January 16, 1903.] 



SCIENCE. 



113 



Y.; Dr. A. G. Hall, University of Michigan; 

 Mr. E. L. Hancock, Purdue University; Pro- 

 fessor L. M. Hoskins, Stanford University; 

 Mr. W. D. A. Westfall, Tale University; Mr. 

 W. F. WHte, State Normal School, New 

 Paltz, N. T. Sixteen apislicants for ad- 

 mission to the society were received. 



At the annual election the following offi- 

 cers and members of the council were chosen : 



President, Thomas S. Fiske. 



Vice-Presidents, W. F. Osgood, Alexander 

 Ziwet. 



Secretary, F. N. Cole. 



Treasurer, W. S. Dennett. 



Librarian, D. E. Smith. 



Committee of Publication, F. N. Cole, Alexander 

 Ziwet, D. E. Smith. 



Memiers of the Council, to serve until December, 

 1905, James Harkness, Heinrich Masehke, Irving 

 Stringham, H. W. Tyler. 



The .report of the librarian shows that the 

 society's library, which was recently deposited 

 in the charge of the Columbia University 

 Library, is rapidly growing and already con- 

 tains nearly one thousand bound volumes. 

 The exchange lists of the Bulletin and the 

 Transactions now include about one hundred 

 and twenty mathematical journals, being 

 nearly all that exist. Many gifts have also 

 been received. It is hoped that the society's 

 collection may ultimately become the most 

 extensive one of the kind in the country. 

 Besides the mathematical journals of the 

 world, it is intended to include a full set of 

 mathematical Americana, thus making the 

 library a historical as well as m.athematieal 

 repository. 



A special feature of the annual meeting 

 this year was the presidential address. Under 

 the title : ' On the Foundations of Mathe- 

 matics,' the retiring president. Professor 

 Eliakim Hastings Moore, advocated the de- 

 sirability of the society exercising a more ef- 

 fective influence on the teaching of element- 

 ary mathematics. The address will appear 

 in Science. A committee was appointed by 

 the council to consider the questions involved. 



The following papers were read at the an- 

 nual meeting: 



E. V. Huntington: 'A complete set of postu- 



lates for the theory of real number ' ( second 

 paper ) . 



E. V. Huntington : ' On the definition of the 

 elementary functions by means of definite inte- 

 grals.' 



C. J. Keyseb : ' On the axiom of infinity.' 



G. H. Darwin : ' The approximate determina- 

 tion of the form of Maclaurin's spheroid.' 



Harris Hancock : ' Remarks on the sufficient 

 conditions in the calculus of variations.' 



L. E. Dickson : ' The abstract group simply 

 isomorphic with the alternating group on six 

 letters.' 



President E. H. Moore : Presidential Address, 

 ' On the foundations of mathematics.' 



W. E. Taylor : ' On the product of an alternant 

 and a symmetric function.' 



E. D. EoE : ' On the coefficients in the product 

 of an alternant and a symmetric function.' 



E. D. Roe : ' On the coefficients in the quotient 

 of two alternants (preliminary communication).' 



E. O. LovETT: 'A transformation group of 

 (2™ — 1 ) {n — 1 ) parameters, and its role in the 

 problem of n bodies.' 



I. E. Rabinovitch : ' On solid lunes of coni- 

 coids, analogous to the circular lunes of Hippo- 

 crates of Chios.' 



E. B. Wilson : ' The synthetic treatment of 

 conies at the present time.' 



A. B. Coble : ' On the invariant theory of the 

 counex (2, 2) of the ternary domain viewed as a 

 connex (1,1) in a five-dimensional space.' 



Edward Kasner : ' The general quadratic sys- 

 tems of conies and quadrics.' 



W. F. Osgood : ' On the transformation of the 

 boundary in the case of conformal mapping.' 



W. F. Osgood : ' A Jordan curve of positive 

 area.' 



Maximb Bochee : ' Singular points of functions 

 which satisfy partial differential equations of the 

 elliptic type.' 



J. W. \0UNG: 'On the automorphic functions 

 associated with the group of character [0, 3; 

 2, 4, 00 1 ' (preliminary report). 



R. W. H. T. Hudson: 'The analytic theory of 

 displacements.' 



H. E. Hawkes : ' Enumeration of the non- 

 quaternion number systems.' 



H. F. Stecker : ' On the parameters in certain 

 systems of geodesic lines.' 



G. D. BiRKHOFF and H. S. Vandivee : ' General 

 theory of the integral divisors of a" — 6", and 

 allied cyclotomic forms.' 



F. Morley: 'On the determinant | (a-,- — aj)—^\.' 



