dhe lioycdS(Soc op Lond
}i. K y^'oCfencCen cUCet sc. tcmtcn 1945 PROCEEDINGS
OF THE
ROYAL SOCIETY OF LONDON
S e r ie s A
CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER.
YOL. XCIII.
LONDON:
P rinted for THE ROYAL SOCIETY a nd S old by HARRISON AND SONS, ST. MARTIN’S LANE, PRINTERS IN ORDINARY TO HIS MAJESTY.
October, 1917. LONDON: HABEISON AND SONS, PBINTEBS IN OEDINAEY TO HIS MAJESTY, ST. MABTIN’S DANE. CONTENTS
SERIES A. VOL. XCIII.
No. A 646.—December 1, 1916. PAGE The Kinetic Theory of Simple and Composite Monatomic Gases: Viscosity, Thermal Conduction, and Diffusion. By S. Chapman, M.A., D.Sc., Fellow and Lecturer of Trinity College, Cambridge. Communicated by Sir J. Larmor, F.R.S. (Abstract) ...... 1 On the Mechanical Relations of the Energy of Magnetisation. By G. H. Livens, The University, Sheffield. Communicated by Sir J. Larmor, F.B.S...... 20 On Phenomena relating to the Spectra of Hydrogen and Helium. By T. R. Merton, D.Sc., and Prof. J. W. Nicholson, M.A., D.Sc. Communicated by A. Fowler, F.R.S. (Abstract) ...... 27
No. A 647.—February 1, 1917. On Multiple Integrals. By Prof. W. H. Young, Sc.D., F.R.S...... 28 On the Order of Magnitude of the Coefficients of a Fourier Series. By Prof. W. H. Young, Sc.D., F.R.S...... 42 The Corrosion and Electrical Properties of Steels. By Sir Robert Hadfield, F.R.S., and Edgar Newbery, D.Sc...... 56 Monoclinic Double Selenates of the Nickel Group. By A. E. H. Tutton, D.Sc., M.A., F.R.S. (Abstract)...... 68 X-Ray Analysis and Topic Axes of the Alkali Sulphates, and their Bearing on the Theory of Valency Volumes. By A. E. H. Tutton, D.Sc., M.A., F.R.S. ... 72 Address of the President, Sir J. J. Thomson, O.M., at #ie Anniversary Meeting, November 30, 1916 ...... 90
No. A 648.—March 1, 1917. Motion of Solids in Fluids when the Flow is not Irrotational. By G. I. Taylor, M.A. Communicated by Prof. H. Lamb, F.R.S...... 99 On Waves in an Elastic Plate. By Horace Lamb, F.RS...... 114 Magnetic Induction and its Reversal in Spherical Iron Shells. By J. W. Nicholson, M.A., D.Sc., Professor of Mathematics in the University of London, and Ernest Wilson, M.Inst.C.E., M.Inst.E.E., Siemens Professor of Electrical Engineering in the University of London, King’s College. Communicated by Prof. J. A. Fleming, F.R.S...... 129 On the Dynamics of Revolving Fluids. By Lord Rayleigh, O.M., F.RS...... 148 IV
No. A 649—April 2, 1917. PAGE A Determination of the Heat of Vaporisation of Water at 100° C. and One Atmosphere Pressure in Terms of the Mean Calorie. By T. Carlton-Sutton, B.Sc., Government Research Scholar in the University of Melbourne, 1914—15. Communicated by Principal E. H. Griffiths, F.R.S...... 155 The Magnetic Storm of August 22, 1916. By C. Chree, Sc.D., LL.D., F.R.S., Superintendent of Kew Observatory ...... 177 Spontaneous Generation of Heat in Recently Hardened Steel. By Charles F. Brush and Sir Robert A. Hadfield, F.R.S...... 188
No. A 650.—May 3, 1917. An Application of the Theory of Probabilities to the Study of a'priori Pathometry. —Part II. By Lieut.-Colonel Sir Ronald Ross, K.C.B., F.R.S., R.A.M.C.T.F., and Hilda P. Hudson, M.A., Sc.D...... 212 An Application of the Theory of Probabilities to the Study of a priori Pathometry. —Part III. By Lieut.-Colonel Sir Ronald Ross, K.C.B., F.R.S., R.A.M.C.T.F., and Hilda P. Hudson, M.A., Sc.D...... 225 The Initial Wave Resistance of a Moving Surface Pressure. By T. H. Havelock, F.R.S., Professor of Applied Mathematics in the University of Durham...... 240 Spectroscopic Observations on the Active Modification of Nitrogen.—V. By the Hon. R. J. Strutt, F.R.S. (Plate 1) ...... 254
No. A 651.—June 1, 1917. The Selective Properties of the Copper Ferrocyanide Membrane. By Frank Tinker, D.Sc. Communicated by Sir Oliver Lodge, F.R.S...... 268 On the Ordinary Convergence of Restricted Fourier Series. By Prof. W. H. Young, Sc.D., F.R.S...... 276 On the Deflection of the Vertical by Tidal Loading of the Earth’s Surface. By Horace Lamb, F.R.S...... 293 Torsional Hysteresis of Mild Steel. By J. J. Guest and F. C. Lea. Communicated by Sir Oliver Lodge, F.RiS...... '...... 313
No. A 652.—July 2, 1917. A Graphical Method of Drawing Trajectories for High-Angle Fire. By W. E. Dalby, F.R.S...... 333 The Dissipation of Energy in the Tides in Connection with the Acceleration of the Moon’s Mean Motion. By R. O. Street, M.A., The University, Liverpool. Communicated by Sir Joseph Larmor, F.R.S...... 348 The Complete Photo-electric Emission from the Alloy of Sodium and Potassium. By William Wilson, Pli.D. Communicated by Prof. O. W. Richardson, F.R.S. 359 Experiments with Mercury Jets. By S. W. J. Smith, M.A., D.Sc., F.R.S., and H. Moss, M.Sc., Imperial College, South Kensington ...... 373 V
PAGE No. A 653.—August 1, 1917. On Residual Magnetism in Relation to Magnetic Shielding. By Ernest Wilson, M.Inst.C.E., M.I.E.E., Siemens Professor of Electrical Engineering, and J. W. Nicholson, M.A., D.Sc., Professor of Mathematics in the University of London. Communicated by Prof. J. A. Fleming, F.R.S...... 393 Gravitational Instability and the Figure of the Earth. By J. H. Jeans, M.A., F. R.S...... 413 X-Ray Analysis of the Crystal-Structure of Rutile and Cassiterite. By C. M. Williams, B.Sc., Fellow of the University of Wales. Communicated by Dr. E. H. Griffiths, F.R.S...... 418 The Composition of the X-Rays from Various Metals. By G. W. C. Kaye, M.A., D.Sc., Captain R.E. (T.). Communicated by Dr. R. T. Glazebrook, F.R.S...... 427 On Magnetic Inertia. By George W. Walker, M.A., A.R.C.Sc., F.R.S., formerly Fellow of Trinity College, Cambridge ...... 442 The Effective Inertia of Electrified Systems Moving with High Speed. By George W. Walker, A.R.C.Sc., M.A., F.R.S., formerly Fellow of Trinity College, Cambridge ...... 448
No. A 654.—September 1, 1917. On the Mode of Approach to Zero of the Coefficients of a Fourier Series. By W. H. Young, F.R.S...... 455 The High-Frequency Resistance of Multiply-Stranded Insulated Wire. By G. W. O. Howe, D.Sc., M.I.E.E. Communicated by Prof. T. Mather, F.R.S.... 468 On Permanent Periodicity in Sunspots. By Sir Joseph Larmor, F.R.S., Cambridge, and N. Yamaga, University of Tokio...... 493 The Lateral Vibrations of Bars of Variable Section. By J. W. Nicholson, M.A., D.Sc., F.R.S., Professor of Mathematics in the University of London ...... 506 Some Cases of Wave Motion due to a Submerged Obstacle. By T. H. Havelock, F.R.S...... 520
No. A 655.—October 9, 1917. Problems Bearing on Residual Affinity. By Spencer Umfreville Pickering, M.A., F.R.S. (Plate 2) ...... 533 The Theory of Decay in Radioactive Luminous Compounds. By J. W. T. Walsh, B.A. (Oxon), B.Sc. (Lond.) Communicated by R. T. Glazebrook, F.R.S...... 550 On the Reflection of Light from a Regularly Stratified Medium. By Lord Rayleigh, O.M., F.R.S...... 565 Absorption Bands of Atmospheric Ozone in the Spectra of Sun and Stars. By A. Fowler, F.R.S., Professor of Astrophysics, and the Hon. R. J. Strutt, F.R.S., Professor of Physics, Imperial College, South Kensington. (Plate 3) ...... 577 Note on the Specific Heat of Water. By W. R. Bousfield, M.A., K.C., F.R.S...... 587 VI
OBITUAEY NOTICES OF FELLOWS AND OTHERS DECEASED. PAGE Sir Henry Roscoe (with portrait) ; Henry Gwyn Jeffreys Moseley ; Raphael Meldola (with portrait) ; Benjamin Williamson ; Sir James Stirling ; Sir William Ramsay (with portrait) ; William Esson...... i—lvii
Index ...... lix