510 



SCIENCE 



[N. S. Vol. XLIV. No. 1136 



The twenty-fifth anniversary of the broadening 

 out of the society into a national organization and 

 the founding of the Bulletin were celebrated at 

 the banquet on Monday evening, at which eighty- 

 four members and friends were present. Brief 

 addresses were made by Professors Piske, W. W. 

 Johnson, Pine, Birkhoff, Hedriek, Webster, Cool- 

 idge and the secretary. 



On Tuesday evening Professor D. E. Smith en- 

 tertained the society with an interesting account 

 of ' ' The relation of the history of economies to the 

 history of arithmetic problems." 



The following papers were read at the summer 

 meeting : 



J. C. Pields: "Direct derivation of the com- 

 plementary theorem." 



C. A. Pischer: "Note on the order of continuity 

 of functions of lines. ' ' 



Olive C. Hazlett: "On the theory of associative 

 division algebras." 



W. C. Eells: "A statistical study of eminent 

 mathematicians. ' ' 



J. L. Coolidge : ' ' The characteristic numbers of 

 real algebraic plane curves." 



B. W. Burgess: "The comparison of a certain 

 case of the elastic curve with its approximation. ' ' 



G. A. Miller: "Orders of operators of congru- 

 ence groups modulo 2 r 3s. ' ' 



John Eiesland: "Sphere geometry (third 

 paper)." 



A. J. Kempner : ' ' Generalization of a theorem 

 on transcendental numbers. ' ' 



C. N. Moore : ' ' On the developments in Bes- 

 sel 's functions. ' ' 



Arnold Dresden : ' ' Supplementary note on the 

 second derivatives of an extremal integral." 



L. E. Dickson : ' ' Extension of the theory of 

 numbers to the rational numbers of certain sets." 



A. G. Webster: "On a theory of acoustic 

 horns. ' ' 



E. H. Moore: "On properly positive Hermitian 

 matrices. ' ' 



L. P. Eiseuhart: "Deformations of transfor- 

 mations of Ribaucour. ' ' 



P. R. Sharpe and Virgil Snyder: "On (2 — 2) 

 point correspondence between two planes. ' ' 



P. H. Saff ord : ' ' Surfaces of revolution in the 

 theory of Lame" 's products. ' ' 



Dunham Jackson: "Note on the parametric rep- 

 resentation of an arbitrary continuous curve. ' ' 



Dunham Jackson: "Note on representations of 

 the partial sum of a Pourier series." 



L. H. Bice: "Determinants of many dimen- 



L. B. Ford : ' ' Regular continued fractions. ' ' 



M. W. Haskell: "The eliminant of a system of 

 forms. ' ' 



E. V. Huntington: "A simple substitute for 

 Duhamel's theorem." 



E. V. Huntington and J. R. Kline: "Sets of in- 

 dependent postulates for betweenness. ' ' 



G. D. Birkhoff: "Dynamical systems with two 

 degrees of freedom (second paper)." 



E. B. Van Vleck: " Non-loxodromie substitu- 

 tions in n variables. ' ' 



L. I. Hewes: "Nomograms of adjustment." 



H. C. M. Morse: "A theorem on the linear de- 

 pendence of analytic functions of a single vari- 

 able. ' ' 



G. A. Pfeiffer: "Note on the linear dependence 

 of analytic functions. ' ' 



G. M. Green: "On the linear dependence of 

 functions of one variable." 



C. L. Bouton: "Iteration and group theory." 



G. M. Green: "On the general theory of sur- 

 faces. ' ' 



W. V. Garretson: "On the asymptotic solution 

 of the non-homogenous linear differential equation 

 of the nth order. A particular solution. ' ' 



Caroline E. Seely: "On series of biorthogonal 

 functions. ' ' 



A. B. Prizell: "Lemma for a new method of 

 generating alephs. ' ' 



John Eiesland : ' ' Transformation theory of the 

 flat complex and its associated line complex. ' ' 



A. B. Schweitzer: "On the type of quasi-transi- 

 tive functional equations (second paper)." 



A. R. Schweitzer: "A problem in quasi-transi- 

 tive functional equations. ' ' 



A. R. Schweitzer: "Some theorems on quasi- 

 transitive functional equations. ' ' 



A. R. Schweitzer: "On the analogy between 

 functional equations and geometric order rela- 

 tions. ' ' 



T. H. Gronwall : ' ' On the power series for log 



(1+2)." 



T. H. Gronwall : "A problem in geometry con- 

 nected with the analytic continuation of a power 

 series. ' ' 



T. H. Gronwall: "On the convergence of Bi- 

 net's factorial series for log T(z) and \j/ (#)." 



T. H. Gronwall : ' ' On the zeroes of the function 

 /3(^) associated with the gamma function." 



The next meeting of the society will be held at 

 Columbia University on Saturday, October 28. 

 The Southwestern Section will meet at the Uni- 

 versity of Kansas on Saturday, December 2. 

 P. N. Cole, 

 Secretary 



