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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..

339

363

By J. H. McDonald 66

By A. A. Bennett 84

PROBLEMS OF POTENTIAL THEORY...

QUATERNIANS and Their GenERALIZATIONS.

By G. C. Evans 89

By L. E. Dickson 109

THE MATHEMATICAL THEORY OF THE APPORTIONMENT OF RepresentatIVES

By E. V. Huntington 123

By G. A. Miller 146

By H. B. Phillips 172

AN OVERLOOKED Infinite System of Groups of Order pq2. .

A FORMULA FOR THE VISCOSITY OF LIQUIDS...

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

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

By E. Hille 303

317

AN INTEGRAL EQUALITY AND ITS APPLICATIONS...

ON THE APPROXIMATE SOLUTIONS IN INTEGERS OF A SET OF LINEAR EQUATIONS..

GEOMETRIC ASPECTS OF THE ABELIAN MODULAR FUNCTIONS OF GENUS FOUR
(II) . . . . .
..By Arthur Coble 245

........

GROUP OF ISOMORPHISMS OF A TRANSITIVE SUBSTITUTION GROUP.

By G. A. Miller 325

EINSTEIN STATIC FIELDS ADMITTING A GROUP G 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.

CHANGES Observed in the Crab NebulA IN TAURUS...

PHYSICS

By F. G. Pease 177

By John C. Duncan 179

5

THE ATTACHMment 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