July 23, 1915] 



SCIENCE 



129 



Among the special essays may be mentioned 

 the following : " Napier and the Invention of 

 Logarithms," by Professor Gibson, of Glas- 

 gow, perhaps the best essay which has ap- 

 peared upon the great Scotch mathematician; 

 " Notes on the Special Development of Cal- 

 culating Ability," by Dr. W. G. Smith, an 

 excellent summary of the history and psychol- 

 ogy of the subject ; " Calculating Machines," 

 by F. J. W. Whipple, a description of the 

 standard engines of calculation written from 

 the standpoint of the practical computer and 

 elaborating the descriptive catalogue prepared 

 for the Fifth International Congress of 

 Mathematicians in 1912 ; " The Calculating 

 Machine of the East: the Abacus," by Dr. C. 

 G. Knott, the efficient secretary of the Royal 

 Society of Edinburgh, and one of the prime 

 movers in the Napier Celebration — a classical 

 essay upon the subject and one which has been 

 out of print for nearly thirty years ; " The 

 Slide Rule," by Dr. G. D. C. Stokes, a his- 

 torical review of the various types of these 

 instruments ; " Integraphs," by Charles 

 Tweedie ; " Integrometers," " Planimeters " 

 and " Harmonic Analysis," by Dr. G. A. Carse 

 and Mr. J. Urquhart ; " Integrating Machines 

 in Naval Architecture," by A. M. Robb ; " A 

 Differentiating Machine," by Dr. J. Erskine 

 Murray ; " Tide-predicting Machines," by 

 Edward Roberts; "A Mechanical Aid in Pe- 

 riodgram Work," " A Mathematical Descrip- 

 tion of Conies " and " The Instrumental Solu- 

 tion of Numerical Equations," by D. Gibb; 

 " Ruled Papers," by E. M. Horsburgh ; " Col- 

 linear-point Nomograms," by Professor 

 D'Ocagne ; " Mathematical Models," by Pro- 

 fessor Crum Brovra ; and " Closed Linkages," 

 by Colonel R. L. Hippisley. Besides these 

 v'^ssays, numerous shorter notes appear, all of 

 thf.m written by experts in their fields. 



A catalogue of the mathematical portraits 

 in the \?ollection of W. W. Rouse Ball, the well- 

 known writer on the history of mathematics, 

 will prove of value to all collectors. 



It is impossible in the space at our disposal 

 to speak in detail of any of the essays, sev- 

 eral of them profusely illustrated and all of 

 an authoritative nat-K'p. Suffice it to say that 



the book should be in every mathematical li- 

 brary and workshop as being the most valuable 

 treatise of its kind that we have in English, 

 and, indeed, about the only one in any lan- 

 guage except such as is found in the articles 

 in the German encyclopedia. 



David Eugene Smith 

 Teachers College, 

 Columbia Univeesity 



Die Elemente der Bntwicklungslehre des Men- 



schen und der Wirheltiere. Anleiiung und 



Repetitorium fur Studierende und Aerzte. 



Von Oscar Heetwig. 5te Auflage. Jena, 



Gustav Fischer, 1915. Pp. x-f464. 416 figs. 



This work, already well known through 



former editions, must be regarded as among 



the opera minora of its distinguished author. 



It is professedly a utilitarian text-book, and 



discussions not adapted to " comprehensive 



brief presentation, suitable for a text-book," 



have been omitted. For further information. 



Professor Ilertwig appropriately refers the 



student to his "Lehrbuch," ninth edition, his 



"Allgemeine Biologic," fourth edition, and 



the imposing " Handbueh der Entwickelungs- 



geschiehte der Wirheltiere," which he edited 



and to which he contributed important 



chapters. 



The fourth edition of the "Elements" was 

 published in 1910 and the present volume, al- 

 though reset throughout, contains only minor 

 changes — chiefly such as are designed to make 

 the book more useful to students of medicine. 

 Except that Hochstetter's series of diagrams 

 of the development of the vena cava inferior 

 has been replaced by KoUmann's drawings of 

 the same subject, all the figures in the last edi- 

 tion have been republished. To these are 

 added sixteen others, eight of which show 

 young human embryos and their adnexa, three 

 illustrate cleft palate, two pertain to the vas- 

 cular system, and the remaining three repre- 

 sent the tunica vasculosa leniis, the human 

 branchial region and one of Keibel's models of 

 the urogenital tract, respectively. None of the 

 new figures is original, for Professor Hertwig 

 is not of those who, on seeing a good drawing, 

 make another much like it to be called their 

 own. He prefers to present to the students a 



