116 



SCIENCE 



[N. S. Vol. XXXVII. No. 942 



Winger, University of Illinois. Sixteen applica- 

 tions for membership were received. 



At the annual election, which closed on Thurs- 

 day morning, the following officers and other mem- 

 bers of the council were chosen: 



President — E. B. Van Vleck. 



Vice-president — M. W. Haskell, B. 0. Peirce. 



Secretary — F. N. Cole. 



Treasurer — J. H. Tanner. 



Librarian — D. E. Smith. 



Committee of Publication — F. N. Cole, E. W. 

 Brown, Virgil Snyder. 



Members of the Council — F. G. Ferry, W. B. 

 Ford, E. C. Maclaurin, Jacob Westlund. 



The treasurer 's report shows a balance of 

 $9,684.92, including the life membership fund of 

 $4,483.69. Sales of publications during the year 

 amounted to $1,730.94. The total membership of 

 the society is now 680, including 64 life members. 

 The total attendance of members at all meetings 

 during the past year was 336, the number of papers 

 presented 179. The library shows a marked 

 growth, the number of catalogued volumes being 

 now 4,560. Much of the increase is due to the 

 generous gifts of several hundred volumes by Dr. 

 Emory McClintock and Dr. G. W. Hill, ex-presi- 

 dents of the society. 



The following papers were read at this meeting : 



E. D. Carmiehael: "On the numerical factors 

 of the arithmetic forms a» ± /3". ' ' 



E. D. Carmiehael: "On non-homogeneous linear 

 equations with an infinite number of variables. ' ' 



E. D. Carmiehael : ' ' Note on Format 's last 

 theorem. ' ' 



W. A. Hurwitz : ' ' Mixed linear integral equa- 

 tions of the first order. ' ' 



H. Galajikian: "On certain non-linear integral 

 equations. ' ' 



W. A. Hurwitz : "On Green 's theorem for the 

 plane. ' ' 



Arnold Emch : ' ' On some properties of closed 

 continuous curves. ' ' 



G. A. Miller: "The product of two or more 

 groups. ' ' 



J. E. Eowe: "Three or more rational curves in 

 collinear relation." 



F. E. Sharpe and F. M. Morgan : ' ' Quartic sur- 

 faces invariant under periodic transformations. ' ' 



H. M. Sheffer: "A set of postulates for the 

 Boolean algebra. ' ' 



J. R. Conner : ' ' The rational sextie curve and 

 the Cayley symmetroid. ' ' 



J. E. Conner: "Multiple correspondences deter- 

 mined by the rational space septimic. ' ' 



L. E. Dickson: "Finiteness of the odd perfect 

 and primitive abundant numbers with a given 

 number of distinct prime factors. ' ' 



L. E. Dickson : ' ' Amicable number triples. ' ' 



J. L. Coolidge: "A study of the circle-cross." 



G. A. Bliss: "The relation satisfied by two 

 dependent functions near a point at which both 

 are singular. " 



J. A. Eiesland : ' ' On the algebraic curves of a 

 tetrahedral complex and the corresponding sur- 

 faces conjugate to it." 



E. H. Moore: "On nowhere negative kernels." 



Daniel Buchanan : ' ' Oscillations near one of the 

 isosceles triangular solutions of the three-body 

 problem. ' ' 



Peter Field : ' ' On constrained motion. ' ' 



G. C. Evans : " On the reduction of certain types 

 of integro-dififerential equations. ' ' 



J. A. Caparo : ' ' Hyperspace and the non-euclid- 

 ean geometry of four dimensions. ' ' 



Jacob Westlund : ' ' On the factorization of ra- 

 tional primes in cubic cyclotomic number fields. ' ' 



E. L. Dodd: "An erroneous application of 

 Bayes 's theorem to the set of real numbers. ' ' 



E. L. Dodd: "The validity of Bertrand's ap- 

 proximation leading to the probability integral." 



Edward Kasner: " Equitangential trajectories 

 in space. ' ' 



C. J. Keyser: "Concerning multiple interpreta- 

 tions of postulate systems and the 'existence' of 

 hj'perspaces. ' ' 



E. J. Wilczynski: "On a certain completely in- 

 tegrable system of linear partial differential equa- 

 tions. ' ' 



L. C. Karpinski: "Algebra in the Quadripar- 

 titum numerorum of Johannes de Muris. ' ' 



L. C. Karpinski : ' ' Hindu numerals among the 

 Arabs. ' ' 



H. B. Phillips : ' ' Directed integration. ' ' 



Joseph Lipke: "Geometric characterization of 

 isogonal trajectories on a surface." 



J. B. Shaw: "Integral invariants of general 

 vector analysis. ' ' 



J. B. Shaw : "On non-linear algebras. ' ' 



D. E. Curtiss : ' ' Proofs of certain formulas sug- 

 gested by Laguerre's work in the theory of equa- 

 tions. ' ' 



Arthur Eanum: "On the projective differential 

 classification of ?i-dimensional spreads generated 

 by 00^ flats." 



I. M. Schottenf els : "Proof that there is but 

 one simple group of order 7!/2." 



L. P. Eisenhart: "Certain continuous deforma- 

 tions of surfaces applicable to quadrics. " 



E. V. Huntington: "A set of independent pos- 

 tulates for ' betweenness. ' ' ' 



A. B. Frizell : ' ' Some terms in the expansion of 

 the infinite determinant." 



T. H. Gronwall: "On Weierstrass 's preparation 

 theorem. ' ' 



T. H. Gronwall: "On series of spherical har- 

 monics (second paper)." 



Cora B. Hennel : ' ' Transformations and invari- 

 ants connected with linear homogeneous difference 

 equations and other functional equations." 



Harris Hancock : ' ' Problems in arithmetical 

 geometry. ' ' 



Harris Hancock: "Generalization of a theorem 

 due to Liouville or to Dedekind, with applications 

 to the geometry of numbers. ' ' 



W. D. MacMillan: "A proof of Wilczynski 's 

 theorem. ' ' 



W. D. MacMillan: "On PoincarS's correction 

 to Bruns 's theorem. ' ' 



