INDEX TO VOLUME 283 (A)

Abragam, A. The Overhauser effect (discussion), 458.Address of the President, Sir Howard Florey, at the Anniversary Meeting, 30 November

1964, v.Analysis of randomized experiments with orthogonal block structure. I. Block structure

and the null analysis of variance (Nelder), 147.Analysis of randomized experiments with orthogonal block structure. II. Treatment

structure and general analysis of variance (Nelder), 163.Appendix to a paper by Donnelly & Schwarz (Roberts), 550.Arpaci, V. S., Clark, J. A. & Larsen, P. S. The dynamics of gas-vapour bubbles in

binary systems, 50.

Bacon, M. D. See Dean & Bacon.Bailyn’s exchange correlation and phonon spectrum of sodium (Dayal & Srivastava), 394.Bakerian Lecture, 1964. Inventive technology: the search for better electric machines

(Williams), 1.Basco, N. & Norrish, R. G. W. The reaction of cyanogen radicals with nitric oxide, 291.Basco, N. The reaction of cyanogen radicals with oxygen, 302.Birks, J. B., Braga, C. L. & Lumb, M. D. ‘Excimer ’ flourescence. VI. Benzene, toluene,

p-xylene and mesitylene, 83.Boyer, R. H. Rigid frames in general relativity, 343.Braga, C. L. See Birks, Braga & Lumb.Brogden, T. W. P. Dynamic polarization work at A.E.R.E., Harwell (discussion), 480.

Calculation of the phonon frequencies in sodium (Sham), 33.Campbell, I. A., Stone, N. J. & Turrell, B. G. The polarization of radioactive gold nuclei

in iron, 379.Charlesby, A. & Partridge, R. H. The identification of luminescence centres in polyethy­

lene and other polymers, 312.Charlesby, A. & Partridge, R. H. Thermoluminescence and phosphorescence in poly­

ethylene under ultra-violet irradiation, 329.Clark, J. A. See Arpaci, Clark & Larsen.Coates, P. B. & Gaydon, A. G. A simple shock tube with detonating driver gas, 18.Crystal structure of graphite-bromine compounds (Eeles & Turnbull), 179.

Dayal, B. & Srivastava, P. L. Bailyn’s exchange correlation and phonon spectrum of sodium, 394.

Dean, P. & Bacon, M. D. Vibrations of two-dimensional disordered lattices, 64.Deformation of metals under small stresses during phase transformations (Greenwood &

Johnson), 403.Direct calculation of the first-order density matrix for atoms (Hall, Jones & Rees), 194.Discussion on magnetic relaxation (Richards and others), 433.Dispersion of Ostwald-de Waele fluid in laminar flow through a cylindrical tube (Fan &

Hwang), 576.Dixon, R. N. & Kroto, H. W. The electronic spectrum of nitrosomethane, CH3NO, 423.Donnelly, R. J. Experiments on the stability of viscous flow between rotating cylinders.

IV. The ion technique, 509.Donnelly, R. J. & Schwarz, K. W. Experiments on the stability of viscous flow between

rotating cylinders. VI. Finite amplitude experiments (With an appendix by P. H. Roberts), 531.

[ 583 ]

Donnelly, R. J. & Tanner, D. J. Experiments on the stability of viscous flow between rotating cylinders. V. The theory of the ion technique, 520.

Dove, J. E. & Moulton, D. McL. Shock wave studies by mass spectrometry. III. Des­cription of apparatus; data on the oxidation of acetylene and of methane, 216.

Dynamic nuclear polarization in crystals (discussion) (Jeffries), 471.Dynamic polarization work at A.E.R.E., Harwell (discussion) (Brogden), 480.Dynamics of gas-vapour bubbles in binary systems (Arpaci, Clark & Larsen), 50.

Eeles, W. T. & Turnbull, J. A. The crystal structure of graphite-bromine compounds, 179.

Electron diffraction investigation of the pen-bonds in perylene (Traetteberg), 557.Electronic spectrum of nitrosomethane, CH3NO (Dixon & Kroto), 423.Endor studies of ligand interactions (discussion) (Hurrell), 448.Endor with europium isotopes (discussion) (Williams), 445.‘ Exeimer ’ flourescenee. VI. Benzene, toluene, p-xylene and mesitylene (Birks, Braga &

Lumb), 83.Experiments on the stability of viscous flow between rotating cylinders. IV. The ion

technique (Donnelly), 509.Experiments on the stability of viscous flow between rotating cylinders. V. The theory of

the ion technique (Donnelly & Tanner), 520.Experiments on the stability of viscous flow between rotating cylinders. VI. Finite

amplitude experiments. (With an appendix by P. H. Roberts) (Donnelly & Schwarz), 531.

Fan, L. T. & Hwang, W. S. Dispersion of Ostwald-de Waele fluid in laminar flow through a cylindrical tube, 576.

Florey, Sir Howard. Address of the President at the Anniversary Meeting, 30 November 1964, v.

Gaydon, A. G. See Coates & Gaydon.Gaydon, F. A. The rectangle, under general equilibrium loading, in generalized plane

stress, 356.Greenwood, G. W. & Johnson, R. H. The deformation of metals under small stresses

during phase transformations, 403.

Hall, G. G., Jones, L. L. & Rees, D. The direct calculation of the first-order density matrix for atoms, 194.

Hilton, Elizabeth. The singularity in the Schwarzschild space-time, 491.Hurrell, J. P. Endor studies of ligand interactions (discussion), 448.Hwang, W. S. See Fan & Hwang.Hypervirial theorems and perturbation theory in quantum mechanics (Robinson), 229.

Identification of luminescence centres in polyethylene and other polymers (Charlesby & Partridge), 329.

Importance of coupling for inelastic collisions between protons and hydrogen atoms (Lovell & McElroy), 100.

Inventive technology: the search for better electric machines (Bakerian Lecture, 1964) (Williams), 1.

Ionization of atomic hydrogen by electron impact (Rudge & Seaton), 262.

Jeffries, C. D. Dynamic nuclear polarization in crystals (discussion), 471.Johnson, R. H. See Greenwood & Johnson.Jones, L. L. See Hall, Jones & Rees.

584 Index

Index 585

Kennedy, S. W. & Patterson, J. H. Mechanisms of structure transformations in thallous nitrate crystals, 498.

Klein-Gordon model particle (Synge), 14.Kroto, H. W. See Dixon & Kroto.

Larsen, P. S. See Arpaci, Clark & Larsen.Lerche, I. Unstable cyclotron waves in relativistic plasma, 203.Levy, A. An optical study of flammability limits, 134.Lovell, S. E. & McElroy, M. B. Importance of coupling for inelastic collisions between

protons and hydrogen atoms, 100.Lumb, M. D. See Birks, Braga & Lumb.

McElroy, M. B. See Lovell & McElroy.Mechanisms of structure transformations in thallous nitrate crystals (Kennedy & Patter­

son), 498.Mims, W. B. Pulsed endor experiments (discussion), 452.Moulton, D. McL. See Dove & Moulton.

Nelder, J. A. The analysis of randomized experiments with orthogonal block structure.I. Block structure and the null analysis of variance, 147.

Nelder, J. A. The analysis of randomized experiments with orthogonal block structure.II. Treatment structure and the general analysis of variance, 163.

Non-linear dispersive waves (Whitham), 238.Norrish, R. G. W. See Basco & Norrish.Nuclear electron double resonance in liquids (discussion) (Richards & White), 459.

Oldroyd, J. G. Some steady flows of the general elastico-viscous liquid, 115.Optical study of flammability limits (Levy), 134.Overhauser effect (discussion) (Abragam), 458.

Partridge, R. H. See Charlesby & Partridge.Patterson, J. H. See Kennedy & Patterson.Polarization of radioactive gold nuclei in iron (Campbell, Stone & Turrell), 379. Presidential Address. Address of the President, Sir Howard Florey, at the Anniversary

Meeting, 30 November 1964, v.Pryce, M. H. L. Resonance and relaxation in cobalt-doped magnesium oxide (discus­

sion), 433.Pulsed endor experiments (discussion) (Mims), 452.

Reaction of cyanogen radicals with nitric oxide (Basco & Norrish), 291.Reaction of cyanogen radicals with oxygen (Basco), 302.Rectangle, under general equilibrium loading, in generalized plane stress (Gaydon), 356 Rees, D. See Hall, Jones & Rees.Resonance and relaxation in cobalt-doped magnesium oxide (discussion) (Pryce), 433. Richards, R. E. and others. A discussion on magnetic relaxation, 433.Richards, R. E. & White, J. W. Nuclear electron double resonance in liquids (discussion),

459.Rigid frames in general relativity (Boyer), 343.Roberts, P. H. Appendix to a paper by Donnelly & Schwarz, 550.Robinson, P. D. Hypervirial theorems and perturbation theory in quantum mechanics,

229.Rudge, M. R. H. & Seaton, M. J. Ionization of atomic hydrogen by electron impact,

262.

Rutherford in nineteenth-century Cambridge (Rutherford Lecture, 1964) (Thomson), 481.

Rutherford Lecture, 1964. Rutherford in nineteenth-century Cambridge (Thomson), 481.

Schwarz, K. W. See Donnelly & Schwarz.Seaton, M. J. See Rudge & Seaton.Sham, L. J. A calculation of the phonon frequencies in sodium, 33.Shock wave studies by mass spectrometry. III. Description of apparatus; data on the

oxidation of acetylene and of methane (Dove & Moulton), 216.Simple shock tube with detonating driver gas (Coates & Gaydon), 18.Singularity in the Schwarzschild space-time (Hilton), 491.Some steady flows of the general elastico-viscous liquid (Oldroyd), 115.Srivastava, P. L. See Dayal & Srivastava.Stone, N. J. See Campbell, Stone & Turrell.Synge, J. L. A Klein-Gordon model particle, 14.

Tanner, D. J. See Donnelly & Tanner.Thermoluminescence and phosphorescence in polyethylene under ultra-violet irradiation

(Charlesby & Partridge), 329.Thomson, Sir George. The Rutherford Lecture, 1964. Rutherford in nineteenth-century

Cambridge, 481.Traetteberg, Marit. An electron diffraction investigation of the peri-bonds in perylene,

557.Turnbull, J. A. See Eeles & Turnbull.Turrell, B. G. See Campbell, Stone & Turrell.

Unstable cyclotron waves in relativistic plasma (Lerche), 203.

Vibrations of two-dimensional disordered lattices (Dean & Bacon), 64.

White, J. W. See Richards & White.Whitham, G. B. Non-linear dispersive waves, 238.Williams F. C. The Bakerian Lecture, 1964. Inventive technology: the search for better

electric machines, 1.Williams, F. I. B. Endor with europium isotopes (discussion), 445.

586 Index

END OF THE TWO-HUNDRED AND EIGHTY-THIRD VOLUME (SERIES A)

PROCEEDINGSOF THE

ROYAL SOCIETY OF LONDON

SERIES A. MATHEMATICAL AND PHYSICAL SCIENCES

VOL 283

Published by the Royal Society Burlington House

Piccadilly London, W. 1

26 January 1965

Printed in Great Britain at the University Printing House, Cambridge (Brooke Crutchley, University Printer)

CONTENTS SERIES A VOLUME 283

No. 1392 5 January 1965PAGE

Address of the President, Sir Howard Florey, at the Anniversary Meeting,30 November 1964 ..........................................................................................v

The Bakerian Lecture, 1964. Inventive technology: the search for better electricmachines. By F. C. Williams, F.R.S. (Plates 1 to 4) . . . . . 1

A Klein-Gordon model particle. By J. L. Synge, F.R.S. . . . . . 14A simple shock tube with detonating driver gas.

By P. B. Coates and A. G. Gaydon, F.R.S. (Plate 5) . . . . . 18A calculation of the phonon frequencies in sodium. By L. J. Sham . . . 33The dynamics of gas-vapour bubbles in binary systems.

By V. S. Arpaci, J. A. Clark and P. S. Larsen . . . . . . 50Vibrations of two-dimensional disordered lattices. By P. Dean and M. D. Bacon 64‘ Excimer ’ fluorescence. VI. Benzene, toluene, p-xylene and mesitylene.

By J. B. Birks, C. L. Braga and M. D. Lumb . . . . . . 83Importance of coupling for inelastic collisions between protons and hydrogen

atoms. By S. E. Lovell and M. B. McElroy . . . . . . 100Some steady flows of the general elastico-viscous liquid. By J. G. Oldroyd . 115An optical study of flammability limits. By A. Levy. (Plates 6 and 7) . . 134

No. 1393 6 January 1965The analysis of randomized experiments with orthogonal block structure

I. Block structure and the null analysis of variance. By J. A. Nelder . 147The analysis of randomized experiments with orthogonal block structure.

II. Treatment structure and the general analysis of variance.By J. A. Nelder . . . . . . . . . . . . 163

The crystal structure of graphite-bromine compounds.By W. T. Eeles and J. A. Turnbull. (Plates 8 to 1 3 ) ....................................179

The direct calculation of the first-order density matrix for atoms.By G. G. Hall, L. L. Jones and D. Rees . . . . . . . 194

Unstable cyclotron waves in relativistic plasma. By I. Lerche . . . . 203Shock wave studies by mass spectrometry. III. Description of apparatus;

data on the oxidation of acetylene and of methane.By J. E. Dove and D. McL. Moulton. (Plate 14) . . . . . . 216

Hypervirial theorems and perturbation theory in quantum mechanics.By P. D. Robinson . . . . . . . . . . . 229

Non-linear dispersive waves. By G. B. Whitham . . . . . . 238Ionization of atomic hydrogen by electron impact.

By M. R. H. Rudge and M. J. Seaton . . . . . . . . 262

No. 1394 19 January 1965The reaction of cyanogen radicals with nitric oxide.

By N. Basco and R. G. W. Norrish, F.R.S. (Plates 15 and 16) . . . 291The reaction of cyanogen radicals with oxygen. By N. Basco. (Plates 17 to 20) 302The identification of luminescence centres in polyethylene and other polymers.

By A. Charlesby and R. H. Partridge . . . . . . . . 312

iv ContentsPAGE

Thermoluminescence and phosphorescence in polyethylene under ultra-violetirradiation. By A. Charlesby and R. H. Partridge . . . . . 329

Rigid frames in general relativity. By R. H. Boyer . . . . . . 343The rectangle, under general equilibrium loading, in generalized plane stress.

By F. A. Gaydon . . . . . . . . . . . 356The polarization of radioactive gold nuclei in iron.

By I. A. Campbell, N. J. Stone and B. G. Turrell . . . . . 379Bailyn’s exchange correlation and phonon spectrum of sodium.

By B. Dayal and P. L. Srivastava . . . . . . . . 394The deformation of metals under small stresses during phase transformations.

By G. W. Greenwood and R. H. Johnson . . . . . . . 403The electronic spectrum of nitrosomethane. CH3NO.

By R. N. Dixon and H. W. Kroto. (Plates 21 and 22) . . . . 423

No. 1395 26 January 1965A Discussion on Magnetic R elaxation

Organized by R. E. Richards, F.R.S.M. H. L. Pryce, F.R.S. Resonance and relaxation in cobalt-doped magnesium

oxide . . . . . . . . . . . . . .F. I. B. Williams. Endor with europium isotopes . . . . . .J . P. Hurrell. Endor studies of ligand interactions . . . . . .W. B. Mims. Pulsed endor experiments . . . . . . . .A. Abragam. The Overhauser effect . . . . . . . . .R. E. Richards, F.R.S. and J. W. White. Nuclear electron double resonance in

liquids . . . . . . . . . . . . . .C. D. Jeffries. Dynamic nuclear polarization in crystals . . . . . T. W. P. Brogden. Dynamic polarization work at A.E.R.E., Harwell

433445448452458

459 471 480

The Rutherford Lecture, 1964. Rutherford in nineteenth-century Cambridge.By Sir George Thomson, F.R.S. . . . . . . . . . 481

The singularity in the Schwarzchild space-time. By Elizabeth Hilton . . 491Mechanisms of structure transformations in thallous nitrate crystals.

By S. W. Kennedy and J. H. Patterson. (Plate 23) . . . . . 498Experiments on the stability of viscous flow between rotating cylinders. IV. The

ion technique. By R. J. Donnelly . . . . . . . . 509Experiments on the stability of viscous flow between rotating cylinders. V. The

theory of the ion technique. By R. J. Donnelly and D. J. Tanner . . 520Experiments on the stability of viscous flow between rotating cylinders.

VI. Finite-amplitude experiments. By R. J. Donnelly and K. W. Schwarz.(With an appendix by P. H. Rober t s. ) . . . . . . . . 531

An electron diffraction investigation of the pen-bonds in perylene.By Marit Traetteberg . . . . . . . . . . . 557

Dispersion of Ostwald-de Waele fluid in laminar flow through a cylindrical tube.By L. T. Fan and W. S. Hwang . . . . . . . . . 576

Index . . . . . . . . . . . . . . 583

THE RO YAL SO C IE T Y IN T E R N A T IO N A L G E O PH Y SIC A L YEAR

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1955-1959

The Royal Society Expedition to Halley Bay in Antarctica was one of the major British contributions to the International Geophysical Year. An extensive research pro­gramme in meteorology, geomagnetism, aurora and airglow, ionospheric physics, radio astronomy, glaciology and seismology was carried out at this Base.

All the experimental observations and derived data are published in a series of four volumes: size royal quarto (125X9! in.). Bound in maroon cloth with gold lettering.

Price £7 ($23.00) each volume.

V olum e I. Foreword. Introduction. The establishment and maintenance of the Royal Society Base. Visual and photographic auroral observations, airglow observations. Geomagnetic observations.

V o l u m e II . Results of ionospheric vertical soundings, absorption and drift measure­ments. Results of radio-star scintillation measurements and of radio-echo obser­vations of aurorae and meteors.

V olum e I I I . Seismological bulletin and notes. Meteorological observations (upper- air radio soundings and radar wind observations; total, diffuse and net radiation measurements total, surface and balloon-borne ozone determination).

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Published by The Royal Society, Burlington House, Piccadilly, London, W. 1.

PROCEEDINGS OF THE ROYAL SOCIETY, SERIES A No 1395 26January 1965 Vol 283

CONTENTS

A D iscussion on Magnetic Relaxation

O rganized by R. E. R ichards, F.R.S.

M. H. L. Pryce, F.R.S. Resonance and relaxation in cobalt-doped mag­nesium oxide . . . . . . . . . .

F. I. B. W illiams. Endor with europium isotopes . . . . .

J. P. H urrell. Endor studies of ligand interactions . . . .

W. B. M ims. Pulsed endor experiments. . . . . . .

A. Abragam. The Overhauser effect . . . . . . .

R. E. R ichards, F.R.S. and J. W. W hite. Nuclear electron double resonance in liquids . . . . . . . . . . .

C. D. J effries. Dynamic nuclear polarization in crystals

T. W. P. Brogden. Dynamic polarization work at A.E.R.E., Harwell

page

433

445

448

452

458

459

471

480

The Rutherford Lecture, 1964. Rutherford in nineteenth-century Cambridge.By Sir GEORGE THOMSON, F.R.S.......................................................481

The singularity in the Schwarzchild space-time.By ELIZABETH H IL T O N ......................................................................491

Mechanisms of structure transformations in thallous nitrate crystals.By S. W. KENNEDY and J. H. PATTERSON. (Plate 23) . . 498

Experiments on the stability of viscous flow between rotating cylinders.IV. The ion technique.By R. J. D O N N ELLY ....................................................................................... 509

Experiments on the stability of viscous flow between rotating cylinders.V. The theory of the ion technique.By R. J. DONNELLY and D. J. T A N N E R ........................................ 520

Experiments on the stability of viscous flow between rotating cylinders.VI. Finite-amplitude experiments.By R. J . DONNELLY and K. W. SCHWARZ. (With an appendix by P. H. Roberts.) . . . . . . . . . . 531

An electron diffraction investigation of the bonds in perylene.By MARIT T R A E T T E B E R G ................................................................... 557

Dispersion of Ostwald-de Waele fluid in laminar flow through a cylindricaltube. By L. T. FAN and W. S. H W A N G ........................................576

Index . . . . . . . . . . . . 583

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