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SCIENCE 



{N. S. Vol. XXX. ^o. 761 



The purpose of this book is stated at the 

 outstart by the author to be an attempt to 

 show biologists that a mathematical treat- 

 ment of biological problems may be in general 

 valid and useful. By such demonstration it is 

 hoped to lessen or eradicate " eine gewisse 

 Scheu " of such methods on the part of work- 

 ers in this field, which Przibram (in com- 

 mon with others) has observed. Both these 

 aims are certainly commendable, and this 

 book will undoubtedly aid — and in certain 

 quarters perhaps greatly aid — in their realiza- 

 tion. 



The general plan of the book, which is an 

 outgrowth of a series of lectures given in the 

 University of Vienna, is to present first in an 

 introductory chapter certain general consid- 

 erations regarding the scope, the limitations, 

 the necessity for and the practical usefulness 

 of mathematical methods in biological in- 

 vestigation. There follows a series of chap- 

 ters intended to show how the general prin- 

 ciples brought out in the introductory 

 chapter apply in the study of specific, con- 

 crete, biological problems. In the practical 

 working out of this scheme it results that the 

 introductory chapter, with the title " Mog- 

 lichkeit mathematischer Biologic," is by long 

 odds the best in the book. The arguments for 

 the possibility, and indeed necessity, of a 

 mathematical biology are stated very clearly, 

 incisively and convincingly. To be sure, such 

 arguments have been as well stated before, but 

 it is encouraging, and augurs well for the 

 wider acceptance of these ideas, that this 

 time they are presented by a biologist von 

 Fach, not by a mathematician. 



The special chapters (H. to IX. inclusive) 

 deal with a variety of general biological prob- 

 lems from the standpoint noted above. 

 Chapter H. (Eaum) discusses the interrela- 

 tions between cell and nuclear volume and 

 surface. Chapter III. (Zeit und Gesehwindig- 

 keit) deals primarily with growth and in par- 

 ticular with rate of growth. Chapter IV. 

 (Energie) has as its chief topic the tempera- 

 ture coeiEcients of various biological phe- 

 nomena. Gleichgewicht is the title of Chapter 

 V. and it deals with certain quantitative as- 



pects of regeneration and molting in arthro- 

 pods. The next chapter has for its title 

 Chance and for its biological topic the dis- 

 tribution (right or left) of asymmetry of the 

 chelae in certain Crustacea. As a supplement 

 to this chapter there is a brief discussion of 

 sex as a " chance " phenomenon. Chapter 

 VII., under the title Kombinationen, deals 

 with the segregation and recombination of 

 characters in Mendelian inheritance. Varia- 

 tion und Selektion are briefly discussed in the 

 next chapter. Chapter IX. deals in an ele- 

 mentary way with psychophysics, particular 

 attention being given to the Weber-Fechner 

 law. A curiously ill-assorted and incomplete 

 bibliography ends the volume. The author 

 states in the preface that the bibliography is 

 not complete. How superfluous this remark 

 is is indicated, for example, by the fact that 

 Pearson's name does not appear at all except 

 as an associate editor of Biometrika, and that 

 Weldon is known only by his 1898 British 

 Association address. Whatever one's opinion 

 may be as to the importance of Pearson's 

 work, it certainly is a fact that he has con- 

 tributed extensively to the subject with which 

 this book has to do, viz.. the application of 

 elementary mathematics to biological prob- 

 lems. That Przibram is aware of this fact 

 appears definitely in the text. To cite Pear- 

 son's fundamental papers in the bibliogra- 

 phy would seem only common justice to the 

 reader. 



The discussions in these special chapters are 

 in every case suggestive. They are, however, 

 neither exhaustive nor thorough. But since 

 they were obviously not intended to be they 

 perhaps can not fairly be criticized on this 

 ground. The greatest weakness of these chap- 

 ters, to the reviewer's way of thinking, is that 

 the standpoint is too exclusively abstract and 

 too little concrete and quantitative. Biology 

 needs definite, quantitative data bearing on its 

 problems, much more than it does theoretical 

 abstractions, even though these be mathemat- 

 ical in form. Of course it is not to be ex- 

 pected that measurements or statistics will be 

 presented in a general work of this character; 

 but it is reasonable to ask that the general 



