PROCEEDINGS

OF THE

ROYAL SOCIETY OF LONDON

S eries A

CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER,

VOL. CXIII.

LONDON:

P rinted for THE ROYAL SOCIETY and S old by

HARRISON AND SONS, Ltd., ST. MARTIN’S LANE, PRINTERS IN ORDINARY TO HIS MAJESTY.

J anuary, 1927. LONDON HARRISON AND SONS, LTD., PRINTERS IN ORDINARY TO HIS MAJB8TY ST. MARTIN’S LANE. r CONTENTS

SERIES A. VOL. CXIIL

No. A 763—November 1, 1926. PAGE The Metallography of Solid Mercury and Amalgams. By VV. Rosenhain, F.R.S., and A. J. Murphy. (Plates 1-3.) ...... 1 The Forces on a Cylinder in a Stream of Viscous Fluid. By L. N. G. Filon, F.R.S...... 7 Experiments on the Production of Large Copper Crystals. By H. C. H. Carpenter, F.R.S., and S. Tarnura. (Plates 4 and 5.) ...... 28 Primary and Secondary Vortices in Oscillating Fluids. Their Connection with Skin Friction. By the late Mrs. H. Ayrton. (Plates 6-9.) Communicated by T. Mather, F.R.S...... 44 On the Motion of a Sphere in a Rotating Liquid. By S. F. Grace. Communicated by Prof. J. Proudman, F.R.S...... 46 The Mechanism of Activation at Catalytic Surfaces. By H. S. Taylor. Communi­ cated by Dr. E. F. Armstrong, F.R.S...... 77 The Scattering of Cathode Rays. By B. F. J. Schonland. Communicated by Sir Ernest Rutherford, Pres.R.S...... 87 Hydrogen Bands in the Ultra-Violet Lyman Region. By S. Werner. (Plate 10.) Communicated by N. Bohr, For. Mem. R.S...... 107 On the Interpretation of X-Ray, Single Crystal, Rotation Photographs. By J. D. Bernal. Communicated by Sir William Bragg, F.R.S...... 117 The Formation of Twinned Metallic Crystals. By H. C. H. Carpenter, F.R.S., and S. Tamura. (Plates 11-16.)...... 161 The Band Spectra of Helium and Hydrogen at Low Temperatures. By J. C. McLennan, F.R.S., H. G. Smith, and C. A. Lea. (Plate 17.)...... 183 The Longitudinal Magneto-Resistance Effect in Single Crystals of Iron. By W. L. Webster. Communicated by Sir Ernest Rutherford, Pres.R.S...... 196 Absorption Spectra of Pyrone Derivatives in the Near Infra-Red. By A. Ross. Communicated by Prof. J. N. Collie, F.R.S...... 208 An apparently Unimolecular Reaction—The Homogeneous Decomposition of Gaseous Propionic Aldehyde. By C. N. Hinshelwood and H. W. Thompson. Com­ municated by N. V. Sidgwick, F.R.S...... 221 IV

PAGE On the Theory of Unimolecular Reactions. By C. N. Hinshehvood. Communicated by N. V. Sidgwick, F.R.S...... 23 The Effect of Temperature on the Viscosity of Air. By F. A. Williams. Communi­ cated by H. B. Dixon, F.R.S...... 233

No. A 764—December 1, 1926. Integrals of the Equations of Electrodynamics with an Application to the Electric Constants of a Transparent Medium. By H. M. Macdonald, F.R.S...... 237 The Initial Stages of the Dehydrogenation and Isomeric Change of Allyl Alcohol. By F. H. Constable. Communicated by Prof. T. M. Lowry, F.R.S...... 254 The Properties of Torsional Vibrations in Reciprocating Engine Shafts—Part I. By G. R. Goldsbrough. Communicated by Prof. T. H. Havelock, F.R.S. 259 The Properties of Torsional Vibrations in Reciprocating Engine Shafts—Part II. By G. R. Goldsbrough and H. Baker. Communicated by Prof. T. H. Havelock, F.R.S...... 272 The Secondary and Tertiary Cathode Rays produced by External and Internal Absorption of Homogeneous X-Rays. By H. R. Robinson and A. M. Cassie. Communicated by Prof. C. G. Barkla, F.R.S...... 282 On the Densities of Particles in Smokes. By H. S. Patterson and R. Whytlaw-Gray. (Plate 18.) Communicated by N. V. Sidgwick, F.R.S...... 302 The Scattering of Light by the Individual Particles in Smokes. By H. S. Patterson and R. Whytlaw-Gray. Communicated by N. V. Sidgwick, F.R.S...... 312 ■ The Spectrum of Fluorine (FI). By H. Dingle. (Plate 19.) Communicated by A. Fowler, F.R.S...... 323 The Thermal Conductivity of Vitreous Silica, with a Note on Crystalline Quartz. By G. W. C. Kaye and W. F. Higgins. Communicated by Sir Joseph Petavel, F.R.S...... 335 The Polymorphism of Silicon Dioxide and the Structure of Tridymite. By R. E. Gibbs. Communicated by Sir William Bragg, F.R.S...... 351 Structure in the Secondary Hydrogen Spectrum—Part V. By O. W. Richardson, F-R-S...... 368 Supplementary Table of Wave-Lengths of New Lines in the Secondary Spectrum of Hydrogen. By D. B. Deodhar. Communicated by O. W. Richardson, F.R.S. ... 420 General korms of Statistical Mechanics with Special Reference to the Requirements of the New Quantum Mechanics. By R. H. Fowler, F.R.S...... 432 On Wireless Interference Phenomena between Ground Waves and Waves deviated by the Upper Atmosphere. By E. V. Appleton and M. A. F. Barnett. (Plate 20.) Communicated by Admiral of the Fleet, Sir Henry Jackson, F.R.S...... 450- V

Conduction of Heat through Powders and its Dependence on the Pressure and Conductivity of the Gaseous Phase. By J. Aberdeen and T. H. Laby. Com­ municated by H. L. Callendar, F.R.S...... 459 A Further Note upon “ Intertraction.” By N. K. Adam. Communicated by Sir William Hardy, F.R.S...... 478

No. A 765—January 1, 1927. Address of the President, Sir Ernest Rutherford, at the Anniversary Meeting, November 30, 1926 ...... 481 On Hilbert’s World-Function. By E. T. Whittaker, F.R.S...... 496 Magnetic Double-Refraction in Liquids. Part I.—Benzene and its Derivatives. By C. V. Raman, F.R.S., and K. S. Krishnan ...... 511 The Vapour Pressures and Melting Points of Sodium and Potassium. By W. Edmond­ son and A. Egerton, F.R.S...... 520 The Chemical and other Thermal Constants of Sodium and Potassium. |By W. Edmondson and A. Egerton, F.R.S...... 533 Theorems concerning Mean Values of Analytic Functions. By G. H. Hardy, F.R.S., A. E. Ingham and G. Polya ...... 542 On the Rate of Maximum Activation by Collision for Complex Molecules with Applica­ tions to Velocities of Gas Reactions. By R. H. Fowler, F.R.S., and E. K. Rideal 570 An X-Ray Study of Isomorphism in Simple Organo-Metallic Series. Part I.— The Tetraphenyls. By W. H. George. (Plates 21-22.) Communicated by Sir William Bragg, F.R.S...... i...... 585

The Equilibrium of Heterogeneous Systems including Electrolytes. Part II.— Equilibrium at Interfaces and the Theory of Electro-capillarity. By J. A. V. Butler. Communicated by F. G. Donnan, F.R.S...... 594 Adhesives and Adhesion: True Chemical Compounds as Adhesives. By J. W. McBain, F.R.S., and W. B. L ee...... 606 The Physical Interpretation of the Quantum Dynamics. By P. A. M. Dirac. Com­ municated by R. H. Fowler, F.R.S...... 621 The Structure of Phenacite, Be2Si04. By W. L. Bragg, F.R.S...... 642 On the Form and Energy of Crystalline Sodium Nitrate. By J. Topping and S. Chapman, F.R.S...... 658 Some Theoretical Determinations of the Structure of Carbonate Crystals.—I. By J. E. Lennard-Jones and B. M. Dent. Communicated by S. Chapman, F.R.S. ... 673 Some Theoretical Determinations of the Structure of Carbonate Crystals.—II. By J. E. Lennard-Jones and B. M. Dent. Communicated by S. Chapman, F.R.S. ... 690 On Measurement of Intensity of Spectrum Lines. By T. R. Merton, F.R.S. (Plate 23.)] 697 VI

PAQB On Temperature and Pressure Regulation in Prismatic Spectrographs. By T. R. Merton, F.R.S...... 704 The Measurement of Absorptive Power. By E. C. C. Baly, P.R.S., R. A. Morton and R. W. Riding ...... 709 Absorption Spectra of Nitrates in the Region 300 (X ft. By R. A. Morton and R. W. Riding. Communicated by E. C. C. Baly, F.R.S...... 717 On the Proportionality of Mass and Weight. By H. H. Potter. Communicated by O. W. Richardson, F.R.S...... Minutes of Meetings of November 4, 11, 18, 30 ; December 2.

Obituary Notices (with portraits)Heike Kamerlingh Onnes; Sir Philip Watts ; James Thomson Bottomley ...... j