December 29, 1905.] 



SCIENCE. 



865 



On the other hand, for the non-technical stu- 

 dent it makes a readable account, but makes 

 it necessary for him to search long if he de- 

 sires to place his specimen. Whatever one 

 may think of the method. President Jordan 

 has used it with skill, and the result is an 

 account probably as attractive as such an ac- 

 count can well be made. Though it does not 

 ignore foreign fishes, it is of particular in- 

 terest to Americans, since it properly gives 

 preference to American forms. The author 

 has given us the cream of his long experience 

 and wide knowledge of American fishes and 

 has made it full and attractive. There is no 

 other account of the sort for American read- 

 ers. He has wisely treated the fossil fishes in 

 their proper sequence along with living fishes. 

 Many systematists will not agree with Presi- 

 dent Jordan concerning the general scheme of 

 classification adopted and in minor details, 

 but that is unavoidable and immaterial in a 

 book of this kind. 



The book is profusely illustrated with half- 

 tones of uniform excellence and with two 

 striking colored plates. Ichthyologists should 

 be especially grateful to Dr. Jordan for the 

 admirable portraits of their colleagues, past 

 and present. There is a valuable index, but 

 the intentional omission of all but a very few 

 references to the literature is to be regretted. 

 Such selected foot-note references as are to be 

 found in the ' Cambridge Natural History ' 

 occupy but little space and are of distinct 

 value, even to the expert. 



The publishers have given us a sightly page 

 with large clear type and serviceable bind- 

 ing. The proof-reader has been sometimes at 

 fault, though fortunately not often in the 

 technical terms. There may be noted only 



* construction ' for contraction (p. 28) ; ' mal- 

 lets ' for mullets (p. 32) ; ' himera ' for 

 Chimera (p. 43) ; ' neutral ' for neural (p. 56) ; 



* ethnoid ' for ethmoid (p. 113) ; ' Acanco- 

 cephala ' for Acanthocephala (p. 344). Other 

 errors will be readily detected by the reader. 

 In his chapter on mythology President Jordan 

 has, apparently by the omission of a deciraal 

 point, added a new myth in making the ' sea- 

 serpent' Begalecus 225 feet long (p. 361), but 



the measurement is correctly given in another 

 place. 



The book as a whole impresses the reader 

 as the work of a busy man. Where the author 

 has wandered from the narrower field of sys- 

 tematic ichthyology, with its attendant prob- 

 lems of distribution and external morphology, 

 he has sometimes fallen into vagueness or 

 error. Where he has depended on compilation 

 he appears usually to have used only the more 

 accessible and older English compendious 

 sources and has thus helped to a longer cur- 

 rency some errors that others had corrected. 

 Where, on the other hand, he has traversed 

 his own familiar ground he has supplied a 

 real need and supplied it admirably. In view 

 of the great merits of his work, as he has 

 himself said of the work of a,nother, we may 

 well ' pass by its faults with the leniency 

 which we may hope that posterity may bestow 

 on our own.' 



Jacob Eeighard. 



Lectures on the Calculus of Variations. By 

 OsKAR BoLZA. (The University of Chicago 

 Decennial Publications, Second Series, Vol- 

 ume XIV.) Chicago, The University of 

 Chicago Press. 1904. 8vo. Pp. xv + 271. 

 It is to be the function of the present gen- 

 eration of mathematical scholars in America 

 to set a standard in mathematical memoirs 

 and treatises which has been almost totally 

 lacking in this country. The mathematical 

 books which have heretofore appeared in 

 America have been with few exceptions of 

 text-book rank; it would be a generous esti- 

 mate which would allow the fingers of both 

 hands upon which to count books which woiild 

 not be within the range of college students in 

 undergraduate classes among the total mathe- 

 matical production of the United States. 

 There are several books in English, published 

 in England, which are available; but the 

 English school of mathematics has labored 

 under such a handicap of lax reasoning and 

 so-called ' general ' statement that many of 

 these can not be used with safety by one who 

 is not already a master of the subject treated. 

 It is, therefore, a very notable occurrence 

 when a mathematical work of really advanced 



