Catalogue of the papers and correspondence of THOMAS BROOKE BENJAMIN FRS (1929-1995) Bodleian Library, Oxford Compiled by Jeannine Alton and Timothy E. Powell Deposited in the Department of Western Manuscripts, 1997 NCUACS 63/1/97 All rights reserved University of Bath T. B. Benjamin NCUACS 63/1/97 The work of the National Cataloguing Unit for the Archives of Contemporary Scientists, and the production of this catalogue, are made possible by the support of the following societies and organisations: The Biochemical Society The Geological Society The Institute of Physics The Royal Society The Higher Education Funding Council for England The Wellcome Trust T. B. Benjamin NCUACS 63/1/97 NOT ALL THE MATERIAL IN THIS COLLECTION MAY YET BE AVAILABLE FOR CONSULTATION. ENQUIRIES SHOULD BE ADDRESSED IN THE FIRST INSTANCE TO: THE KEEPER OF WESTERN MANUSCRIPTS BODLEIAN LIBRARY OXFORD T. B. Benjamin NCUACS 63/1/97 LIST OF CONTENTS GENERAL INTRODUCTION SECTION A BIOGRAPHICAL A.1-A61 Career, honours and awards A.1 - A.25 Music Poetry A.26 - A.32 A.33 - A.55 Photographs A.56 - A.61 SECTION B NOTES, DRAFTS AND CALCULATIONS B.1 - B.165 University teaching B.1-B.17 SECTION C SECTION E E.1-E.18 SECTION D SOCIETIES AND ORGANISATIONS D.1-D.5 LECTURES, CONFERENCES AND VISITS C.1-C.41 Other notes, drafts and calculations B.18-B.165 MATHEMATICS AND HIGHER EDUCATION National Conference of University Professors (NCUP) INDEX OF CORRESPONDENTS CORRESPONDENCE Articles and writings E.15-E.18 SECTION F F.1-F.20 T. B. Benjamin NCUACS 63/1/97 GENERAL INTRODUCTION PROVENANCE The papers were received from Mrs Natalia Benjamin (widow) and via Professor John Toland, School of Mathematical Sciences, University of Bath, at various dates in 1996. OUTLINE OF THE CAREER OF THOMAS BROOKE BENJAMIN Benjamin was born on 15 April 1929 in Wallasey, Merseyside, and educated at Wallasey Grammar School. He studied electrical engineering at Liverpool University 1947-1950, before moving to Yale University on a Rotary Foundation Fellowship to take an M.Eng. Benjamin then went to Cambridge University where he took his doctorate on cavitation in fluids. He was elected Fellow of King’s College, Cambridge in 1955, and appointed Assistant Director of Research 1958-1967 and Reader in Hydrodynamics 1967-1970, working in the Department of Applied Mathematics and Theoretical Physics, Cambridge University, on problems of fluid dynamics such as thin films, wave instability, drag reduction, and vortex breakdown. He was elected Fellow of the Royal Society in 1966, at the early age of 36. the Fluid Mechanics Research Institute, to promote interaction between mathematicians and experimentalists in advanced fluid mechanics. In 1979 he accepted appointment to the Sedleian Chair of Natural Philosophy at Oxford, which carried with it Fellowship of The Queen’s College. In addition to his contributions to the study of fluid dynamics, Benjamin retained a lifelong interest in music, as executant (piano and strings), conductor and composer. Somewhat later in life, he also In 1970 Benjamin moved as Professor of Mathematics to the University of Essex, where he set up Apart from periods as visiting professor at overseas universities, principally in America, Benjamin the marriage was dissolved in 1974. In 1978 he married Natalia Court, by whom he had a daughter. Benjamin was twice married: in 1956 to Helen Ginsburg, by whom he had a son and two daughters; remained in Oxford until his death on 16 August 1995. tumed to the composition of poetry. T. B. Benjamin NCUACS 63/1/97 DESCRIPTION OF THE COLLECTION The material is presented as shown in the List of Contents. Additional explanatory notes, information and cross-references are appended where appropriate to the separate sections and the individual entries. The surviving documentation of many aspects of Benjamin's career, is unfortunately sparse; several of his career moves seem to have resulted in the loss or destruction of papers. Section A, Biographical, provides a useful outline of the principal events of Benjamin’s life including his appointment to the Sedleian Professorship at Oxford. His non-professional interests, music and poetry, are well recorded, with examples of Benjamin’s own scores and writings on music, and poems, almost all wrtten in 1980. Section B, Notes, drafts and calculations, is the largest in the collection. It includes material relating to university courses taught by Benjamin and a considerable quantity of notes and other material relating to research, publications and lectures, much of it undated and difficult to assign as to category. higher education, especially the National Conference of University Professors of which he was a founder and first Chairman. Section F, Correspondence, is slight. a lecturer can be seen. It covers the years 1970-1994. Section D, Societies and organisations, is slight and does not convey the full involvement of Benjamin in the life of professional mathematical societies, or of his contribution to the publication of learned journals (he was a founder editor of the influential Journal of Fluid Mechanics). Section C, Lectures, conferences and visits, is far from being a complete record of Benjamin’s travel Section E, Mathematics and higher education, records Benjamin's concem with various aspects of and conference commitments, although something of the extent of his travels and his reputation as There is also an index of correspondents. T. B. Benjamin NCUACS 63/1/97 ACKNOWLEDGEMENTS We are pleased to acknowledge the help of Mrs Natalia Benjamin and Professor John Toland in making the papers available and in helping to date and identify some of the documents and photographs. Jeannine Alton Timothy E. Powell BATH 1997 T. B. Benjamin NCUACS 63/1/97 SECTION A BIOGRAPHICAL A.1-A.25 CAREER, HONOURS AND AWARDS A.26-A.32 MUSIC A.33-A.55 POETRY A.56-A.61 PHOTOGRAPHS T. B. Benjamin NCUACS 63/1/97 Biographical CAREER, HONOURS AND AWARDS Miscellaneous curricula vitae and biographical information, compiled at various dates. Includes ‘main accomplishments over last three years’ (1989-1992), listing recent significant honours and publications. List of publications to 1993. References to publications in the form Bibliog. ... refer to this list. Obituary notices and tributes: The Times The Independent The Daily Telegraph The Guardian King’s College Cambridge Annual Report The Queen’s College Oxford Record Yale University, Dunham Laboratory, 1950-1952. Manuscript ‘Progress Report of Research Work by B. Benjamin during University of Liverpool, October 1947-July 1950. Letter from unidentified University friend, mainly about music, written shortly before Benjamin’s departure for America. See A.30 for Benjamin’s musical activities at Liverpool. Record of courses attended. Press cuttings. Service of Thanksgiving 27 January 1996; Order of service, addresses by D.G. Crighton, T. Mullin, J.F. Toland. session 1950-1951’, press cuttings. Benjamin spent 1950-1952 as a Rotary Foundation Fellow, obtaining an M.Eng. for work on the effects of ultrasonic frequencies on cavitation in liquids. T. B. Benjamin NCUACS 63/1/97 Biographical Award of William Hopkins Prize of the Cambridge Philosophical Society 1969 ‘for outstanding work on the mechanics of fluids’. Notification, letter of congratulation. See A.31 for Benjamin’s musical activities at Cambridge. University of Essex, 1970-1978. Benjamin was Professor of Mathematics at Essex 1970-1978, where he set up and directed the Fluid Mechanics Research Institute. In 1974 there was a period of serious student unrest at the University. Press cuttings on Benjamin and on research grants for Fluid Mechanics Research Institute 1971. List of visiting professors and seminars at Institute, 1974-1975. List of 91 research reports published by Institute, 1971-1977. See A.32 for Benjamin’s musical activities at Essex. Sedleian Professorship of Natural Philosophy Oxford. Press cuttings on student unrest at Essex, including letters to the press, interviews etc by Benjamin; brief correspondence, 1974. A-C. Benjamin's application for the Chair November 1977, his acceptance of it February 1978, formal acknowledgement of his resignation from Essex February 1978. Correspondence with references. A.11-A.15 Letters of congratulation on the Sedleian Chair. A.114 T. B. Benjamin NCUACS 63/1/97 Biographical S-W and unidentified. for Correspondence and papers about Science Research Council grant to Benjamin at Mathematical Institute Oxford. Includes correspondence with T. Mullin who came to work on the project as a post-doctoral researcher and became a long-term collaborator. hydrodynamic phenomena’ bifurcation ‘Studies of Distinction award, 1994. Undergraduate report on Benjamin’s lecture course, nd. Miscellaneous teaching, seminar and lecture schedules 1981-1982. Letter on proposed collaboration between Meteorological Office and Oxford University, 1994. Offer of Visiting Professorship, Mathematics Research Center, University of Wisconsin-Madison, 1980. on nonlinear systems’, ca.1987. Draft of application to Science and Engineering Research Council for further grant for research on ‘Combined mathematical and experimental research T. B. Benjamin NCUACS 63/1/97 Biographical Honorary Doctorate, University of Bath, June 1989. Oration by University Orator (J. Honorands. F. Toland), Benjamin’s reply on behalf of Brief correspondence on Benjamin’s election to Council of the Royal Society and nomination as a Vice-President, 1990. Honorary Doctorate, Brunel University, July 1991. Photocopy of certificate only. Election as Foreign Member, Académie des Sciences, Institut de France, 1993. Arrangements for presentation, oration. Honorary Doctorate, University of Liverpool, July 1993. Election Engineers, 1994. to Honorary Membership, American Society of Mechanical the Society’s International Congress in Correspondence, oration, Benjamin’s speech at the ceremony. Election to Membership, New York Academy of Sciences, 1995. The award was conferred at Chicago, November 1994. Correspondence about honour, arrangements for conferral, biographical information, press release, letters of congratulation. Certificate of membership only. T. B. Benjamin NCUACS 63/1/97 Biographical player, orchestral Benjamin was involved with music throughout his life. As an undergraduate at Liverpool he played a major part in the university’s Music Society as violin manager and chairman, and as a composer. He wrote light-hearted music for reviews, pantomimes and performances by ‘Pantopera’, and more serious works which were regularly performed and attracted favourable critical comment. The university string orchestra, which he founded, performed widely in Liverpool and outside. choir-master, conductor and Michael At this time, when musical talent at Liverpool was unusually strong - John Shirley-Quirk, were among contemporaries - Benjamin was almost drawn to a full-time career in music. Having decided in favour of science, he kept music firmly in second place at Cambridge, but at Essex he again played an important part in the orchestral and choral concerts of the University Music Society. Moores and Routledge Patricia Scores and writings on music are at A.26-A.29. The remainder of the material bears witness to his activities through critical comment and printed notices. Extracts from English metaphysical poets, String Quartet 1948. Photocopied manuscript score. ‘Comedy Overture’ 1953. Photocopied manuscript score. Manuscript paper, probably for reading to musical composition and patronage, nd. ‘The Progresse of The Soule’. typescripts with manuscript indication of possible musical settings, nd. Chancellor. Programmes, Music announcements, various dates 1948-1951. Music at Cambridge, 1954, 1956. Music at Essex 1972. of congratulation a society, on the history of Includes letter from Vice- press comments, at Liverpool. publicity, T. B. Benjamin NCUACS 63/1/97 POETRY Biographical Poems written almost entirely in 1980. Indexed by Benjamin’s title. ‘A saying to my liking’. Manuscript and typescript versions. ‘Encounter. explanatory note. Manuscript and typescript versions, the latter with an ‘First thoughts’. Manuscript. ‘Four from which Childe Roland went’ (on Essex University). Typescript. ‘Gulls in fields’ and ‘The mooring cord’. Typescript. ‘In Warsaw’. Manuscript sketch, typescript. ‘Haiku on science’. with an explanatory note. Heavily corrected manuscript draft, typescript version ‘Homage’. Manuscript with corrections, typescript with an explanatory note. ‘The mooring cord ‘and untitled. Typescript. ‘K.529, Act |’. Manuscript, typescript with an explanatory note. ‘Lesson’. Typescript. ‘Le monde ancien presque oublié’ (in French). Manuscript. T. B. Benjamin NCUACS 63/1/97 Biographical ‘The neutron beam’. Manuscript sketches. ‘Nightmare’. Manuscript, typescript with an explanatory note. ‘The old railway’. Manuscript and typescript sketches. ‘Rayleigh’. Manuscript with corrections and an explanatory note. ‘Reflection’. Manuscript and typescript versions. ‘Sleeping baby’. Manuscript and typescript versions. ‘Soliloquy’. Manuscript. ‘Sonic boom’. Manuscript and two typescript versions. ‘The worry worm’. Manuscript and typescript versions. ‘Students 1975’. Multiple manuscript and typescript drafts. Sketches and drafts. T. B. Benjamin NCUACS 63/1/97 PHOTOGRAPHS Biographical These are all copies made available by Mrs Benjamin. Conducting at Liverpool, ca. 1950. West Freedom Railway, Wisconsin, 1980. Lecturing at Florida, ca. 1991. Third Anniversary of the founding of the National Conference of University Professors, 1992. With his daughter Victoria, 1992. On election as Associé Etranger, French Academy of Sciences, 1993. T. B. Benjamin NCUACS 63/1/97 SECTION B NOTES, DRAFTS AND CALCULATIONS The papers in this section were received via Professor John Toland, University of Bath, in 1996. It includes material for research, lecture notes and drafts for publications but it has not always been possible to distinguish between these categories. UNIVERSITY TEACHING OTHER NOTES, DRAFTS AND CALCULATIONS B.18-B.143 Shorter notes, drafts, calculations B.144-B.156 Incomplete longer drafts B.157-B.164 Miscellaneous B.165 Notebook T. B. Benjamin NCUACS 63/1/97 UNIVERSITY TEACHING Notes, drafts and calculations Material relating to university courses on identified topics. Further teaching material which cannot be so clearly assigned is to be found in Other notes, drafts and calculations (B.18-B.168). Applications of Dfifferential] E[quation]s. Typescript problem sheet 2 for ‘MODS, Trinity Term’; manuscript lecture notes paginated 1-25 with 3pp notes on ‘Parametric excitation’. ‘BS Notes’. Contents of Benjamin’s folder so inscribed divided into four for ease of reference: manuscript notes re course on Applied and Numerical Analysis. Review of course; work sheets; ‘material not used 1994’. Applied Functional Analysis. Lecture notes, paginated 1-65. 2 folders. Typescript class papers and manuscript lecture notes; manuscript draft examination question on ‘Topics in Analysis’. ‘M.Sc. course (8 lectures Mich. Term)’. Contents of Benjamin’s folder so inscribed divided into two for ease of reference: manuscript notes for lectures on PDEs, paginated 1-22. Manuscript Theoretical Mechanics work sheets. Nd. Photocopied manuscript Pure Maths test sheets, Spring 1975. Sleeman re Manuscript Benjamin’s participation in IMA Symposium, 8 May 1980. transparencies; notes letter from and B.D. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations B.11, B.12 Contents of Benjamin’s folder divided into two for ease of reference. B.11 Manuscript and typescript worksheets. Manuscript lecture notes paginated 1-38. B.13-B.17 M.Sc. course on Waves and Compressible Flow. B.13 Manuscript lecture notes, paginated 1-20, with later annotations 1988, 1989, 1990; manuscript draft exam question. Miscellaneous pages of manuscript lecture notes. Manuscript and typescript class papers 1, 2, various versions. Manuscript and typescript class papers 3-5, various versions. Manuscript and typescript class papers 6-8, various versions. OTHER NOTES, DRAFTS AND CALCULATIONS form Bibliog. ... Presented in a single sequence arranged as far as possible by subject. Some of the material was found in Benjamin's own folders and envelopes, sometimes with an indication of the subject of the material inscribed thereon, but the bulk of the papers were found loose and unordered. The papers include drafts of publications and lectures, teaching material, research notes and calculations and transparencies for illustrating lectures. The bulk of the material is undated. Where applicable reference has been made to the bibliography at A.1 in the T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Air lubrication of tape’. Manuscript draft paginated 1-13. ‘Asymptotics of new solitary wave’. Incomplete manuscript calculation paginated 1-6. ‘More about asymptotics’. Manuscript calculation paginated 1-4. Manuscript draft beginning ‘4. paginated 1-5, latest bibliographical reference 1974. Estimates for axisymmetric steady motions’ ‘Generalized BBM equation’. Photocopied manuscript calculation paginated 1-11, reference 1987. latest bibliographical See also C.10 ‘BICC wire-unwinding problem’. 6pp photocopied typescript by D.C.Handscomb, 26 February 1981. Manuscript notes and transparencies for lecture on bifurcation theory. See also C.10. ‘R.R. Huilgol Théor. Méc. Univ Paris VI June at Bath Slides 1-5’. Contents of envelope so inscribed. Multi-parameter Bifu Probs ~ 15 Transparencies for lecture. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Notes about Boussinesq system’. Manuscript draft paginated 1-3 20 February 1995. ‘Operator needed in modified Boussinesq system’. Manuscript calculation paginated 1-3. ‘Chaotic bubbles’. Contents of Benjamin’s envelope so inscribed. Transparencies and figures for lecture. ‘Free vibrations of bubbles’. Manuscript draft paginated 1-9, latest bibliographical reference 1964. ‘Capillary problem’. Contents of Benjamin’s folder so inscribed. Summary, Introduction, ‘2. Equations of equilibrium’ paginated 1-8. Axisymmetric drop’ and conclusion paginated 1-13, list of references; ‘Nonlinear capillary problem’. Contents of Benjamin's envelope so inscribed. Manuscript calculations. Part General formulation and the case of axial symmetry’ by Benjamin and Incomplete manuscript draft of ‘Liquid drops suspended by soap films. 1. A.D. Cocker, 1983. Bibliog. 60. ‘4. graphs and data provided by colleague in March and April 1983. Manuscript notes and calculations. ‘Cones Uniqueness’. Contents of Benjamin’s folder so inscribed divided into two for ease of reference. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Contraction mapping principle’. Photocopied manuscript calculations paginated 1-8 (lacks p7), with typescript question on the contraction mapping principle. ‘The contraction ratio for a sluice-gate on whose vertical parts the fluid velocity is zero’. Manuscript calculation. ‘New aspects of unsteady Couette flow’. Typescript draft paginated 1-11 ca.1980, and manuscript notes, figures etc found therewith. Bibliog. 55. See also C.13. ‘Slides: Degree thfeor]y.’ Contents of Benjamin’s envelope so inscribed divided into two for ease of reference. Miscellaneous transparencies. B.38-B.40 ‘Discontinuities’. Contents of Benjamin’s envelope so inscribed divided into three for ease of reference. Manuscript drafts, latest bibliographical reference 1986. Letter from W.G. Pritchard, 31 October 1989 enclosing photographs of film thickness during experiments; set of 16 transparencies, latest bibliographical reference 1980. Manuscript calculation paginated 1-4. Energy demand in the United Kingdom. Manuscript note paginated 1-4, latest reference 1972. ‘Outline of existence theory’. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations Manuscript draft beginning ‘[...| My own interest pragmatic’. in f.a. is essentially Conference lecture on ‘nonlinear positive operators (“positone” problems)’ paginated 1-6. Flows. Manuscript notes ‘what happens in various flow situations where nonlinear effects are delicately balanced’. and transparencies for conference lecture on ‘Gas dynamics’. Manuscript calculation paginated 1-5. ‘Gravity current in Strat. fluids’. Contents of Benjamin’s folder so inscribed divided into two for ease of reference. Manuscript calculations. ‘Gravity currents’. Contents of Benjamin’s envelope so inscribed. ‘Hamiltonian Structure’. Manuscript calculation paginated 1-3. Letter from M. Mcintyre to H. Huppert re lecture by Benjamin, 9 May 1988; set of 12 transparencies. Miscellaneous manuscript notes and calculations. 3 folders. ‘The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics’ by Benjamin, University of Essex Fluid Mechanics Research Institute Report no.67 September 1975. Bound volume with manuscript notes and calculations intercalated. ‘Stability of Hill vortex’. Contents of Benjamin’s folder so inscribed divided into four for ease of reference. B.50-B.53 B.51-B.53 T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Some recent work on the Hodgkin-Huxley nerve equations’. 6pp photocopied typescript draft. Manuscript draft beginning hydrodynamic problem’ paginated 1-6, latest bibliographical reference 1987. ‘Appendix. A formulation of the complete Manuscript draft beginning ‘Appendix: Formulation of hydrodynamic problem’ paginated 1-3. Contents of Benjamin’s folder: manuscript notes, figures and transparencies for lectures on hydrodynamic stability, 1980s. ‘Generalization of results for ILW eqn’. Manuscript draft paginated 1-10, September 1994. Manuscript draft paginated 1-8, September 1994. ‘Simple theory of instability’. Photocopied manuscript notes paginated 1-4. ‘Proof that periodic steady soins of the ILW eqn are parameterized in exactly the same way as those of KdV eqn’. Incomplete manuscript draft on ‘intemal waves’ paginated 35-76. Latest bibliographical reference 1967. 2 folders. Possibly related to Bibliog. 29. sheets. Manuscript calculations, some on verso of 1965 duplicated typescript course ‘K & de V eqn’. Contents of Benjamin’s folder so inscribed. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Generalized KdV equation’. Manuscript draft paginated 1-24, latest bibliographical reference 1987. ‘Slides Benjamin’s envelope so inscribed. Lecture on genferalize]d KdV eqn _ Hull 13/5/93)’. Contents of Transparencies. ‘Kelvin - Amol’d’. Manuscript bibliographical reference 1967. calculation paginated 1-13, with later addition. Latest ‘Reappraisal Structure’ by Benjamin and T.J. Bridges. Bibliog. 74. Kelvin-Helmholtz problem’. the of Part 1. Hamiltonian Manuscript draft for publication. 3 folders. Navier-Stokes problems. Transparencies. Manuscript draft paginated 1-21. ‘Some qualitative properties of Nagumo’s Nerve Axon Equation’. ‘Applications of Leray-Schauder degree theory to problems of hydrodynamic Stability’. Bibliog. 41. Photocopied manuscript draft paginated 1-8, 23 July 1973. 13pp typescript draft by M. Green, ca.1972, with covering letter inviting Benjamin to comment and to add his name to the paper; manuscript note by Benjamin on ‘Nagumo’s equation’ paginated 1-8. ‘Necessity of upstream influence ahead of cavity in swirling flow, when angular velocity is not uniform’ T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations Incomplete manuscript draft beginning ‘Chapter 3. systems with one space variable’ paginated 1-31 bibliographical reference 1984. Nonlinear dispersive (lacks pp7-11), latest Lecture to Faculty of Mathematics, Cambridge University, on non-linear equations. Manuscript draft paginated 1-10. See also C.12. Contents of Benjamin’s folder: manuscript notes and transparencies on work with P. Olver. Possibly related to Bibliog. 56. ‘New approach to 1-D nonlinear hyperbolic systems’. Manuscript calculation. ‘Positive-operator theory’. ‘Introduction’ paginated 1-13 (lacks p3); two different drafts of ‘2. General Theory’ paginated 1-4 and 1-5. ‘3. Planar motions’ paginated 1-16; ‘3.5 Confined flows with disconnected sets of S’ paginated 1-5; photocopied manuscript calculation paginated 1-6. ‘Planar motions of a perfect fluid’. Contents of Benjamin’s envelope so inscribed divided into two for ease of reference: manuscript drafts, latest bibliographical reference 1977. Probably Benjamin’s comments on draft sent to him to referee. Manuscript Th{eore]m’ paginated :-iii. draft paginated Manuscript ‘Notes’ chiefly on Ro paginated 1-8. 1-10; manuscript ?appendix ‘Existence T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Lecture on rimming flows’. Contents of Benjamin's envelope so inscribed. Typescript draft paginated transparencies. 1-12, latest bibliographical reference 1988; Manuscript drafts on rimming flows, September 1989. ‘Thin rimming flows’ paginated 1-9; ‘Second-order approximation for rimming flows’ paginated 1-7; ‘Notes on stability of thin rimming flows’ paginated 1-6. Miscellaneous manuscript calculations and notes found with preceding. ‘Spherical vortex’. Manuscript calculation. ‘The solitary wave with surface tension’. Bibliog. 58. See also C.17. ‘4. Instability’. B.87-B.89 Incomplete manuscript draft on bibliographical reference 1987. solitary waves paginated 11-77. Latest Manuscript draft for publication paginated 1-13 + references. Incomplete manuscript draft beginning ‘6. Conclusion. The topological method of analysis expounded in section 2 has been applied to three specific solitary wave problems’ by Benjamin, J. L. Bona and D. K. Bose, paginated 1-8, latest bibliographical reference 1981. Possibly related to Bibliog. 73. ‘5. Generalized BBM solitary waves’, ‘6. Conclusion’. ‘2. Properties relating to solitary-wave solutions’; ‘3. Stability’. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Proper “regularization” of solitary-wave equation’. Manuscript calculation paginated 1-3, 8 September 1993. ‘Integrals of generalised equations with periodic and solitary-wave solutions’. Manuscript draft paginated 1-8, September 1994. ‘Surface solitary waves: outline of theory’. Manuscript draft paginated 1-24. ‘Notes on solitary-wave problem’. Manuscript draft paginated 1-14. Contents of Benjamin’s envelope. Manuscript notes and transparencies on solitary waves. Transparencies on stability of solitary waves, latest bibliographical reference 1987. ease of reference. Manuscript list of ‘Conférences par T.B. Benjamin’ on stability and related mathematical problems; manuscript draft beginning ‘Maintenant pour ma premiére conférence, je voudrais introduire plusieurs idées et définitions fondamentales’, paginated 1-13. ‘Stability’. Contents of Benjamin’s folder so inscribed divided into two for Contents of Benjamin’s envelope. Solitary waves. Transparencies. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations Manuscript ‘Proposed outline photocopied manuscript ‘Notes on [Chapter] 5’, paginated 1-10. the sequel for to BBM’ paginated 1-5; In two different hands, neither Benjamin’s. Miscellaneous manuscript calculations. ‘Stability of kinematic waves (general, approximate theory)’. Manuscript calculation paginated 1-4. Incomplete manuscript draft beginning ‘3. The effect of surface tension on Stability’ paginated 10-16. ‘Existence d'autres solutions stationnaires dans le cas ou A, est négative’. Manuscript drafts in French. for publication paginated 1-46, latest bibliographical Possibly related to Manuscript draft paginated 1-24. ‘Stationary waves on a running stream’. Manuscript draft reference 1969. ‘Steady flows drawn from a steady stratified reservoir’. Bibliog. 52. steady flow; transparencies. Contents of Benjamin’s envelope: manuscript outline of two lectures on Manuscript notes and figures for lecture on steady flows paginated 1-16. Notes and pages of drafts found therewith. T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations Incomplete manuscript draft beginning ‘3.3 stable steady flow paginated 17-24, latest bibliographical reference 1964. Existence and regularity of ‘Steady flows of ideal fluid in rectangular channet’. Manuscript draft paginated 1-7. Manuscript draft beginning ‘My object today is to show you what can be done to solve the exact equations of steady motion for stratified fluids’ paginated 1-8, latest bibliographical reference 1963. ‘Complete theory of steady waves in a two-fluid solution’. Manuscript draft paginated 1-28, September 1994. ‘Steady wave solutions of generalized KdV and BBM equations and systems, including case of non4ocal operators’. Manuscript draft paginated 1-13, September 1994. ‘Notes on the multiplicity of flows in the Taylor experiment’. Bibliog. 57. Manuscript draft for publication by Benjamin and T. Mullin paginated 1-15. Manuscript draft of Benjamin's contribution to Festschrift for M.J. Lighthill on his Sixtieth birthday (1984) beginning ‘[...] We had independently noticed several facts that classified the theory of steady long waves in a horizontal water channel’, paginated 1-20. famous experiment’. Latest bibliographical reference 1978. Incomplete manuscript draft beginning ‘The purpose of this paper is to review the mathematical problem posed by realistic models for Taylors Manuscript calculation on ‘events observed in paginated 1-8. the Taylor experiment’ T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations Manuscript draft beginning ‘Outline of theoretical issues’ on ‘high multiplicity in the Taylor experiment’ paginated 16-30, latest bibliographical reference 1981, and pages of drafts found therewith. ‘Thin films’. Manuscript draft and transparencies for lecture at unidentified ‘international center of mathematical research’. ‘Tensors’. Manuscript notes paginated [1]-18. B.118-B.120 ‘Transitions in parallel flows’. Contents of Benjamin’s folder so inscribed divided into three for ease of reference. Includes letter to Benjamin from Marten Landanhl re alterations to draft paper, 21 February 1962, manuscript draft by Landahl, 20 March 1962, manuscript draft titled ‘Possible title: Progress Report on theoretical studies conceming Boundary Layers over compliant surfaces’, paginated 1-3. B.119, B.120 ‘Two-dimensional flows’. still a mysterious subject’, Manuscript notes and drafts. 2 folders. Manuscript draft is paginated 1-3; transparencies found therewith. ‘Turbulence beginning Photocopied manuscript notes paginated 7-10 and figures found therewith. dimensional motions’ paginated 1-7, latest bibliographical reference 1984. Manuscript considerations regarding 2-D flows’ paginated 1-7. this comparatively simple case of two- Manuscript draft beginnning ‘In draft beginnning ‘[...1 some elementary but important T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Unsteady wave motions of small but FINITE amplitude’. Manuscript draft paginated 6-10, latest bibliographical reference 1967. ‘Cellular flows of cylinder, by Benjamin and S.K. Pathak. Bibliog. 68. a viscous liquid partly fills that a horizontal rotating Incomplete manuscript draft for publication. See B.127, B.128. ‘Benjamin & Pathak horizontal rotating cylinder’ [...]’. “Cellular flows of a viscous liquid that partly fills a Transparencies and figures for lecture. See B.126, B.128. ‘Pathak paper’. Contents of Benjamin’s folder so inscribed. Transparencies. See B.126, B.127. B.129, B.130 Contents of Benjamin’s folder divided into two for ease of reference. ‘Notes on the problem of buckling instability in sheets and columns of highly viscous liquid’ by Benjamin, 24pp photocopied manuscript, November 1967. Manuscript calculations. Manuscript draft of lecture on viscous fluid in a stationary solution, Grenoble, France (in French) paginated 1-23. ‘Visc. sheet’. Contents of Benjamin's folder so inscribed divided into two for ease of reference. Manuscript notes and calculations on viscosity. B.129 B.132, B.133 T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations ‘Viscous flow down inclined plane’. Manuscript calculation paginated 1-12. B.135, B.136 ‘Vortex stab.’ Contents of Benjamin’s envelope so inscribed divided into two for ease of reference. Manuscript notes and calculations. ‘Notes on water-wave theory (Part Il)’. Manuscript notes for in autumn course on mathematical and numerical methods in fluid dynamics, International Centre for Theoretical Physics, Trieste, 17 September - 15 December 1973. Paginated 1-22. lecture ‘Water waves’. Contents of Benjamin’s envelope so inscribed. Manuscript notes paginated transparencies. 1-8, latest bibliographical reference 1984; B.139, B.140 introduction and set of 19 transparencies for lecture on Manuscript draft paginated 1-8. ‘Variational principle for steady water waves’. Contents of Benjamin’s envelope divided into two for ease of reference. Manuscript mathematical theory of water waves. Manuscript calculations. ‘1973 Waves in strat. fluids’. Contents of Benjamin’s folder so inscribed. Manuscript draft for lecture paginated 1-15; manuscript notes. "Waves of finite amplitude in film’. T. B. Benjamin NCUACS 63/1/97 Incomplete longer drafts Notes, drafts and calculations B.144-B.146 Manuscript draft for lectures, latest bibliographical reference 1984. B.144 Beginning ‘Shallow-water theory’ paginated 1-23. Beginning ‘KdV theory’ paginated 30-40. Beginning ‘Planar (2-D) motions’ paginated 52-86. B.147-B.151 Lectures material. Contents of Benjamin’s set of envelopes. The inscriptions on the envelopes are reproduced in the catalogue entries. ‘Lecture 1’. Manuscript draft paginated 1-8; transparencies ‘Lecture 2’. Transparencies. ‘Water Waves _ 5’. Transparencies. ‘B[enjamin]-O[no] Eqn 4’. Manuscript draft paginated 1-7; transparencies. ‘Inviscid FM & Planetary waves 7’. Manuscript calculations; transparencies. latest bibliographical reference 1982. ‘2. Systems of differential equations with one space variable’ paginated 1-27, ‘1. General theory’ paginated 1-26, latest bibliographical reference 1974. B.152-B.156 Manuscript drafts ?for lecture series. B.152 T. B. Benjamin NCUACS 63/1/97 Notes, drafts and calculations Systems ‘4. bibliographical reference 1976. several with space variables’ paginated 1-17, latest Surface solitary waves’ paginated 1-26, latest bibliographical reference ‘5. 1981. ‘6. Water waves’ paginated 1-42, latest bibliographical reference 1983. Miscellaneous B.157-B.160 Miscellaneous sets of manuscript calculations. 4 folders. B.161, B.162 Miscellaneous manuscript sections of drafts. 2 folders. Notebook Two photographs of ?flow in normal and abnormal cells. Data and graphs, some sent to Benjamin by unidentified colleague. Hardback notebook used for data and calculations 16 November 1978 - 21 January 1979, paginated 1-126. T. B. Benjamin NCUACS 63/1/97 SECTION C LECTURES, VISITS AND CONFERENCES Benjamin lectured and travelled widely, and was visiting professor for varying periods at many He attended numerous conferences, several of which he universities, particularly in America. helped to organise. The documentation for these activities is unfortunately very sparse and may survive only in the form The material below, listed in of brief correspondence, or the notification of a meeting or lecture. It covers the chronological order, nevertheless gives some idea of this aspect of Benjamin's career. years 1970 - 1994. Where applicable reference has been made to the bibliography at A.1 in the form Bibliog. ... A small group of notes and drafts is included at C.37 - C.41. Some of the shorter notes and drafts in or conference papers, and are cross-referenced when such Section identification may reasonably be made. B may refer to lecture T. B. Benjamin NCUACS 63/1/97 Lectures, conferences and visits to Visit distinguished visiting professor, spring semester 1970. of Technology, Clarkson College Potsdam, New York, as Benjamin taught on ‘Special Topics in Fluid Mechanics’. Information only. Fluid Dynamics Symposium, McMaster University, Hamilton, 27 August 1970. Ontario, 25- Benjamin gave a Keynote Address on ‘New ideas about waves in fluids’. Programme only. McGill University Montreal Quebec, seminars in mechanics. Special seminar by Benjamin on ‘The Stability of Solitary Waves’, 18 December 1970. (Bibliog. 34). Notice only. honour of the 7Oth birthday Announcement only. Benjamin was a principal lecturer (Bibliog. 38). Seventh Summer Seminar in applied mathematics, on ‘Nonlinear wave motion’, Clarkson College of Technology, Potsdam New York, 6-28 July 1972. Intemational Symposium in of Sydney Goldstein, on ‘Modern developments in fluid dynamics’, Haifa, Israel, 16-23 December 1973. Notice only. Benjamin lectured on ‘Modern mathematics and mechanics’. Benjamin spoke on ‘New ideas about hydrodynamic stability’. Edinburgh Mathematical Society, 1 June 1974. Programme, list of participants. T. B. Benjamin NCUACS 63/1/97 Lectures, conferences and visits University of Essex Association Science and Technology Section, December 1975. 5 Benjamin spoke on ‘Science and music’. Notice only. Autumn course on ‘Applications of Analysis to Mechanics’, International Centre for Theoretical Physics, Trieste, 22 September - 10 December 1976. Benjamin was a co-Director. Circular letters only. Institute of Mathematics and its Applications, Debate, Winchester College, 14 March 1977. Benjamin opposed the motion ‘that academic scientists and mathematicians should be employed in more useful activity’. Notice only. Notice only. Laboratoire de Mécanique de Paris VI, See also B.23, B.24. Special seminar, Théorique, 22 April 1977. Université Benjamin spoke on ‘Quelques nouvelles idées concemant les phénoménes de bifurcation dans les fluides’ (related to Bibliog. 42, 43). Minutes only, with contributions by Benjamin. Meeting of Conference of Professors of Applied Mathematics, University College London, 28 September 1977. T. B. Benjamin NCUACS 63/1/97 Lectures, conferences and visits Rouse Ball Lecture, Faculty of Mathematics, Cambridge, 4 May 1979. Benjamin lectured on ‘New Uses for nonlinear analysis’. Notice only. Possibly related to B.74. ‘New aspects conference paper, 1981 (Bibliog. 55). of unsteady Couette flow’, abstract for collaborative See also B.35. International Union of Theoretical and Applied Mechanics (IUTAM), Second Symposium on Nimbrecht, Germany, 28 August - 4 September 1981. the Mechanics of Continua, Stability in Benjamin served on the Scientific Committee. Brief correspondence, participants. List of speakers and symposia only. Programme, participants, information. ‘New ideas about waves in fluids’. Society for Industrial and Applied Mathematics (SIAM) symposium, 1982. Benjamin was on the organising committee and gave some of the lectures. Benjamin spoke at the symposium on ‘Methods in Non-linear Analysis’ at SIAM ‘ 82. NATO/London Mathematical Society Advanced Study Institute on ‘Systems of nonlinear partial differential equations’, Oxford, 26 July - 7 August 1982. See also B.85. Manuscript for short talk, nd. but kept with paper by A.E. Green ‘The solitary wave with surface tension’ commenting on Benjamin’s paper of the same title (Bibliog. 58), 1982. T. B. Benjamin NCUACS 63/1/97 Lectures, conferences and visits International Mathematical Union General Assembly, Warsaw, August 1983 (postponed from 1982). Information only. Talk to Sussex Branch, Mathematical Association, Brighton, January 1984. Correspondence, Benjamin’s manuscript notes. L.S.G. Kovasznay Distinguished Lecture, Houston, Texas, April 1984. Benjamin lectured on ‘Old questions and new answers in fluid dynamics’. Notice of lecture only. 17th IUTAM Assembly, Denmark, 19-25 August 1984. 16th IUTAM Intemational Congress, Lyngby, Information only. Notice of lecture only. ‘Report evaluate Mathematics’ (Chicago), in collaboration, March 1986. Visiting Committee to the of Distinguished Lecture, Houston, April 1985. Benjamin led the Royal Society’s delegation. Benjamin spoke on ‘A novel stability problem in hydrodynamics’. July 1987. Invitation at conference on ‘Mathematical problems in fluid dynamics and plasma physics’, Oberwolfach, Germany, to present a main lecture the Department of T. B. Benjamin NCUACS 63/1/97 Lectures, conferences and visits Penn State University Applied Mathematics Seminars, Fall Semester 1988. Benjamin headed a Departmental Colloquium on ‘Hydrodynamic bifurcation phenomena’, 23 September. ‘Vortex breakdown’, September, and lectured on 1 Programme only. ‘Nonlinear Phenomena in honour of Benjamin’s sixtieth birthday, held at Penn State University, 13-15 April 1989. Fluid Mechanics’, Conference in Benjamin spoke on ‘Several outstanding problems in hydrodynamics’. Programme, lists of participants. Alicia Golebriewska Herrmann Memorial Lecture, California, 28 September 1989. Stanford University, Benjamin lectured on ‘Vortex breakdown: a partially solved enigma’. Notice only. Differential Department of Applied Mathematics and of Cambridge, Programme only. Benjamin spoke on ‘Self-propulsion of asymmetrically vibrating bubbles’. University Theoretical Physics, George Batchelor Symposium, 16 March 1990. ‘Albert Ellis: an appreciation’, tribute by Benjamin to be read at memorial service, Notice. Benjamin spoke on ‘Hamiltonian theory for continuous equations’ and ‘Stable and unstable solitary wave solutions of generalised KdV and BBM equations’. Manuscript, 22 April 1990. North November 1990. British Equations Seminar, Sheffield University, 6 T. B. Benjamin NCUACS 63/1/97 C.31, C.32 Lectures, conferences and visits NSF-CBMS Regional Conference on Nonlinear Dispersive Wave Systems, University of Central Florida, Orlando, 11-15 March 1991. Benjamin was Principal Speaker and gave a course of ten lectures. Notice, programme. British (incorporating Theoretical Mechanics Colloquium), Oxford, 9-12 April 1991. Mathematics Colloquium Applied 33rd British Benjamin was Chairman and gave the opening and closing remarks. Conference booklet with programme, abstracts, list of participants. Miscellaneous on university teaching and research adopted at colloquium and Benjamin’s account of the meeting prepared for publication. correspondence resolution including papers, and (SRHE) 1991 for Research into Higher Education Information, programme. Programme, participants, abstracts. Benjamin spoke on ‘A new kind of solitary waves’. Canadian Applied Mathematics Society Conference on ‘Wave Phenomena Il: modem theory and applications’, Alberta, Canada, 15-18 June 1992. Society Annual Conference on ‘Research and higher education in Europe’. Leicester, 17-19 December 1991. List of guests only. Meteorological Office/Oxford University Lunch, 6 December 1994. Benjamin lectured on ‘The mystery of vortex breakdown’. Royal Society Bakerian Lecture, London, 12 November 1992. Notice only. T. B. Benjamin NCUACS 63/1/97 Lectures, conferences and visits Lectures and notes by Benjamin. Manuscript note on the work of Benjamin’s group at Oxford (in French), nd. 1p only. Manuscript note on proposed consortium to be set up by European Science Foundation (in French), nd. 1p only. Manuscript lecture in French, nd. 12pp. ‘Supplement’ to ‘Lecture by T.B. Benjamin’, nd. 2pp typescript. 1p manuscript note (poor condition) on public perception of mathematics. T. B. Benjamin NCUACS 63/1/97 SECTION D SOCIETIES AND ORGANISATIONS See Section E for material relating to Benjamin’s involvement with the National Conference of University Professors and the organisation of higher education. CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE (CNRS) 1975-1978 Benjamin was a member of the Comité de Direction, Laboratoire de Mécanique Théorique, Université de Paris VI, 1975-1978. Information and agenda for meetings. INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS 1976 Benjamin was a Vice-President 1976-1978. was the Duke of Edinburgh. The President at this period 1976-1982 1976-1977, 1982, membership lists, INTERNATIONAL SOCIETY FOR THE INTERACTION OF MECHANICS AND MATHEMATICS Benjamin was a founder member, member of the organising committee, and Vice-President of this new society founded at Lecce, Italy, in May 1975. Papers for meeting of Council at Buckingham Palace, 11 March 1976. Includes correspondence and report from Benjamin on co-operation with French mathematicians. Benjamin. Minutes of meeting of Council 24 November 1977, the first attended by JOINT MATHEMATICAL COUNCIL OF THE UNITED KINGDOM Correspondence information on new society etc. papers and Benjamin was a member 1977-1978. T. B. Benjamin NCUACS 63/1/97 Societies and organisations ROYAL SOCIETY/INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS MATHEMATICAL EDUCATION COMMITTEE Benjamin was Chairman 1979-1985. Minutes of meeting, of Benjamin’s Society/IMA Mathematical Education Committee’, and of a draft report by the Committee on ‘A-level mathematics: the balance of pure and applied.’ brief correspondence 1982. the Includes drafts Royal Members of ‘Memorandum to Papers by others on the subject are also included. T. B. Benjamin NCUACS 63/1/97 SECTION E MATHEMATICS AND HIGHER EDUCATION Much of this section (E.1-E14) is given to the National Conference of University Professors (NCUP) of which Benjamin was a founder and first Chairman. He was active in writing for its Policy Documents, and in contributing more generally in articles and letters to the press to the discussion of current issues in educational policy such as selection, curriculum content, quality control and appraisal. Some of these appear at E.15-E.18. E.1-E.14 NATIONAL CONFERENCE OF UNIVERSITY PROFESSORS (NCUP) E.15-E.18 ARTICLES AND WRITINGS T. B. Benjamin NCUACS 63/1/97 Mathematics and higher education NATIONAL CONFERENCE OF UNIVERSITY PROFESSORS (NCUP) The NCUP was founded in 1989. A preliminary meeting was held in March and at a more formal meeting at Manchester in December officers were elected and a constitution approved. Benjamin was the first Chairman, serving until 1992, and subsequently as a member of Council. The NCUP was set up as a non-political independent organisation. Its aims, as set out in its brochures were: to support university professors in carrying out their responsibilities for the maintenance of academic standards; to provide a forum for discussion and a corporate voice on matters of concern to the nation’s university system; to improve public perceptions about the work of universities; to act as a means of collecting and disseminating information relevant to universities. The Conference held an Annual Assembly, commissioned policy documents for general circulated newsletters and information to its members. specific issues of concem and publication on involved Benjamin was closely or contributed to, the policy documents, made representations to ministers, conducted correspondence and wrote articles and letters to the press as NCUP Chairman. Some of these survive only as press-cuttings at E.6. Drafts for other publications or reports are at E.2-E.4. activities; wrote, these he all in Includes circulars information on NCUP 1989-1995. Proof with corrections by Benjamin. Policy Document 1: ‘Quality-control of Teaching Standards’ (Bibliog.75). General and newsletters, arrangements for first assembly at Manchester December’ 1989, press releases, constitution, annual assemblies London 1990, 1992 (includes Benjamin’s last annual report on retirement as Chairman), 1995. See also E.18. Benjamin’s heavily-corrected manuscript draft; proof with corrections by Benjamin. Policy document 4: ‘Improving public opinion of universities’ (Bibliog. 81). Policy Document 2: ‘The Role of the Professoriate’. (Bibliog. 77). Manuscript draft, title ‘Public perceptions of higher education’. T. B. Benjamin NCUACS 63/1/97 Mathematics and higher education Published versions of Policy Documents 1, 2, and 3 (‘Higher education: a new framework’ Bibliog. 79). Articles and letters to the press by Benjamin 1990-1992. These are press-cuttings only. Most are written by Benjamin as Chairman NCUP, a few are in Benjamin’s own right advocating two-level university courses. They include items listed as Bibliog. 76, 78, 80. Miscellaneous press-cuttings, news items and comments on NCUP 1989- 1992. Correspondence. general exchanges with informing Benjamin’s publications etc. them of Includes correspondence re meetings with ministers, to members arising from letters correspondence colleagues and activities, circular current 1989. 1990 August-December. 1990 May-July. Education. Includes account of meeting with Minister for Higher 1993. Correspondence on public image of universities. 1992 January. presentation of universities and academics. Correspondence with 1992 February-April. Sheppard, fictional R. on the T. B. Benjamin NCUACS 63/1/97 ARTICLES AND WRITINGS Mathematics and higher education ‘The importance of mathematics in the secondary school’, nd. ca.1980. ‘The public image of mathematics’, nd. ‘Advice on the composition of mathematical theses’, June 1987. ‘Public perception of Higher Education’, Oxford Rev. of Education, 19, 1993 (Bibliog. 84). A fuller version of NCUP Policy Document 4. See also E.4, E.12, E.14. T. B. Benjamin NCUACS 63/1/97 SECTION F CORRESPONDENCE 1982, 1993 Bridges, T. J. Crighton, D. G. Dixon, B. 1989 On Benjamin’s 1967 paper (Bibliog. 27) as a Citation Classic. Dixon, H. B. F. Francis, J. ca.1967-1969 Granger, R. A. 1985 (The envelope, with a note to memorialist, about the letter, has been retained). J.F. Toland, Benjamin’s Royal Society On Benjamin's article for festschrift edited by Granger (published 1988, Bibliog.71). Letter re paper by Benjamin on gravity flows, enclosing photograph of water wave. Hopf, E. Herczynski, A. T. B. Benjamin NCUACS 63/1/97 Correspondence Keller, J. J. On Benjamin’s work on vortex breakdown. Lakshmikantham, V. 1976 Journal of Nonlinear Analysis; Benjamin was on the Board of Associate Editors. Leibovich, S. 1994 Photocopy of Benjamin’s reply only, on a paper submitted by him to J. Fluid Mechanics. Lighthill, M. J. 1984, 1988, 1990 Mitterrand, F. 1981 Neale, M. C. Price, W.G. 1994 1988 Committee of the Scholarships Benjamin’s Commission for the 1851 Exhibition. work the Science for Phillips, O. M. Photocopy of Benjamin’s reply only, on his paper Bibliog. 72. Benjamin’s draft only, of his letter of congratulation on Mitterrand’s election as President of France (in French). Trans. Photocopy of Benjamin’s reply only, on a paper submitted by him to Phil. On Benjamin’s Bakerian Lecture. Restrepo, J. 1995 T. B. Benjamin NCUACS 63/1/97 Correspondence Sneddon, I. N. Wilson, J. H. Unidentified Letter re data on shape transitions. T. B. Benjamin NCUACS 63/1/97 INDEX OF CORRESPONDENTS ACRIVOS, Andy ALLEN, Michael ARNOLD, Douglas N. ATIYAH, Sir Michael (Francis) BARNARD, George Alfred BATCHELOR, George Keith BINNIE, Alfred Maurice BLAKE, Robert Norman William, Baron BONA, Jerry L. BONE, Geoffrey BRIDGES, Thomas J. BRYSON, (James) Graeme A.11 E.14 FA A.11,A.21 A.11 A.11 A.11 A.11 2 A.11 F.3 A.11 CRIGHTON, David George A.11, F.4 DRAZIN, Philip GIBSON, Alan F. GORDON, Manfred GRANGER, Robert A. GREEN, Mike FRANCIS, John DEERE, Malcolm FERSHT, Alan Roy FRAENKEL, Eduard DI PRIMO, Dick DIXON, Bemard E.13 A.12 ES F.5A A.12 FERNANDES, John H. EDMUNDS, David Eric DIXON, Henry Berkeley Franks A.12 FRIEDLANDER, Frederick Gerard GREEN, Albert Edward T. B. Benjamin NCUACS 63/1/97 Index of correspondents GRIST, Edward HERCZYNSKI, Andrzej HOCKING, Leslie HUNT, Julian Charles Roland JACKSON, Robert Victor JEFFREY, Alan JOSEPH, Daniel J. KELLER, Jakob J. KINGMAN, Sir John (Frank Charles) LAKSHMIKANTHAM, V. LEIBOVICH, Sidney LIGHTHILL, Sir (Michael) James LIONS, J. L. E.8 A.13 A.10, A.13 F.9 A.13 F.10 F.11 F.12 A.10, MAJOR, John MULLIN, Tom McINTYRE, M McLEOD, Bryce NEUMANN, Peter NEWELL, Alan C. B.48 A.13 A.14 A.14 E.10 A.14 A.14 A.16 MAHONEY, John J. MAIR, William Austyn NEALE, Michael Cooper MOFFATT, Henry Keith MOORE, Derek William B.36 PRICE, Williams Geraint PHILLIPS, Owen Martin PEARSON, Anthony A.14 A.14 A.19 PRITCHARD, W. G. A.14 F.16 NOHEL, John A. F.14 A.14, F.15 T. B. Benjamin NCUACS 63/1/97 Index of correspondents QUINLAN, Sir Michael (Edward) RATCLIFFE, John Ashworth RESTREPO, Juan RILEY, Norman RILEY, Patrick A. SCHULLER, Thomas SEWELL, Michael John SHEPPARD, Richard SLEEMAN, Brian D. SLOMAN, Sir Albert (Edward) SNEDDON, Ian Naismith STEWARTSON, Keith STUART, John Trevor THORPE, Steven C.13 A.5 feat7Z A.14 E.10 E.10 A.15 E12 B.8 A.9, A.15, A.32 F.18 A.15 A.15 A.15 WOODS, Leslie Colin WRIGHT, John VAN WIJNGAARDEN, | WILSON, James Harold, Baron ZORSKI, Henryk

# BENJAMIN, Thomas Brooke v1

Published: 13 September, 2023 Author: admin