CONTENTS 
OifFicERS AND Members of the Academy, November 16, 1920 ix 
Report of the Autumn Meeting, 1919, of the National Academy of Sciences 43 
Report of the Annual Meeting, 1920, of the National Academy of Sciences 442 
The Kilauea Volcano Observatory Committee Report 706 
Errata 716 
Index 717 
NATIONAL RESEARCH COUNCIL 
The Larger Opportunities for Research on the Relations of Solar and 
Terrestrial Radiation By C. G. Abbot 82 
Notes from the Minutes of the Meetings in January and February, 1920, 
OF THE Executive Board and Interim Committee of the National Re- 
search Council 335 
Report of the Meetings of the International Research Council and of 
THE Affiliated Unions Held at Brussells, July 18-28, 1919 340 
Report on the Organization of the International Astronomical Union . . . 349 
A Survey of Research Problems in Geophysics 545 
Present Status of Geodesy and Some Problems of This Branch of 
Geophysics By William Bowie 545 
The Problems of Seismology By Harry Fielding Reid 555 
The Status and Problems of Meteorology By C. F. Marvin 561 
Some of the Chief Problems in Terrestrial Magnetism and Electricity 
By Louis A . Bauer 572 
The Problems and Functions of the Section of Physical Oceanography 
OF THE American Geophysical Union By G. W. Littlehales 580 
The Problems of Volcanology By Henry W. Washington 583 
An Outline of Geophysical Chemical Problems By Robert S. Sosman 592 
MATHEMATICS 
The Commutativity of One-Parameter Transformations in Real Variables 
By A. C. Lunn 24 
Groups Generated by Two Operators, si, S2, Which Satisfy the Conditions 
si^ = S2^, (siSi)^ = 1, SiS2 = 52^1 By G. A. Miller. 70 
Note on Geometrical Products By C. L. E. Moore and H. B. Phillips 155 
The Starting of a Ship By James K. Whittemore 182 
A Thermodynamic Study of Electrolytic Solutions , . .By F. L. Hitchcock 186 
Functionals Invariant under One-Parameter Continuous Groups of Trans- 
formations IN THE Space of Continuous Functions By I. A. Barnett 200 
On Kummer's Memoir of 1857 Concerning Fermat's Last Theorem 
By H. S. Vandiver 266 
On the Distortion in Conformal Mapping when the Second Coefficient in 
the Mapping Function has an Assigned Value By T. H. Gronwall 300 
Conformal Mapping of a Family of Real Conics on Another 
By T. H. Gronwall 312 
On the Class Number of the Field n{e^i^/P^) and the Second Case of Fer- 
mat's Last Theorem ByH.S. Vandiver 416 
iii 
