Proceedings of the National Academy of Sciences of the United States of America

FEB 1 1922

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PUBLISHED MONTHLY

Publication Office: Eschenbach Printing Company, Easton, Pa.
Editorial Office: Massachusetts Institute of Technology, Cambridge
Home Office of the Academy: Washington, D. C.

CONTENTS

LIST OF PUBLICATIONS OF THE NATIONAL ACADEMY OF SCIENCES AND OF THE

NATIONAL RESEARCH COUNCIL.

INDEX.....

MATHEMATICS

ON THE ROOTS of Bessel'S FUNCTIONS.

NORMALIZED GEOMETRIC SYSTEMS.

PROBLEMS OF POTENTIAL THEORY..

THE MATHEMATICAL THEORY OF THE APPORTIONMENT OF REPRESENTATIVES

AN OVERLOOked Infinite System of Groups of Order pq2.

E. V. Huntington 123

By G. A. Miller 146

A FORMULA FOR THE VISCOSITY OF LIQUIDS.
By H. B. Phillips 172

GEOMETRIC Aspects of the Abelian ModULAR FUNCTIONS OF GENUS FOUR....

EQUATIONS....

AN ALGORISM FOR DIFFERENTIAL INVARIANT THEORY..

THE AVERAGE OF AN ANALYTIC FUNCTIONAL AND THE

THE AVERAGE OF AN ANALYTIC FUNCTIONAL......

SEMI-COVARIAnts of a General System of LINEAR HOMOGENEOUS Differential

By E. B. Stouffer 273

.By O. E. Glenn 276

BROWNIAN Movement

By N. Wiener 294

AN INTEGRAL EQUALITY AND ITS APPLICATIONS...
By E. Hille 303

ON THE APPROXIMATE SOLUTIONS IN INTEGers of a Set oF LINEAR EQUATIONS.... 317

GEOMETRIC ASPECTS OF THE ABELIAN MODULAR FUNCTIONS OF GENUS FOUR
By Arthur Coble 245

339

363

(II)...

GROUP OF ISOMORPHISMS OF A TRANSITIVE SUBSTITUTION GROUP.....

By Arthur B. Coble 245

By N. Wiener 253

ASTRONOMY

By G. A. Miller 325

EINSTEIN STATIC FIELDS ADMITTING A GROUP G2 OF CONTINUOUS TRANS-

FORMATIONS INTO THEMSELVES..
By L. P. Eisenhart 328

CHANGES OBSERVED IN the Crab NebuLA IN TAURUS..

PHYSICS

INTERNAL MOTION IN THE Spiral Nebula MESSIER 33.. By A. van Maanen

MEASUREMENT of the Diameter of ALPHA ORIONIS BY THE INTERFEROMETER

By A. A. Michelson and F. G. Pease 143

STUDIES OF MAGNITUDES IN STAR CLUSTERS XIII. VARIABLE STARS IN N. G. C.

7006.....
.By Harlow Shapley and Beatrice W. Mayberry 152

THE ANGULAr Diameter of Alpha BOOTIS BY THE INTERFEROMETER.

By F. G. Pease 177

By John C. Duncan 179

THE ATTACHMent of ElectRONS TO NEUTRalMolecules IN AIR. By L. B. Loeb

On the REFLECTION AND RE-EMISSION OF ELECTRONS FROM METAL SURFACES:

AND A METHOD OF MEASURING THE IONIZING Potential of SUCH SURFACES

By R. A. Millikan and I. G. Barber 13

iii

POSITIVE RAY ANALYSIS OF Magnesium. .

THE ENERGY CONTENT OF THE DIAPASON .

THE PELTIER EFFECT.....

THE OPEN MERCURY MANOMETER READ BY DISPLACEMENT INTERFEROMETRY

THERMO-ELECTRO ACTION AND THERMAL CONDUCTION IN METALS: A SUMMARY

By E. H. Hall 98

NOTE ON A METHOD OF DETERMINING THE DISTRIBUTION OF PORE SIZES IN A

POROUS MATERIAL..
..By E. W. Washburn 115

THE DIFFUSION OF AIR THROUGH WATER IN THE LAPSE of Years.

....

By Carl Barus 133

THE DESTRUCTION OF PHOSPHORESCENT ZINC SULFIDES by ULTRA VIOLET LIGHT

By Leonard B. Loeb and Lloyd Schmiedeskamp 202

ACOUSTIC PREssure DistriBUTIONS, CHIEFLY in ReserVOIRS AND PIPES...

By Carl Barus 207

AN APPARATUS FOR DETERMINATION of the GASES IN BLOOD AND OTHER Solu-

TIONS. . . . . . .
By Donald D. Van Slyke 229

A REMEASURement of the Radiation CONSTANT, h, BY Means of X-RAYS...

By William Duane, H. H. Palmer, and Chi-Sun Yeh 237

THE U-TUBE ABSOLUTE ELECTROMETER........

.By Carl Barus 242

ON THE CALCULATION OF THE X-RAY ABSORPTION FREQUENCIES OF THE CHEMICAL

ELEMENTS...
...By William Duane 260

ON THE CALCULATION OF THE X-RAY ABSORPTION FREQUENCIES OF THE Chemical

ELEMENTS (SECOND NOTE)..
By W. Duane 267

THE EVALUATION OF QUANTUM INTEGRALS.
By E. C. Kemble 283

THE FURTHER EXTENSION OF THE ULTRA-VIOLET SPECTRUM AND THE PROGRESSION

WITH ATOMIC NUMBER OF THE SPECTRA OF Light ElemeNTS. By R. A. Millikan 289

MEASUREMENTS OF THE DEVIATION FROM OHM'S LAW IN METALS AT HIGH CURRENT

DENSITIES..
.By P. W. Bridgman 299

THE MOBILITIES OF ELECTRONS.
.By L. B. Loeb 307

THE GROWTH and Decay of PHOTO-THERMIONIC CURRENTS FROM Oxide Coated

.By H. D. Arnold and Herbert E. Ives 323

EXPERIMENTS ON THE ELECTRICAL CONDUCTION OF A HYDROGEN ALLOY..

By D. P. Smith 28
THE CORRELATION OF COMPOUND. IONIZATION AND SOLUBILITY IN SOLUTIONS.
OUTLINE OF A MODIFIED IONIZATION THEORY..
.By J. Kendall 56
STUDIES ON CATALYSIS I. THE REDUCTION OF URACIL TO HYDROURACIL. . . . . . . .
By T. B. Johnson and E. B. Brown 75
THE APPLICATION of a Differential THERMOMETER IN EBULLIOSCOPY.....
By A. W. C. Menzies and S. L. Wright 77
A DIFFERENTIAL, THERMOMETER.
.By A. W. C. Menzies 81
THE EFFECT OF TEMPERATURE AND OF The ConcentrATION OF HYDROGEN IONS
UPON THE RATE OF DESTRUCTION OF ANTISCORBUTIC VITAMIN (VITAMIN C)....
By H. C. Sherman, V. K. LaMer and H. L. Campbell 279

GEOLOGY AND PALEONTOLOGY

SOME GEOLOGIC CONCLUSIONS FROM GEODETIC DATA....
By W. Bowie 23

ORIGIN AND HISTORY OF THE BEAR FAMILY IN THE WESTERN HEMISPHERE WITH

PARTICULAR Reference to the RELATION OF THIS QUESTION TO PROBLEMS

OF GEOGRAPHICAL HISTORY.
.By John C. Merriam 183

ADAPTIVE RADIATION AND CLASSIFICATION OF THE PROBOSCIDEA..By H. F. Osborn 231
MELANOVANADITE, A NEW Mineral from MINA RAGRA, Pasco, Peru...

By Waldemar Lindgren 249

BOTANY

THE VASCULAR ANATOMY OF NORMAL AND VARIANT SEEDLINGS OF Phaseolus

vulgaris...
.By J. A. Harris and E. W. Sinnott 35

ZOOLOGY

THE PRESENT STATUS OF THE LONG-CONTINUED PEDIGREE CULTURE OF Para-