320 



SCIENCE 



[N. S. Vol. LI. No. 1317 



Eentals amounting- to $2,367,000 will go to 

 the university under the terms of a lease ar- 

 ranged by Levi L. Barbour, the Detroit manu- 

 facturer, with the stipulation that the money 

 shall be used for educating women of the Far 

 East. 



Cornell University has received a gift of 

 $100,000 for a new dormitory, to be named for 

 the donors' parents, from W. G. Mermen and 

 his sister, Mrs. Emma Mennon Williams, of 

 Detroit. 



Bates College is to receive $500,000 from 

 the fund to be raised by the Northern Baptist 

 Convention. 



On recommendation of the medical faculty 

 of Cornell University, women who are stu- 

 dents in medicine may hereafter take the first 

 year's work at the Medical College in New 

 York City. 



Professor Walter Edward McCourt, head 

 of the department of geology of Washington 

 University, has been appointed dean of the 

 schools of engineering and architecture of 

 Cornell University. He will assume the 

 duties of his new position at once. The ap- 

 pointment was made to fill the vacancy caused 

 by the resignation of Professor A. S. Langs- 

 dorf. 



Professor E. T. Bartholomew, of the de- 

 partment of botany of the University of Wis- 

 consin has accepted a research professorship 

 in the Graduate School of Tropical Agricul- 

 ture at Eiverside, Cal., in comieetion with the 

 University of California. His special work 

 will be the investigation of the diseases of 

 lemons and other citrus fruits. 



Sir Archibald E. Garrod has been ap- 

 pointed to be regius professor of medicine in 

 the University of Oxford in succession to the 

 late Sir William Osier. 



DISCUSSION AND CORRESPONDENCE 



MODERN INTERPRETATION OF DIFFER- 

 ENTIALS 



To the Editor of Science: Without at- 

 tempting to discuss the hist;orical questions in- 

 volved, I wdsh to iwint out that the theory of 



" diiierentials " given by Professor A. S. 

 Hathaway in Science for February 13, 1920, 

 would prove highly misleading to the modern 

 student. 



Professor Hathaway defijies A'y as N^y, 

 where N is some multiplier and Ay a simple 

 increment, and then defines dy as the limit of 

 A'y as Ay aipproaches zero. The inevitable 

 consequence of such a definition is that dy = 0, 

 which is obviously futile. 



In view of the continual recrudescence of 

 such fallacies (with or without a historical 

 background), it may be worth while to repeat 

 here the modern interpretation of the differen- 

 tial, though this may be found correctly stated 

 in any good test-book of calculus. 



Consider the graph of a function y==f(x), 

 with the tangent line drawn at the point 

 X = .Tj, y = 2/j. Give x an arbitrary increment 



which, since x is the independent variable, may 

 be denoted indifferently by Ax or dx. Corre- 

 sponding to any such increment in x we have 

 the increment of y, called Ay, extending up to 

 the curve, and the differential of y, called dy, 

 extending up to the tangent. Now when Ax 

 (or dx) is made to approach zero, the ratio 

 dy/dx remains constant, being the slope of the 

 tangent line, while the ratio Ay/ Ax is a vari- 

 aible, approaching the slope of the tangent as 

 a limit. But the limit of Ay taken by itself is 

 zero, and the limit of dy taken iy itself is 

 also zero. 



There are thus two very good reasons why 



