INDEX TO VOLUME 323 (A)

Appendices to a paper by Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’Connor (Waters & Waters), 480; (Dodson), 484.

Application of integral equation methods to the numerical solution of some exterior bonndary-value problems (discussion) (Burton & Miller), 201.

Application of the Zeeman effect to the precise measurement of pulsed magnetic fields (King & Learner), 431.

Ashpole, C. W., Formosinho, S. J. & 'Porter, G. Pressure dependence of intersystem crossing in aromatic vapours, 11.

Astrophysical significance of the dissipation of turbulence in a dense baryon fluid (Jones),111 .

Baker, J. M. & Marsh, D. Interactions between Nd3+ ions beyond the first neighbour shell in LaCl3 and LaBr3, 341.

Basco, N. & Dogra, S. K. Reactions of halogen oxides studied by flash photolysis. I. The flash photolysis of chlorine dioxide, 29.

Basco, N. & Dogra, S. K. Reactions of halogen oxides studied by flash photolysis. II. The flash photolysis of chlorine monoxide and of the CIO free radical, 401.

Basco, N. & Dogra, S. K. Reactions of halogen oxides studied by flash photolysis. III. The production and reactions of BrO and CIO radicals in the halogen-sensitized decomposition of chlorine dioxide, 417.

Boley, B. A. & Yagoda, H. P. The three-dimensional starting solution for a melting slab, 89.

Bryant, F. J., Hagston, W. E. & Radford, C. J. The effects of preferential pairing and its detection using electron radiation damage, 127.

Bulewicz, Elzbieta M. & Padley, P. J. Photometric investigations of the behaviour of chromium additives in premixed H2-f-02 + N2 flames, 377.

Burton, A. J. & Miller, G. F. The application of integral equation methods to the numerical solution of some exterior boundary-value problems (discussion), 201.

Chee-Seng, Lim. Isotropic radiation from a steadily pulsating multidimensional distribution, 555.

Clough, P. N., Curran, A. H. & Thrush, B. A. The e.p.r. spectrum of vibrationally excited hydroxyl radicals, 541.

Computing experience with hyperbolic partial differential equations (discussion) (Elliott), 263.

Coordinate conditions in a Riemannian space for coordinates based on a subspace (Florides & Synge), 1.

Curran, A. H. See Clough, Curran & Thrush.

Dale, D. See Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’Connor.Davies, A. K., McKellar, J. F. & Phillips, G. O. Photochemistry of the piperidino-

anthraquinones, 69.Difference approximations for initial boundary-value problems (discussion) (Kreiss), 255.Discussion on numerical analysis of partial differential equations (Wilkinson and others),

151.Dodson, Eleanor. Appendix to a paper by Venkatesan, Dale el al., 484.Dogra, S. K. See Basco & Dogra.

[ 581 ]

Effects of preferential pairing and its detection using electron radiation damage (Bryant, Hagston & Radford), 127.

Elliott, L. A. Computing experience with hyperbolic partial differential equations (dis­cussion), 263.

E.p.r. spectrum of vibrationally excited hydroxyl radicals (Clough, Curran & Thrush), 541.Experience with the linear Boltzmann equation (discussion) (Hill), 293.

Finite-difference and finite-element methods of approximation (discussion) (Walsh), 155.Finite-difference methods in numerical weather prediction (discussion) (White), 285.Finite-difference techniques for a harmonic mixed boundary problem having a reentrant

boundary (discussion) (Whiteman), 271.Elorides, P. S. & Synge, J. L. Coordinate conditions in a Riemannian space for co­

ordinates based on a subspace, 1.Formosinho, S. J. See Ashpole, Eormosinho & Porter.Fox, L. Some experiments with singularities in linear elliptic partial differential equations

(discussion), 179.

Gourlay, A. R. Some recent methods for the numerical solution of time-dependent partial differential equations (discussion), 219.

Hagston, W. E. See Bryant, Hagston & Radford.Hill, J. G. Experience with the linear Boltzmann equation (discussion), 293.Hinotani, K. SeeKrishnaswamy, Menon et aHodgkin, Dorothy C. See Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’Connor.

Interactions between Nd3+ ions beyond the first neighbour shell in LaCl3 and LaBr3 (Baker & Marsh), 341.

Introductory remarks to a discussion (Wilkinson), 153.Isotropic radiation from a steadily pulsating multidimensional distribution (Chee-

Seng), 555.Ito, N. See Krishnaswamy, Menon et al.

Jonah, D. A. & King, M. B. A method for predicting the variation with temperature of the solubilities of gases in non-polar liquids, 361.

Jones, P. B. Astrophysical significance of the dissipation of turbulence in a dense baryon fluid, 111.

Kendall, K. & Tabor, D. An ultrasonic study of the area of contact between stationary and sliding surfaces, 321.

King, M. B. See Jonah & King.King, P. W. & Learner, R. C. M. The application of the Zeeman effect to the precise

measurement of pulsed magnetic fields, 431.Kolar Gold Fields neutrino experiment. I. The interactions of cosmic ray neutrinos

(Krishnaswamy, Menon, Narasimham, Hinotani, Ito, Miyake, Osborne, Parsons & Wolfendale), 489.

Kolar Gold Fields neutrino experiment. II. Atmospheric nuons at a depth of 7000 hg cm-2 (Kolar) (Krishnaswamy, Menon, Narasimham, Hinotani, Ito, Miyake, Osborne, Parsons & Wolfendale), 511.

Kreiss, H.-O. Difference approximations for initial boundary-value problems (discussion), 255.

582 Index

Index 583

Krishnaswamy, M. R., Menon, M. G. K., Narasimham, V. S., Hinotani, K., Ito, N., Miyake, S., Osborne, J. L., Parsons, A. J. & Wolfendale, A. W. The Kolar Gold Fields neutrino experiment. I. The interactions of cosmic ray neutrinos, 489.

Krishnaswamy, M. R., Menon, M. G. K., Narasimham, V. S., Hinotani, K., Ito, N., Miyake, S., Osborne, J. L., Parsons, A. J. & Wolfendale, A. W. The Kolar Gold Fields neutrino experiment. II. Atmospheric muons at a depth of 7000 hg cm-2 (Kolar), 511.

Lasers and light scattering. Review Lecture (Smith), 305.Learner, R. C. M. See King (P. W.) & Learner.Lee, A. E. & Singer, K. E. Studies of the tungsten-oxygen surface reaction by means

of reflexion high energy electron diffraction, 523.Longuet-Higgins, M. S. A numerical disproof of a conjecture in projective geometry, 443.

McKellar, J. F. See Davies, McKeller & Phillips.Marsh, D. See Baker & Marsh.Menon, M. G. K. See Krishnaswamy, Menon etMethod for predicting the variation with temperature of the solubilities of gases in non­

polar liquids (Jonah & King), 361.Miller, G. F. See Burton & Miller.Mitchell, A. R. Variational principles and the finite-element method in partial differential

equations (discussion), 211.Miyake, S. See Krishnaswamy, Menon et al.Moore, F. H. See Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’Connor.Morton, K. W. Stability and convergence in fluid flow problems (discussion), 237.

Narasimham, V. S. See Krishnaswamy, Menon et al.Nockolds, C. E. See Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’ConnorNumerical disproof of a conjecture in projective geometry (Longuet-Higgins), 443.

O’Connor, B. H. See Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’Connor.Osborne, J. L. See Krishnaswamy, Menon et al.Padley, P. J. See Bulewicz & Padley.Parsons, A. J. See Krishnaswamy, Menon et al.Phillips, G. O. See Davies, McKellar & Phillips.Photochemistry of the piperidinoanthraquinones (Davies, McKellar & Phillips), 69.Photometric investigations of the behaviour of chromium additives in premixed H2-f

0 2 +N 2 flames (Bulewicz & Padley), 377.Porter, G. See Ashpole, Formosinho & Porter.Pressure dependence of intersystem crossing in aromatic vapours (Ashpole, Formosinho

& Porter), 11.Pseudo-viscosity methods and nonlinear hyperbolic equations (Raviart), 277.Radford, C. J. See Bryant, Hagston & Radford.Raviart, P. A. Pseudo-viscosity methods and nonlinear hyperbolic equations (discussion),

277.Reactions of halogen oxides studied by flash photolysis. I. The flash photolysis of chlorine

dioxide (Basco & Dogra), 29.Reactions of halogen oxides studied by flash photolysis. II. The flash photolysis of

chlorine monoxide and of the CIO free radical (Basco & Dogra), 401.Reactions of halogen oxides studied by flash photolysis. III. The production and re­

actions of BrO and CIO radicals in the halogen-sensitized decomposition of chlorine dioxide (Basco & Dogra), 417.

584 IndexReview Lecture. Lasers and light scattering (Smith), 305.

Singer, K. E. See Lee & Singer.Smith, R. A. Review Lecture. Lasers and light scattering, 305.Some convergence results in elliptic difference-equations (discussion) (Thomee), 191.Some experiments with singularities in linear elliptic partial differential equations

(discussion) (Fox), 179.Some recent applications of asymptotic error expansions to finite-difference schemes

(discussion) (Widlund), 167.Some recent methods for the numerical solution of time-dependent partial differential

equations (discussion) (Gourlay), 219.Stability and convergence in fluid flow problems (discussion) (Morton), 237.Structure of vitamin B12. IX. The structure of cobyric acid, factor V ia (With appendices

by Waters & Waters and by Dodson) (Venkatesan, Dale, Hodgkin, Nockolds, Moore & O’Connor), 455.

Studies of the tungsten-oxygen surface reaction by means of reflexion high energy electron diffraction (Lee & Singer), 523.

Synge, J. L. See Florides & Synge.

Tabor, D. See Kendall & Tabor.Thomee, V. Some convergence results in elliptic difference equations (discussion), 191.Three-dimensional starting solution for a melting slab (Boley & Yagoda), 89.Thrush, B. A. See Clough, Curran & Thrush.

Ultrasonic study of the area of contact between stationary and sliding surfaces (Kendall & Tabor), 321.

Variational principles and the finite-element method in partial differential equations (discussion) (Mitchell), 211.

Venkatesan, K., Dale, D., Hodgkin, Dorothy C., Nockolds, C. E., Moore, F. H. & O’Connor, B. H. The structure of vitamin B12. IX. The crystal structure of cobyric acid, factor V ia (With appendices by N. Waters & Joyce Waters, and by Eleanor Dodson), 455.

Walsh, Joan. Finite-difference and finite-element methods of approximation (discussion), 155.

Waters, Joyce. See Waters (N.) & Waters.Waters, N. & Waters, Joyce. Appendix to a paper by Venkatesan, Dale, Hodgkin,

Nockolds, Moore & O’Connor, p. 480.White, P. W. Finite-difference methods in numerical weather prediction (discussion), 285.Whiteman, J. R. Finite-difference techniques for a harmonic mixed boundary problem

having a reentrant boundary (discussion), 271.Widlund, O. B. Some recent applications of asymptotic error expansions to finite

difference schemes (discussion), 167.Wilkinson, J. H. and others. A discussion on numerical analysis of partial differential

equations, 151.Wilkinson, J. H. Introductory remarks to a discussion, 153.Wolfendale, A. W. See Krishnaswamy, Menon et al.

Yagoda, H. P. See Boley & Yagoda.

E N D OP THE THREE H U N D R E D AN D T W ENTY THIRD VOLUME (SERIES A)

PROCEEDINGS OF THE ROYAL SOCIETY

OF LONDON

SERIES A VOLUME 323MATHEMATICAL AND PHYSICAL SCIENCES

1971

P U B L ISH E D BY THE ROYAL SO C IET Y 6 C A R L T O N H O U S E T E R R A C E L O N D O N SW1Y5AG

Printed in Great Britain at the University Printing House, Cambridge

CONTENTS

SE R IE S A VOLUME 323 N u m b e r 1552 25 M a y 1971

Coordinate conditions in a Riemannian space for coordinates based on a subspace.By P. S. Elorides and J. L. Synge, F.R.S. 1

Pressure dependence of intersystem crossing in aromatic vapours.By C. W. Ashpole, S. J. Formosinho and G. Porter, F.R.S. 11

Reactions of halogen oxides studied by flash photolysis. I. The flash photolysis ofchlorine dioxide. By N. Basco and S. K. Dogra. (Plates 1 and 2) 29

Photochemistry of the piperidinoanthraquinones.By A. K. Davies, J. F. McKellar and G. O. Phillips 69

The three-dimensional starting solution for a melting slab.By B. A. Boley and H. P. Yagoda 89

Astrophysical significance of the dissipation of turbulence in a dense baryon fluid.By P. B. Jones 111

The effects of preferential pairing and its detection using electron radiationdamage. By F. J. Bryant, W. E. Hagston and C. J. Radford 127

N u m b e r 1553 8 J u n e 1971A D I S C U S S I O N ON N U M E R I C A L A N A L Y S I S OF P A R T I A L

D I F F E R E N T I A L E Q U A T I O N S

O R G A N I Z E D B Y J. H. W I L K I N S O N , F.R.S.

Introductory remarks. By J. H. Wilkinson, F.R.S. page 153Finite-difference and finite-element methods of approximation.

By Joan Walsh 155Some recent applications of asymptotic error expansions to finite-difference

schemes. By O. B. Widlund 167Some experiments with singularities in linear elliptic partial differential equations.

By L. Fox 179Some convergence results in elliptic difference equations. By V. Thomee 191The application of integral equation methods to the numerical solution of some

exterior boundary-value problems. By A. J. Burton and G. F. Miller 201Variational principles and the finite-element method in partial differential

equations. By A. R. Mitchell 211Some recent methods for the numerical solution of time-dependent partial dif­

ferential equations. By A. R. Gourlay 219Stability and convergence in fluid flow problems. By K. W. Morton 237Difference approximations for initial boundary-value problems. By H.-O. Kreiss 255Computing experience with hyperbolic partial differential equations.

By L. A. Elliott 263Finite-difference techniques for a harmonic mixed boundary problem having a

reentrant boundary. By J. R. Whiteman 271Pseudo-viscosity methods and nonlinear hyperbolic equations.

By P. A. Raviart 277Finite-difference methods in numerical weather prediction. By P. W. White 285Experience with the linear Boltzmann equation. By J. G. Hill 293

IV Contents

N u m b e r 1554 24 J u n e 1971Review Lecture. Lasers and light scattering. By R. A. Smith, F.R.S. page 305An ultrasonic study of the area of contact between stationary and sliding surfaces.

By K. Kendall and D. Tabor, F.R.S.Interactions between Nd3+ ions beyond the first neighbour shell in LaCl3 and

LaBr3. By J. M. Baker and D. MarshA method for predicting the variation with temperature of the solubilities of gases

in non-polar liquids. By D. A. Jonah and M. B. King Photometric investigations of the behaviour of chromium additives in premixed

H2 + 0 2 + N2 flames. By Elzbieta M. Bulewicz and P. J. Padley Reactions of halogen oxides studied by flash photolysis. II. The flash photolysis

of chlorine monoxide and of the CIO free radical.By N. Basco and S. K. Dogra. (Plate 3)

Reactions of halogen oxides studied by flash photolysis. III. The production and reactions of BrO and CIO radicals in the halogen-sensitized decomposition of chlorine dioxide. By N. Basco and S. K. Dogra. (Plates 4 and 5)

The application of the Zeeman effect to the precise measurement of pulsed magnetic fields. By P. W. King and R. C. M. Learner. (Plate 6)

N u m b e r 1555 6 J u l y 1971A numerical disproof of a conjecture in projective geometry.

By M. S. Longuet-Higgins, F.R.S. page 453The structure of vitamin B12. IX. The crystal structure of cobyric acid, factor V 1

By K. Yenkatesan, D. Dale, Dorothy Crowfoot Hodgkin, F.R.S., C. E. Nockolds, F. H. Moore and B. H. O’Connor. (With appendices by N. Waters & Joyce Waters, and by Eleanor Dodson)

The Kolar Gold Fields neutrino experiment. I. The interactions of cosmic ray neutrinos. By M. R. Krishnaswamy, M. G. K. Menon, F.R.S., V. S. Narasim- ham, K. Hinotani, N. Ito, S. Miyake, J. L. Osborne, A. J. Parsons and A. W.Wolfendale 489

The Kolar Gold Fields neutrino experiment. II. Atmospheric muons at a depth of 7000 hgcm-2 (Kolar). By M. R. Krishnaswamy, M. G. K. Menon, F.R.S.,V. S. Narasimham, K. Hinotani, N. Ito, S. Miyake, J. L. Osborne, A. J. Parsons and A. W. Wolfendale 511

Studies of the tungsten-oxygen surface reaction by means of reflexion high energyelectron diffraction. By A. E. Lee and K. E. Singer. (Plates 7 to 10) 523

The e.p.r. spectrum of vibrationally excited hydroxyl radicals.By P. N. Clough, A. H. Curran and B. A. Thrush 541

Isotropic radiation from a steadily pulsating multidimensional distribution.By Lim Chee-Seng 555

Index 581

321

341

361

377

401

417

431

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PROCEEDINGS OF THE ROYAL SOCIETY, SERIES A

Number 1555 6 July 1971 Volume 323

CONTENTSL onguet-H iggins, M. S. pages 443-454

A numerical disproof of a conjecture in projective geometry

Venkatesan , K., D ale , D ., H odgkin , D orothy Crowfoot,N ockolds, C. E., Moore, F. H. & O’Connor, B. H.The structure of vitamin B12. IX. The crystal structure of cobyic acid, factor V la. (With appendices by N. Waters & Joyce Waters and Eleanor Dodson)

455^87

Krishnasw am y , M. R., Menon , M. G. K., N arasimham , V. S., H inotani, K., I to, N., Miy a k e , S., Osborne , J. L., P arsons, A. J. & WOLFENDALE, A. W.The Kolar Gold Fields neutrino experiment. I. The interactions of cosmic ray neutrinos

489-509

Krishnasw am y , M. R., Menon , M. G. K., N arasimham , V. S., H inotani, K., I to, N., Miy a k e , S., Osborne , J. L., P arsons, A. J. & WOLFENDALE, A. W.The Kolar Gold Fields neutrino experiment. II. Atmospheric muons at a depth of 7000 hg cm-2 (Kolar)

511-522

L e e , A. E. & Singer , K. E.Studies of the tungsten-oxygen surface reaction by means of reflexion high energy electron diffraction. [Plates 7 to 10]

523-539

Clough, P. N., Curran , A. H. & Thrush , B. A.The e.p.r. spectrum of vibrationally excited hydroxyl radicals

541-554

Ch e e -Seng , Lim

Isotropic radiation from a steadily pulsating multidimensional distribution

555-580

I n d ex 581-584

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