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

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...

QUATERNIANS AND THEIR GENERALIZATIONS.

THE MATHEMATICAL THEORY OF THE APPORTIONMENT OF REPRESENTATIVES

By

By J. H. McDonald 66

By A. A. Bennett 84

By G. C. Evans 89

By L. E. Dickson 109

E. V. Huntington 123

AN OVERLOOKED Infinite System of Groups of Order pq2. 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..

By Arthur B. Coble 245

.By N. Wiener 253

Differential

By E. B. Stouffer 273

By O. E. Glenn 276

BROWNIAN MOVEMENT

THE AVERAGE of an ANALYTIC FUNCTIONAL.

SEMI-COVARIAnts of a General System of LINEAR Homogeneous

EQUATIONS.

AN ALGORISM for DifferENTIAL INVARIANT THEORY.

THE AVERAGE OF AN ANALYTIC FUNCTIONAL AND THE

339
363

.....

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

ASTRONOMY

(II)...

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

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.

1

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

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