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Ready Reckoners
October-December 2005 (vol. 27 no. 4)
pp. 64-80
Bruce O.B. Williams, Birkbeck College, University of London
Roger G. Johnson, Birkbeck College, University of London
Multiplication is vital to the conduct of commerce but is time-consuming and error-prone. Many aids were developed over two centuries to address these issues. This article surveys the development of the most widely used of these, the ready reckoner. The underlying principles of reckoner design are explained. To explain their range of use, over 1,250 entries from the major national library catalogues and elsewhere have been classified by application, target user, date, price and format. A sample of different styles are illustrated.

1. D. Fenning, The Ready Reckoner, or Trader's Most Useful Assistant, Crowder, 1757.
2. W. Leybourne, Panarithmologia, or the Trader's Sure Guide, Dunton and Harris, 1673.
3. O. Ore, Number Theory and Its History, Dover Publications, 1988. Originally published by Mc-Graw-Hill, 1948.
4. W. Webster, Webster's Tables, Flesher, London, 1634.
5. F. Barrême, Le Livre des Comptes Faits [Book of Sums Done], Thierry, 1689 (in French).
6. M. Campbell-Kelly ed. History of Mathematical Tables, Oxford Univ. Press, 2003.
7. D.E. Smith, Rara Arithmetica— A Catalogue of the Arithmetics Written before 1601, Chelsea Publishing, 1853.
8. A. De Morgan, Arithmetical Books from the Invention of Printing to the Present Time, Taylor and Walton, 1847.
9. J.W.L. Glaisher, "Mathematical Tables," Proc. British Assoc. for the Advancement of Science, London, 1873, p. 2.
10. A. Fletcher, J.C.P. Miller, and L. Rosenhead, An Index of Mathematical Tables, Scientific Computing Service, 1946.
11. Collins National Ready Reckoner, Collins, 1959, quote from preface.
12. H.A. Klein, The Science of Measurement: A Historical Survey, 1988 ed., Dover, 1974.
13. F. Tapson, A Dictionary of Units, 2003; .
14. B.O.B. Williams, Check Figures— A Once Ubiquitous Tool for Book-keepers, published in Slide Rule and Calculation monographs, Slide Rule Circle, UK, 2002, pp. 59-98.
15. US Census Bureau, Historical Statistics of the US Colonial Times to 1970, 2000.
16. E. Martin, Calculating Machines (Die Rechenmaschinen): Their History and Development, P. Kidwell and M. Williams, eds., MIT Press, 1992.
17. B.W. Boering, "Biography of a Machine: Comptometer"; .
18. "National Calculating Service & Sumlock Comptometer Colleges"; .
19. T.A. Russo, Antique Office Machines: 600 Years of Calculating Devices, Schiffer Publishing, 2001.
20. "43 Percent Quicker with Decimals," Office Magazine, Aug. 1960.
21. E.M. Horsburgh, Handbook of the Napier Tercentenary Celebration, G. Bell and Sons, 1914; reprint 1982.
22. M.R. Williams, "From Napier to Lucas: The Use of Napier's Bones in Calculating Instruments," Annals of the History of Computing, vol. 5, no. 3, 1983, pp. 279-296.
23. G. Ifrah, The Universal History of Numbers, Harvill Press, 1998, p. 567.
24. J. Dilson, The Abacus: The World's First Computing System, St. Martin's Press, 1968, p. 84.
25. C.G. Knott, Napier Tercentenary Memorial Volume, Longmans, Green and Co., 1915.
26. S.L. Laundy, A Table of Products, by the factors 1 to 9 of all numbers from 1 to 100,000, by the aid of which multiplication may be performed by inspection. With an introduction explanatory of its use, etc., Charles & Edwin Layton, 1856.
27. J.W.L. Glaisher, "Multiplication by a Table of Single Entry," Philosophical Magazine, 1878.
28. P.M. Hopp, Slide Rules, Their History, Models, and Makers, Astragal Press, 1999.
29. E.J. Chamberlain, "Long Scale Slide Rules," J. Oughtred Society, vol. 8, Spring 1999.
30. W. Feely and C. Schure, "The Fuller Calculating Instrument," J. Oughtred Society, vol. 4, no. 1, 1995.
31. P.M. Hopp, Slide Rules, Their History, Models, and Makers, p. 114.
32. Instruments Catalogue, W.F. Stanley and Co. Ltd, 1928, p. 307.
33. J. Keyworth, Catalogue, Bank of England Museum, Bank of England, 2003.
34. L. de Brabandere, Calculus: Les Machines du calcul non électriques [Calculus: Non-Electric Calculating Machines], Mardaga, 1994 (in French).
35. Shell Group Archives, GHS/2B/72. (A note in Shell Group Archives GHS/2B/72 records that "we had 4 in 1923, worked by women".)
36. Office Magazine, June 1923.
37. L.J. Comrie, "Hollerith and Powers Tabulating Machines," Trans. Office Machine Users Assoc. (1929-30), Office Machine Users Assoc., pp.25-37.
38. A.L. Norberg, "Punched Card Technology," Technology and Culture, vol. 31, no. 4, 1990, pp. 753-779.
39. P. Faulstich, "Brunsviga,Brain of Steel," Historische Burowelt, vol. 37, 1994.
40. C. Barnes, Otis King Calculators: A History of Production, Colin Barnes, 1999.
41. S. Johnston, "Making the Arithmometer Work," J. Scientific Instrument Soc., vol. 52, Mar. 1997.
42. M.N. Wise, The Values of Precision, Princeton Univ. Press, 1995, p. 318.
43. "Some Useful Ready Reckoners," The Organiser, July-Nov. 1908, p. 191.
44. Office Magazine, June 1923.
45. W. Campbell, Office Management, Pitman, 1933.
46. H.P. Cemach, Elements of Punched Card Accounting, Pitman, 1951.
47. "Good Ideas from Unilever Ready-Reckoners," Office Magazine, Nov. 1958.
48. A.F. Warburton, "Calculator Terminology," Office Magazine, Jan. 1959.
49. L.M. Nation-Tellery, Office Magazine, Sept. 1960.
50. J.C. Oehlschlager, The Ready Reckoner or the Business Man's Companion, Winnipeg, Canada, undated.
51. W. Leybourne, Ready Reckoner or Trader's Sure Guide, Dilly, Rivington, et al., London, 1798.
52. Ibid., p. 83.
53. J. Gall Inglis, The Express Ready Reckoner, Gall and Inglis, Edinburgh, 1920, quote from preface.
54. S. Simpson and E. Wise, The Readiest Reckoner Ever Invented, 13th ed., William Tegg, 1862, quote from foreword.
55. R. Anlezark, A Commercial Ready Reckoner on an entirely new system etc., Palmer & Howe, 1871.
56. The World's Ready Reckoner and Rapid Calculator, Laird and Lee, 1911, p. 254.
57. Pitman's Office Desk Book and Ready Reckoner, Isaac Pitman and Sons, 1934.
58. D. Fenning, The Ready Reckoner, or Trader's Most Useful Assistant, quote from the introduction.
59. D. Fenning, The Ready Reckoner, or Trader's Most Useful Assistant, 1788, Crowder, title page.
60. S. Simpson and E. Wise, The Readiest Reckoner Ever Invented, Sharpe and Hailes, 1811, quote from preface.
61. S. Simpson and E. Wise, The Readiest Reckoner Ever Invented, 13th ed., William Tegg, 1862, quote from preface. Rooks checked the original calculations: a common practice and perhaps good marketing.
62. D. Neave, Moulders' Ready Reckoner, Aberdeen Univ. Press, ca. 1880, p. 5 of preface; author Williams' copy.
63. Advertisement for C.H. Dowling, A Series of Metric Tables, Crosby Lockwood and Co., 1886. Advertisements are in the unnumbered pages at the back of Chadwick.
64. Shorthose, Commercial Ready Reckoner, 10th ed., George Allen & Unwin, 1921.
65. D. Swade, "The 'Unerring Certainty of Mechanical Agency': Machines and Table Making in the Nineteenth Century," History of Mathematical Tables, M. Campbell-Kelly, ed., Oxford Univ. Press, 2003, p. 152.
66. G. Brown and C. O'Brien, The Rich Man's Ready Reckoner, Wolfe Publishing, 1970, preface.
67. "Financial compound interest and annuity tables. Fifth edition. (Second printing.) Computed by Financial Publishing Company under editorial supervision of Charles H. Gushee. Financial Publishing Co. Boston, Mass. London: Routledge and Kegan Paul." Gushee is a book of tables (undated). Quote is from title page to show that it was produced by computer.
68. H. Perrin, Nuttall's Metric Conversion Tables, Warne, 1973.
69. D. Swade, "The 'Unerring Certainty of Mechanical Agency': Machines and Table Making in the Nineteenth Century," pp. 147-149.
70. A. Weedon, Victorian Publishing— The Economics of Book Production for a Mass Market 1836–1916, Ashgate, 2003.
71. Brendon and Son Ltd. to Routledge, 19 Feb. 1926, Routledge Archive, Univ. College, London.
72. J. Whitaker, Reference Catalogue of Current Literature, J. Whitaker & Sons, dates covered: 1874-2003.
73. Cumulative Book Index, H.W. Wilson, dates covered: 1912-1999.
74. W. Chadwick, Combined Number and Weight Calculator, Crosby Lockwood and Co., 1886.
75. Model Ready Reckoner, Warne, Frederick, and Co., 1888.
76. B.O.B. Williams, "Ready Reckoners and Tabular Calculators," Proc. 9th Int'l Meeting of Slide Rule Collectors, Dutch Slide Rule Collectors Circle, Amsterdam, 2003.

Index Terms:
Ready reckoners, pre-electronic computing, computing aids, multiplication aid
Bruce O.B. Williams, Roger G. Johnson, "Ready Reckoners," IEEE Annals of the History of Computing, vol. 27, no. 4, pp. 64-80, Oct.-Dec. 2005, doi:10.1109/MAHC.2005.64
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