600 



SCIENCE 



[Vol. LV, No. 1431 



Outlines of Certain Fields of Research: 



(a) "Foundations of geometry," by Professor 

 Oswald Veblen, Princeton University. 



(b) "Calculus of variations," by Professor 

 G. A. Bliss, University of Chicago. 



(It is frequently urged that college and univer- 

 sity teachers should be engaged in some form of 

 productive work, but many college instructors do 

 not knoTP promising lines of investigation and do 

 not know how and where to find the literature 

 which will inform them what has already been 

 done in various lines. A suggestion has been 

 made that the Assoeia.tion can do a valuable 

 service if on its programs and through the Amer- 

 ican Mathematical Monthly university teachers 

 map out for college teachers possible lines of 

 research growing readily out of college courses. 

 These papers afford a beginning of such sugges- 

 tions.) 



' ' Courses in mechanics for students majoring 

 in mathematics," by Professor E. V. Hunting- 

 ton, Harvard University. 



' ' Topology of three-dimensional manifolds in 

 three dimensions, ' ' by Professor Norman Miller, 

 Queen's University. 



' ' Functionality in mathematical instruction in 

 schools and colleges," by Professor E. E. Hed- 

 rick. University of Missouri. 



' ' An example in the inversion of upper limits 

 and bounds, ' ' by Professor Samuel Beatty, Uni- 

 versity of Toronto. 



"New mathematical periodicals," by Pro- 

 fessor G. A. Miller, University of imnois. 



' ' Proof of the fundamental theorem regarding 

 the length of a curve," Professor J. L. Synge, 

 University of Toronto, by invitation. 



At the business meeting the following officers 

 for 1922 were elected : 



President: E. C. Archibald, Brown University. 

 Vice-presidents: E. D. Carmiehael, University 

 of Illinois, and B. F. Finkel, Drury College. 



Trustees: L. P. Eisenhart, Princeton Univer- 

 sity; E. V. Huntington, Harvard University; 

 D. N. Lehmer, University of California; G. A. 

 Miller, University of Illinois; E. J. Wilczynski, 

 University of Chicago. 



The trustees elected to membership 58 indi- 

 vidual members and 4 institutional members. 



The financial report indicated an estimated 

 surplus of $240 on the year's business. 



The full proceedings of the meeting were 

 published in the Monthly for March, 1922. 

 W. D. Cairns, 

 Secretary-Treasurer 



THE AMERICAN MATHEMATICAL 

 SOCIETY 



The twenty-eighth annual meeting of the 

 society and the forty-eighth regular meeting of 

 the Chicago section were held at the Uni- 

 versity of Toronto on Wednesday and Thurs- 

 day, December 28-29, in affiliation with the 

 meetings of the American Association for the 

 Advancement of Science. The regular sessions 

 of the society were held on Wednesday, Presi- 

 dent Bliss occupying the chair, relieved by 

 Professors P. P. Smith and C. N. Haskins. On 

 Thursday morning there was held a joint 

 session with Sections B and C of the American 

 Association and the American Physical Society, 

 and on Thursday afternoon a joint session 

 with Section A and the Mathematical Associa- 

 tion of America. The attendance included 84 

 members. At the meeting of the council on 

 Wednesday, 61 persons were elected to mem- 

 bership in the society. 



At the annual election the following officers 

 and other membere of the Council were chosen : 

 Vice-presidents, R. D. Carmiehael and D. E. 

 Smith; secretary, R. G. D. Richardson; treas- 

 urer, W. B. rite; librarian, R. C. Archibald; 

 committee of publication, E. R. Hedrick, 

 W. A. Hurwitz, J. W. Young; members of the 

 Council, to serve until December, 1924, J. W. 

 Alexander, Henry Blumberg, L. L. Dines, F. R. 

 Sharpe, 



The total membership of the society is now 

 1,005, including 85 life members. The total 

 attendance of members at all meetings, includ- 

 ing sectional meetings, during the past year 

 was 420; the number of papers read was 175. 

 At the annual election 169 votes were cast. 

 The treasurer's report shows a balance of 

 $10,604.22, including the life membership fund 

 of $7,528.87. Sales of the society's publica- 

 tions during the year amounted to $3,222.16. 

 The library now contains 6,014 volumes, ex- 

 cluding 500 unbound dissertations. 



The program of the joint session of Thurs- 

 day morning was as follows : 



I. Atomic nuclei and extra-nuclear electronic 

 configuration, by Professor J. C. McLennan, retir- 

 ing vice-president of Section B. 



II. Symposium on quantum theory: for Sec- 

 tion C, Dr. R. C. Tolman; for the American Math- 

 ematical Society, Professor H. B. Phillips; for 



