Abstract
This chapter explores the extent to which elite astronomy and mathematics influenced the practice of navigation in Britain in the period some historians celebrate as the birth of scientific navigation.2 Although some writers, particularly those closest to the practice, consider navi-gation to be an art, most tell of the ‘science’ of navigation and most put the start of scientific navigation with the advent of the Nautical Almanac.3 Obviously these developments, from intuition to reliance on a mathematically based procedure, were not instantaneous or without problems.
[W]e may be said to receive from the Mathematics […] Increase of Fortune, and conveniences of Labour […] we have safe Traffick through the deceitful Billows, pass in a direct Road through the tractless Ways of the Sea
Isaac Barrow, 17341
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Notes
Isaac Barrow, The Usefulness of Mathematical Learning Explained and Demonstrated, (London: Stephen Austen, 1734), p. xxviii–xxix.
Eric G. Forbes, ‘The Bicentenary of the Nautical Almanac (1767)’, British Journal for the History of Science, 3 (1967), 393–94
Eric G. Forbes, The Birth of Scientific Navigation: The Solving in the Eighteenth Century of the Problem of Finding Longitude at Sea (London: National Maritime Museum, 1974).
On navigation as an art, see William Edward May, A History of Marine Navigation (Henley-on-Thames: Foulis, 1973), p. xiii.
J. E. D. Williams, From Sails to Satellites: The Origin and Development of Navigational Science (Oxford: Oxford University Press, 1992)
D. H. Sadler, Man is Not Lost (London: HMSO, 1968), p. 4.
Derek Howse ‘The Lunar-Distance Method of Measuring Longitude’ in The Quest for Longitude, ed. by William J. H. Andrewes (Cambridge Mass: Harvard Collection of Historical Scientific Instruments, 1996), pp. 149–65 (p. 159).
Eugene Wigner, ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences,’ Communications in Pure and Applied Mathematics, 13 (1960), 1–14.
Ivor Grattan Guiness, ‘Solving Wigner’s Mystery: The Reasonable (Though Perhaps Limited) Effectiveness of Mathematics in the Natural Sciences’, Mathematical Intelligencer, 30 (2008), 7–17
Quoted in Alan Shapiro, ‘Experiment and Mathematics in Newton’s Theory of Colour’ in Newton, ed. by I. Bernard Cohen and Robert Westfall (New York and London: W. W. Norton and Co, 1995), pp. 191–202 (p. 193).
Reproduced in Nicholas Kollerstrom, Newton’s Forgotten Lunar Theory (Santa Fe: Green Lion Press, 2000), p. 3.
For example Keith Devlin, Life by the Numbers (New York: Wiley, 1998)
Donald M. Davis, The Nature and Power of Mathematics (Princeton: Princeton University Press, 1993)
H. L. Resnikoff and R. O. Wells junior, Mathematics in Civilisation (New York: Dover Books, 1973), especially p. 5.
Nathan Altshiler Court, Mathematics in Fun and Earnest (Dial Press, 1958), pp. 96–107
For example, the King George III Collection of scientific instruments, which represents mid-eighteenth century courses of natural philosophy, contains items relating to isochronous pendulums and pyrometry, both resulting from the pursuit of longitude; see A. Q. Morton and J. A Wess, Public and Private Science: The King George III Collection (Oxford: Oxford University Press, 1993).
John Gascoigne, Science in the Service of Empire: Joseph Banks, the British State and the Uses of Science in the Age of Revolution (Cambridge: Cambridge University Press, 1998), p. 24.
Talk by Andrew Lambert, ‘Science and the Maritime Nation: 350 years of the Royal Society and the Royal Navy’, National Maritime Museum, Greenwich, 1 October 2010.
John Keay, The Honourable Company: A History of the East India Company (New York: Macmillan, 1991) p. 220.
Ramskrishna Mukherjee, The Rise and Fall of the East India Company: A Sociological Appraisal (New York and London: Monthly Review Press, 1974), p. 255
Andrew S. Cook, ‘Establishing the Sea-Routes to India and China’, in The Worlds of the East India Company, ed. by H. V. Bowen, Margarette Lincoln and Nigel Rigby (Woodbridge: Boydell, 2002), pp. 119–36.
Dava Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time (New York: Walker, 1995)
Derek Howse, Nevil Maskelyne: The Seaman’s Astronomer (Cambridge: Cambridge University Press, 1989).
J. A. Bennett, The Divided Circle: A History of Instruments for Astronomy, Navigation and Surveying (Oxford: Phaidon/Christie’s, 1987) p. 130.
Isaac Newton, A Treatise on the Method of Fluxions and Infinite Series, with its application to the geometry of curved lines (London: 1737), p. iii.
Quoted in Nick Kollerstrom and Bernard D. Yallop, ‘Flamsteed’s Lunar Data, 1692–1695, Sent to Newton’, Journal for the History of Astronomy, 26 (1995), 237–46 (p. 237).
Curtis Wilson, ‘Newton and Celestial Mechanics’, in The Cambridge Companion to Newton, ed. by I. Bernard Cohen and George E. Smith (Cambridge: Cambridge University Press, 2002), pp. 202–26 (p. 211).
Richard Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge: Cambridge University Press, 1980), p. 541.
Derek Howse, Greenwich Time and the Longitude (London: Philip Wilson, 1997), p. 57.
D. T. Whiteside ‘Newton’s Lunar Theory: From High Hope to Disenchantment’, Vistas in Astronomy, 19 (1975), 317–28
Rob Iliffe, Newton: A Very Short Introduction (Oxford: Oxford University Press, 2007), p. 111.
I. Bernard Cohen, Newton’s Theory of the Moon’s Motion (Folkstone: Dawson, 1975), p. 31.
Isaac. Newton, Philosophic naturalis principia mathematica Auctore Isaaco Newtono, 3rd edition (London: Guil and Joh Innys, 1726), p. 464.
James Bradley, ‘An Account of the New Discovered Motion of the Fixed Stars’, Philosophical Transactions, 35 (1727), 637–60. The model with which he demonstrated the principle in his lecture at the Ashmolean Museum as Savilian Professor of Astronomy in 1729 is now the property of the Clarendon Laboratory and resides in the Science Museum, London, 1876–1029.
Steven A. Wepster, Between Theory and Observations: Tobias Mayer’s Explorations of Lunar Motion, 1751–1755 (New York and London: Springer, 2009), p. 29.
Tobias Mayer, Mathematischer Atlas, in welchem auf 60 Tabellen alle Theile der Mathematic vorgestellet und […] durch deutliche Beschreibung u. Figuren entworfen werden (Augsburg: Johann Andreas Pfeffel, 1745)
Nevil Maskelyne (ed.), Tables Requisite to be Used with the Nautical Ephemeris for Finding the Latitude and Longitude at Sea (London: Commissioners of Longitude, 1781).
Mary Croarken, ‘Tabulating the Heavens: Computing the Nautical Almanac in 18th-Century England’, IEEE Aannals of the History of Computing, 25 (2003), 48–61.
E. G. R. Taylor, The Haven-Finding Art: A History of Navigation from Odysseus to Captain Cook (London: Hollis and Carter, 1956), p. 263.
Nevil Maskelyne, The British Mariner’s Guide (London: Printed for the author, 1763), p. iv.
E. G. R. Taylor and M. W. Richey, The Geometrical Seaman: A Book of Early Nautical Instruments (London: Hollis & Carter, 1962), p. 57.
Thomas Haselden, The Description and Use of that Most Excellent Invention The Mercator’s Chart (London: for the author, 1722), p. 4.
Benjamin Donn, The Description and Use of Donn’s Improved Navigation Scale (London, c.1780).
Jane Wess ‘Avoiding Arithmetic, or the Material Culture of not Learning Mathematics’, Journal of the British Society for the History of Mathematics, 27 (2012), 82–106.
Jean Randier, Marine Navigation Instruments (London: Murray, 1980), p. 124
William Puddicombe, The Mariner’s Instructor, being an Easy and Expeditious Method whereby a Master may Teach the Art of Navigation in a Short Time (London: R. Trewman, 1773), pp. 133–34.
Henry Wilson, Navigation New Modelled (London: 1777), p. vi.
Alexander Ewing, A Synopsis of Practical Mathematics (Edinburgh: William Smellie and Co, 1771), p. 131.
Benjamin Martin, The Mariner’s Mirror; or, A new Treatise on Navigation (London: Robert Sayer, 1782), Part II, Preface.
William Nicholson, The Navigator’s Assistant, containing the Theory and Practice of Navigation (London: 1784), pp. viii–ix.
Samuel Dunn, The Lunar Method Shorten’d in Calculation and Improv’d. (London: 1788).
W. E. May, ‘How the Chronometer Went to Sea’, Antiquarian Horology, 9 (1976), 638–63 (p. 644).
Andrew MacKay, The Description and Use of the Sliding Gunter in Navigation (Aberdeen: Printed for the Author, 1802)
Andrew MacKay, The Complete Navigator; or, An Easy and Familiar Guide to the Theory and Practice of Navigation, etc (London: 1804).
P. C. H. Clissold, ‘An Eighteenth Century Voyage’, Journal of the Institute of Navigation, 9 (1956), 191–97 (p. 192).
William Mountaine, A Description of the Lines Drawn on a Gunter scale (London: for Messrs Nairne and Blunt, 1778).
Willem F. J. Mörzer Bruyns, Sextants at Greenwich (Oxford: Oxford University Press, 2009)
Willem F. J. Mörzer Bruyns, ‘Navigational instruments in the collection of the Science Museum, London: A report’, Bulletin of the Scientific Instrument Society, 108 (2011), 34–43.
Harriet Wynter and Anthony Turner, Scientific Instruments (London: Studio Vista, 1975) p. 81
Gerard L’E. Turner, Nineteenth Century Scientific Instruments (London: Sotheby’s Publication, 1983), p. 265.
J. B. Hewson, History of the Practice of Navigation (Glasgow: Brown Son & Ferguson, 1951), p. 84.
Allan Chapman, Dividing the Circle: The Development of Critical Angular Measurement in Astronomy 1500–1850 (Chichester: John Wiley & Sons, 1995), p. 81.
Alan Stimson, ‘Influence of the Royal Observatory on Marine Measuring Instruments’, Vistas in Astronomy, 20 (1976), 123–30 (p. 130).
Anita McConnell, Jesse Ramsden (1735–1800): London’s Leading Scientific Instrument Maker (Aldershot: Ashgate, 2007) pp. 146–47.
N. W. Emmott: ‘Captain Vancouver and the Lunar Distance’, Journal of the History of Navigation, 27 (1974), 141–45.
George Vancouver, A Voyage of Discovery to the North Pacific Ocean and Round the World 1791–1795, ed. by W. Kaye Lamb (London: Hakluyt Society, 1984).
For example May, ‘How the Chronometer Went to Sea’, p. 641. Several memoirs are bound together in the BL under Alexander Dalrymple, Nautical Memoirs, 3 vols (London: W. Faden, 1787). Dalrymple was Hydrographer to the EIC and later to the Admiralty.
John McCluer, Description of the Coast of India, (London: George Bigg, 1789), p. 1.
Alexander Dalrymple, An Account of the Passage of the ship ‘Atlas’ Cat Allen Cooper, to the Eastwards of Banka, 1785 (London: George Bigg, 1789), p. iv.
Alexander Dalrymple, Memoirs of the Chart of the Straights of Sunda and Banka (London: George Bigg, 1787).
John McCluer, Continuation of the Description of the Coast of Malabar (London: George Bigg, 1791), p. 2.
Alexander Dalrymple, Account of the Passage of the Warren Hastings, Capt John Pascal Larkins, by the Mackesfield Straight of East Banka, 1788 (London: George Bigg, 1789).
J ames Horsburgh, Observations on the Navigation of the Eastern Seas, published by Alexander Dalrymple (London: W. Bennett, 1797).
Alexander Dalrymple, Memoir of a Chart from Cape Mons to Acheen (London: George Bigg, 1795), p. 18.
Alexander Dalrymple, General Collection of Nautical Publications (London: G. Bigg, 1783), p. 7.
Andrew S. Cook, ‘Alexander Dalrymple and John Arnold: Chronometers and the Representation of Longitude on East India Company Charts’, Vistas in Astronomy, 28 (1985), 189–95.
Harry Dickinson, Educating the Royal Navy: Eighteenth and Nineteenth Century Education and Training for Officers (Abingdon: Routledge, 2007), suggests a culture of resistance to experts and land-based training arising from the established system of on-board training and patronage. However, this would not explain the absence of lunar distance in textbooks.
Morris Kline, Mathematics and the Physical World (Mineola NY: Dover Publications Inc., 1959), p. vii.
Isaac Barrow, The Usefulness of Mathematical Learning Explained and Demonstrated, (London: Stephen Austen, 1734), pp. xxviii–ix.
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Wess, J. (2015). Navigation and Mathematics: A Match Made in the Heavens?. In: Dunn, R., Higgitt, R. (eds) Navigational Enterprises in Europe and its Empires, 1730–1850. Cambridge Imperial and Post-Colonial Studies Series. Palgrave Macmillan, London. https://doi.org/10.1057/9781137520647_11
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DOI: https://doi.org/10.1057/9781137520647_11
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