Early Journal Content on JSTOR, Free to Anyone in the World This article is one of nearly 500,000 scholarly works digitized and made freely available to everyone in the world by JSTOR. Known as the Early Journal Content, this set of works include research articles, news, letters, and other writings published in more than 200 of the oldest leading academic journals. The works date from the mid-seventeenth to the early twentieth centuries. We encourage people to read and share the Early Journal Content openly and to tell others that this resource exists. People may post this content online or redistribute in any way for non-commercial purposes. Read more about Early Journal Content at http://about.jstor.org/participate-jstor/individuals/early- journal-content. JSTOR is a digital library of academic journals, books, and primary source objects. JSTOR helps people discover, use, and build upon a wide range of content through a powerful research and teaching platform, and preserves this content for future generations. JSTOR is part of ITHAKA, a not-for-profit organization that also includes Ithaka S+R and Portico. For more information about JSTOR, please contact [email protected]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA VOLUME 2, 1916 EDITORIAL BOARD ARTHURA. NOYES, Chairman EDWIN B. WILSON,Managing Editor ARTHUR L. DAY, Home Secretary GEORGEE. HALE, Foreign Secretary J. J. ABEL J. M. COULTER W. H. HOLMES W. B. CANNON C. B. DAVENPORT J. P. IDDINGS J. McK. CATTELL SIMONFLEXNER R. A. MILLIKAN J. M. CLARKE E. B. FROST E. H. MOORE E. G. CONKLIN R. G. HARRISON ALEXANDER SMITH Publication Office: Williams & Wilkins Company, Baltimore Editorial Office: Massachusetts Institute of Technology, Cambridge Home Office of the Academy: Washington, D. C. TABLE OF CONTENTS PAGE OFFICERS AND MEMBERS OF THE ACADEMY, NOVEMBER 15, 1915 ................... x REPORT OF THE ANNUAI, MEETING, APRIL, 1916.................................. 300 A WARDOF M EDALS.......................................................... 307 RESEARCH GRANTS FROM THE TRUST FUNDS OF THE ACADEMY............... 307, 743 PRELIMINARY REPORT UPON THE POSSIBILITY OF CONTROLLING THE LAND SLIDES ADJACENT TO THE PANAMA CANAL .......................................... 193 SYMPOSIUM ON TIHE EXPLORATION OF THE PACIFIC ............................... 391 REPORT OF THE AUTUMN MEETING, NOVEMBER, 1916............................. 744 NOTICES OF BIOGRAPHICALMEMOIRS ........................................... 737 INDEX....................................................................... 751 ERRATA. ...................................................................... 192 NATIONAL RESEARCH COUNCIL PAGI PRELIMINARY REPORT OF THE ORGANIZING COMMITTEE TO THE PRESIDENT OF THE ACADEMY................................................................. 507 REPORT OF THE FIRST MEETING OF THE COUNCIL................................ 602 REPORTS OF THE MEETINGS OF THE EXECUTIVE COMMITTEE.........605, 738 ORGANIZATIONOF THE RESEARCH COUNCIL...................................... 607 REPORT OF THE SECOND MEETING OF THE COUNCIL............................. 738 SCIENTIFIC RESEARCH FOR NATIONAL DEFENSE AS ILLUSTRATED BY THE PROBLEMS OF AERONAUTICS(ABSTRACT) ........... By Lieut. Col. George 0. Squier, U. S. A. 740 MATHEMATICS PAGE UPPER LIMIT OF THE DEGREE OF TRANSITIVITY OF A SUBSTITUTION GROUP By G. A. Miller 61 AN EXTENSION OF FEUERBACH'S THEOREM..........................By F. Morley 171 DEFORMATIONS,OF TRANSFORMATIONSOF RIBAUCOUR............By L. P. Eisenhart 173 ON THE LINEAR DEPENDENCE OF FUNCTIONS OF SEVERAL VARIABLES, AND CERTAIN COMPLETELY INTEGRABLE SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS.... By Gabriel M. Green 209 POINTSETS ANDALLIED CREMONA GROUPS (PART II) ............By Arthur B. Coble 244 ON A THEOREMOF LUCAS....................................By M. B. Porter 247 INTERPRETATION OF THE SIMPLEST INTEGRAL INVARIANT OF PROJECTIVE GEOMETRY By E. J. Wilczynski 248 ON THE FOUNDATIONS OF PLANE ANALYSIS SITUS ... ...........By Robert L. Moore 270 A GENERAL THEORY OF SURFACES.......... By Edwin B. Wilson and C. L. E. Moore 273 DIFFERENTIAL EQUATIONS AND IMPLICIT FUNCTIONS IN INFINITELY MANY VARIABLES By William L. Hart 309 NOTE ON LUCAS' THEOREM....................................By M. B. Porter 335 A VARIABLESYSTEM OF SEVENSON Two TWISTEDCUBIC CURVES....By H. S. White 337 A PROOF OF WHITE'S PORISM..................................By A. B. Coble 530 ON CERTAIN ASYMPTOTIC EXPRESSIONS IN THE THEORY OF LINEAR DIFFERENTIAL EQUATIONS......................................By W. E. Milne 543 ON NEWTON'SMETHOD OF APPROXIMATION....................By Henry B. Fine 546 POINT SETS AND CREMONAGROUPS (PART III) ...............By Arthur A. Coble 575 SOME PROBLEMS OF DIOPHANTINE APPROXIMATION: A REMARKABLE TRIGONOMETRI- CAL SERIES ............................. By G. H. Hardy and J. E. Littleswood 583 iii iv CONTENTS PAGE NEWTON'S METHOD IN GENERAL ANALYSIS ................... By Albert A. Bennett 592 A SET OF INDEPENDENT POSTULATES FOR CYCLIC ORDER, By Edward V. Huntington 630 CERTAIN GENERAL PROPERTIES OF FUNCTIONS................By Henry Blumberg 646 ASTRONOMY PAGE A POSSIBLE ORIGIN FOR SOME SPIRAL NEBULAE ................ By GeorgeF. Becker 1 STUDIES OF MAGNITUDES IN STAR CLUSTERS, I. ON THE ABSORPTION OF LIGHT IN SPACE .. ............ .............................. By Harlow Shapley 12 :STUDIES OF MAGNITUDES IN STAR CLUSTERS, II. ON THE SEQUENCE OF SPECTRAL TYPES IN STELLAR EVOLUTION ...........................By Harlow Shapley 15 ON THE ALBEDOOF THE PLANETS AND THEIR SATELLITES...... By Henry Norris Russell 74 THE MINUTE STRUCTURE OF THE SOLAR ATMOSPHERE ........................... By GeorgeE. Hale and Ferdinand Ellerman 102 MONOCHROMATICPHOTOGRAPHY OF JUPITER AND SATURN ..........By R. W. Wood 109 ON THE OBSERVED ROTATIONS OF A PLANETARY NEBULA ..................... By W. W. Campbell and J. H. Moore 129 A SHORT PERIOD CEPHEID WITH VARIABLE SPECTRUM ..........By Harlow Shapley 132 THE SPECTRUM OF 5 CEPHEI ............ By Walter S. Adams and Harlow Shapley 136 INVESTIGATIONS IN STELLAR SPECTROSCOPY, I. A QUANTITATIVE METHOD OF CLASSI- FYING STELLA SPECTRA ................................By Walter S. Adams 143 INVESTIGATIONS IN STELLAR SPECTROSCOPY, II. A SPECTROSCOPIC METHOD OF DE- TERMINING STELLAR PARALLAXES ..................... By Walter S. Adams 147 INVESTIGATIONS IN STELLAR SPECTROSCOPY, III. APPLICATION OF A SPECTROSCOPIC METHOD OF DETERMINING STELLAR DISTANCES TO STARS OF MEASURED PARALLAX By Walter S. Adams 152 INVESTIGATIONS IN STELLAR SPECTROSCOPY, IV. SPECTROSCOPIC EVIDENCE FOR THE EXISTENCE OF Two CLASSES OF M TYPE STARS..........By Walter S. Adams 157 DISCOVERY OF EIGHT VARIABLE STELLAR SPECTRA ................By Harlow Shapley 208 SYSTEMATIC MOTION AMONG STARS OF THE HELIUM TYPE ........By Benjamin Boss 214 THE SITUATION IN REGARD TO ROWLAND'S PRELIMINARY TABLE OF SOLAR SPECTRUM WAVE-LENGTHS ......................................By Charles E. St. John 226 CHANGES IN THE FORM OF THE NEBULA N. G. C. 2261.......... By Edwin P. Hubble 230 'ON SOME RELATIONS BETWEEN THE PROPER MOTIONS, RADIAL VELOCITIES, AND MAG- NITUDES OF STARS OF CLASSES B AND A.................... By C. D. Perrine 289 ASYMMETRY IN THE PROPER MOTIONS AND RADIAL VELOCITIES OF STARS OF CLASS B AND THEIR POSSIBLE RELATION TO A MOTION OF ROTATION.... By C. D. Perrine 292 THE PYRANOMETER: AN INSTRUMENT FOR MEASURING SKY RADIATION .............. By C. G. Abbot and L. B. Aldrich 333 THE WORK OF THE AMERICAN METEOR SOCIETY IN 1914 AND 1915.................. By Charles P. Olivier 372 AN APPARENT DEPENDENCE OF THE APEX AND VELOCITY OF SOLAR MOTION, AS DE- TERMINED FROM RADIAL VELOCITIES, UPON PROPER MOTION..By C. D. Perrine 376 PRELIMINARY EVIDENCE OF INTERNAL MOTION IN THE SPIRAL NEBULA MESSIER 101 By A. van Maanen 386 'ON THE SUGGESTED MUTUAL REPULSION OF FRAUNHOFER LINES .................... By Charles E. St. John 458 THE ROTATION AND RADIAL VELOCITY OF THE SPIRAL NEBULA N. G. C. 4594........ By Francis G. Pease 517 A SIMPLE METHOD FOR DETERMINING THE COLORS OF THE STARS ................ By Frederick H. Seares 521 'STUDIES OF MAGNITUDES IN STAR CLUSTERS, III. THE COLORS OF THE BRIGHTER STARS IN FOUR GLOBULAR SYSTEMS ...................... By Harlow Shapley 525 CONTENTS v PAGE PRELIMINARY RESULTS ON THE COLOR OF NEBULAE .......... By Frederick H. Seares 553 SPECTROGRAPHIC OBSERVATIONS OF RELATIVE MOTIONS IN THE PLANETARY NEBULAE By W. W. Campbell and J. H. Moore 566 PHYSICS AND ENGINEERING PAGE EXPERIMENTAL EVIDENCE FOR THE ESSENTIAL IDENTITY OF THE SELECTIVE AND NOR- MAL PHOTO-ELECTRICEFFECTS ............ By R. A. Millikan and W. H. Souder 19 CONCOMITANT CHANGES IN TERRESTRIAL MAGNESIUM AND SOLAR RADIATION ...... By L. A. Bauer 24 QUANTUM RELATIONS IN PHOTO-ELECTRIC PHENOMENA ........By R. A. Millikan 78 THE EMISSION QUANTA OF CHARACTERISTIC X RAYS ........By David L. Webster 90 THE ELECTROMOTIVE FORCE PRODUCED BY THE ACCELERATION OF METALS ........ By Richard C. Tolman and T. Dale Stewart 189 THE HIGH FREQUENCYSPECTRUM OF TUNGSTEN.... By Albert W. Hull and Marion Rice 265 DYNAMICAL STABILITY OF AEROPLANES....................By Jerome C. Hunsaker 278 THEORY OF AN AEROPLANE ENCOUNTERINGGUSTS ........ By Edwin Bidwell Wilson 294 NOTE ON THE PHOSPHORESCENCEOF URANYL SALTS...........By Edward L. Nichols 328 ON THE MOBILITIES OF GAS IONS IN HIGH ELECTRIC FIELDS. .By Leonard B. Loeb 345 TIE LIGHT EXCITATION BY SLOW PosrrIVE AND NEUTRAL PARTICLES .............. By A. J. Dempster 374 CHANNELED GRATING SPECTRA,