PROCEEDINGS

OF THE

ROYAL SOCIETY OF LONDON

S e r ie s A

CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER.

VOL. LXXXIV.

LONDON:

Printed for THE ROYAL SOCIETY and Sold b HARRISON AND SONS, ST. MARTIN’S LANE PRINTERS IN ORDINARY TO HIS MAJESTY.

February, 1911. LONDON: HARRISON AND SONS, PRINTERS IN ORDINARY TO HIS MAJESTY ST. MARTIN’S DANE. CONTENTS. ------

SERIES A. VOL. LXXXIV.

No. A 567.—June 9, 1910. PAGE On the Viscous Flow in Metals, and Allied Phenomena. By E. N. da C. Andrade, B.Sc., Physics Research Scholar, University College, London. Communicated by Prof. F. T. Trouton, F.R.S...... 1 The Refraction and Dispersion of Argon, and Redeterminations of the Dispersion of Helium, Neon, Krypton, and Xenon. By Clive Cuthbertson, Fellow of University College, London, and Maude Cuthbertson. Communicated by Prof. F. T. Trouton, F.R.S...... 13 The Total Ionisation produced in Different Gases by the Cathode Rays ejected by X-Rays. By R. D. Kleeman, D.Sc., B.A., Mackinnon Student of the Royal Society, Emmanuel College, Cambridge. Communicated by Prof. W. H. Bragg, F.R.S...... 16 The Incidence of Light upon a Transparent Sphere of Dimensions comparable with the Wave-Length. By Lord Rayleigh, O.M., F.R.S...... 25 On the Improbability of a Random Distribution of the Stars in Space. By Karl Pearson, F.R.S., University College, London ...... 47 : The Liberation of Helium from Minerals by the Action of Heat. By D. Orson Wood, B.Sc., A.R.C.Sc. Communicated by Prof, the Hon. R. J. Strutt, F.R.S. 70

No. A 568.—July 8, 1910. On Scandium.—Part II. By Sir William Crookes, D.Sc., LL.D., For. Sec. R.S. (Abstract) ...... 79 On the Rotatory Character of some Terrestrial Magnetic Disturbances at Greenwich and on their Diurnal Distribution. By Robert B. Sangster. Communicated by Dr. C. Chree, F.R.S...... 1 85 On the Direction of Motion of an Electron ejected from an Atom by Ultra-Violet Light. By R. D. Kleeman, D.Sc., B.A., Mackinnon Student of the Royal Society, Emmanuel College, Cambridge. Communicated by Prof. Sir J. J. Thomson, F.R.S...... 92 On the Absorption of Gases by Charcoal. By Miss I. F. Homfray, D.Sc. Com­ municated by Sir William Ramsay, K.C.B!, F.R.S...... 99 IV

1'AGE Flow of Water in Curved Pipes. By John Eustice, B.Sc., Professor of Engineering, Hartley University College, Southampton. Communicated by Sir J. Larmor, Sec. R.S...... 107

Obituary Notices of Fellows deceased :— Sir Benjamin Baker ; Edward John Boutli ; Dmitri Ivanovitch Mendeleeff ; George Gore ; Julius Thomsen ; William James Russell; Simon Newcomb...... i—xxxviii

No. A 569.—July 28, 1910. The Effect of Pressure upon Arc Spectra. No. 3.—Silver ; No. 4.—Gold. By W. G. Duffield, D.Sc. Communicated by Prof. A. Schuster, F.R.S. (Abstract) 118 Studies of the Processes Operative in Solutions. XI.—The Displacement of Salts from Solution by "Various Precipitants. By H. E. Armstrong, F.R.S., and J. Vargas Eyre, Ph.D...... 123 The Distribution of Velocity in the /3-Rays from a Radioactive Substance. By J. A. Gray, B.Sc., 1851 Exhibition Scholar, University of Melbourne. Com­ municated by Prof. E. Rutherford, F.R.S. (Plate 1) ...... 136 The Decrease of Velocity of the /3-Particles on Passing through Matter. By William Wilson, M.Sc., Hon. Research Fellow of the University of Manchester. Communicated by Prof. E. Rutherford, F.R.S...... 141 Rate of Emission of a-Particles from Uranium and its Products. By J. N. Brown, A.R.C.S. Communicated by Prof, the Hon. R. J. Strutt, F.R.S...... 151 On Radiation in a Gaseous Explosion. By Bertram Hopkinson, F.R.S...... 155 The Effect of Small Traces of Water Vapour on the Velocities of Ions produced by Rontgen Rays in Air. By Robert Tabor Lattey. Communicated by Prof. J. S. Townsend, F.R.S...... 173 On the Variation with Temperature of the Viscosities of the Gases of the Argon Group. By A. O. Rankine, D.Sc., Assistant in the Department of Physics, University College, London. Communicated by Prof. F. T. Trouton, F.R.S. ... 181 Additional Refractive Indices of Quartz, Vitreous Silica, Calcite, and Fluorite. By J. W. Gifford. Communicated by Prof. S. P. Thompson, F.R.S...... 193 The Accumulation of Helium in Geological Time.—IV. By the Hon. R. J. Strutt, F.R.S., Professor of Physics, Imperial College of Science, South Kensington ... 194

No. A 570.—September 15, 1910. The Wave-making Resistance of Ships : a Study of Certain Series of Model Experiments. By T. H. Havelock, M.A., D.Sc., Armstrong College, Newcastle- on-Tyne. Communicated by Prof. Sir Joseph Larmor, Sec. R.S...... 197 Dispersion of Light by Potassium Vapour. By Prof. P. V. Bevan, Royal Holloway College. Communicated by Prof. Sir J. J. Thomson, F.R.S. (Plate 2) ...... 209 V

PAGE On the Scattering of Homogeneous /3-Ravs and the Number of Electrons in the Atom. By J. A. Crowther, M.A., Fellow of St. John’s College, Cambridge. Communicated by Prof. Sir J. J. Thomson, F.R.S...... 226 Aerial Plane Waves of Finite Amplitude. By Lord Rayleigh, O.M., F.R.S...... 247

No. A 571.—October 21, 1910.

The Origin and Growth of Ripple-mark. By Mrs. Hertha Ayrton. Communicated by the late Prof. W. E. Ayrton, F.R.S. (Plates 3 and 4)...... 285 The Absorption Spectra of Sulphur Vapour at Different Temperatures and Pressures and their Relation to the Molecular Complexity of this Element. By J. Ivon Graham, B.Sc. (Lond.), A.R.C.Sc.I., Royal College of Science, Dublin. Com­ municated by Prof. W. N. Hartley, F.R.S. (Plate 5) ...... 311 A Determination of the Ratio of Mass to Weight for a Radioactive Substance. Bv L. Southerns, B.A. (Cantab.), B.Sc. (Lond.), Whitworth Scholar, 1851 Exhibition Scholar, Emmanuel College, Cambridge. Communicated by Sir J. J. Thomson, F.R.S...... 325 On the Spontaneous Crystallisation and the Melting and Freezing Point Curves of Mixtures of Two Substances which form Mixed Crystals and possess a Minimum or Eutectic Freezing Point.—Mixtures of Azobenzene and Benzyl- aniline. By Miss F. Isaac, formerly Research Fellow of Somerville College. Communicated by Principal H. A. Miers, F.R.S...... '...... 344 On the Improbability of a Random Distribution of the Stars in Space. By F. W. Dyson, M.A., F.RS...... 369 The Conditions Necessary for Discontinuous Motion in Gases. By G. I. Taylor, B.A., Trinity College, Cambridge. Communicated by Prof. Sir Joseph Larmor, Sec. RS...... 371 On the Radium Content of Basalt. By the Hon. R. J. Strutt, F.R.S., Professor of Physics, Imperial College of Science, South Kensington ...... 377 Measurements of the Rate at which Helium is Produced in Thorianite and Pitchblende, with a Minimum Estimate of their Antiquity. By the Hon. R. J. Strutt, F.R.S., Professor of Physics, Imperial College of Science, South Kensington...... 379

No. A 572.—December 15, 1910. Observations on the Anomalous Behaviour of Delicate Balances, and an Account of Devices for Increasing Accuracy in Weighings. By J. J. Manley, Hon. M.A. Oxon., Daubeny Curator, Magdalen College, Oxford. Communicated by Prof. E. B. Elliott, F.R.S. (Abstract)...... 389 The Damping of Sound by Frothy Liquids. By A. Mallock, F.R.S...... 391 On the Determination of the Tension of a recently-formed Water-Surface. By N. Bohr, Copenhagen. Communicated by Lord Rayleigh, O.M., F.R.S...... 395 VI

PAGE The Tidal Observations of the British Antarctic Expedition, 1907. By Sir George Darwin, K.C.B., F.R.S...... 403 On a Mistake in the Instructions for the Use of a Certain Apparatus in Tidal Reductions. By Sir G. H. Darwin, K.C.B., F.R.S...... 423 On the Sequence of Chemical Forms in Stellar Spectra. By Sir Norman Lockyer, K.C.B., F.R.S. (Plate 6)...... 426 A Spectroscopic Investigation of the Nature of the Carriers of Positive Electricity from Heated Aluminium Phosphate. By Frank Horton, M.A., D.Sc., Fellow of St. John’s College, Cambridge. Communicated by Sir J. J. Thomson, F.R.S...... 433 Colour-Blindness and the Trichromatic Theory of Colour Vision. Part II.— Incomplete Red or Green Blindness. By Sir W. de W. Abney, K.C.B., D.Sc., F.R.S...... 449 On the Sensibility of the Eye to Variations of Wave-length in the Yellow Region of the Spectrum. By Lord Rayleigh, O.M., F.R.S...... 464

No. A 573.—January 26, 1911. Address of the President, Sir Archibald Geikie, K.C.B., at the Anniversary Meeting on November 30, 1910 ...... 469 Influence of Viscosity on the Stability of the Flow of Fluids. By A. Mallock, F.R.S...... 482 Optical Dispersion : An Analysis of its Actual Dependence upon Physical Conditions. By T. H. Havelock, M.A., D.Sc., Armstrong College, Newcastle- on-Tyne. Communicated by Prof. Sir Joseph Larmor, Sec. R.S...... 492 The Spectrum of Halley’s Comet. By Charles P. Butler, A.R.C.Sc., F.R.P.S., F.R.A.S. Communicated by Sir Norman Lockyer, K.C.B., F.R.S. (Plate 7)... 523 The Distribution of Electric Force in the Crookes Dark Space. By F. W. Aston, B.Sc., A.I.C., Trinity College, Cambridge. Communicated by Sir J. J. Thomson, F.R.S...... 526 The Density of Niton (“ Radium Emanation ”) and the Disintegration Theory. By Dr. R. Whytlaw Gray and Sir William Ramsay, K.C.B., F.R.S., University College, London...... 536

No. A 574.—February 15, 1911. On Atmospheric Oscillations. ByHorace Lamb, F.R.S...... 551 Sturm-Liouville Series of Normal Functions in the Theory of Integral Equations. By James Mercer, M.A. (Cantab.), D.Sc. (Liverpool), Fellow of Trinity College, Cambridge. Communicated by Prof. A. R. Forsyth, Sc.D., LL.D., F.R.S. (Abstract) ...... 573 Conduction of Heat through Rarefied Gases.—II. By Frederick Soddy, M.A. F.R.S., and Arthur John Berry, B.A., Physical Chemistry Laboratory, University of Glasgow...... 576 Vll

PAGE An Electrostatic Voltmeter for Photographic Recording of Atmospheric Potential. Bv George W. Walker, A.R.C.Sc., M.A., Superintendent of Eskdalemuir Observatory. Communicated by Dr. W. N. Shaw, E.R.S...... 585 The Measurement of End-Standards of Length. By P. E. Shaw, B.A., D.Sc. Communicated by Prof. Poynting, F.R.S...... 589 On the Absolute Expansion of Mercury. By H. L. Callendar, M.A., LL.D., F.R.S., and H. Moss, B.Sc., A.R.C.S., Demonstrator of Physics, Imperial College of S c ie n c e and Technology, S.W. (Abstract) ...... 595 A Geometrical Proof of the Theorem of a Double Six of Straight Lines. By H. F. Baker, Sc.D., F.R.S...... 597

OBITUARY NOTICES OF FELLOWS DECEASED.

Sir Benjamin Baker; Edward John Routli ; Dmitri Ivanovitch Mendeleeff; George Gore; Julius Thomsen; William James Russell; Simon Newcomb... i—xxxviii

Index ...... xxxix

ERRATUM.

P. 209. To title of paper add “ Communicated by Sir J. J. Thomson, F.R.S.