June 11, 1920] 



SCIENCE 



593 



women for degrees in the university. The 

 Cambridge University Syndicate appointed 

 to consider the question is divided in opinion; 

 half have reported in favor of admission to 

 full membership, and half in favor of a 

 separate university at Cambridge. 



Dr. David Kinley, professor of economics 

 and dean of the graduate school of the Uni- 

 versity of Illinois, has been elected president 

 to succeed Dr. Edmund Janes James. 



Dr. Lauder W. Jones, dean of the School 

 of Chemistry and also of the College of 

 Engineering and Architecture of the Univer- 

 sity of Minnesota, has accepted an appoint- 

 ment as professor of organic chemistry at 

 Princeton University. 



Alice M. Boring, of the Peking Union 

 Medical College, China, has been appointed 

 assistant professor of zoology at Wellesley 

 College, beginning with the academic year 

 1920-21. 



Dr. Ellswoeth D. Elston, of Cornell Uni- 

 versity, has been appointed assistant professor 

 of geology at Dartmouth College. 



Associate Professor J. Wemyss Anderson, 

 has been appointed to the recently established 

 John William Hughes Chair of Engineering 

 Refrigeration at Liverpool University. 



DISCUSSION AND CORRESPONDENCE 



MODERN INTERPRETATION OF DIFFER- 

 ENTIALS AGAIN 



To THE Editor of Science : I regret that in 

 my criticism (Science, March 26) of Pro- 

 fessor Hathaway's exposition of differentials 

 (Science, February 13) I was led by an un- 

 wise desire for brevity into making a state- 

 ment which, in its unqualified form, will not 

 stand analysis. The statement that " lim NAy 

 is inevitably zero " is certainly not true un- 

 less N remains finite, and Professor Hathaway 

 is quite justified (Science, May 7) in chiding 

 me for this error, since his N is not restricted 

 to finite values. 



At the same time I can not feel that I was 

 essentially mistaken in contending that his 

 presentation of differentials " would prove 

 highly misleading to the modern student." 



It is true that when he defines the differ- 

 ential dy as the limit of NAy for lim Ay = 0, 

 he does allow the multiplier N to vary (as 

 I should have stated) ; but it is also true that 

 he gives no indication whatever as to the 

 manner in which N is to vary; and without 

 some such indication his lim,it of NAy, and 

 hence his differential, dy, remain wholly 

 undefined! 



On page 167 (I quote verbatim this time, 

 to avoid the danger of renewed injustice), his 

 formal interpretation of differentials is given 

 as follows : they are " ordinary arithmetical 

 increments, but in a variation defined as in 

 the first ratio, or as the variables begin to 

 increase, or, in the instantaneous state, which 

 are all one." 



I maintain that such vague statements are 

 not likely to convey to any student's mind " a 

 rigorous theory, neglecting no quantity, how- 

 ever small, leaving no unexplained symbol." 

 They are much more likely to leave him with 

 the traditional impression that differentials 

 are really as Bishop Berkeley called them, the 

 " ghosts of departed quantities," or, in Pro- 

 fessor Osgood's phrase, abominable "little 

 zeroes," unworthy of a place in mathematical 

 discussion. 



The objeet of my brief letter was, as stated, 

 not to discuss historical questions (the im- 

 portance and value of which no one can 

 deny) but merely to contrast the obscurity of 

 Professor Hathaway's presentation with the 

 clearness and simplicity of the modern treat- 

 ment — the treatment which has been the com- 

 monplace of every treatise of recognized 

 standing since the middle of the nineteenth 

 century. 



Edward V. Huntington 



Harvard Univeksitt 



POPULAR scientific LITERATURE 



To THE Editor of Science: In the issues of 

 Science for Eebruary 20 and 27 Mr. F. L. 

 Ransome, of the U. S. Geological Survey, 

 published a most interesting article on the 

 " Functions and Ideals of a National Geo- 

 logical Survey." 



In this article, attention was given to the 



