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 CouUNCIL.

INDEX..

339

363

AN OVERLOOKED Infinite System of Groups of Order pq2....By G. A. Miller 146

A FORMULA FOR THE VISCOSITY OF LIQUIDS...

GEOMETRIC ASPECTS OF THE Abelian MODULAR FUNCTIONS OF GENUS FOUR......

By H. B. Phillips 172

By Arthur B. Coble 245

By N. Wiener 253

THE AVERAGE OF AN ANALYTIC FUNCTIONAL.

SEMI-COVARIANTS of a General System of LINEAR HOMOGENEOUS Differential

EQUATIONS..

By E. B. Stouffer 273

By O. E. Glenn 276

AN ALGORISm for DiffeRENTIAL INVARIANT THEORY...

THE AVERAGE OF AN ANALYTIC FUNCTIONAL AND THE 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

GROUP OF ISOMORPHISMS OF A TRANSITIVE SUBSTITUTION GROUP...

(II)...

By G. A. Miller 325

EINSTEIN STATIC FIELDS ADMITTING A GROUP G2 OF CONTINUOUS TRANS-

FORMATIONS INTO THEMSELVES.
By L. P. Eisenhart 328

ASTRONOMY

INTERNAL MOTION IN THE Spiral Nebula MESSIER 33........By A. van Maanen 1
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
CHANGES OBSERVED IN THE CRAB NEBULA IN TAURUS........By John C. Duncan 179

PHYSICS

5

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