This Article 
 Bibliographic References 
 Add to: 
Charles Babbage's Table of Logarithms (1827)
July-September 1988 (vol. 10 no. 3)
pp. 159-169

In 1827 Charles Babbage published his Table of Logarithms of the Natural Numbers, from 1 to 108,000. His logarithms were generally considered to be the most accurate in his day and were reprinted on numerous occasions, well into the 20th century. This paper describes Babbage's motivation for producing the tables, and the measures taken to ensure their accuracy. An assessment is given of Babbage's contribution to the art of table making.

1. Archibald, R. C. 1948.Mathematical Table Makers, New York: Scripta Mathematica.
2. Babbage, C. 1822. The Science of Number Reduced to Mechanism.Works of Babbage 2, London: Pickering and Chatto (in press).
3. Babbage, C. 1824. Rates of the Protector.Works of Babbage 4, London: Pickering and Chatto (in press).
4. Babbage, C. 1826.A Comparative View of the Various Institutions for the Assurance of Lives, London: J. Mawman.
5. Babbage, C. 1827a.Table of Logarithms of the Natural Numbers, from 1 to 108,000, London: J. Mawman.
6. Babbage, C. 1827b. Notice Respecting Some Errors Common to Many Tables of Logarithms.Mem. Astron, Soc. 3, pp. 65-67.
7. Babbage, C. 1829. An Essay on the General Principles which Regulate the Application of Machinery to Manufactures and the Mechanical Arts.Encyclopaedia Metropolitana 8, pp. 1-84.
8. Babbage, C. 1831a.Specimen of Logarithmic Tables Printed with Different Coloured Inks on Variously Coloured Papers, London: B. Fellowes.
9. Babbage, C. 1831b.Table of Logarithms of the Natural Numbers from 1-108,000 on Different Coloured Papers, London: B. Fellowes.
10. Babbage, C. 1832.On the Economy of Machinery and Manufactures, London: Charles Knight.
11. Baily, F. 8 Nov. 1826. Letter to Charles Babbage, British Library Add MS 37183 f357.
12. Bauschinger, J. and Peters, J. 1910.Logarithmic-Trignometrical Tables..., Leipsig: Englemann.
13. Berg, M. 1980.The Machinery Question and the Making of Political Economy, Cambridge University Press.
14. Bowden, B. V. 1953.Faster than Thought, London: Pitman.
15. Briggs, H. 1624.Arithmetica Logarithmetica..., London.
16. Bromley, A. 1980. Charles Babbage's Analytical Engine, 1838.Annals of the History of Computing 4, pp. 196-217.
17. Callet, F. 1795.Tables Portatives..., Paris.
18. Colby, T. 9 Sept. 1826. Letter to Charles Babbage, British Library Add MS 37183 f328.
19. Colby, T. 10 Oct. 1826. Letter to Charles Babbage, British Library Add MS 37183 f338.
20. Colby, T. 15 Sept. 1836. Letter to Charles Babbage, British Library Add MS 37189 f411.
21. Colby, T. 25 Jun. 1840. Letter to Charles Babbage, British Library Add MS 37191 f410.
22. Comrie, L. J. 1948.Chambers's Six-Figure Mathematical Tables, Edinburgh: Chambers.
23. de Morgan, A. 1861. Table.English Cyclopedia: Arts and Sciences 7, London: Charles Knight, cols. 976- 1016.
24. DNB1. 1885-1900. Francis Baily (1774-1844).Dictionary of National Biography 2, Oxford University Press, pp. 899-904.
25. DNB2. 1885-1900. Thomas Frederick Colby (1784- 1852).Dictionary of National Biography 11, Oxford University Press, pp. 711-715.
26. Dubbey, J. M. 1978.The Mathematical Work of Charles Babbage, Cambridge University Press.
27. Fletcher, A., Miller, J. C. P., Rosenhead, L., and Comrie, L. J. 1962.An Index of Mathematical Tables, 2nd edition, Oxford: Blackwell.
28. Franksen, O. I. 1984.Mr. Babbage's Secret: the Tale of Cypher--and APL, Birkerod, Denmark: Strandberg.
29. Gardiner, W. 1742.Tables of Logarithms..., London.
30. Glaisher, J. W. L. 1911a. Logarithm.Encyclopedia Britannica 16, 11th edition, New York, pp. 868-877.
31. Glaisher, J. W. L. 1911b. Table.Encyclopedia Britannica 16, 11th edition, New York, pp. 868-877.
32. Henderson, J. 1926.Bibliotheca Tabularum Mathematicum: Part I: Logarithmic Tables, (Tracts for computers, 13), Cambridge University Press.
33. Hutton, C. 1822.Mathematical Tables, 6th edition, London.
34. Hyman, A. 1984.Charles Babbage: Pioneer of the Computer. Oxford: Oxford University Press.
35. Lardner, D. 1834. Babbage's calculating engine.Edinburgh Reuiew 120, pp. 263-327.
36. Milne, J. R. 1915. The arrangement of mathematical tables.Napier Tercentenary Memorial Volume(ed. C. G. Knott), London: Longman's, Green and Co., pp. 293-316.
37. Morrison, P. and E. 1961.Charles Babbage and His Calculating Engines, New York: Dover.
38. Nagy, K. 9 Apr. 1833, Letter to Charles Babbage, British Library Add MS 37187 f471.
39. Taylor, M. 1792.Mathematical Tables..., London.
40. Tucker, R. 1872.Mathematical and Scientific Library of the Late Charles Babbage, London: printed by C. F. Hodgson and Son.
41. Vega, G. 1794.Thesaurus Logarithmorum..., Leipsig.
42. Vlacq, A. 1628.Arithmetica Logarithmica, Gouda.
43. Williams, M. R. 1981. The Scientific Library of Charles Babbage.Annals of the History of Computing 3, pp. 235-240.
44. M. Williams,A History of Computing Technology, Prentice-Hall, Englewood Cliffs, N.J., 1985.
45. Young, J. R. 1834.Mathematical Tables..., London.

Martin Campbell-Kelly, "Charles Babbage's Table of Logarithms (1827)," IEEE Annals of the History of Computing, vol. 10, no. 3, pp. 159-169, July-Sept. 1988, doi:10.1109/MAHC.1988.10023
Usage of this product signifies your acceptance of the Terms of Use.