remarks have much truth in 

 them: -"Nous sommes habitue's depuis longtemps a 

 considerer 1' apparition d'un traite" eidmentaire de mathe"- 

 matiques comme tin evenement pe'dagogique ou commer- 

 cial n'a) ant lien de commun avec la science pure. Si l'on 

 met a part quelques honorables exceptions, e'est toujours 

 le meme livre qui reparait sous une couverture de couleur 

 differente, avec quelques pages transposees, quelques pro- 

 positions secondaires introduites ou supprimees, quelques 

 demonstrations modine"es sinon perfectionnees, quelques 

 developpements de plus suivant les tendances des pro- 

 grammes officiels. Quant a la maniere d'exposer les 

 principes fondamentaux de la science, rien n'est change". 

 Les decouvertes qu'on a faites dans les hautes mathe- 

 matiques depuis 1111 siecle et qui out si admirablement 

 eclairci les difficultes que presentaient encore les elements 

 d'algebre semblent etrangeres a. nos auteurs, qui ex- 

 pliquent les imaginaires comme au temps de Bdzout et 

 de Lacroix, et pre'sentent parfois a leurs lecteurs des 

 notions geomctriques en arriere de beaucoup sur celles 

 qu'exposait Euclide ii y a plus de deux mille ans. . . . 

 En Angleterre, 1'enseignement est reste ce qu'il e"tait au 

 temps de Barrow et de Simpson ; heureusement le vieil 

 Euclide a etc" choisi et fidelement conserve" a l'abri des 

 pretendus perfectionnements des traite"s modernes." 



M. Victor Schlegel is a pupil of H. Grassmann, and 

 his present work is inspired by the bold views of the 

 author of the " Ausdehnungslehre." It consists of four 

 volumes devoted to arithmetic, algebra, plane and solid 

 geometry, and plane and spherical trigonometry. Vol. i., 

 " Arithmetik und Combinatorik " (182 pp.), treats of ele- 

 mentary algebra and of the theory of combinations. 

 " Le tout est expose avec une concision qui n'exclut pas 

 la clarte", et avec une rigueur irreprochable." The re- 

 viewer's attention is especially directed to an analysis of 

 vol. ii., " la partie vraiment originale de I'ouvrage." In 

 222 pages are laid down the principles of plane geometry, 

 the ideas in which are those first introduced, we believe, 

 by Grassmann. A full statement is given of the funda- 

 mental hypotheses, and the treatise consists of two sec- 

 tions. The first, "Geometry of Figures in Motion," 

 naturally discusses the geometry of the straight line and 

 of the plane ; the second, " Geometry of Figures at 

 Rest." A collection of 737 exercises closes the book. 

 The following remark by M. Hou. 1 is deserving of a place 

 here : — " La tendance de la nouvelle e"cole a remplacer le 

 raisonnement par le coup d'ceil nous semble e"minemment 

 dangeureuse. Le sentiment de la forme est un prdcieux 

 auxiliaire, auquel les illustres inventeurs de la geome"trie 

 pure ont du une grande partie de leurs decouvertes : mais 

 rien en mathe"matiques ne peut dispenser de la demon- 

 stration, d'autant plus que cette partie de la tache est en 

 general la plus aisde. Dans le cas actuel, la marche 

 d'Euclide n'est pas plus longue, et ne laisse aucun doute 

 dans l'esprit." 



The third volume, Rectilineal (or Plane) Trigonometry, 

 is founded, in like manner with the second, on a trea- 

 tise on the subject published by Grassmann in 1865. 



