1 See Andrewes, William (ed.), The Quest for Longitude, Cambridge, MA: Harvard UniversityGoogle Scholar, Collection of Historical Scientific Instruments, 1996, for papers on these themes; and Sobel, Dava, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, New York: Walker, 1995Google Scholar, for a popular account. Boistel, Guy, ‘Training seafarers in astronomy: methods, naval schools and naval observatories in eighteenth- and nineteenth-century France’, in Aubin, David, Bigg, Charlotte and Sibum, Hans-Otto (eds.), The Heavens on Earth, Durham, NC: Duke University Press, 2010, pp. 148–173Google Scholar, offers a revisionist view, emphasizing continuity of technique over rupture.

2 Guyot, Edmond, Histoire de la détermination des longitudes, La Chaux de Fonds: La Chambre Suisse de l'horlogerie, 1955Google Scholar, is the only comprehensive (albeit technical) history of longitude measurement.

3 Stachurski, Richard, Longitude by Wire: Finding North America, Columbia: University of South Carolina Press, 2009Google Scholar; Galison, Peter, Einstein's Clocks, Poincaré's Maps, London: Hodder and Stoughton, 2003Google Scholar, Chapter 10.

4 Hoskin, Michael (ed.), The Cambridge Concise History of Astronomy, Cambridge: Cambridge University Press, 1999, p. 154Google Scholar.

5 Preston, E., ‘Appendix 6: Proceedings of the International Geodetic Association Conference and Geodetic Operations in the United States’, Report of the Superintendent of the Coast Survey 1898 (1899), pp. 247–253Google Scholar, 250.

6 The only existing work on the history of the joining of the observatories of Greenwich and Paris is Debarbat, Suzanne, ‘Courte histoire des raccordements des observatoires de Paris et Greenwich’, XYZ (1999) 79, pp. 77–82Google Scholar.

7 The concept and effectiveness of mutual grounding of methods of measurement is explored in Chang, Hasok, ‘Circularity and reliability in measurement’, Perspectives on Science (1995) 3, pp. 153–172CrossRefGoogle Scholar; and Chang, , Inventing Temperature: Measurement and Scientific Progress, New York: Oxford University Press, 2004Google Scholar. The term ‘web of measurement’ is from the former.

8 This is what Hasok Chang has called an ‘epistemic iteration’: an unpredictable, peripatetic, yet self-correcting form of improvement. See Chang, Hasok, ‘Scientific progress: beyond foundationalism and coherentism’, Royal Institute of Philosophy Supplements (2007) 61, pp. 1–20Google Scholar, for a discussion.

9 See Mackenzie, Donald, Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance, Cambridge, MA: The MIT Press, 1993Google Scholar, for this argument, which he makes in respect of nuclear weapon guidance systems in the context of the many historical case studies of individual new weapons.

10 See Aubin, ‘Introduction’, in Aubin, Bigg and Sibum, op. cit. (1), pp. 1–32, for a wider discussion.

11 See Martin, Jean-Pierre and McConnell, Anita, ‘Joining the observatories of Greenwich and Paris’, Notes and Records of the Royal Society (2008) 62, pp. 355–372Google Scholar. In this paper I refer to measurements of longitude in units of minutes and seconds of time, as opposed to the alternative units of degrees, minutes and seconds of arc. The two are simply converted, as the earth rotates 360 degrees in 24 hours, or one degree every four minutes.

12 Herschel, John, ‘Account of a series of observations, made in the summer of the year 1825, for the purpose of determining the difference of meridians of the Royal Observatories of Greenwich and Paris’, Philosophical Transactions of the Royal Society of London (1826) 116, pp. 77–126Google Scholar, is the primary account of the determination by rocket; Henderson, Thomas, ‘On the difference of meridians of the Royal Observatories of Greenwich and Paris’, Philosophical Transactions of the Royal Society of London (1827) 117, pp. 286–296Google Scholar, corrects a minor error in Herschel's results, giving 9 minutes and 21.5 seconds, and this was the value published by the Nautical Almanac.

13 ‘Chronometer accuracy – verification of the longitude of Paris’, Nautical Magazine (1838) 7, pp. 402–408. The chronometric value was 9 minutes and 21.28 seconds, about two-tenths of a second adrift from that obtained by rocketry.

14 See Bouvard, A., ‘Note sur la détermination de la différence entre les méridiens de Paris et Greenwich’, Connaisance des temps pour l'an 1825 (1822), pp. 344–363Google Scholar, giving a value from lunar culminations of 9 minutes and 20.5 seconds; and Kater, Henry, ‘An account of trigonometrical operations in the years 1821, 1822 and 1823, for determining the difference of longitude between the Royal Observatories of Paris and Greenwich’, Philosophical Transactions of the Royal Society of London (1828) 118, pp. 153–239Google Scholar, giving a value by triangulation of 9 minutes and 20.18 seconds.

15 Herschel, op. cit. (12), p. 107.

16 See Stachurski, op. cit. (3), especially Chapters 7 and 8.

17 See Howse, Derek, Greenwich Time and the Longitude, London: Philip Wilson Publishers, 1997Google Scholar, Chapter 4, on ‘Greenwich Time for Great Britain’.

18 George Biddell Airy to Sir F.J. Baring, First Lord of the Admiralty, 26 November 1851; secretary of the South Eastern Railway to Airy, 17 September 1851; Final Memorandum dated 20 December 1851; Jacob Brett to Airy, 20 September 1851; Office of Public Works to Airy, 3 January 1852, all Royal Greenwich Observatory Papers, University Library Cambridge (subsequently RGO), Box 6/610.

19 Airy, George Bidell, Difference of Longitude between the Observatories of Brussels and Greenwich, London: George Barclay, 1854, pp. 1–3Google Scholar, sets out the early history of the establishment of the connections.

20 Airy, George Biddell and Le Verrier, Urbain, ‘Nouvelle détermination de la différence de longitude entre les observatoires de Paris et de Greenwich’, Comptes rendus de l'Académie des sciences (1854) 39, pp. 553–566Google Scholar, 558.

21 Airy and Le Verrier, op. cit. (20), describes the measurement, and says that fuller details would be published in a special mémoire, but I do not believe they ever were. Airy, op. cit. (19), is a fuller account of the techniques.

22 See Schaffer, Simon, ‘Astronomers mark time: discipline and the personal equation’, Science in Context (1988) 2, pp. 115–145CrossRefGoogle Scholar; and Canales, Jimena, A Tenth of a Second: A History, Chicago: The University of Chicago Press, 2009Google Scholar, for an introduction to the literature on the personal equation.

23 This relies on the fact that a delay in transmission will increase an observed longitude difference when sent in one direction, and decrease it in the other.

24 See Howse, op. cit. (17), Appendix II, for a brief explanation of the techniques of time-finding by astronomy, and of the types of error to which transit instruments are subject. Azimuth error refers to deviation from the north–south plane, collimation to deviation between the physical axis and optical axis of the instrument, and level refers to the horizontality of the instrument's pivots.

25 Telegram, Le Verrier to Airy, 27 May 1854, RGO 6/635.

26 Telegram, Airy to Le Verrier, 3 June 1854, RGO 6/635.

27 Report of the Astronomer Royal to the Board of Visitors, Read at the Annual Visitation … (subsequently Report to the Board of Visitors) 1855, p. 11.

28 Bouvard's work had by then been refined by the French astronomer Goujon. See Goujon, Emile, ‘Différence de longitude entre les observatoires de Paris et Greenwich’, Comptes rendus de l'Académie des sciences (1847) 24, p. 430Google Scholar.

29 See Airy and Le Verrier, op. cit. (20), pp. 562–566. The astronomical technique, based on measurement of the right ascension (the astronomical equivalent of longitude) of the Moon, is described in Bouvard, op. cit. (14).

30 Airy and Le Verrier, op. cit. (20), p. 564.

31 Sheepshanks, Richard and Quetelet, Adolphe, ‘Sur la différence des longitudes des Observatoires Royaux de Greenwich et de Bruxelles’, Mémoires de l'Académie royale de Bruxelles (1841) 16, pp. 3–18Google Scholar, has details of the earliest examples of corrections for the personal equation at Greenwich.

32 Airy and Le Verrier, op. cit. (20), p. 562.

33 See the Nautical Almanac for the Year 1858 (1854), p. 537; and Connaissance des temps pour l'an 1857 (1854), Additions, p. 4.

34 Clarke, A.R., Comparison of the Standards of Length of England, France, Belgium, Prussia, Russia, India and Australia, London: HMSO, 1866, p. viGoogle Scholar.

35 James, Henry, Extension of the Triangulation of the Ordnance Survey into France and Belgium …, London: Ordnance Survey, 1863, p. 57Google Scholar.

36 See ‘Jonction géodésique des triangulations de la France avec l'Angleterre et détermination de la différence en longitude entre les observatoires de Paris et de Greenwich’, Mémorial du Dépôt général de la guerre IX, Supplément (1865). The computed value for the difference in longitude was 9 minutes and 21.07 seconds, compared to the previous geodetic value of 9 minutes and 21.18 seconds.

37 See Torge, Wolfgang, ‘The International Association of Geodesy 1862 to 1922: from a regional project to an international organisation’, Journal of Geodesy (2005) 78, pp. 558–568Google Scholar, for a brief history.

38 See Bruhns, C. and Hirsch, A. (eds.), Bericht über die Verhandlungen der vom 21. bis 30. September zu Wien abgehaltenen Dritten allgemeinen Conferenz der Europäischen Gradmessung, Berlin: Georg Reimer, 1872, pp. 75–91Google Scholar, for details of the project and its then state of completion.

39 See Albrecht, Theodor, ‘Ausgleichung des zentraleuropäischen Längennetzes’, Astronomische Nachrichten (1905) 167, pp. 145–161CrossRefGoogle Scholar, for a chronological list. My example is for the year 1875.

40 Hilgard, J.E., ‘Appendix 13: preliminary report on the determination of transatlantic longitudes’, Report of the Superintendent of the Coast Survey 1872 (1875), pp. 227–234Google Scholar, 231.

41 Stachurski, op. cit. (3), p. 104.

42 See Airy, George Biddell, ‘On the method of observing and recording transits lately introduced in America, and on some other connected subjects’, Monthly Notices of the Royal Astronomical Society (1849) 10, pp. 26–34Google Scholar; and Starchsuki, op. cit. (3), Chapter 7. Maunder, E. Walter, The Royal Observatory Greenwich, London: The Religious Tract Society, 1900, pp. 156–159Google Scholar, gives a practitioner's account of the use of a transit and chronograph.

43 A value of 9 minutes and 20.97 seconds is given in J.E. Hilgard, ‘Appendix 18: transatlantic longitudes’, Report of the Superintendent of the Coast Survey 1874 (1877), pp. 163–242, and differs slightly from the preliminary determination reported in Hilgard, op. cit. (40).

44 Hilgard, op. cit. (40), p. 231.

45 See Albrecht, Theodor, ‘Ueber der Genauigkeitsgrad der telegraphischer Längenbestimmungen’, Astronomische Nachrichten (1877) 89, pp. 305–316Google Scholar.

46 Faye, A., ‘Rapport verbale sur le Protocole de la Conférence géodésique tenue à Berlin en avril 1862’, Comptes rendus de l'Académie des sciences (1863), 56, pp. 28–34Google Scholar, 33.

47 Annales du Bureau des longitudes, Paris: Gauthier-Villars, 1882, p. A3. M. Schiavon, ‘Geodesy and mapmaking in France and Algeria: between army officers and observatory scientists’, in Aubin, Bigg and Sibum, op. cit. (1), pp. 199–224, describes ‘The lessons from the war with Prussia’ for French geodesy. Boistel, G., L'observatoire de la marine et du Bureau des longitudes au parc Montsouris, 1875–1914, Paris: IMCCE, 2010Google Scholar, gives a history of the Montsouris observatory.

48 The accounts of the exercise are Annales du Bureau des longitudes, vol. 2, Paris: Gauthier-Villars, 1882Google Scholar; and Bestimmung der Längendifferenzen zwischen Berlin und Paris, Berlin und Bonn, Bonn und Paris, Berlin: Stankiewicz, 1878. These show a discrepancy in the Paris–Berlin determination of about two-tenths of a second. A correction to the adjustment from the Montsouris to the Cassini meridians in Paris, explained in Albrecht, Theodor, ‘Ausgleichung des deutschen Längenbestimmungsnetzes’, Astronomische Nachrichten (1879) 95(9), pp. 129–142Google Scholar, roughly halved the problem. This paper also compares many telegraphic longitude determinations with their values derived from the compensation of longitudes. See also Figuier, L., L'année scientifique et industrielle, année 1879, Paris: Hachette, 1879. pp. 12–14Google Scholar, for a contemporary view.

49 Report to the Board of Visitors 1877, p. 20.

50 Maunder, op. cit. (42), p. 175.

51 The various indirect determinations are set out in Turner, H., ‘Note on the recent determination of the longitude of Paris’, Monthly Notices of the Royal Astronomical Society (1891) 51, pp. 155–163Google Scholar.

52 The Nautical Almanac for 1883 adopted 9 minutes and 20.9 seconds, which was changed in 1886 to 9 minutes and 21.0 seconds.

53 Christie, William, Telegraphic Determinations of Longitude Made in the Years 1888 to 1902, Edinburgh: HMSO, 1906, p. 1Google Scholar.

54 See Perrier, Georges, ‘Notice sur la vie et les travaux de Léon Bassot’, Notices et discours de l'Académie des sciences, vol. 1, Paris: Gauthier-Villars 1937, pp. 593–619Google Scholar; ‘Obituary Notices: Gilbert Defforges’, Monthly Notices of the Royal Astronomical Society (1916) 76, pp. 289–292 (‘La longitude, c'est un métier’ on p. 290); Aitken, R.G., ‘Herbert Hall Turner, 1861–1930’, Publications of the Astronomical Society of the Pacific (1930) 42, pp. 277–280Google Scholar; and Wright, David, ‘Thomas Lewis: a lifetime of double stars’, Journal of the British Astronomical Association (1992) 102, pp. 95–101Google Scholar.

55 Although on the face of it less precise than the large observatory-mounted meridian circle telescopes used in the first Paris–Greenwich measurement, the portable transit instruments were the only practical way of making simultaneous measurements with two teams. They also had the advantage that by regular reversal during the observation process errors of collimation could be better managed.

56 Christie, op. cit. (53), pp. 1–111, is a comprehensive account of the measurement.

57 Turner, op. cit. (51), p. 161. At this stage the British determination was 9 minutes and 20.85 seconds, and the French 9 minutes and 21.04 seconds, a difference of about two-tenths of a second.

58 Ledger, RGO 7/269, underlining in original.

59 The chronology is summarized in the Reports to the Board of Visitors 1890 and 1891.

60 See Turner, op. cit. (51); followed by Bassot, Léon and Defforges, Gilbert, ‘Sur la détermination récente de la longitude Paris–Greenwich’, Monthly Notices of the Royal Astronomical Society (1891) 51, pp. 407–413Google Scholar; and Turner, H.H., ‘On the recent determination of the longitude Greenwich–Paris, reply to Colonel Bassot and Commandant Defforges’, Monthly Notices of the Royal Astronomical Society (1891) 51, pp. 413–419Google Scholar.

61 Bassot and Defforges, op. cit. (60), p. 413.

62 Report to the Board of Visitors 1891, p. 18.

63 The procedure for measuring and correcting for pen parallax, the phenomenon whereby two pens do not necessarily react absolutely simultaneously to a signal, is described in Christie, op. cit. (53), p. 22.

64 Report to the Board of Visitors 1893, p. 23.

65 Report to the Board of Visitors 1895, p. 22.

66 Report to the Board of Visitors 1900, p. 21.

67 ‘Appendix 9: Proceedings of the Geodetic Conference held at Washington D.C., January 9 to February 24 1894’, Report of the Superintendent of the Coast Survey 1893 (1895), pp. 223–424, 294.

68 As mentioned above, the Paris–Berlin determination was corrected by one-tenth of a second after publication. As another example, we see various values for the Paris–Greenwich discrepancy of 1888, of which the lowest was as little as 0.15 seconds in Report to the Board of Visitors 1891, p. 18.

69 Ratcliff, Jessica, The Transit of Venus Enterprise in Victorian Britain, London: Pickering & Chatto, 2008, p. 148Google Scholar.

70 Preston, op. cit. (5).

71 See Hirsch, A. (ed.), Bericht über die Verhandlungen der vom 3. bis 12. Oktober zu Stuttgart abgehaltenen Zwölften allgemeinen Conferenz der Internationalen Gradmessung, Berlin: Georg Reimer, 1899, pp. 127–129Google Scholar and Appendix A.IV. Albrecht was head of the Königlich-Preußische Geodätische Institut at Potsdam, one of the leading centres of European geodesy.

72 Darwin to Christie, 19 October 1898, RGO 7/262.

73 Loewy to Christie, 23 November 1898, RGO 7/262.

74 Loewy, Maurice, ‘Détermination faites en 1902 de la différence de longitude entre les méridiens de Greenwich et de Paris’, Comptes rendus de l'Académie des sciences (1904) 139, pp. 1010–1015Google Scholar, makes the points about finance and about the Service géographique de l'Armée. See also Loewy, , Rapport annuel sur l’état de l'Observatoire de Paris pour l'année 1901, Paris: Imprimerie nationale, 1902, p. 3Google Scholar, on the finance, which resulted from the intervention of the Bureau des longitudes. The institutional apparatus of French geodesy throughout the later nineteenth century, involving the Observatory, Bureau des longitudes, Army and Navy, was one of some complexity and disharmony. See Boistel, op. cit. (47), for a bibliography of the extensive literature.

75 The French preference had been for an earlier measurement; see Henri Poincaré to Christie, 23 June 1898, RGO 7/262; and Christie to Poincaré, 3 August 1899, Archives du Bureau des longitudes, C6.

76 Loewy to Christie, 7 December 1898, RGO 7/262.

77 ‘Obituary: Henry Park Hollis’, Monthly Notices of the Royal Astronomical Society (1940) 100, pp. 249–250. He was the only participant in the 1892 determination who had not also worked on that of 1888.

78 Loewy, op. cit. (74), p. 1012. Bigourdan twice won the Lalande prize, awarded by the Académie des sciences, for advances in astronomy. Renan fell ill and had to be replaced before completion of the determination, but later became known as an expert practitioner in the determination of longitude by wireless.

79 The complete accounts of the exercise are Christie, op. cit. (53); and Bigourdan, Guillaume, ‘Détermination de la différence de longitude entre les méridiens de Greenwich et de Paris’, Annales de l'Observatoire de Paris (1910) 26, pp. B1–B214Google Scholar.

80 Collimation error was determined by observations of a terrestrial mark, by nadir observations and by observations of the same star with instrumental reversals, to deduce a single correction for each transit instrument.

81 Simon Newcomb, director of the United States Nautical Almanac, had published his catalogue of fundamental stars in 1899, with new values for astronomical constants that remained accepted for decades.

82 ‘Convention concernant le plan d’éxecution de la nouvelle détermination …’, (undated), RGO 7/262. The execution of the project can be followed in the Rapports annuel sur l’état de l'Observatoire de Paris pour l'année 1901 to 1904, Paris: Imprimerie nationale.

83 Daily Express, 20 March 1902.

84 La Presse, 15 December 1902.

85 See Bartky, Ivan, One Time Fits All, Stanford: Stanford University Press, 2007Google Scholar, Chapter 8, on the adoption of time zones; and Bigourdan, Guillaume, ‘Chapitre II : les fuseaux horaires’, Annuaire pour l'an 1914 publié par le Bureau des longitudes, pp. B51–B68Google Scholar.

86 See Christie to Loewy, 25 March 1902; Christie to Dyson, 25 March 1902; and Loewy to Christie, 28 March 1902, RGO 7/262.

87 Loewy to Christie, 4 June 1903, RGO 7/262.

88 See Loewy, op. cit. (74), p. 1013.

89 Christie to Loewy, 8 December 1904, RGO 7/262.

90 See Christie, op. cit. (53); and Loewy, op. cit. (74), for the full results. In summary they were as follows. British: 9 minutes and 20.977 seconds in spring and 9 minutes and 20.910 seconds in autumn (unweighted mean 9 minutes and 20.943 seconds, weighted mean 9 minutes and 20.932 seconds); French: mean 9 minutes and 20.974 seconds.

91 Loewy to Christie, 8 November 1904, RGO 7/262.

92 See Bigourdan, op. cit. (79), for the final French values, of which the mean was 9 minutes and 20.994 seconds. The statistically derived probable error was about one-hundredth of a second.

93 Guyot, op. cit. (2), p. 253.

94 See Albrecht, op. cit. (39). Albrecht lists a number of other compensations carried out in years past, as more data became available. The seven Paris–Greenwich values were the French and English results from 1888, 1892 and 1902, together with the US Coast Survey value from 1872.

95 Albrecht to Christie, 23 November 1904, RGO 7/262.

96 Schiavon, op. cit. (47), pp. 199–200.

97 Kuhn, Thomas, ‘The function of measurement in modern physical science’, Isis (1961) 52, pp. 161–193Google Scholar, 168.

98 See, for example, Hunt, Bruce, ‘Michael Faraday, cable telegraphy and the rise of field theory’, History of Technology (1991) 13, pp. 1–19Google Scholar; and Hunt, , ‘The ohm is where the art is: British telegraph engineers and the development of electrical standards’, Osiris (1994) 9, pp. 48–63Google Scholar.

99 See Ditisheim, Paul, ‘Différence de longitude Greenwich–Paris’, Monthly Notices of the Royal Astronomical Society (1920) 80, pp. 809–812Google Scholar. The result was within a few thousandths of a second of the telegraphic value of 1902.

100 This is the result quoted in Stachurski, op. cit. (3), p. 204. The complete data, not quite so flattering, is in Smith, E., ‘Appendix 4: telegraphic longitudes: the Pacific arcs from San Francisco to Manila 1903–1904 completing the circuit of the Earth’, Report of the Superintendent of the Coast Survey 1904 (1904), pp. 257–311Google Scholar.

101 See Bartky, op. cit. (85), Chapter 9, on ‘The French take the lead’.

102 The reliance by the Admiralty on foreign radio time signals has been historically misunderstood. The speculation has been that the British were happy to use foreign time transmissions in time of peace, and expected all wireless time transmission to cease in time of war. The origins of this incorrect notion are to be found in Howse, op. cit. (17), p. 155. The reality is that in the few months after the start of the First World War, the Admiralty made plans for continuation of wireless time signals in the event of the Eiffel Tower being, as they put it, ‘tampered with’. The transmissions were to be made by the Marconi Company from Poldhu in Cornwall, the site of their first transatlantic transmissions. Time was to be provided telegraphically by the Greenwich Observatory. See Admiralty to Astronomer Royal, 30 September 1914, RGO 8/146.

103 There were three World Longitude Campaigns using wireless, in 1926, 1933 and 1957. They have so far received little attention from historians.

104 Letter from Greenwich Observatory (author unclear) to Baillaud, 1 August 1912, RGO 8/146.