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Draft of a paper entitled 'Sur une propriété générale d'une certaine classe de fonctions transcendantes (par Mr.N.H.Abel de Christiana)', apparently in the hand of Niels Henrik Abels hand, later printed as 'Remarques sur quelques propriétés generales d'une certaine sorte de fonctions transcendantes' in Oeuvres complètes de N.H.Abel...redigées...par B.Holmboe (1859), vol.I (section XV), pp.288-98.

The collection, 1835-1850, contains letters and printed papers, notices and unpublished printed material, which Airy received during his time as a member of the Senate of the University of London. The Airy correspondence has a special importance because much of the early archival material of the University of London was destroyed and so often the only record of its activities is in the Senate and Committee Minutes. Airy was particularly interested in the constitution of the University, the developments of the mathematics syllabus, the syllabuses for certificates in hydrography and civil engineering and the introduction of the religious examination.

Papers of Jacob Vale Asbury, 1816-1843, comprising a manuscript volume by Asbury, containing notes of the lectures of John Abernethy given at St Bartholomew's, 25 Jul 1816; notes titled Observations on the Pulse, by Dr Fordyce, 18 Sep 1816; notes titled Lectures on the Principle Operations of Surgery by Sir Everard Home, 1812; notes titled Cases and Original Observations, 1842; tables of statistics on the population of Enfield, and Great Britain; and mathematical calculations on the cubic inches of water in a box.

Notebooks on lectures on mathematics, languages and political economy attended by Bagehot when a student at University College London.

Notebook compiled by Jonathan Baker containing mathematical problems and tables, dated 29 July 1765. The notebook was also used for entering his accounts between 1782 and 1796, with some later, more general, additions to 1800, mostly relating to his work as a cobbler, but also accounts of household expenses and rents received. The accounts mention places between Cirencester and Newnham.

Papers of Harry Bateman including three notebooks, two (numbered six and seven) containing notes from the lectures of E T Whittaker at Trinity College Cambridge 1903-1904; one containing formulae connected with the Legendre and Bessel functions, with Trinity examination paper 1880 and printed testimonial by Rutherford.

Manuscript transcript by Richard Bateman, 1612, of a work by Benedictus Victorius Faventius containing a calculator or computer for increasing or diminishing figures, which was printed by Benedict Hector, bookseller of Bologna, in 1512. The text was copied by Bateman from a treatise of a revised edition by Dom. Gaetanus, Doctor of Medicine.

Manuscript volume, 1694: Rechenbuch. An arithmetic book containing problems, including calculations for finding the date of Judgement Day, the Golden Number, etc, together with astrological information. Some of the problems are set out in verse.

Papers of Jean-Baptiste Biot, c 1800-1937, including correspondence and a translation of Biot's Memoir on the Circular Zodiac of Denderah.

Twenty-three manuscript notebooks on mathematical statistics which include 'The theory of deviation from an average', the introduction to 'An algebra of evolution', and 'Problems relating to the mathematical treatment of statistics: periodicity and deviation'.

Mathematical and scientific papers of George Boole.

Letter from Henry Peter Brougham of [Westmorland] to [Augustus] De Morgan, 11 Sep [1857]. Referring to an article in Notes and Queries [2nd series, Volume 4] and discussing mathematical subjects. Autograph, with signature.

Copies of reviews of books on mathematical subjects, mainly for the ASLIB Book Review, 1957-1977.

Thirteen volumes of manuscript notes and calculations about magic squares.

Nine foolscap pages of handwritten mathematical calculations and notes by Arthur Cayley entitled 'Areal Co-ordinates' (December 1891)

Letter from Michel Chasles of Paris to Augustus De Morgan, 17 May 1850. On mathematical matters.

Autograph, with signature.

Letter from Michel Chasles of Paris to Augustus De Morgan, 31 Aug 1852. On mathematical matters.

Autograph, with signature.

Letter from Michel Chasles of Paris to Augustus De Morgan, 4 Oct 1852. On mathematical matters.

Autograph, with signature.

Letter from Michel Chasles of Paris to Augustus De Morgan, 8 Apr 1848. On algebraical formulae.

Autograph, with signature.

Records relating to the City and Guilds College (formerly the Central Institution of the City and Guilds Institute), 1876-1995, comprising a history, 1896; printed reports and schemes for the new institution, 1876-1884; speeches and accounts of the opening of the Central Institution, 1884; correspondence relating to the Jubilee, 1933-1935; programmes of the Central Institution, 1884-1931; letter books of the Secretary to the City and Guilds College Delegacy, 1911-1927; papers relating to the City and Guilds College Centenary, 1885-1985, and visitor's book (FC);
minutes of the Board of Studies, 1885-1913; report on equipment, 1889 (FE);
papers relating to the Engineering Board, notably minutes, 1915-1965, 1980-1984; correspondence and papers, 1911-1935; conference on postgraduate courses, 1962-1965; Chairman's notes and correspondence, 1955-1961; correspondence of the Research Committee, 1932-1951; senior appointments, 1913-1933 (FF);
papers of the Delegacy, notably minutes and reports, annual reports of the Dean of the Central Institution, 1911-1968; correspondence, 1910-1937, including research grants, 1915-1921; appointment of members, 1936-1970; minutes and accounts of the Finance and Special Committees, 1911-1924; correspondence and reports of the Organisation Committee, 1930-1931; chairmans' notes and correspondence, 1954-1968, donations, 1934-1936 (FG);
papers relating to links with Imperial College and the University of London, notably history of the City and Guilds London Institute, 1910; joint meetings and committee relating to the Delegacy, 1907-1910, 1955; correspondence of the Delegacy concerning the University of London, 1911-1921; degree and diploma examinations, 1926-1930; suspension of the Delegacy, 1966-1976 (FH);
papers relating to staff roles, including staff conference with Imperial College, 1911-1912; powers and duties of the Rector, 1918 and Deanship, 1931-1936; organisation and administration, 1918; papers relating to the Chemistry department, comprising regulations, examination papers and course notes of Professor Henry Edward Armstrong, 1884-1897; papers relating to the Civil and Mechanical Engineering Department, comprising notebook of Professor William Ernest Dalby on courses, 1904-1908; notes on lectures given by Professor William Cawthorne Unwin, 1885-1887; lecture and laboratory notebooks of C E H Salmon, 1894-1896; examination papers, 1913; correspondence relating to the Unwin Library, 1933-1934; papers relating to the Mechanics and Mathematics department, comprising notes on lectures given by Professor Olaus Henrici, 1885-1889; examination papers, 1888-1929; papers relating to the Electrical Engineering department, comprising notes on lectures given by Professor William Edward Ayrton, 1885-1887, notebooks of C Percy Taylor, 1892-1895 (FK);
records relating to students, 1884-1913 (FP); matriculation and entrance examination results; 1905-1938, examination results, 1887-1913 (FQ); registers of students, 1884-1948, tuition fees ledgers, 1911-1918, attendance registers, 1919-1940 (FR); Central Gazette and other journals, 1889-1906 (FSG).

Letter from Josiah Latimer Clark of Westminster Chambers, 11 Victoria Street, London to Sydney Lupton, 2 Dec 1891. 'Your most delightful book of tables and constants is I presume on every table ...'. Writing in reply to a letter from Lupton, saying that he hopes to correct his own figures before long, since Lupton had referred him to an article by Professor [George Carey] Foster in Watts' Dictionary [of Chemistry].

Autograph, with signature.

Scientific and other papers sent to the Royal Society, presented at meetings of Fellows, or commissioned by the Society. They form a complementary series to the Early Letters, both of which were superseded by the Letters and Papers. Many of these items, referred to as the 'Guard Books', are duplicated in the Register Book of the Society. The classification is a simplified form of the 'Philosophical Transactions' abridgment by John Lowthorp. This arrangement was completed in 1741 by Thomas Birch. The majority of the papers in these volumes are manuscript, but a few printed documents occur throughout the series. Some of the papers are earlier in date than the grant on 15 July 1662 of the First Charter to the Society. The Committee of Trades seems to have been associated with the earlier meetings of those philosophers who subsequently became Fellows, and produced a number of practical papers, some of which were written in 1639 and which are mostly found in Volume 3(i). There are still earlier documents, mostly in Volume 25, which may have been included in the gift, in 1667, of the Arundel Library.

Undated lecture notes on geometry: two closely written sheets pasted onto an otherwise unused notebook.

Undated mathematical fragments.

Notes on physics and mathematics.

Letter from Matthew Collins of 40 Upper Pitt Street, Liverpool to Augustus De Morgan, 8 Apr 1853. Covering note, enclosing a pamphlet, On Clairaut's theorem ... (1853).

Autograph, with signature. A note in De Morgan's hand states that the content of the pamphlet, published in the Cambridge and Dublin Mathematical Journal, new series vol IX (1854), were plagiarized from a lecture given by Mr James MacCullagh in 1846.

Papers of Thomas George Cowling including correspondence with Neil Oscar Weiss, 1964-1989 and P A Gilman, 1980-1982.

Correspondence between Augustus De Morgan and George Boole, Professor of Mathematics at Queen's College Cork, dated 1842-1864. The collection also includes letters from John Stuart Mill, and letters from various correspondents mostly dated 1846-1848.

Papers of the De Morgan family, [1756-1928], comprising material relating to the suffragette movement, such as photographs, newpapers, press cuttings and pamphlets; correspondence of Augustus de Morgan, with correspondents including Sir Frederick Richard Pollock, Sir George Biddle Airy, Sir John William Lubbock, John Wrottesley (2nd Baron Wrottesley), John Radford Young, Sir John Frederick William Herschel, John Finlaison, and General Sir John Briggs; correspondence of William Frend de Morgan, mainly with members of his family and Sir Edward Coley Burne Jones; material relating to the de Morgan and Frend families, notably family photographs, drawings, letters, legal documents and memorabilia; letters from Sophia and Mollie de Morgan to Joan Antrobus; manuscript and typescript copies of stories and essays by William and Mary de Morgan; papers relating to Sophia de Morgan's Memoir of her husband Augustus, including letters, reviews and working notes; bundle of letters containing correspondence concerning a petition to the women of America from the women of England about the abolition of slavery; printed material, mainly works by Augustus de Morgan; letters to Francis Baily, [1820-1940]; letters from Thomas Henderson to Thomas Galloway, 1834-1842; 5 watercolours of Scotland by Frances Shakerley, [1920-1930].

Notes for an introductory lecture in the Faculty of Arts and Laws at University College London.

Manuscript of De Morgan's introductory lecture delivered at the opening of classes in mathematics at University College London on 5 November 1828. Appended are notes for another lecture.

Student's notes on lectures on Algebraic Geometry and the Calculus, given by Augustus De Morgan at University College London from 11 March to 13 May 1847.

Mathematical fragments, letters, and papers.

Augustus De Morgan's mathematical tracts, copied by John Power Hicks from the original manuscripts in the Library of University College London.

'Elements of statics', a volume written for publication at the proposal of the Society for the Diffusion of Useful Knowledge, though it was never actually published. De Morgan used it as evidence of his work and knowledge when applying for the Mathematics Chair at University College London in 1827.

Papers of Augustus de Morgan, 1859, comprise a letter to Mrs Bax [grandmother of the composer Sir Arnold Bax], enquiring whether she is comfortably settled at her new address; an obituary of Professor De Morgan is attached to the second sheet.

Papers of Augustus de Morgan, 1833-1870, comprise letters sent and received by De Morgan. Correspondents include: Miss Anne Sheepshanks and [her brother] Rev Richard Sheepshanks, Vice-Admiral W H Smyth, and Professor [Philip] Kelland of the University of Edinburgh.

Copy of the draft of the first work published by Augustus de Morgan, 'The Elements of Arithmetic', 1830.

A collection of tracts on fortification and geometry, 17th and 18th centuries: Folio 1 Della Fortificatione; Folio 53 Geometrica Prattica; Folio 83 Della sfera; Folio 104-115 Blank sheets and oddments; Folio 116 Del Misurare da Contano; Folio Il quaduarete Geometrico; Folio Aritmetica.

A collection, compiled in 1723, of mathematical material, principally for the use of navigation.

A complete ternary square table up to 256,000 followed by a quaternary square table by Solomon Moses Drach, 1866.

A system of mathematical tables inscribed on title page ' James Elgar May 8th 1756'. Originally entitled 'A system of mathematical tables by James Elgar and John Newton' and bound with 'Tabulae Mathematicae' by John Newton.

Paper by Alexander J Ellis 'On clinant geometry, as a means of expressing the general relatings of points on a plane, realising imaginaries, and extending the theories of anharmonic ratios', communicated by Arthur Cayley, Esq. F.R.S. Febr. 1863. Abstract printed in the Proceedings of the Royal Society, vol.12, pp 442-3 Carbon copy of MS, with figures drawn in ink. Text and figures on rectos only. Paper wrappers inscribed 'Prof Augustus De Morgan, with the Author's respects'. Part of A De Morgan's library, given to the University by Lord Overstone in 1871. Former shelf-mark L(P.C.6).

A commentary on Newton's 'Principia' by Nicholas Fatio, with an introductory note in English by Dr Johnstone about Fatio, his life, religious beliefs, death and dispersal of his books.

Papers of Rev George Fisher. The earliest items are two books of mathematical theorems, 1811 and 1813. There are volumes of notes and observations for both Fisher's Arctic voyages and for his period in the Mediterranean, accounts of later scientific work and abstracts of observations made by other scientists. This is the material which formed the basis of the scientific papers which he published in the Philosophical Transactions and elsewhere. There are letterbooks for Greenwich Hospital School from 1836 to 1863 (excepting the years 1858, 1859 and 1860) and other reports and papers relating to the School There are a number of items collected by Fisher The most important are Peter Puget's journal for March to May 1793 in the Chatham, storeship for Vancouver's expedition; a meteorological log also giving details of ship arrivals and departures at Madras, 1815 to 1816; Franklin's (q.v.) lunar observations on board the Trent in 1818 and Parry's (1790-1855) meteorological journal on his first two voyages in search of the North-West Passage in 1819 to 1820 and 1821 to 1823.

Copy of 'The radix; a new way of looking at logarithms...in five problems by Robert Flower' made in 1877 by Alexander John Ellis with supplementary notes by Ellis including biographical information on Flower.

Papers of Professor Andrew Russell Forsyth, [1898-1921], comprising papers and lectures concerning mathematics, notably relating to Abels theorem, Abelian functions, binary forms, quintic equations and other modular functions, Fourier's and other series, algebraic functions, 1909, differential equations of mathematical physics, 1917-1921, elements of theory of functions, 1915-1916, elliptic functions, 1898, 1914-1915, spherical harmonic series, expansion in polynomials, expansion theorems, solid geometry, differential equations of dynamics.

A geometrical exercise book with Frederick's name and the dates 4 May 1795 and 17 May 1796 on the cover. Each page bears a theorem and its accompanying diagram, up to the 21st theorem of the 5th book. The exercises are occasionally relieved by a pencil sketch of a head or half-figure.

Papers of Professor Albrecht Fröhlich, 1916-2001, reflecting his mathematical research, publications and correspondence with colleagues. Papers are divided into six sections comprising biographical papers; research papers; publications; papers relating to visits, conferences and lectures; correspondence and theses and examinations.

Biographical papers include obituaries, memoirs and papers relating to memorials including a service in the Chapel of Robinson College Cambridge, 10 Feb 2002; autobiographical papers including copy of Fröhlich's entry for Personal Records of Fellows of the Royal Society; papers relating to Fröhlich's career, honours and awards including his Ph.D. thesis 'On some topics in the theory of representation of groups and in class field theory', and correspondence and papers relating to his university appointments and some of his principal honours, including election to the Fellowship of the Royal Society.

Research papers chiefly comprise mathematical workings, notes and drafts: notably relating to work on the decomposition of primes [1950] and work on Galois module theory and Gauss sums.

Publications comprise published material by Fröhlich, 1950-2000, drafts and unpublished drafts, including work with Charles Terence Clegg Wall on Brauer groups, 'Galois modules and the functional equation', and draft of a longer text entitled 'mathematical theory of ostensive and consequently of empirical predicates'.

Visits, conferences and lectures include papers relating to Fröhlich's conference attendance and overseas visits 1956-1998, documentation of his participation in mathematics meetings held at the Mathematisches Forschungsinstitut, Oberwolfach, Germany and papers relating to Visiting Professorships, including invitations, programmes, and texts or abstracts of lectures.

Correspondence,1950-2000, on subjects including progress of Fröhlich's research, discussions of problems with mathematical workings and drafts of papers. Notable correspondents include Fröhlich's Ph.D. supervisor Hans Arnold Heilbronn, colleagues Jean-Pierre Serre, Olga Taussky-Todd, Stephen Virgil Ullom and Charles Terence Clegg Wall, and former research students Colin J. Bushnell, Martin J. Taylor and Stephen Mark Johnson Wilson.

Theses and examinations comprise, theses of Ph.D. students supervised or examined by Fröhlich, including his research students at King's College London and examination papers, some with Fröhlich's manuscript calculations of answers, 1980-1990.

Manuscript volume containing an eighteenth century treatise on geometry, entitled 'Geometrie Pratique'. The chapter headings are: 'Livre premier: des logarithmes', 'Livre II: De la trigonometrie rectiligne', 'Livre IV: De la construction des figures', 'Livre V: De la longimetrie', 'Livre VI: De la planimetrie', 'Livre VII: De la stereometrie'.