June 26, 1913] 



NATURE 



421 



tains extracts from numerous workers, and, owing 

 to the limited time available, the portion relating 

 to the internal anatomy has been taken entirely 

 from Stephens and Christophers's work on malaria, 

 &c. The bionomics and natural enemies are next 

 considered, and prove extremely interesting and 

 instructive, much original work having been per- 

 formed, especially in connection with the former 

 subject. A few pages on technique follow, 

 and we then reach the part dealing with the 

 relation of mosquitoes to man. This, of necessity 

 a somewhat lengthy contribution, covers some 130 

 pages, and deals successively with the carrying of 

 disease by mosquitoes in general, malaria, yellow 

 fever, dengue, filariasis, suggested relations 

 with other diseases, and the effect of mosquito 

 bites. 



Under malaria an account is given of the 

 organisms concerned in its production, and of 

 the demonstration of its carriage ; thirty-three 

 species of Anopheles, some of doubtful validity, 

 being cited as transmitters. The general biology 

 of the Anopheline mosquitoes is also satisfactorily 

 dealt with, and the section concludes with refer- 

 ence to the distribution, appearance, and dis- 

 appearance of the disease. Yellow fever is treated 

 on similar lines, the bionomics of the mosquito, 

 under the name of Aedes calopus, being con- 

 sidered in great detail. As regards filariasis, 

 lourteen species are enumerated, and have appar- 

 ently been directly incriminated as transmitting 

 agents. 



More than one hundred pages are devoted to 

 the consideration of economic loss from mos- 

 quitoes, the subject being discussed in relation to 

 disease, real estate, and agriculture. Under this 

 section, too, we find references to the flight and 

 transportation of these flies, and lastly an exhaus- 

 tive treatise on protective and remedial work in 

 connection with mosquitoes generally. The 

 volume concludes with numerous examples of 

 mosquito control and an extensive bibliography. 



Vol. ii. is devoted exclusively to plates. These 

 deal with the structure of the male genital organs 

 of a large number of species, the wings of certain 

 Anophelines, and the earlier stages in the life- 

 cvcle. Illustrations are g'iven of numerous species 

 of larva;, including no fewer than fiftv-nine plates 

 relating to their detailed structure. Many of the 

 plates are beautifully executed, and the authors 

 are to be congratulated upon the production of this 

 volume, which points out very clearly the large 

 amount of original work performed. 



The work will undoubtedly prove a most valu- 

 able addition to the literature of the subject, and 

 will be heartily welcomed by all who are interested 

 in these noxious insects. 



XO. 22/8, VOL. 91] 



_L u 



TWO FRENCH MATHEMATICAL BOOKS. 



(1) Notions tic Mathdmatiques. By Prof. A. Saintc- 

 Lague. Avec Preface de Prof. G. Kcenigs. 

 Pp. vii + 512. (Paris: A. Hermann et Fils, 

 1 9 1 3.) Price 7 francs. 



(2) Proprictis Cindmatiques Fondamentales des 

 Vibrations. By M. Guillet. Notes de Dr. M. 

 M. Aubert. Pp. 405. (Paris : Gauthier- 

 Villars, 1913.) Price 16 francs. 



HE development of mathematical teachi- 

 ng in this country has been greatly 

 influenced during the last decade by foreign 

 methods. For this, if for no other reason, English 

 teachers will do wisely to watch the evolution of 

 these methods, and this can most easily be done 

 by studying the tendencies of recent text-books. 



M. Sainte-Lague's work on the elements of 

 mathematics is one which will repay such study. 

 Unlike the majority of school-books dealing with 

 this subject, it is not intended for the beginner, 

 but aims at giving a condensed account of results 

 and processes essential to those who have to use 

 mathematics in simple practical applications. 



The book is divided into four parts, devoted 

 respectively to arithmetic, algebra, trigonometry, 

 and geometry. Those principles which are con- 

 tinually used in practical applications are kept 

 to the front, and exercises which merely require 

 skill in manipulation are generally excluded. Thus 

 the algebra contains no reference to permutations 

 and combinations, and the binomial and exponen- 

 tial theorems are left to a more advanced stage. 

 On the other hand, the use of logarithms and of 

 the slide rule is explained, and the section on 

 arithmetic contains a valuable chapter on errors 

 and approximate calculations. 



It is remarkable that, although the derived func- 

 tion is used and defined, no use is made of the 

 classical notation of the differential and integral 

 calculus. In the section on trigonometry the dis- 

 cussion of the inscribed and circumscribed circles 

 is omitted, and the solution of triangles is com- 

 pressed into a very few pages. One or two results 

 of spherical trigonometry are included. 



The book works throughout in grades, instead 

 of degrees; to the English reader this will cer- 

 tainly prove a stumbling-block. The grade has 

 never won recognition outside France, and has not 

 displaced the degree for astronomical purposes. 



The section on geometry is the longest in the 

 book. Space geometry is introduced very early. 

 The method of superposition is employed through- 

 out, and the theory of parallels is based on the 

 notion of the motion of translation of a rigid body. 

 Although, according to the best authorities, this 

 I may be faulty from the logical point of view, it 



