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Mathematicians on board: introducing lunar distances to life at sea

  • JIM BENNETT (a1)
Abstract

Nevil Maskelyne, the Cambridge-trained mathematician and later Astronomer Royal, was appointed by the Royal Society to observe the 1761 transit of Venus from the Atlantic island of St Helena, assisted by the mathematical practitioner Robert Waddington. Both had experience of measurement and computation within astronomy and they decided to put their outward and return voyages to a further use by trying out the method of finding longitude at sea by lunar distances. The manuscript and printed records they generated in this activity are complemented by the traditional logs and journals kept by the ships’ officers. Together these records show how the mathematicians came to engage with the navigational practices that were already part of shipboard routine and how their experience affected the development of the methods that Maskelyne and Waddington would separately promote on their return. The expedition to St Helena, in particular the part played by Maskelyne, has long been regarded as pivotal to the introduction of the lunar method to British seamen and to the establishment of the Nautical Almanac. This study enriches our understanding of the episode by pointing to the significant role played by the established navigational competence among officers of the East India Company.

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This article derives from a paper prepared for the Longitudes Examined conference at the National Maritime Museum, Greenwich, in 2014 and I am grateful to the organizers for this stimulus, to the Board of Longitude Project and its institutional supporters for the wonderful online resource for the Board of Longitude on the Cambridge Digital Library, and to two anonymous referees for their careful reading and helpful comments.

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1 On the plans for the expedition see Howse, Derek, Nevil Maskelyne: The Seaman's Astronomer, Cambridge: Cambridge University Press, 1989, pp. 1826; on Maskelyne's observing project on St Helena see Nicky Reeves, ‘Constructing an instrument: Nevil Maskelyne and the zenith sector, 1760–1774’, Cambridge University PhD thesis, 2009.

2 It is not clear whether, in nautical terminology, we should refer to Maskelyne and Waddington being ‘in’ or ‘on’ these ships; the former would be used for the crew, the latter for passengers. They were not crew, of course, but we shall see that they sometimes became involved with the life of the ship in ways not expected of a passenger.

3 The chronometer method is ‘so-called’ because historians of horology will not allow any timepiece extant at this time to qualify for the title of ‘chronometer’.

4 For Maskelyne see Howse, op. cit. (1); Derek Howse, ‘Maskelyne, Nevil (1732–1811), astronomer and mathematician’, in Oxford Dictionary of National Biography, at http://ezproxy-prd.bodleian.ox.ac.uk:2167/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-18266, accessed 16 August 2018; Higgitt, Rebekah, ed., Maskelyne: Astronomer Royal, London: Robert Hale, 2014. For Waddington see Jim Bennett, ‘“The Rev. Mr. Nevil Maskelyne, F.R.S. and myself”; the story of Robert Waddington’, in Higgitt, op. cit., pp. 59–88; Bennett, ‘Waddington, Robert (d. 1779)’, forthcoming in Oxford Dictionary of National Biography.

5 Selected from a large literature: (for its substantial bibliography) Andrewes, William J.H., ed., The Quest for Longitude, Cambridge, MA: Collection of Historical Scientific Instruments, Harvard University, 1996; (for its balanced approach) Dunn, Richard and Higgitt, Rebekah, eds., Finding Longitude, Glasgow: Collins and Royal Museums Greenwich, 2014.

6 Harrison, John, A Description Concerning Such Mechanism as Will Afford a Nice, or True Mensuration of Time, London, 1775, p. 58.

7 Harrison op. cit. (6), pp. 63, 61, 66.

8 Routes into discussion of these issues can be found in Smith, Pamela H., The Body of the Artisan: Art and Experience in the Scientific Revolution, Chicago and London: The University of Chicago Press, 2004; Roberts, Lissa, Schaffer, Simon and Dear, Peter, eds., The Mindful Hand: Inquiry and Invention from the Late Renaissance to Early Industrialisation, Amsterdam: Koninkliijke Nederlandse Akademie van Wetenschappen, 2007; Long, Pamela O., Artisan/Practitioners and the Rise of the New Sciences, 1400–1600, Corvallis: Oregon State University Press, 2011.

9 Bennett, Jim, ‘The travels and trials of Mr Harrison's timekeeper’, in Bourguet, Marie-Noëlle, Licoppe, Christian and Sibum, H. Otto, eds., Instruments, Travel and Science: Itineraries of Precision from the Seventeenth to the Twentieth Century, London: Routledge, 2002, pp. 7595.

10 Nevil Maskelyne, ‘Journal of voyage to St Helena’, Cambridge University Library MS RGO 4/150, at https://cudl.lib.cam.ac.uk/view/MS-RGO-00004-00150, accessed 14 August 2018.

11 Maskelyne, op. cit. (10), ff. 5v–9r.

12 Maslekyne, Nevil, ‘A letter … containing the results of observations of the distance of the moon from the sun and fixed stars, made in a voyage from England to the Island of St. Helena, in order to determine the longitude of the ship’, Philosophical Transactions (1761–1762) 52, pp. 558577, 573; Maskelyne, , The British Mariner's Guide: Containing, Complete and Easy Instructions for the Discovery of the Longitude at Sea and Land, London, 1763, pp. 106107.

13 Maskelyne to Thomas Birch, 8 November 1760, British Library MS Add 4313, f. 236.

14 Maskelyne, op. cit. (10), ff. 5v–6r; ‘X’ refers to a difference or divergence.

15 Mountaine, William and Dodson, James, ‘A letter … concerning the variation of the magnetic needle; with a sett of tables annexed’, Philosophical Transactions (1757–1758) 50, pp. 329349; Jonkers, A.R.T., Earth's Magnetism in the Age of Sail, Baltimore: Johns Hopkins University Press, 2003, pp. 189195.

16 The comment on the measurement of variation is based on the author's reading of a number of captain's journals in the British Library.

17 Captain Charles Haggis, journal of the Prince Henry, British Library IOR/L/MAR/B/325G. The journal also provides evidence of Haggis's care and competence as a navigator, both when Maskelyne is on board and afterwards. Haggis, for example, makes frequent and regular determinations of magnetic variation from measurements of solar azimuth or amplitude (or both), and later in the voyage he uses the new method of double altitudes for finding latitude from the sun, as a check on latitude determined by meridian altitude; this is discussed later in this article.

18 Maskelyne, op. cit. (10), ff. 6v–7r.

19 Mountaine, William and Dodson, James, ‘An attempt to point out, in a concise manner, the advantages which will accrue from a periodic review of the variation of the magnetic needle, throughout the known world’, Philosophical Transactions (1753–1754) 48, pp. 875880.

20 Mountaine and Dodson, op. cit. (15), p. 330.

21 Maskelyne, op. cit. (10), f. 6v. Maskelyne refers to his observations of 11 February in his paper in Philosophical Transactions: Maskelyne, ‘A letter’, op. cit. (12), p. 577.

22 Maskelyne, The British Mariner's Guide, op. cit. (12), p. 107.

23 Waddington to Thomas Birch, 13 May 1761, British Library MS Add. 4320, f. 83.

24 Maskelyne to Thomas Birch, 13 May 1761, British Library MS Add 4313, f. 242. The quadrant was of twenty inches radius and Bird was the leading maker of astronomical measuring instruments; Maskelyne affirmed, ‘I was secured from any errors in the construction of the quadrant, by the known skill of the artist’. Maskelyne, ‘A letter’, op. cit. (12), p. 559.

25 Howse, op. cit. (1), p. 29.

26 Maskelyne, op. cit. (10), ff. 6v–7.

27 Maskelyne, op. cit. (10), ff. 1r, 1v, 2v. See also Maskelyne, op. cit. (24), f. 242v.

28 Maskelyne, op. cit. (10), ff. 3v–5r.

29 The ‘limb’ is the edge of the apparent disc of the moon.

30 Maskelyne, ‘A letter’, op. cit. (12).

31 Halley, Edmond, Astronomical Tables: with Precepts Both in English and Latin for Computing the Places of the Sun, Moon, Planets, and Comets, London, 1752, sig (d) ff. Note also Halley, , ‘A proposal of a method for finding the longitude at sea within a degree’, Philosophical Transactions (1731–1732) 37, pp. 185195.

32 For secondary accounts of the lunar method see Cotter, Charles H., A History of Nautical Astronomy, London: Hollis & Carter, 1968; May, W.E., A History of Marine Navigation, Henley on Thames: Foulis, 1973; Howse, Derek, Greenwich Time: And the Discovery of the Longitude, Oxford: Oxford University Press, 1980; Hewson, J.B., A History of the Practice of Navigation, Glasgow: Brown, Son & Ferguson, 1983; Howse, ‘The lunar-distance method of measuring longitude’, in Andrewes, op. cit. (5), pp. 150–162. Note also Schaffer, Simon, ‘Swedenborg's lunars’, Annals of Science (2014) 71, pp. 226. Still useful is Mackay, Andrew, The Theory and Practice of Finding the Longitude at Sea or Land, London, 1793. For Lacaille see Glass, Ian Stewart, Nicolas-Louis De La Caille, Astronomer and Geodesist, Oxford: Oxford University Press, 2012, esp. pp. 37, 114, 128–129, 140.

33 Waddington to Pigott, 26 May 1761, Royal Astronomical Society, RAS MSS Pigott, 84.

34 Maskelyne, op. cit. (24), f. 242v.

35 Maskelyne, ‘A letter’, op. cit. (12), p. 564.

36 Maskelyne, op. cit. (10), f. 3v.

37 Senex, John, Zodiacus Stellatus fixas omnes hactenus cognitas, ad quas Lunae Appulsus ullibi; Terrarum Telescopio Observari poterunt, complexus, London, 1718; Warner, Deborah J., The Sky Explored: Celestial Cartography, 1500–1800, New York: A.R. Liss, 1979, pp. 239242.

38 Maskelyne, op. cit. (10), f. 4v.

39 Maskelyne, op. cit. (10), f. 10v.

40 Haggis, op. cit. (17), 10 February 1761.

41 Haggis, op. cit. (17), 11, 19, 28 February, 9, 10, 13, 18, 25, 26, 29 March 1761.

42 For some of the literature on this see Cook, Andrew S., ‘Establishing the sea routes to India and China: stages in the development of hydrographical knowledge’, in Bowen, H.V., Lincoln, Margarette and Rigby, Nigel, eds., The Worlds of the East India Company, Woodbridge: Boydell Press, 2002, pp. 119136; Miller, David Philip, ‘Longitude networks on land and sea: the East India Company and longitude measurement “in the wild”, 1770–1840’, in Dunn, Richard and Higgitt, Rebekah, eds., Navigational Enterprises in Europe and Its Empires, 1730–1850, Basingstoke: Palgrave Macmillan, 2015, pp. 223247. For a recent analysis of the relationship of practice with theory, though mainly treating a slightly later period, see Jane Wess, ‘Navigation and mathematics: a match made in heaven?’, in Dunn and Higgitt, op. cit., pp. 201–222.

43 Harrison, Richard, A New Sett of Logarithmic Solar Tables, Calculated and Constructed for Determining the Latitude at Sea, by Taking Two Altitudes either in the Forenoon or Afternoon, with the Intermediate Time by a Common Watch, London, 1759.

44 Maskelyne, op. cit. (24), f. 242; Haggis, op. cit. (17), 25, 26, 27, 28, 29 May; 1, 2, 3 June, and passim. We can be sure that Haggis was using Harrison's treatise, since he begins the record of his first observation, 25 May, with: ‘By the New Logarithmic Solar Tables, Calculated and constructed for determining the Latitude at Sea, by taking two Altitudes …’, cf. the title at note 43.

45 Maskelyne, The British Mariner's Guide, op. cit. (12), pp. 70–79. Note also the contemporary interest of Pemberton, Henry, ‘Some considerations on a late treatise intituled, A New Set of Logarithmic Solar Tables, &c. intended for a more commodious method of finding the latitude at sea, by two observations of the sun’, Philosophical Transactions (1759–1760) 51, pp. 910929. Harrison, op. cit. (43), p. 31v, note also sig. A2. Dodson, who had died in 1757, is not mentioned.

46 Harrison, op. cit. (43), sigs. A2–A2v.

47 Maskelyne, ‘A letter’, op. cit. (12), p. 560.

48 Maskelyne, The British Mariner's Guide, op. cit. (12), pp. 53–56.

49 Maskelyne, op. cit. (24), f. 242v. Eleven was a mistake, which he corrected in later accounts to seven or to eight.

50 Maskelyne, The British Mariner's Guide, op. cit. (12), p. 107; cf. Maskelyne, ‘A letter’, op. cit. (12), p. 574. Waddington concurs, reporting as early as 13 May that the accounts kept by the mates were out by between ten and eleven degrees. Waddington, op. cit. (23), f. 83.

51 Waddington, op. cit. (23), f. 83.

52 Maskelyne's determination of the longitude of St Helena by Jupiter's satellites was 5° 44′ west of London (i.e. not Greenwich, which was five minutes to the east of the London meridian, generally taken as St Paul's Cathedral). Maskelyne, The British Mariner's Guide, op. cit. (12), p. 107. The final longitude by account in Maskelyne's Journal is 1° 28′ east (the prime meridian is not specified but was probably London); the captain's journal 1° 37′ east (surely of London); we do not have Waddington's journal but his letter to Birch of 13 May records his longitudes to, at best, half a degree, the final one being one degree east (though he does specify London). Waddington, op. cit. (23), f. 83.

53 Waddington to Pigott, 26 May 1761, Royal Astronomical Society, RAS MSS Pigott, 84.

54 Maskelyne, op. cit. (10), ff. 39v–40r.

55 Waddington, Robert, A Practical Method for Finding the Longitude and Latitude of a Ship at Sea by Observations of the Moon, London, 1763, pp. 2526; Maskelyne, op. cit. (10), ff. 7v–8r. See also Maskelyne, ‘A letter’, op. cit. (12), p. 577.

56 Maskelyne, op. cit. (10), f. 8r; Haggis, op. cit. (17), 18 March 1761.

57 Waddington, op. cit. (55), p. 11, note also pp. 12–23. See also Waddington to Pigott, 7 January 1762, Royal Astronomical Society, RAS MSS Pigott, 85.

58 Captain William Webber, journal of the Oxford, British Library IOR/L/MAR/B/588D.

59 Bennett, op. cit. (4), pp. 67–80.

60 On this aspect of Martin's confusing output of publications see Millburn, John R., Benjamin Martin: Author, Instrument-Maker, and ‘Country Showman’, Leiden: Noordhoff, 1976, pp. 6971; Waddington, Robert, ‘To find the longitude of a ship at sea, by observations of the distance of the sun and moon, or of the moon and a known fixed star of a small latitude’, in Martin, Benjamin, Miscellaneous Correspondence in Prose and Verse (June–August 1762) 4, pp. 879881, 895–897, 911–912.

61 Waddington, op. cit. (55), pp. 12–23.

62 Waddington, op. cit. (60), p. 897.

63 Webber, op. cit. (58), 2 September 1761.

64 This example is repeated in A Practical Method, Waddington, op. cit. (55), pp. 27–28.

65 Waddington, op. cit. (55), pp. 23–25.

66 Waddington, op. cit. (55), p. 13.

67 Maskelyne, The British Mariner's Guide, op. cit. (12), pp. 108–110.

68 Captain James Dewar, journal of the Warwick, British Library IOP/L/MAR/B/585H, ff. 149 (21 April 1762), 150v (26 April and 27 April), 151 (28 April), 152 (2 May).

69 Maskelyne, The British Mariner's Guide, op. cit. (12), pp. 14–52, 14.

70 Cambridge University Library, Board of Longitude Confirmed Minutes RGO 14/5, pp. 78–81.

71 Captain Charles Mears, journal of the Ermont, British Library IOR/ L/MAR/B/535D, see longitude determinations in 1763: 5 March, 3, 16 June; in 1764: 19, 22 April, 20, 22 May, 19, 20, 21, 22, 23 June, 6, 7 July. Mears also tries finding the latitude by two altitudes of the sun ‘According to the Revd Mr Maskelyn's [sic] method’ on 9, 10, 11, 12, 13 July 1764. Captain James Dewar, journal of the Speaker, British Library IOR/ L/MAR/B/548 A, see longitude determinations in 1764: 22 May, 6, 8, 21, 22 June, 5, 12, 16, 17, 23 July, 2, 4, 5, 31 August, 5, 7, 21 September, 1, 3, 29 October, 1 November.

72 Cambridge University Library, Board of Longitude Confirmed Minutes RGO 14/5, p. 80.

73 For a discussion of the challenges of making such judgements see Bennett, op. cit. (9).

74 Maskelyne, The British Mariner's Guide, op. cit. (12), p. 117.

75 For a slightly earlier case of significant and innovative navigational skill on the part of a lifelong seaman and Hudson's Bay captain, Christopher Middleton, see Jim Bennett, ‘Adventures with instruments: science and seafaring in the precarious career of Christopher Middleton’, forthcoming in Notes and Records: The Royal Society Journal of the History of Science.

76 Maskelyne, The British Mariner's Guide, op. cit. (12), p. 104.

This article derives from a paper prepared for the Longitudes Examined conference at the National Maritime Museum, Greenwich, in 2014 and I am grateful to the organizers for this stimulus, to the Board of Longitude Project and its institutional supporters for the wonderful online resource for the Board of Longitude on the Cambridge Digital Library, and to two anonymous referees for their careful reading and helpful comments.

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