PROCEEDINGS

OF THE

OYAL SOCIETY OF LONDON

Series A

CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER.

VOL. LXXXV.

LONDON:

P rinted for THE ROYAL SOCIETY and S old by HARRISON AND SONS, ST. MARTIN’S LANE, PRINTERS IN ORDINARY TO HIS MAJESTY.

N ovember, 1911. LONDON: HARRISON AND SONS, PRINTERS IN ORDINARY TO HTS MAJESTY, ST. MARTIN’S LANE. CONTENTS

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SERIES A. VOL. LXXXV.

No. A 575.—March 14, 1911. P AG-E The Chemical Physics involved in the Precipitation of Free Carbon from the Alloys of the Iron-Carbon System. By W. H. Hatfield, B. Met. (Sheffield University). Communicated by Prof. W. M. Hicks, F.R.S. (Plates 1—5) ...... 1 On the Fourier Constants of a Function. By W. H. Young, Se.D., F.R.S...... 14 The Charges on Ions in Gases, and some Effects that Influence the Motion of Negative Ions. By Prof. John S. Townsend, F.R.S...... 25 On the Energy and Distribution of Scattered Rontgen Radiation. By J. A. Crowtlier, M.A., Fellow of St. John's College, Cambridge. Com­ municated by Prof. Sir J. J. Thomson, F.R.S...... *...... 29 The Origin of Magnetic Storms. By Arthur Schuster, F.R.S...... 44 On the Periodicity of Sun-spots. By Arthur Schuster, F.R.S...... 50 The Absorption Spectx*a of Lithium and Caesium. By Prof. P. V. Bevan, M.A., Royal Holloway College. Communicated by Sir J. J. Thomson, F.R.S...... 54 Dispersion in Vapours of the Alkali Metals. By Prof. P. V. Bevan, M.A., Royal Holloway College. Communicated by Sir J. J. Thomson, F.R.S. (Plates 6 and 7) ...... 58 Report on the Separation of Ionium and Actinium from Certain Residues and on the Production of Helium by Ionium. By B. B. Boltwood, Ph.D., John Hailing Fellow, University of Manchester. Communicated by Prof. E. Rutherford, F.R.S...... 77

No. A 576.—April 11, 1911. he Relative Atomic Weights of Nitrogen and Sulphur. By F. P. Burt and F. L. Usher. Communicated by Sir William Ramsay, F.R.S...... 82 The Production and Properties of Soft Rontgen Radiation. By R. Whi#lington, B.A., St. John’s College, Allen Scholar of the University of Cambridge. Communicated by Sir J. J. Thomson, F.R.S...... 99 Experiments on Stream-line Motion in Curved Pipes. By John Eustice, B.Sc., Professor of Engineering, Hartley University College, Southampton. Com­ municated by Sir Joseph Larmor, Sec. R.S...... 119 IV

PAGE Secondary y-Rays produced by /3-Rays. By J. A. Gray, B.Sc., 1851 Exhibition Scholar, University of Melbourne. Communicated by Prof. E. Rutherford, F.R.S...... 131 On the Measurement of Specific Inductive Capacity. By Charles Niven, F.R.S., Professor of Natural Philosophy, University of Aberdeen ...... 139 Note on the Electrical Waves occurring in Nature. By W. H. Eccles, D.Sc., A.R.C.S., and H. Morris Airey, M.Sc., F.R.A.S. Communicated by Sir A. W. Rucker, F.R.S...... 145 Obituary Notices of Fellows Deceased :— William Edward Ayrton ; Bindon Blood Stoney; Friedrich Wilhelm Kohlrausch ;Sir Charles Todd, K.C.M.G. ; Greville Williams . i—xx

No. A 577.—May 10, 1911. A Theory of the Chemical Action of the Electric Discharge in Electrolytic Gas. By Rev. P. J. Kirkby, Fellow of New College, Oxford. Communicated by Prof. J. S. Townsend, F.R.S...... 151 Atmospheric Electricity over the Ocean. By G. C. Simpson, D.Sc., and C. S. Wright, B.A. Communicated by Arthur Schuster, F.R.S...... 175 On the Ionic Solubility-product. By James Kendall, M.A., B.Sc. (Vans Dunlop Scholar in Chemistry, University of Edinburgh). Communicated by Prof. James Walker, F.R.S...... 200

Bakerian Lecture.—A Chemically Active Modification of Nitrogen, Produced by the Electric Discharge. By the Hon. B. J. Strutt, F.R.S., Professor of Physics, Imperial College of Science, South Kensington. (Plate 8) ...... 219

No. A 578.—June 9, 1911. The Ionisation of Heavy Gases by X-Rays. By R. T. Beatty, M.A., B.E., Emmanuel College, Clerk Maxwell Student of the University, Cambridge. Communicated by Sir J. J. Thomson, F.R.S...... 230 The Variation of Ionisation with Velocity for the /3-Particles. By W. Wilson, M.Sc., Honorary Fellow of the University of Manchester. Communicated by Prof. E. Rutherford, F.R.S...... 240 The Association of Lead with Uranium in Rock-Minerals, and its Application to the Measurement of Geological Time. By Arthur Holmes, A.R.C.S., B.Sc., Imperial College of Science and Technology. Communicated by Prof, the Hon. R. J. Strutt, F.R.S...... 248

The Path of Electron in Combined Radial Magnetic and Electric Fields. By H. Stanley Allen, M.A., D.Sc., Senior Lecturer in Physics at University of London, King’s College. Communicated by Sir Joseph Larmor, Sec. R.S...... 257 On the Dynamical Nature of the Molecular Systems which emit Spectra of the Banded Type. By Prof. E. T. Whittaker, Sc.D., F.R.S...... 262 V

PAGE On some Mineral Constituents of a Dusty Atmosphere. By W. N. Hartley, D.Sc., F.R.S., Royal College of Science, Dublin ...... •...... 271 On the Absolute Measurement of Light: A Proposal for an Ultimate Light Standard. By R. A. Houstoun, M.A., Ph.D., D.Sc., Lecturer in Physical Optics in the University of Glasgow. Communicated by Prof. Andrew Gray, F.R.S...... 275 On a Method of making Visible the Paths of Ionising Particles through a Gas. By C. T. R. Wilson, M.A., F.R.S. (Plate 9 ) ...... 285 The Vacuum Tube Spectra of Mercury. By Frank Horton, D.Sc., M.A., Fellow of St. .John’s College, Cambridge. Communicated by Sir J. J. Thomson, F.R.S.... 288 The Specific Heat of Water. By W. R. Bousfield, M.A., K.C., and W. Eric Bousfield, B.A. Communicated by Prof. Sir J. Larmor, Sec. R.S. (Abstract) 302 Memoir on the Theory of the Partitions of Numbers. Part V.—Partitions in Two- dimensional Space. By Major P. A. MacMalion, D.Sc., F.R.S. (Abstract) ... 304 An Optical Method of Measuring Vapour Pressures: Vapour Pressure and Apparent Superheating of Solid Bromine. By Clive Cuthbertson, Fellow of University College, London, and Maude Cuthbertson. Communicated by Prof. F. T. Trouton, F.R.S...... 306

No. A 579.— July 5, 1911. The Influence of Planets on the Formation of Sun-spots. By Arthur Schuster, F.R.S...... 309 The Production of Characteristic Routgen Radiations. By R. Whiddington, B.A., St. John’s College, Cambridge. Communicated by Sir J. J. Thomson, F.R.S.... 323 Experiments on the Compression of Liquids at High Pressures. By the Hon. C. A. Parsons, C.B., F.R.S., and S. S. Cook, B.A. Cantab...... 332 Energy Transformation of X-Rays. By Prof. W. H. Bragg, M.A., F.R.S., and H. L. Porter, B.Sc., Demonstrator of Physics, University of Leeds ...... 349 The Mechanical Viscosity of Fluids. By T. E. Stanton, D.Sc., M.Inst.C.E. Communicated by R. T. Glazebrook, F.R.S...... 366 Spectroscopic Investigations in connection with the Active Modification of Nitrogen.—I. Spectrum of the Afterglow. By A. Fowler, F.R.S., Assistant Professor of Physics, Imperial College of Science and Technology, and the Hon. R. J. Strutt, M.A., F.R.S., Professor of Physics, Imperial College of Science and Technology, South Kensington. (Plate L0) ...... 377

No. A 580.—August 15, 1911. ihe Constitution of the Alloys of Aluminium and Zinc. By Walter Rosenhain, B.A., D.Sc., and Sydney L. Archbutt, A.I.C. (of the National Physical Laboratory). Communicated by R. T. Glazebrook, C.B., F.R.S. (Abstract)... 389 On the Anode and Cathode Spectra of Various Gases and Vapours. By G. Stead, B.A., Formerly Scholar of Clare College, Cambridge. Communicated by Sir J. J. Thomson, F.R.S...... 393 VI

PAGE On a Class of Parametric Integrals and their Application in the Theory of Fourier Series. By W. H. Young, Sc.D., F.R.S...... 401 On a Mode of Generating Fourier Series. By W. H. Young, Sc.D., F.R.S...... 415 A Silica Standard of Length. By G. W. C. Kaye, D.Sc., B.A. Communicated by It. T. Glazebrook, F.R.S...... 430 The Distribution of Slide in a Right Six-face subject to Pure Shear. By E. N. da C. Andrade, B.Sc., Jessel Scholar of the University of London. Communicated by Prof. Karl Pearson, F.R.S...... 448 The Pupil of an Optical System with regard to Perspective. By Conrad Beck. Communicated by Silvanus P. Thompson, F.R.S...... 462 On Dr. Johnstone Stoney’s Logarithmic Law of Atomic Weights. By Lord Rayleigh, O.M., F.R.S...... 471 On Small Longitudinal Material Waves accompanying Light Waves. By J. H. Poynting, F.R.S...... 474

No. A 581.—October 18, 1911. On the Boiling Point of Water. By The Earl of Berkeley, F.R.S., and M. P. Appleby, M.A., B.Sc. (Oxon) ...... 477 On the Boiling Points of some Saturated Aqueous Solutions. By The Earl of Berkeley, F.R.S., and M. P. Appleby, M.A., B.Sc, (Oxon) ...... 489 Pendulum Clocks and their Errors. By H. R. A. Mallock, F.R.S...... 505 The Effect of Temperature upon the Ductility of Zinc. By W. B. Haines, B.Sc., Physics Research Scholar, University College, London. Communicated by Prof. F. T. Trouton, F.R.S...... 1 526 The Flame arising from the Nitrogen-burning Arc. By the Hon. R. J. Strutt, F.R.S., Professor of Physics, Imperial College of Science, South Kensington ... 533 Radiation in Explosions of Coal-gas and Air. By W. T. David, B.A., B.Sc., Trinity College, Cambridge. Communicated by Prof. B. Hopkinson, F.R.S. (Abstract) 537 The Heating Effect of the Currents in Precise Measurements of Electrical Resistance. By R. T. Glazebrook, F.R.S., W. R. Bousfield, K.C., and F. E. Smith ...... 541

No. A 582.—November 30, 1911. An Experimental Investigation of Gibbs’ Tliei’modynamical Theory7 of Interfacial Concentration in the Case of an Air-Water Interface. By7 Prof. F. G. Donnan, F.R.S., and J. T. Barker, D.Sc...... 557 On the Gaseous Condensable Compound, Explosive at Low Temperatures, produced from Carbon Disulphide Vapour by the Action of the Silent Electric Discharge.—II. By Sir James Dewar, M.A., Sc.D., LL.D., F.R.S., Jacksonian Professor in the University of Cambridge, and Humphrey Owen Jones, M.A., D.Sc., Jacksonian Demonstrator in the University of Cambridge ...... 574 Vll

PAGK Production of S

OBITUARY NOTICES OF FELLOWS DECEASED. William Edward Ayrton ; Bindon Blood Stoney ; Friedrich Wilhelm Kohlrausch ; Sir Charles Todd, K.C.M.G. ; Greville Williams...... i- x x 1 Index ...... xxi

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