December 9, 1904.] 



SCIENCE. 



799 



On the whole, the author's aim seems to he 

 realized, although it takes over 200 pages. 

 The frequency polygon, as a whole, is properly 

 declared to be the unit of comparison which 

 its constants by no means fully replace. The 

 methods of determining the average, standard 

 derivation and probable error are fully set 

 forth and the explanation of the method of 

 calculating the coefficient of correlation is 

 particularly good. 



Great stress is laid — properly enough in a 

 book intended for psychologists whose ma- 

 terial is not always directly measurable — on 

 measurement by position and the transmuta- 

 tion of position into units of amount. Such 

 a transmutation is easily effected when the 

 frequency distribution is approximately nor- 

 mal. A little table, based on the table of the 

 normal probability integral, is given, showing 

 the deviation from the mean (in units of the 

 standard deviation) of each per cent, class 

 from 1 to 50. A handy table is also given 

 showing the average deviation of any number 

 of consecutive percentage classes. Of course, 

 there is nothing new in this, but it helps to 

 have the importance of the measure by rela- 

 tive position insisted on in a popular treatise 

 of this sort, because it is not popularly under- 

 stood. 



In treating the measure of differences em- 

 phasis is laid on the importance of comparing 

 the entire distributions rather than the aver- 

 ages only. The degree of overlapping of the 

 frequency polygons gives the best insight into 

 the degree of difference. 



Under ' Measurement of Relationships ' the 

 measurement of correlation is considered and 

 the' Pearsonian method of analysis is plainly 

 and fully set forth. In the' chapter on ' Re- 

 liability of Measures ' the determination of 

 the probable error of the average and of a 

 difference between two averages is fully de- 

 scribed. 



The book abounds in tables giving various 

 statistical data. There is appended a multi- 

 plication table up to 100X100; also a table 

 of squares and square roots. A table of the 

 normal probability integral (apparently copied 

 without credit from the reviewer's ' Statistical 

 Methods ') is found on page 148. A feature 



of the work is a set of ' Problems ' at the end 

 of each chapter. 



The reviewer has noted in passing several 

 defects which are mentioned here in order 

 that they may be guarded against in the 

 second edition. Part of Pig. 12 seems to be 

 inverted. The ' Mode ' is repeatedly spoken 

 of where empirical and not theoretical mode 

 is meant. The distinction should always be 

 clearly made. Also, the mode is not the 

 'apex of the slope' (p. 73), but the abscissa 

 of the apex. The method suggested of find- 

 ing the mode is unnecessarily clumsy. The 

 mode is approximately equal to the mean less 

 3 X (i^iean — median). Tables XXXI. and 

 XXXIL, the first value of o would seem to 

 be a misprint for 2.57. 



On the whole, we believe the book will be 

 found very useful, especially in making more 

 familiar the frequency polygon and leading 

 to its more frequent publication in statistics 

 in place of the bare average. And so we trust 

 that it will be widely studied and its recom- 

 mendations followed. 0. B. Davenport. 



American Hydroids. Part II. The Sertu- 

 laridw. With 41 plates. By 0. C. Nut- 

 ting. Special Bulletin, U. S. National 

 Museum. 1904. 



The first part of this magnificent work, on 

 the Plumularidse, appeared in 1900, and was 

 noticed at some length in our columns. Much 

 of what was said about Part I. is equally 

 applicable to Part II., and need not be re- 

 peated. Some idea of the value of the work 

 may be gained from the fact that not more 

 than 20 species of Sertularidte from American 

 waters have heretofore been discussed in any 

 single publication, and now Professor Nutting 

 presents us with complete descriptions and 

 figures of no less than 130! These species, 

 distributed by the author in ten genera, have 

 been named by the following writers : Nutting, 

 37; Allman, 16; Linnajus, 12; S. P. Clark, 9; 

 Kirchenpauer, 8; Hartlaub and Mereschkows- 

 ky, each 5 ; Ellis and Solander, Hincks, Trask, 

 d'Orbigny and H. B. Torrey, each 3 ; Levinsen, 

 Alder, Bale, Marktanner-Turneretscher, Mur- 

 ray and Lepechin, each 2 ; and J. E. Gray, 

 IfcCready, Versluys, Poeppig, Stimpson, Sars, 



