948 



SCIENCE. 



[N. S. Vol. XI. No. 285. 



In the first place, the author has in several 

 instances failed to embody the latest fruits of 

 historical research. Thus, in connection with 

 the graphical representation of imaginaries he 

 fails to mention Wessel ; in speaking, of non- 

 Euclidean geometry he refers to Saccheri, but 

 not to Lambert and Taurinus ; in tracing the his- 

 tory of trigonometry he apparently overlooked 

 the researches of Suter and Braunmiihl, who 

 show that the Arabs distinguished themselves 

 by original work much more than was formerly 

 supposed ; he makes no mention of the Bakh- 

 shali manuscript, which throws considerable 

 light on early Hindu arithmetic. As a rule, the 

 facts presented are stated accurately. Among 

 the exceptions are the following : Athelard of 

 Bath is mentioned as the first translator of 

 Euclid from the Arabic into Latin, but there is 

 ground for the belief that earlier translations 

 existed. Boyer attributes to Benjamin Peirce a 

 research which seems to be due entirely to 

 Charles S. Peirce ; he misspells the name of 

 Crozet, the author of the first American text on 

 descriptive geometry ; he gives Antissa instead 

 of Antinoeia as the birthplace of Serenus. 



In the next place, the book is deficient be- 

 cause it does not trace the evolution of theories. 

 Something on the growth of mathematical ideas 

 we have a right to expect even in a short his- 

 tory. If the reader consults this work on the 

 introduction of the notion of infinity or of con- 

 tinuity, on the evolution of the theory of limits, 

 on the number concept, or on the foundations 

 of algebra, he will receive little satisfaction. 

 But these topics are all of vital importance in 

 elementary as well as in advanced mathematics. 

 Floeian Cajoei. 



Colorado College, Colorado Springs. 



Elementary Chemistry. For High Schools and 

 Academies. By A. L. Aeey, C.E., Eochester 

 (N. Y.) High School. New York, The Mac- 

 millan Co. 1899. 



The author has adopted the theoretically 

 ideal plan of forcing the student to note the 

 various features of chemical reactions without 

 any suggestion as to the phenomena which one 

 is expected to observe. Very few students 

 have cultivated and trained their power of ob- 

 servation, and one of the most advantageous 



purposes of the study of a science is to develop 

 this side of their nature. This can only be 

 done by teaching him what he sees and how he 

 should see it and thus gradually training his 

 powers of observation until he is able to ob- 

 serve new phenomena for himself and becomes 

 independent of the observations of others. 

 Several dangerous experiments are placed in 

 the early part of the book with no notice of the 

 precautions to be taken, and if this book was 

 put into the hands of an inexperienced worker 

 there would probably be disastrous results. 



J. E. G. • 



Laboratory Exercises with Outlines for the Study of 

 Chemistry, to accompany any Elementary Text. 

 By H. H. Nicholson, Professor of Chemistry 

 in the University of Nebraska, and S. Aveey, 

 Professor of Chemistry in the University of 

 Idaho. New York, Henry Holt & Co. 1899. 

 This book is intended as a laboratory guide 

 to be used in connection with a text-book. It 

 is well arranged and the descriptions are clear 

 and logical, and with conscientious use of a 

 reference book should produce the desired re- 

 sults. In cases where dangerous materials are 

 to be handled too much caution cannot be given. 

 In exercise 3 the student is directed to rub in a 

 mortar a piece of sulphur and a crystal of potas- 

 sium chlorate the size of a grain of wheat. One 

 who had never had experience with students 

 just beginning the study of chemistry would be 

 surprised at the dififerences of opinion as to the 

 size of a grain of wheat. 



J. E. G. 



School Chemistry. By Chas. Baskeeville, 



Ph.D. The University of North Carolina. 



Richmond, Va., B. F. Johnson Publishing 



Co. 1899. 



The author wrote this book for use in summer 

 schools for teachers. In attempting to cover the 

 whole field in a short course he has prepared a 

 work which will not give a student the necessary 

 foundation either for teaching the elements of 

 the subject or continuing its study with advan- 

 tage. A few subjects thoroughly understood 

 would probably be of more value than a little 

 knowledge of many, so far as its use by the class 

 of students for whom it is intended is concerned. 

 The author has no doubt supplemented it by 



