April 8, 1921] 



SCIENCE 



343 



1920, to December, 1921), Charlotteville, Virginia. 

 Professor D. E. Curtiss, Northwestern University, 

 will give the retiring address at Toronto (1921- 

 1922). 



A joint dinner for mathematicians and astron- 

 omers was given at the Quadrangle Club of Chi- 

 cago University on Wednesday evening, Decem- 

 ber 29. 



The following announcements concerning mem- 

 bers of Section A are of special interest: 



(1) Professor E. H. Moore, head of the depart- 



ment of mathematics of the University of 

 Chicago, was elected president of the 

 American Association for the Advance- 

 memt of Science. 



(2) Professor G. A. Bliss, of the University of 



Chicago, was elected president of the Ameri- 

 can Mathematical Society. 



(3) Professor G. A. Miller, of the University of 



Illinois, was elected president of the 

 Mathematical Association of America, and 

 member of the executive committee of the 

 council of the American Association for 

 the Advancement of Science. 



(4) The American Mathematical Society and the 



Mathematical Association of America were 

 invtited by the American Association for the 

 Advancement of Science to become affiliated 

 societies. As soon as these organizations 

 officially accept the offer to affiliate, they 

 will be represented on the council of the 

 association by their respective secretaries. 

 Professor R. G. D. Eichardson, of Brown 

 University, and Professor W. D. Cairns, of 

 Oberlin College. 

 At the sessions of the American Mathematical 

 Society on Wednesday afternoon and on Thurs- 

 day, the following papers were read: 



Construction of douhly periodic functions with 

 singular points in the period parallelogram: 

 Professoe W. Paul Webber. 



Boundary value problems with regular singular 

 points: Professor H. J. Ettlinger. (Sec- 

 ond paper.) 



Note on the permutdbility of functions which have 

 the same Schmidt fundamental functions: Pro- 

 fessor E. W. Chittenden. 



On Tcernels which have no Fredholm fundamental 

 functions: Professor Chittenden. 



Note on convergence in mean: Professor Chit- 

 tenden. 



Determination of the spherical transformation in 

 Grassmann's extensive algebra: Dr. A. E. 

 Schweitzer. 



On the relation of iterative compositional equa- 

 tions to Lie's theory of transformation groups: 

 Dr. Schweitzer. 



Isotliermally conjugate nets: Professor E. J. 



WiLCZYNSKI. 



Transformation of conjugate nets into conjugate 

 nets: Professor Wilcztnski. 



Conditions under which one of two given closed 

 linear point sets may he thrown into the other 

 one iy a continuous transformation of a plane 

 into itself: Professor B. L. Moore. 



A closed connected set of points which contains no 

 simple continuous arc: Professor Mooke. 



On the history of symbols for n-factorial: Pro- 

 fessor Florian Cajori. 



Homogeneous polynomials with a multiplication 

 theorem: Professor L. E. Dickson. 



Applications of algebraic and hypercomplex num- 

 bers to the complete solution in integers of 

 quadratic diophantine equations in several vari- 

 ables: Professor Dickson. 



Arithmetic of quaternions: Professor Dickson. 



Determination of all general homogeneous poly- 

 nomials expressible as determinants with linear 

 elements: Professor Dickson. 



I-con jugate operators of an abelian group: Pro- 

 fessor G. A. Miller. 



The integrals and associated divergent series: Pro- 

 fessor W. D. MacMillan. 



Elementary geometry in n-dimensions : Professor 

 E. P. Baker. 



Note on an ambiguous case of approximation: 

 Professor Dunham Jackson. 



On the method of least m-th powers for a set of 

 simultaneous equMions: Professor Jackson. 



Note on the convergence of weighted trigonome- 

 tric series: Professor Jackson. 



On polynomials and their residue systems: Pro- 

 fessor Aubrey J. Kempner. (Second paper.) 



Expansion of the double frequency function into a 

 series of Eermite's polynomials: Professor E. 

 E. Smith. 



On amicable numbers and their generalizations: 

 Professor T. E. Mason. 



On the complete characterization of the set of 

 points of "approximate" continuity: Pro- 

 fessor Henry Blumberg. 



Comparison of different line- geometric representa- 

 tions for functions of a complex variable: Dr. 

 Gladys E. C. Gibbens. 



On tlie trigonometric representation of an ill-de- 

 fined function : Professor Dunham Jackson. 



An adaptation of Bing 's paradox, involving an 

 arbitrary a priori probability: Professor Ed- 

 ward L. DODD. 



A convergence theorem of Osgood's with an ap- 

 plication: Professor O. D. Kellogg. 



Invariant points under trajisformations in func- 

 tion space: Professors G. D. Birkhoff and 0. 

 D. Kellogg. 



Fundamental points of potential theory: Pro- 

 fessor G. C. Evans. 



Functionals of summahle functions: Professor 

 W. L. Hart. 

 The papers of Professors Moore, Dodd and 



Evans, and the paper of Dr. Gibbens were read by 



title. 



The New York meeting of the society was re- 

 ported in Science of February 25. 



At the sesMons of the Mathematical Association 



of America on Tuesday and Wednesday afternoon 



the following papers were read: 



