Charles Babbage: Mathematical and Scientific Notebooks and Papers

Archive Collection

Scope and Content

Schooldays (pre-university)

A bundle of around 30 sheets containing notes and exercises mainly on mathematical topics, with a few notes on Latin, Greek, German, and English grammar.

2 hard-backed notebooks bearing the date 1806, used for exercises in arithmetic.

A hard-backed notebooks bearing the date 1807, used for exercises in algebra.

A notebook bearing the date 1807, used for exercises in geometry.

Drafts and printer's proofs of published papers

A paper folder marked on the outside 'Three papers - Analytical Society 1813' and containing the following MSS, signed 'C. Babbage, Peterhouse': (a) Solutions of two problems requiring the application of mixed differences; (b) Memoir on the summation of certain series of sines, cosines, etc. There is also a draft dealing with the inscription of circles under a hyperbola and with the solution of functional equations.

Incomplete page proofs (pp. 21-95 only) for the Memoirs of the Analytical Society, published in 1813. They are in a wrapper addressed to Babbage at St Peter's College.

Two double sheets containing a draft of the opening section of a paper by Babbage entitled 'Demonstration of some of Dr Matthew Stewart's general theorems, to which is added an account of some new properties of the circle' for the Journal of science and the arts, v. 1 p. 6, Royal Institution, London, 1817. There is also an undated draft of a letter to an unknown recepient containing the words 'The two following theorems are the key to many of Stewart's'.

The draft of a paper entitled 'Observations on the notation employed in the Calculus of Function', 8 pages, for Transactions of the Cambridge Philosophical Society, v. 1 p. 63, 1822.

Early Mathematical interests

A notebook of ten pages, without a cover, containing a sketch for a work on functional equations.

A shorter draft of the above work, presumably earlier, on the same subject.

Three sheets and a smaller sheet concerned with functional equations.

A notebook of 22 pages, without a cover, containing a copy of a paper entitled 'On series containing sines and cosines and their positive powers'. Inside are two loose sheets of mathematical jottings.

A small package containing a MS entitled 'Memoir on the properties of certain functions' by Babbage. A note by Henry Babbage states that it was given to the Analytical Society. There are also writings on mathematical topics.

A notebook containing an essay entitled 'On equations not satisfying the conditions of integrability'. Henry Babbage, in a note dated 1904, states that it is in his father's hand, but that he cannot date it.

A rough verion of an essay of around 30 pages entitled 'Notation'. Babbage published an article on this subject in the Edinburgh Encyclopaedia, 1830.

A sheet headed 'Astronomy' and containing what are apparently notes for a work on that subject.

A copy of an essay entitled 'Remarks on interpolation' by C. Babbage, 6 pages.

A thin grey notebook containing a copy of a mathematical essay beginning with the statement of a problem in functional equations. Inside are loose sheets of jottings.

A bundle of miscellaneous mathematical notes and scribbling papers.

Scientific notes and experiments

A stiff marbled notebook containing a 'Journal of pendulum experiments', dated Portland Place, 1828. It contains a transcript from Isaac Barrow on the duty and reward of bounty to the poor.

Three pages containing a draft by Babbage of a paper entitled 'Description of a pendulum barometer'. There is a note by Henry Babbage to the effect that the date is unknown. There is also a double sheet of the same size containing a rough mathematical treatment of the pendulum barometer.

A double undated sheet headed 'Notes respecting some experiments to be made for the purpose of ascertaining the laws of actions of the Voltaic battery'.

A single sheet containing a transcription (in French) of part of a note by Le Verrier on planetary motion in Comptes rendus, 1849. There is also a sheet entitled 'Notes on a paper by Fuss, 1808', with reference to the Memoirs of the Imperial Academy of St Petersburg, 1811.

Smith's Prize

A large brown folder inscribed 'Smith's Prize examination papers, CB'. Babbage examined the Smith's Prizes in his role as Lucasian Professor. The folder is evidently his working file. It contains printed copies of examination papers for the years 1828, 1830-1836, and 1838. There are also what appear to be drafts of questions, including, in some cases, a note of the source of the idea. As well as the printed Smith's Prize papers there is a set of handwritten copies of unidentified papers of questions, marked in pencil with the years 1829-1837; for the years 1836 and 1837 there are in addition draft copies with revisions and five or six extra copies in various hands of the final version. The folder also contains printed Bell's scholarship papers for 1827, 1830-1832, and 1834-1837.

Mathematical and Astronomical Tables

A proof copy printed from stereotype plates of part of the great French table made under the direction of Prony. The table was never published. There is a note by Babbage to the effetc that this copy was given to him by Didot on his first visit to Paris.

Manuscript of a table of logarithms, with a note by Babbage stating that it was copied with permission from the original MS at the Observatory of Paris.

A double sheet containing a copy of some series for computing logarithmic differences.

A bundle consisting mainly of correspondence and working papers from the year 1827 relating to the comparisons made by Babbage of logarithmic and trignometric tables from various sources. The letters are from Henry Jenkins to Dr Young, from David Booth to Babbage, from Woollgar to Davies Gilbert, and from Davies Gilbert to Babbage. A single sheet has noted on it some errors in Taylor's tables. On the back are 'Hints for Travellers'. The bundle includes a bill from the printer for printing Babbage's table of logarithms, and some correspondence with a bookbinder.

A copy of the ultimate edition, dated 1889, of Babbage's logarithms. It contains Henry Babbage's autograph together with details of the financial arrangements made by him with William Clowes, the printer.

A single sheet containing a note dated 21 Mar. 1858 and initiated by Babbage recording a conversation with Mr Hind, Director of the Nautical Almanac, about Hansen's new lunar tables.

A single sheet annotated 'RS 25 Feb 1859 vol. IV Observatory of Paris' and containing brief mathematical notes.


A single sheet headed 'On a method of expressing the action of machinery', evidently an introductory paragraph for a projected account.

A double sheet on one side of which is a notation for division in the Analytical Engine. There is also a single sheet of the same size with a rough notation, apparently also for a division, on one side, and some jottings and a couple of rough sketches on the other. A third sheet has roughly written on it in pencil a notation for a difference engine.

Notebooks and scribbling books

A small notebook endorsed on the first page 'St Michael's Hill, 29 July 1825' and full of miscellaneous notes on things that caught Babbage's attention at the time. There is an index at the front.

An account book used as a notebook. Much of it is taken up with notes on the rotating of needles by electricity, with records of experiments done with something called the 'akarimeter', and with sundry chemical notes, included tabulated data on the properties of chemical elements. These have dates between 1826 and 1830.

A small notebook inscribed 'Atoms 1848'. It contains about ten pages of mathematical jottings.

Eighteen pages from a notebook sparsely filled with notes about manufacturing processes and indexed. A note by Henry Babbage states that the material was probably collected for Babbage's book Economy of manufactures

A thick notebook, labelled 'Atoms 1854' on the flyleaf. It has nearly 600 pages, most of them written on. There is an index at the front. There is no cover or spine. The first 400 pages are devoted mainly to mathematical calculations, with a short note on sedimentary rocks. One page has a note on seventeenth and eighteenth century books on cyphers, followed by several pages headed 'Rules for dictionary of decyphering'. Then come some 60 pages of notes written during the period November 1856 to February 1858 when Babbage was working out various details of the Analytical Engine. They are concerned with anticipatory carriage and related issues. The latter part of the book is mainly taken up with mathematical calculations, but there are a number of references to the Analytical Engine. One, dated 19 July 1863, deals with hoarding carriage and is marked 'very important'

Nine leaves from a large notebook. The entries bear dates in the 1850s. There are some brief notes made by Babbage for letters to his son.

A large book in a thick paper cover inscribed in copper plate 'Problems on curves related to the various orders of contact'. However, much of the book contains material on other subjects, including the calculus of functions. At the end of the book, opened backwards, is a transcript of a mathematical dissertation in Latin.

A small notebook with a leather cover containing 'Hints to be pursued'. There are ten pages of ideas and problems bearing dates between September 1818 and January 1823.


Note by Babbage dated 14 Dec. 1865 describing a meeting of the Royal Society at Burlington House.

Draft of a letter by an unidentified writer beginning 'Dear Higman'.

A single sheet with a few lines written on it in a mysterious rectilinear script.

A double sheet containing a note in French, apparently copied from a French Journal of 1773. On the back are mathematical jottings.

A number of mechanically drawn curves, with a note by Henry Babbage saying that nothing is known of their origin or use.

Clifford's lecture

Professor W.K. Clifford's notes for a lecture on Babbage and his work at the Royal Institution on 24 May 1872. The notes were sent to Henry Babbage after Clifford's death by his widow. Included in the same folder is a letter from Mrs Clifford to Henry Babbage, referring to an unanswered letter from Henry to Clifford, and returning a book Henry had lent him.

Computations by Henry Babbage

A bundle of papers endorsed 'My computations of the powers of ', covering work done in the early months of 1878. There is a note dated 5 March 1878 stating that they are calculations of differences to be used in the Difference Engine to make a table of sines for every minute of the quadrant to thirty (altered in pencil to twenty-one) places. A further note added in August 1879 states that the first Difference Engine was abandoned in 1879 due to expense.

Administrative / Biographical History

Charles Babbage (1792-1871), mathematician and scientist, studied at Trinity College and Peterhouse, Cambridge 1811-1814, and was Lucasian Professor of Mathematics at Cambridge, 1828-1839. He was the inventor of a mechanical computer.

Conditions Governing Access

Open for consultation by holders of a Reader's Ticket valid for the Manuscripts Reading Room.

Acquisition Information

Transferred from the Scientific Periodicals Library, Cambridge, 1989.


Description compiled by Robert Steiner, Department of Manuscripts and University Archives.

Other Finding Aids

Additional Manuscripts Summary Catalogue. There is also a more detailed entry in the main catalogue.


For information on other papers of Babbage see The manuscript papers of British scientists 1600-1840 (Royal Commission on Historical Manuscripts, Guides to sources for British history), 1982.

Corporate Names