June 2, 1922] 



SCIENCE 



601 



the American Physical Society, Dr. Saul Dushman. 

 The joint session on Thursday afternoon has 

 already been reported under Section A. 



The following papers were read at the regu- 

 lar sessions of the society- 



Differential geometry of an m-dimensional mani- 

 fold in a euclidean space of n dimensions: C. E. 

 Wilder. 



Differential geometry of an m-dimensional 

 manifold in a euclidean space of n dimensions. 

 Second paper: C. E. Wilder. 



A modification of Peano 's postulates for posi- 

 tive integers : M. H. Ingraham. 



Siemann geometry and its generalizations: 

 L. P. Eisenhart and Oswald Veblen. 



Tlie problem of apportionment. The method of 

 the loeighted geometric mean: E. W. Burgess. 



Necessary and sufficient conditions in the prob- 

 lem of apportionment: E. V. Huntington. 



Commutativity of contact transformations of 

 mechanics: S. D. Zeldin. 



Substitutions which are commutative with every 

 substitution of an intransitive group : G. A. Miller. 



Seeming contradictions in the theory of groups: 

 G. A. Miller. 



Convergence-factors in Cesdro-summable series: 

 W. A. Hurwitz. 



Note en the determination of the rectilinear sec- 

 ular trend of an ordered series of statistical rela- 

 tives: W. L. Crum. 



Provisions for depreciation based directly upon 

 appraisal: C. H. Forsyth. 



Plane algebraic curves invariant under a given 

 quadratic Cremona transformation: Arnold Emch. 



Canonical systems and the general problem of 

 dynamics: Joseph Lipka. 



Exder squares: H. P. MacNeish. 



The expression of general forms as determinants 

 whose elements are forms. Preliminary report : 

 H. S. Everett. 



The arithmetic mean of the least and greatest 

 of n measurements: E. L. Dodd. 



Convex distribution of the zeros of Stiirm-Liou- 

 ville functions: Einar Hille. 



On Kellogg 's diophantine problem: D. E. Cur- 

 tiss. 



The isodyadic quintic equation: J. S. C. 

 Glashan. 



On the isodyadic septimic equation: J. S. C. 

 Glashan. 



Criteria for relative root distributions: C. F. 

 Gunimer. 



The algebraic theory of algebraic functions: 

 Samuel Beatty. 



All algebraic proof of the existence of the 

 branches of an algebraic function: I. E. Pounder. 



On the determinant of an hermitian matrix of 

 quaternionic elements: E. H. Moore. 



Some properties of the surfaces which repre- 

 sent the real and imaginary components of a 

 function of a complex variable: E. J. Wilczynski. 



Note on differential invariants : O. E. Glenn. 



Hesse's associated points and the Weddle sur- 

 face: Louise D. Cummings. 



Some of the principles of the operation with 

 series applied to a partial fraction problem: I. J. 

 Schwatt. 



Expansion of powers of infinite series: I. J. 

 Schwatt. 



A symbolic theory of formal modular invari- 

 ants: Olive C. Hazlett. 



The equivalence of expansions in orthogonal 

 functions: Norbert Wiener and J. L. Walsh. 



The next meeting of the society was held in 

 New York City on February 25, this being the 

 only meeting held in New York during the 

 spring. 



R. G. D. Richardson, 



Secretary 



The two hundred and twenty-second regular 

 meeting of the American Mathematical Society, 

 being the seventeenth regular Western meeting, 

 and the forty-ninth regular meeting of the 

 Chicago Section, was held at the University of 

 Chicago on Friday and Saturday, April 14 and 

 15, 1922, in honor of the twenty-flfth anniver- 

 sary of the Chicago Section. The attendance 

 at these meetings was approximately one hun- 

 dred and fifty, and included one hundred and 

 four members of the society. 



At the meeting of the council, ten persons 

 were elected to membership in the society. 

 Professor A. B. Coble was reelected a member 

 of the editorial committee of the Transactions 

 for a term of three years, beginning October 1, 

 1922. 



The council accepted for the society the 

 trust of the Eliakim Hastings Moore Fund, 

 tendered through Professor Arnold Dresden, 

 chairman of the committee that had collected 

 the fund; this fund is to be used for the pub- 

 lication of mathematical books and memoirs, 

 and the award of prizes. In this connection 

 a pleasant feature was the presentation at the 

 dinner on Friday evening of a testimonial to 

 Professor Moore from his fonner students and 



