August 4, 1916] 



SCIENCE 



173 



for a final decision; the former for a much- 

 needed rule as to whether or not " a generic 

 name is to be considered identical whether the 

 ending is masculine, feminine or neuter " if 

 from the same root; the latter for an official 

 opinion as to whether a lapsus calami does or 

 does not exist in the case of LibeU[ula] amer- 

 icanus Drury. 



In the meantime we feel that our action is 

 as clear and consistent as is possible, our aim 

 being to follow the official decisions of the 

 International Code, and, in cases where ac- 

 tion has not as yet been taken, to follow that 

 course which, after careful consideration, we 

 believe most likely to coincide with the later 

 rulings of that body. 



We naturally do not relish our work being 

 used as a striking illustration of the hopeless- 

 ness of unanimity among systematists on 

 nomenclatorial matters, but we could hardly 

 hope for a less gloomy viewpoint from one of 

 the authors of " The Entomological Code " the 

 first rule of which recommends in the vernac- 

 ular "everybody for himself." 



Morgan Hebaed 



Chestnut Hill, Pa. 



sylvester and cayley 

 On page 781 of the last volume of Sci- 

 ence there appeared a criticism relating to a 

 statement in my recent book entitled " His- 

 torical Introduction to Mathematical Litera- 

 ture." The statement in question seems to be 

 the following : " Cayley and Sylvester were 

 students at Cambridge at the same time and 

 formed then a lifelong friendship," which ap- 

 pears on page 259. In view of the fact that a 

 " colossal error " is said to have been com- 

 mitted it may be of interest to compare the 

 given sentence with the following quotation 

 from the third edition, page 484, of " A Short 

 Account of the History of Mathematics," by 

 W. W. E.Bali: 



He (Sylvester) too was educated at Cambridge, 

 and while there formed a life-long friendship with 

 Cayley. 



The same statement appears in the fifth edi- 

 tion (1912) of Ball's " History " and an equiv- 

 alent form of it is found in the reviewed and 



augmented French translation of the third edi- 

 tion. 



The fact that Ball has been connected with 

 Trinity College, Cambridge, for a long time 

 and that he was Fellow of this college during 

 many years while Cayley was professor in the 

 University of Cambridge led me to place more 

 confidence in the given statement as a reliable 

 historical fact than I should otherwise have 

 done. While I do not now recall all the evi- 

 dence at hand when writing the sentence 

 which has been the subject of said criticism, it 

 appears to me that the given evidence is suffi- 

 cient to warrant this sentence until it can be 

 proved that this evidence is unreliable. 



G. A. Miller 



University of Illinois 



SCIENTIFIC BOOKS 



Fundamental Conceptions of Modern Mathe- 

 matics, Variables and Quantities, with a 

 Discussion of the General Conception of 

 Functional Relation. By Bobert B. Eich- 

 ardson and Edward H. Landis. Chicago and 

 London, The Open Court Bublishing Com- 

 pany, 1916. Fp. xxi + 216. 

 According to the announcement near the end 

 of the present volume " that portion of ' Fun- 

 damental Conceptions of Modern Mathe- 

 matics ' dealing with algebraic mathematics 

 will consist of thirteen parts." The volume 

 under review is Part I. and has as subtitle 

 " Variables and Quantities with a Discussion 

 of the General Conception of Functional Eela- 

 tion." The magnitude of this undertaking and 

 the fundamental character of the questions 

 considered combine to direct unusual attention 

 to the project, and hence the present volume 

 is of interest not only on its own account, but 

 also on account of the hopes or fears it may 

 inspire as regards the remaining volumes of 

 the projected series. 



A striking feature of this volume, which will 

 doubtless create at the start an unfavorable 

 impression on many mathematical readers, is 

 the somewhat harsh criticism of some of the 

 work of many eminent mathematicians, in- 

 cluding Baire, Bauer, Pringsheim, Eiemann, 

 Eussell, Weber, and many others. For in- 



