July 8, 1898.] 



SCIENCE. 



53 



foundatiou is laid for the teaching of the prin- 

 ciples and rules. 



In the teaching of algebra he would make 

 plain the theory of imaginaries, when the ex- 

 traction of the square root comes up ; and would 

 introduce an exposition of geometric quantity 

 before taking up the equation of the second de- 

 gree. He predicts that the day when the geo- 

 metric calculus will be introduced in the regular 

 course of instruction is not far off. In the con- 

 cluding chapter he deplores the too great cen- 

 tralization of mathematics in Paris to the injury 

 of the rest of France. 



In conclusion we recommend the volume to 

 the notice of every live mathematician, and to 

 every one interested in the nature of human 

 knowledge. Alexander Macfaelane. 



Elements of Comparative Zoology. By J. S. 



KiNGSLEY, S.D., Professor of Zoology in 



Tufts College. New York, Henry Holt & 



Co. 1897. 



This book of 357 pages embodies an attempt 

 to combine the text-book proper with the lab- 

 oratory manual in such proportions as to meet 

 the demand of the beginner. It is contended 

 in the preface that "a knowledge of isolated 

 facts, no matter how extensive, is of little value 

 in education, excepting as the powers of obser- 

 vation are trained in ascertaining those facts." 

 In accordance with this idea, the author lays 

 stress upon the more obvious features of the 

 types considered, and seeks to lead the student 

 to an intelligent appreciation of the significance 

 of those features in studies under the title of 

 'Comparisons.' For example, a bony and a 

 cartilaginous fish are studied separately, and 

 then the facts acquired by the student are cor- 

 related by a series of questions which require 

 a careful comparison. In this way twenty-flve 

 types are studied and compared, the types rep- 

 resenting all the main divisions of the animal 

 kingdom, and being chosen from the most 

 readily accessible materials. 



The text of the work is based upon the sys- 

 tematic relations and discusses the orders 

 seriatim. 



There is one detail of arrangement, however, 

 which will not appear to everybody to be en- 

 tirely happy. In the discussion of the fishes 



the Selachii and Teleosts are treated at some 

 length, and then follows the part bearing upon 

 Pisces. When one comes to the sub-classes he 

 is referred back to Selachii and Teleosts. This 

 may prove somewhat confusing, although the 

 motive is evidently to emphasize the groups of 

 which types have been studied. 



There are numerous illustrations and dia- 

 grams, the latter in many cases being particu- 

 larly suggestive. 



The part devoted to the laboratory work is 

 arranged in the form of simple directions for 

 dissection and questions to lead the student to 

 as independent a method as possible. The 

 criticism that will be forthcoming will be that 

 the laboratory work is meager — that students, 

 even in the high school, frequently want to 

 know more than the laboratory guide leads them 

 to. This, however, is a minor criticism, since 

 the teacher, if up to the mark, can supplement 

 the work according to his judgment. 



The introduction contains suggestions in re- 

 gard to the carrying on of laboratory work ; 

 apparatus, which is reduced to a minimum as 

 to both quantity and simplicity ; materials for 

 dissection, and reference books. 



The whole is a small, handy volume, neatly 

 bound and well printed on good paper. 



F. E. Lloyd. 



The Phytogeography of Nebraska. 1. General 

 Survey, by Roscoe Pound, PhD., Director 

 of the Botanical Survey of Nebraska, and 

 Frederic E. Clements, A.M., Assistant In- 

 structor in Botany in the University of Ne- 

 braska. Lincoln, Neb. 1898. 8vo., 329 pp., 

 with four maps. Presented by the authors to 

 the Faculty of the University of Nebraska as 

 a thesis for the degree of Doctor of Philoso- 

 phy. 



From the preface we learn that this work is 

 the result of nearly five years of active study of 

 the floral covering of Nebraska, carried on by 

 the members of the Botanical Seminar in the 

 Botanical Survey of the State. The systematic 

 study of the vegetation of Nebraska was begun 

 by Dr. Bessey in 1884, and has since been car- 

 ried on by him and his students, all previous 

 collecting having been more or less desultory 

 and unreliable. The Botanical Survey was or- 



