Publication Office: Eschenbach Printing Company, Easton, Pa. Editorial Office: Massachusetts Institute of Technology, Cambridge

Home Office of the Academy: Washington, D. C.

CONTENTS

PAGE

ix

OFFICERS AND Members OF THE ACADEMY, November 16, 1920...

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.

INDEX...

NATIONAL RESEARCH COUNCIL

716

717

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

340

REPORT OF the MeetinGS OF THE INTERNATIONAL RESEARCH COUNCIL AND OF

THE AFFILIATED UNIONS Held at BrussELLS, JULY 18-28, 1919. . . . . .

REPORT ON THE ORGANIZATION OF THE INTERNATIONAL ASTRONOMICAL UNION... 349

A SURVEY OF RESEARCH PROBLEMS IN GEOPHYSICS..

PRESENT STATUS OF GEODESY AND SOME PROBLEMS OF THIS BRANCH OF

GEOPHYSICS...

THE PROBLEms of SeisMOLOGY.

545

By William Bowie 545

By Harry Fielding Reid 555

By C. F. Marvin 561

THE STATUS AND PROBLEMS OF METEOROLOGY.

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. . . . . . . . . . .

THE PROBLEMS OF VOLCANOLOGY.

...By G. W. Littlehales 580

By Henry W. Washington 583

AN OUTLINE of GeophysiCAL CHEMICAL PROBLEMS.... By Robert S. Sosman 592

m

=

MATHEMATICS

.....

THE COMMUTAtivity of One-Parameter TransFORMATIONS in Real VariABLES

By A. C. Lunn 24

GROUPS GENERATED BY Two Operators, S1, S2, WHICH Satisfy the CONDITIONS

S2′′, (S1S2)k = 1, 5152 = S2S1.
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(e2ix/p") AND THe Second Case of Fer-
MAT'S LAST THEOREM.

.By H. S. Vandiver 416