August 4, 1910] 



SCIENCE 



175 



little about the mathematical literature. For 

 instance, we find on page 33 of the present 

 volume the statement that mathematical works 

 afford no reply to the question which of the 

 ordinary complex numbers should be regarded 

 as positive and which as negative. The fact 

 is that the terms positive and negative are 

 commonly applied only to real numbers and 

 the reviewer does not see an advantage result- 

 ing from the use of these terms in connection 

 with complex numbers as proposed by the 

 authors of this volume. For a very elementary 

 generalization of the terms positive and nega- 

 tive numbers we may refer to volume 15 (1908) 

 of the American Mathematical Monthly, page 

 115. 



As regards form the volume under review 

 could have been made more useful by the addi- 

 tion of headings of sections. If the series is 

 continued it is to be hoped that the future 

 volumes will be improved along this line as 

 well as along the line of more complete refer- 

 ences and less prolixity in the development of 

 the special views of the authors. "While the 

 many shortcomings of the present volume have 

 forced the reviewer to the conclusion that the 

 series will be used by only a small number of 

 mathematicians unless the future volumes 

 should exhibit a marked improvement over the 

 one before us, he recognizes the need of a 

 scholarly work on the general subjects selected 

 by the authors of this volume, and he would 

 like to hope that the later volumes of the 

 series may tend to fill this want. 



G. A. Miller 



University of Illinois 



Harvey's Views on the Use of the Circulation 

 of the Blood. By John G. Curtis. Colum- 

 bia University Press, ISTew York, 1915. 8vo. 

 Pp. 194, 4 pis. 



It is a great source of inspiration to feel 

 that one belongs to a goodly company possess- 

 ing a common ideal and a common interest. 

 What enthusiasm is aroused in us by a great 

 International Congress of scientists! Here 

 the appeal is made to our social sense, but 

 there is a second powerful appeal, that to our 

 historic sense. This comes when we realize 

 that we of to-day are but the visible part of 



a long line of precursors who have been our 

 teachers and the teachers of our teachers and 

 have handed down through the ages the enthu- 

 siasm for knowledge and truth which we con- 

 sider our dearest heritage. Just as none of us 

 can afford to be provincial, so none of us can 

 afford to neglect the history of scientific 

 thought. That would be to affirm the impor- 

 tance of evolution in theory while denying it 

 in practise. 



At this time when proper international rela- 

 tions are interrupted it is a solace to turn from 

 the present to the past and to strengthen our 

 acquaintance with the illustrious scientists 

 of former times. This is especially desirable 

 when we can do so in the company of one 

 whose familiarity with ancient viewpoints 

 makes him a competent expounder of that 

 which time has rendered obscure. 



The theme of Professor Curtis's book is 

 clearly stated in the title. To make Harvey's 

 views intelligible to us we are introduced to 

 the illustrious ancients from whom, next to 

 nature, Harvey drew most of his learning or 

 who colored learned opinion in Harvey's time. 

 Harvey's importance as a discoverer has long 

 been recognized, but for a lucid explanation of 

 his place in the history of scientific thought 

 we have waited for this book. Our sincere 

 thanks are due to Professor Lee, who has com- 

 pleted and published the manuscript left by 

 Professor Curtis. 



Nutrition. — According to Aristotle and 

 Galen (who borrowed the idea from Plato) 

 the parts feed themselves tranquilly from the 

 blood vessels, which act as irrigating ditches in 

 the garden. So why, asks Harvey, this rush 

 of such great quantities of blood through all 

 parts of the body? Although Harvey recog- 

 nized that such a mechanism as the circula- 

 tion was most useful in explaining intestinal 

 absorption in that it did away with the classic 

 belief that in the portal vessels there were two 

 currents, one carrying blood to the intestines 

 and the other carrying absorbed food to the 

 liver, still he could not believe that the sole 

 use of the circulation was the feeding of the 

 parts. 



Respiration. — In his quest of the meaning 



