912 



SCIENCE. 



[N. S. Vol. XXIII. No. 598. 



proposed solutions upon wet and dry 

 tobaccos, always with satisfactory results. 

 James M. Bell. 

 BuKEAti OF Soils, 

 U. S. Department of Agkicultube, 

 Washington, D. C. 



SCIENTIFIC BOOKS. 

 Sur le developpment de I'analyse et ses rap- 

 ports avec diverses sciences. By Emile 

 PiCARD. Paris, Gauthier-Villars. 1905. 

 In this little volume of 167 pages Professor 

 Picard has republished the lectures which he 

 came to America to deliver at the decennial 

 celebration of Clark University in 1899 and 

 at the St. Louis Congress of Arts and Science 

 in 1904. The book thus has a special interest 

 for American readers, but quite apart from 

 this it will prove stimulating to all lovers of 

 mathematics who feel the need from time to 

 time of taking comprehensive views of the 

 great divisions of their subject under the 

 guidance of a master. 



Parts of these lectures give information of 

 a general character concerning some of the 

 most recent advances in such subjects as the 

 theory of differential equations and of alge- 

 braic functions of two variables, in both of 

 which fields M. Picard is one of the leading 

 workers. These sections, which necessarily 

 presuppose a considerable mathematical train- 

 ing on the part of the reader, have been 

 brought down to date by footnotes added 

 since the lectures were delivered. They would 

 be even more useful than they are if provided 

 with more precise bibliographical references. 

 Other sections will be found accessible to 

 readers of much less mathematical attainment, 

 and we can not indicate the kind of inspira- 

 tion and enjoyment to be derived from them 

 better than by giving a few typical quotations. 

 Without wishing to generalize too much, it may 

 be said that mistakes are sometimes useful, and 

 that during really creative periods an incomplete 

 or approximate truth may be more fruitful than 

 the same truth accompanied by the necessary re- 

 strictions (p. 5). 



After having explained that it is not always 

 wise to restrict one's attention to analytic 

 functions (that is to functions which may be 



developed by Taylor's theorem) in spite of the 

 fact that these functions are -in a certain 

 sense sufficiently general for all ' practical ' 

 purposes and that their theory forms an ele- 

 gant mathematical system complete in itself, 

 the author goes on: 



In general, let us admire highly systematized 

 theories, but let us distrust a little their scholastic 

 appearance which is in danger of stifling the in- 

 ventive impulse (p. 30). 



In speaking of the development of mechan- 

 ics in the eighteenth century the author says: 



Formal mathematical developments played at 

 tliat time the main part; and the language of 

 analysis was indispensable for the greatest de- 

 velopment of these principles. There are moments 

 in the history of science, and perhaps of society, 

 when the mind is upheld and carried forward by 

 the words and symbols which it has created, and 

 when generalizations present themselves with the 

 least effort (p. 131). 



True rigor is fruitful, and is thereby distin- 

 guished from another kind of rigor, purely formal 

 and tiresome, which casts a shadow on the prob- 

 lems which it touches (p. 148). 



Those who had the privilege of hearing M. 

 Picard when he was in America will miss 

 from this volume only the charm of the 

 spoken word, while finding there all the at- 

 tractive qualities of style for which the author 

 is so justly noted. 



Maxime Bochek. 



Harvard University. 



SCIENTIFIC JOURNALS AND ARTICLES. 

 The May number of the Botanical Gazette 

 contains the following papers : A. D. E. Elmer 

 contributes his third paper on ' New and Note- 

 worthy Western Plants,' describing numerous 

 new species from California; J. Y. Bergen 

 discusses certain strand plants about the Bay 

 of Naples, chiefly in reference to the toxic 

 effect of sodium chloride, and shows wide 

 variation in this regard; H. D. House de- 

 scribes with the help of illustrations new and 

 noteworthy North American species of clover; 

 Charles E. Lewis describes the basidium of 

 Amanita hisporigera, having traced the nu- 

 clear divisions in connection with spore- 

 formation. The number closes with the usual 

 full review of current literature. 



