528 



SCIENCE. 



[N. S. Vol. XI. No. 275 



it shall have been finished. It is the inten- 

 tion of your commissioners to make careful 

 studies of the material relating to beri-beri, 

 dysenterjr, malarial and typhoid fevers, 

 leprosy, and the bubonic plague, which has 

 been collected. These studies, with the ex- 

 ception of that relating to dysentery, will 

 be carried out upon preserved material, and 

 the labor involved, which has been divided 

 between Baltimoi-e and Philadelphia, will 

 necessitate that some time must elapse be- 

 fore the finished report is forthcoming. 

 The task of completing the study of the 

 bacillus isolated from cases of dysentery 

 has been assigned to Dr. Flexner, who 

 was principally engaged with that theme 

 during the residence in Manila. In order 

 to carry out the experiments as designed, 

 an outlay for experimental animals and 

 their maintenance will need to be made. 

 It is known to you that the original sum so 

 generously contributed by friends of the 

 University and appropriated for the use of 

 your commission has been exhausted, and 

 that private means have been drawn upon 

 to defray a part of the expense involved. 

 We would respectfully draw attention to 

 this fact and to the further expenses to be 

 incuri-ed, and request direction as to your 

 wishes regarding these matters. 



We wish to express our deep gratitude to 

 Messrs. Flint and Gay, whose untiring 

 efforts during our residence in Manila made 

 it possible to accomplish far more than we 

 could have done unaided. It is a pleasure 

 to acknowledge also many kindnesses on 

 the part of Mr. John W. Garrett. 



That we are deeply indebted to the oifi- 

 cers in the Medical Service of the U. S. 

 Army and N"avy for opportunities and aid is 

 evident from the report preceding. Courte. 

 sies and kindnesses extended by various 

 citizens of Manila, European and native, 

 are here also gratefully acknowledged. 

 Simon Flexner, 

 Lewellts F. Baekee. 



A POPULAR ACCOUNT OF SOME NEW FIELDS 

 OF THOUGHT IN MATHEMATICS* 



At the beginning of the nineteenth cen- 

 tury elementary arithmetic was a Freshman 

 subject in our best colleges. In 1802 the 

 standard of admission to Harvard College 

 was raised so as to include a knowledge of 

 arithmetic to the ' Eule of Three.' A boy 

 could enter the oldest college in America 

 prior to 1803 without a knowledge of a mul- 

 tiplication table. t From that time on the 

 entrance requirements in mathematics were 

 rapidly inci-eased, but it was not until after 

 the founding of Johns Hopkins University 

 that the spirit of mathematical investiga- 

 tion took deep root in this country. 



The lectures of Sylvester and Cayley at 

 Johns Hopkins University, the founding of 

 the American Journal of 3Iaihematics and the 

 young men who received their training 

 abroad co-operated to spread the spirit of 

 mathematical investigation throughout our 

 land. This led to the formation of the 

 American Mathematical Society eight years 

 ago as well as to the starting of a new re- 

 search journal. The Transactions of the Amer- 

 ican Mathematical Society, at the beginning of 

 this year. While these were some of the 

 results of mathematical activity, they, in a 

 still stronger sense, tend to augment this 

 activitj'. 



In Europe such men as Descartes, I^ew- 

 ton, Leibniz, Lagrange and Euler laid the 

 foundation for the development of mathe- 

 matics in many directions. These men, 

 as well as a few of the most prominent 

 in the early part of the nineteenth century, 

 were not specialists in mathematics. They 

 were familiar with all the fields of mathe- 

 matical activitj' in their day and some of 

 them were well known for their contribu- 

 tions in other fields of knowledge. The last 



* Eead at the regular winter term meeting of the 

 Alpha Chapter of Sigma Xi, Cornell University. 



t Cajori, The teaching and history of mathematics, 

 1890, p. 60. 



