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ABSTRACT
In the 1760s, the international debate on the solution to determining longitude at sea is at its acme. Two solutions emerge, the mechanical and the astronomical ones. The Portuguese mathematician and astronomer José Monteiro da Rocha (1734–1819) is well aware of that debate. For him, Harrison’s No. 4 marine timekeeper cannot be seen as a solution. The desirable solution could only be astronomical. In a manuscript from c. 1765, which unfortunately he fails to publish, Monteiro da Rocha is very critical of Lacaille's lunar-distance method (1759) and proposes another one. In this paper, we intend to analyse Monteiro da Rocha’s criticisms and proposals, trying to understand how this manuscript fits into the international longitude debate and the Portuguese scientific scenario at the time. Concurrently, we will re-examine the classical historiography around the English vs. French priority proposal of the lunar-distance method, purging it from its mythologies to shift it towards a more open, less linear history.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 ‘Methodo de achar a longitude geografica no mar y na terra pelas observaçoens y calculos da Lua para uso da navegação Portuguesa’, Lisboa, Biblioteca Nacional de Portugal, Colecção Pombalina, MS 511. This manuscript it was revealed in 2005 at the national library of Portugal, until this time it was entirely unknown and had never been mentioned in the historiography.
2 MS BNP 511, fl.17v.
3 As stated by the French mathematician Pierre Bouguer and expert for the ‘Ministre de la Marine’, see Guy Boistel, ‘Pierre Bouguer, commissaire pour la marine et expert pour les longitudes : un opposant au développement de l’horlogerie de marine au XVIIIe siècle ?’, in Pierre Bouguer (1698–1758): un savant et la marine dans la première moitié du XVIIIe siècle, Revue d’Histoire des Sciences, 63: 1 (2010), 121–159.
4 Nicolas-Louis de Lacaille, ‘Mémoire sur l'observation des longitudes en mer par le moyen de la Lune’, Histoire de l'Académie Royale des Sciences pour 1759 (1765), 63–98. The memoire was read at a session of the Académie des Sciences in 1759 and published in the late 1765 or early 1766 (it was reviewed in the Journal des Sçavans of november 1766, 713–725 (1st excerpt), and december 1766, 769–785 (2nd excerpt and astronomy items), p. 770 for a short review of Lacaille’s memoir).
5 In the Table XII Monteiro da Rocha gives an example of moon’s longitude ephemerides tabulated every 4 h for the meridian of Lisbon to the days 25, 27, 29 and 31 of December 1767.
6 Lacaille (1765: 98) for the ‘Modèle de calculs pour un Almanach Nautique […] pour les derniers jours de Mai 1754’, computed lunar distances for May 1754.
7 The NA for 1767 was available from printer on 6 January 1767, Finding Longitude: How Ships, Clocks and Stars Helped Solve the Longitude Problem, ed. by Richard Dunn and Rebekah Higgitt (Glasgow: Harper Collins Publishers, 2014), p. 73.
8 Guy Boistel, ‘From Lacaille to Lalande: French work on lunar distances, nautical ephemerides and lunar tables, 1742–85’, in Navigational Enterprises in Europe and its Empires, 1730–1850’, ed. by Richard Dunn and Rebekah Higgitt, (Basingstoke: Palgrave/Macmillan, 2016), pp. 47–64.
9 By way of example, it is the recently published book The History of Celestial Navigation, Rise of the Royal Observatory and Nautical Almanacs, Seidelmann, P. Kenneth, Hohenkerk, Catherine Young (Eds.), (Springer Nature Switzerland AG 2020), which, as the title suggests, aims to make the history of the nautical almanacs and ends up focusing exclusively on the 18th century in the English Nautical Almanac. The exception is Jim Bennett's chapter which, although in passing, quotes the French contribution of the Lacaille's project. In the book, there is no chapter dedicated to the French Connaissance des temps which contributed significantly to the development of celestial navigation and the problem of longitudes, and on whose model Maskelyne builds his Nautical Almanac.
10 It is by no means a subject played almost exclusively by Harrisson and Maskelyne, both British. See Dunn and Higgitt 2014. For Holland see Karel Davids, ‘The Longitude Committee and the Practice of Navigation in the Netherlands, c. 1750-1850’, in Navigational Enterprises in Europe and its Empires, 1730–1850’, ed. by Richard Dunn and Rebekah Higgitt, (Basingstoke: Palgrave/Macmillan, 2016), pp. 32–46.
11 Guy Boistel, ‘Lalande et la Marine. Un engagement sans faille mais non désintéressé’, in Jérôme Lalande (1732–1807). Une trajectoire scientifique, ed. by Guy Boistel, Jerome Lamy and Collette Le Lay, (Rennes: Presses Universitaires de Rennes, 2010), pp. 67–80.
12 A huge and more detailed presentation of the BNP Ms.511 manuscript in context is to be found in a book in preparation by the authors.
13 For Monteiro da Rocha life and work see Fernando B. Figueiredo, ‘da Rocha, José Monteiro’, in Biographical Encyclopedia of Astronomers, ed. by Thomas Hokey et al., 2nd edn (New York: Springer, 2014), pp. 513–515; and John O'Connor and Edmund Robertson, ‘José Monteiro da Rocha’, in MacTutor History of Mathematics Archive.
14 José Anastácio da Cunha, ‘Contra os vícios, que impedem o progresso das Sciencias’, in Composições Poéticas, ed. by Inocêncio Francisco da Silva (Lisboa: Imprensa, 1839), pp. 90–96.
15 Rodrigues, Francisco; A Formação Intelectual do Jesuíta, Porto: Livraria Magalhães & Moniz Editora, 1917, pp. 441–442.
16 See Fernando B. Figueiredo, ‘A contribuição de José Monteiro da Rocha para o cálculo da órbita de cometas’ (unpublished MPhil thesis, University Nova de Lisboa, 2005). Years later, in the 1780s, already as a professor at the University of Coimbra, Monteiro da Rocha will address the mathematical problem of the orbits of comets, presenting to the Lisbon Academy of Sciences a memoir about the determination of parabolic orbits of comets. In that characteristically scientific work on one of the leading scientific problems that occupied the astronomical community of the time, Monteiro da Rocha presents a method for solving the problem of the determination of the parabolic orbit of a comet making use of three observations, which is essentially the same method proposed by W. Olbers (1758–1840) and published under Von Zach’s sponsorship two years before, in 1797. See Fernando B. Figueiredo and João Fernandes, ‘José Monteiro da Rocha (1734–1819) and His 1782 Work on the Determination of Comet Orbits’, in Journal for the History of Astronomy 2020; 51(4), pp. 461–481.
17 See Fernando B. Figueiredo, ‘Astronomical and Nautical Ephemerides in late 18th century Portugal’, in Martina Shiavon & Laurent Rollet (dir.), Pour une histoire du Bureau des longitudes (1795–1930) (Nancy: PUN - Editions Universitaires de Lorraine, 2017), pp. 147–173.
18 For example, in the biography of Lacaille written by I.S. Glass, Lacaille’s work on longitudes is referred almost ‘en passant’ (Ian Stewart Glass, Nicolas-Louis de La Caille, Astronomer and Geodesist (Oxford: University Press, 2013), pp. 128–29). In the Biographical Encyclopedia of Astronomers Marco Murara makes the same, giving the idea that this issue was marginal in Lacaille’s scientific work (Marco Murara, ‘La Caille [Lacaille], Nicolas-Louis de’, in Biographical Encyclopedia of Astronomers, ed. by Thomas Hokey et al., 2nd edn (New York: Springer, 2014), pp. 536–537).
19 Boistel 2016 and Guy Boistel, ‘L’astronomie nautique au XVIIIe siècle en France : tables de la Lune et longitudes en mer’, 3 vols, (PhD Thesis, University of Nantes, 2001).
20 Royal warrant, quoted in Derek Howse, Greenwich Time and the Longitude (London: Philip Wilson/National Maritime Museum, 1997), p. 42
21 Boistel 2001 and Guy Boistel, ‘Pierre-Louis Moreau de Maupertuis: un inattendu préposé au perfectionnement de la navigation (1739–1745)’, in Annales 2003 de la Société d’histoire et d’archéologie de l’arrondissement de Saint-Malo (2004), 241–261.
22 Edmond Halley, ‘A Proposal of a Method for Finding the Longitude at Sea within a Degree, or Twenty Leagues. By Dr. Edmond Halley, Astr. Reg. Vice-President of the Royal Society. With an Account of the Progress He Hath Made Therein, by a Continued Series of Accurate Observations of the Moon, Taken by Himself at the Royal Observatory at Greenwich’, Philosophical Transactions of the Royal Society of London, 37 (1731), pp. 185–195.
23 See Boistel 2001, pp. 299–302.
24 French title: ‘préposé au perfectionnement de la navigation or de la Marine sous toutes ses formes’.
25 See Boistel 2016, p. 49.
26 Following Bouguer’s death in 1758, his position was split between the mathematician Alexis-Claude Clairaut (1713–1765) and the astronomer Pierre-Charles Lemonnier (1715–1799), both experts on lunar tables and their nautical uses yet with differing views and methods. Jérôme Lalande replaced Clairaut after his death in May 1765.
27 A Caleb Smith quadrant appears in Robert Willoughby, Portrait of a Merchant Captain, 1805, oil on canvas, 76 X 63, 5 cm, National Maritime Museum, Greenwich.
28 Jean Baptiste Nicolas Denis Après de Mannevillette, ‘Principes du calcul astronomique, provenant du cabinet de d’Après de Mannevillette’ (c.1754), Paris, Vincennes, Fonds du Dépôt des Cartes et Plans, Service Historique de la Défense, SH 53.
29 Nicolas-Louis de Lacaille, ‘Projet pour rendre la méthode des longitudes sur mer praticable au commun des navigateurs [1754]’, Paris, Archives Nationales (AN), Ms Marine 2 JJ 69 (J.-N. Delisle’s papers, item 16), and Nicolas-Louis de Lacaille, ‘Instruction détaillée pour l’observation et le calcul des longitudes sur mer par la distance de la Lune aux étoiles ou au Soleil [1754]’, French Archives nationales, Ms Marine 3 JJ 13 (items 3 and 9).
30 In 1754, in a letter to Jean-Dominique Maraldi (1709-88, said Maraldi II), Lacaille had sent him a table with pre-computed distances between the Moon and Spica, calculated at 3-hour intervals for 13 April 1753, which are which are the central basis of his idealized almanac project. Letter from Lacaille to Jean-Dominique Maraldi (said Maraldi II), January 20, 1754, Paris, Archives nationales, fonds Marine, MS 2 JJ 69 (Delisle’s papers), item 16.
31 Paris, Archives nationales, fonds Marine, MS 2 JJ 69 (Delisle’s papers), fol. 109.
32 See Bennett, Jim (2014). ‘‘The Rev. Mr. Nevil Maskelyne, F.R.S. and Myself’: The Story of Robert Waddington’. Maskelyne: Astronomer Royal. London: Robert Hale Ltd, pp. 59–88.
33 Mary Croarken, ‘Providing longitude for all’, Journal for Maritime Research, 4.1 (2002), 106–126, doi: 10.1080/21533369.2002.9668324
34 The first Cosmografo-mor to be appointed was the famous mathematician and astronomer Pedro Nunes (1502–78), in 1529.It will be with Pedro Nunes that a significant change will occur in the Portuguese nautical practice, passing from a common practice supported upon an empirical basis for a truly scientific one, based and founded in mathematical and astronomical principles.
35 In the ‘Aula da Esfera’ was taught geometry, arithmetic, rudiments of algebra, spherical trigonometry and their application to nautical science, optics, cosmography, and astronomy, marine and military architecture. See Henrique Leitão, ‘Sphaera Mundi’, in Sphaera Mundi: A Ciência na Aula da Esfera, Manuscriptos Científicos do Colégio de Santo Antão nas Colecções da BNP, ed. by Henrique Leitão, (Lisboa: BNP, 2008), pp. 19–23; see also Ugo Baldini, ‘The teaching of mathematics in Jesuit Colleges of Portugal from 1640 to Pombal’, in The Practice of Mathematics in Portugal, ed. by Luis Saraiva and Henrique Leitão, (Coimbra: Imprensa da Universidade de Coimbra, 2004), pp. 293–465.
36 Helder Pinto, ‘A Matemática na Academia Politécnica do Porto’, (unpublished Ph.D thesis, University of Lisbon, 2012), pp. 27–30.
37 ‘Planetario Lusitano’, was calculated for the meridian of Lisbon (probably the Jesuit Santo Antão observatory’s meridian) and consisted of 3 sheets per month with the ephemeris of (I) the Sun, (II) the Moon, and (III) positions of the planets (Mercury, Venus, Mars, Jupiter, and Saturn) for the years 1758, 1759 and 1760. For more see Jefferson dos Santos Alves, ‘O Planetario Lusitano de Eusébio da Veiga e a Astronomia em Portugal no século XVIII’ (unpublished master’s thesis, Federal University of Rio de Janeiro, 2013).
38 Princípios Gerais da Astronomia Para o uzo das Sciencias Naturais, e Bellas Letras Necessarios ao Estudo da Mocidade Portugueza, s.l.: s.n., s.d., Lisboa, Ecléctica Livraria Alfarrabista, MS 106.
39 Nuno Ferreira, ‘A institucionalização do ensino da náutica em Portugal (1779–1807)’, (unpublished PhD thesis, University of Lisbon, 2014). See also Ortega-del-Cerro, Pablo. ‘Theory and Praxis of the Professionalisation of the Portuguese Navy: The Navy Officer Corps, 1750–1807.’ International Journal of Maritime History, 2020, 32(3), pp. 551–572.
40 Custódio Gomes Villas-Boas (1741–1808), Francisco Antonio Ciera (1763–1814) and Francisco Garção Stockler (1759–1829), first professors of the ARM and ARGM and former students of Monteiro da Rocha at the University of Coimbra, have been the men responsible for the introduction of the lunar-distance methods in Portugal into the institutional framework of the ‘Ephemerides Nauticas ou Diario Astronomico’ (nautical ephemerides, or astronomical diary) published in 1788 by the Royal Academy of Sciences of Lisbon. Those ephemerides were not calculated directly from the astronomical tables but copied from the English Nautical Almanac and reduced to the meridian of Lisbon.
41 Fernando B. Figueiredo, ‘Les éphémérides nautiques et astronomiques de l’observatoire naval de Lisbonne et de l’observatoire astronomique de l’université de Coimbra, à la fin du XVIIIe siècle’, in Entre Ciel et Mer. Des observatoires pour l’enseignement de l’astronomie, des sciences maritimes et le service de l’heure en France et en Europe, de la fin du XVIIIe au début du XXe siècle: institutions, pratiques et cultures, Cahiers François Viète, ed. by Guy Boistel and Olivier Sauzereau, serie II n° 8–9 (2016), pp. 161–178. See also Fernando B. Figueiredo, Astronomical and Nautical Ephemerides in late 18th century Portugal, in Pour une histoire du Bureau des longitudes (1795–1930), ed. by Martina Shiavon and Laurent Rollet (Lorraine: PUN-Editions Universitaires, 2017), pp. 147–173.
42 The introduction is preceded by a four-page dedication to Pombal, where Monteiro da Rocha is seeking help with the publication.
43 For the MS BNP 511 index see appendix.
44 Its principles are described by William Bourne of Gravesend (c.1535–1582) in The Regiment for the Sea and Other Writings on Navigation (1574). Its first Portuguese description dates only from the 18th century, by Francisco Xavier do Rêgo in his book Tratado Completo de Navegação (1755); although it is mentioned in a Portuguese manuscript from 1720.
45 William Mountaine and James Dodson, An account of the Methods used to describe Lines on Dr. Halley's Chart of the terraqueous Globe, showing the variation of the magnetic needle about the year 1756 in all the known seas (London: W. and J. Dodson, 1758.
46 Gowan Knight, ‘An account of some magnetical experiments, shewed before the Royal Society, by Mr. Gowan Knight, on Thursday the 15th of November’, Philosophical Transactions of the Royal Society of London, 43 (1744), 161–166. See François Bellec, ‘Les hypothèses de Joao de Lisboa. Déviation magnétique et fausses pistes’, in Le Calcul des longitudes. Un enjeu pour les mathématiques, l’astronomie, la mesure du temps et la navigation, ed. by Jullien Vincent, (Rennes: PUR, 2002), pp. 37–59.
47 Monteiro da Rocha quotes the Histoire de l'Académie de Berlin (1757): Leonard Euler, ‘Recherches sur la déclinaison de l'aiguille aimantée’, Histoire de l'Académie de Berlin pour l’année 1757, (1759), 250–251; and William Mountaine and James Dodson, ‘A Letter to the Right Honourable the Earl of Macclesfield, President, the Council, and Fellows, of the Royal Society, concerning the Variation of the Magnetic Needle; With a Sett of Tables Annexed, Which Exhibit the Result of Upwards of Fifty Thousand Observations, in Six Periodic Reviews, from the Year 1700 to the Year 1756, Both Inclusive; And are Adapted to Every Five Degrees of Latitude and Longitude in the More Frequented Oceans’, Philosophical Transactions (1683–1775), 50 (1757), 329–349.
48 The historiography incorrectly refers that the old idea of building a clock that could carry on board the accurate time of the departure port was proposed in 1530 by Gemma Frisius (1508–1555). In fact, was Fernando Colombo (1488–1539) the first person to proposing such a thing in 1524, at the Junta de Badajoz–Elvas. In 1760, after forty years of work Harrison was able to build a technical marvel, the maritime timekeeper H4. The H4 was first tested on a trip to Jamaica. Having left England on November 18, 1761, it reached the destination on January 27, 1762 with only 5 s of delay. In a second trip that took place between March 28 and July 18 of the year 1764, this time to Barbados, the H4 would be three times more accurate than what was stipulated by the Longitude Act of 1714 (up to a variation of two minutes in 60 days). From then on, the idea of having a clock on board becomes a strong opponent to astronomical methods for the determining the longitude at sea. Monteiro da Rocha cite the Connaissance des Mouvements Célestes pour 1765 (Paris, 1763) where the H4 voyage is described.
49 Monteiro da Rocha refers the experiences with the marine chair invented by Christopher Irwin (dates unknown) and constructed by Jeremiah Sisson (1720–1783) for steadier astronomical observation on board, described in the Mémoires pour l'histoire des sciences et des beaux-arts by Delisle : Joseph-Nicolas Delisle, ‘Démonstration de l'exactitude des épreuves faites avec la Chaise Marine de M. Irwin, pour trouver les longitudes sur Mer par les Satellites de Jupiter, par M. De Lisle, de l'Académie Royale des Sciences’, Mémoires pour l'histoire des sciences et des beaux-arts, (1761), avril, article LX, pp.1092–1100.
50 See the appendix for bibliographical references that Monteiro da Rocha does throughout the manuscript.
51 § I. 'General idea about principal points and circles of the celestial sphere'; § II. 'Explanation of the of calculations, which are to be practiced in the determination of the longitude'; § IV. 'Explanation and use of the instruments, to be applied in the observations of Longitude' [§ I. ‘Idea geral dos pontos e círculos principais da Esfera’; § II. 'Uso dos cálculos, que se hão de praticar na determinação da longitude'; § IV. 'Uso dos Instrumentos, que se devem aplicar nas observações da Longitude']
52 It is very interesting to note that Monteiro da Rocha also gives the sinus and tangent series expansions, to be used when the trigonometric tables are absent, ‘we shall have the following formulas demonstrated by the superior analysis [and the formulas are followed]’ (MS BNP 511, fl.30).
53 That question of errors is dealt in two chapters: ‘Longitude criterion observed’ and ‘Warnings concerning some places of uncertain longitude’, («Critério da Longitude observada» and «Advertência sobre os lugares de Longitude duvidosa») §. XIII and XIV, MS BNP 511, fls. 87v–95.
54 «With six or seven very accurate observations, the pilot can easily get a value which its maximum error will be inferior to 16' or 18' of degree», MS BNP 511, fl. 40v.
55 See Boistel 2016.
56 «Après avoir lu avec plaisir ce traité, il me fut facile d’en appliquer les règles aux méthodes que je cherchais ; car en regardant les parallaxes, les réfractions […] & tous les petits mouvements comme des erreurs d’observations, j’en ai déduit des méthodes de calculs si simples, que j’ai cru devoir en rapporter quelques-unes, afin qu’elles servent d’exemple pour trouver les autres dans le besoin.», Nicolas-Louis de Lacaille, ‘Calcul des différences dans la trigonométrie sphérique‘, Histoire de l'Académie Royale des Sciences pour 1741 (1744), 238–260 – (lu les 10 et 14 février 1742 (sic)), p. 240.
57 Boistel 2001: 340–353 and Boistel 2006.
58 The Davis quadrant, invented in 1595 by John Davis (1550–1605), only in the year 1712 would it be proposed, by the royal cosmographer Manuel Pimentel (1650–1719), to be adopted by the Portuguese navy.
59 About the accuracy of observing instruments see Nicolàs de Hilster, Navigation on Wood, Wooden Navigational Instruments 1590–1731: An analysis of early modern western instruments for celestial navigation, their origins, mathematical concepts and accuracies (PhD thesis, Vrije Universiteit, Amsterdam, 2018). The author as also a very useful site about the subject http://www.dehilster.info/index.php.
60 About the octants Monteiro writes: «The instrument for observing heights must be a good octant, which is at least two palms of radius; and graduated by the method of Pedro Nunes, which the foreign call Nonius method. My preference falls on the octant of Robert Smith, whose advantage was made famous by the renowned navigators Middleton, Adisson and Sparrel. But since its use is not so common in the navy, Hadley's octant may be used instead because our pilots know how to use it. But they must be large, and having its scale graduated in minutes, with precision by the method of Nonius; So that in the observations we have always by certain a minute, and if being possible by the judgment of the observer to have some precision in seconds.» (original PT: «O instrumento para observar as alturas deve ser um octante bom, que tenha pelo menos dois palmos de raio; e esteja graduado pelo methodo de Pedro Nunes, que os estrangeiros chamam método de Nonius. Pelo meu voto era preferível o octante de Roberto Smith, de cuja vantagem fizeram experiência os celebres navegantes Middleton, Adisson e Sparrel. Mas como o seu uso não é tão comum a marinha, poderá servir em seu lugar o Octante de Hadley, de que sabem usar os nossos pilotos; contanto que seja grande, e tenha a graduação de minuto em minuto com exacção pelo método de Nonius; de sorte que nas observações seja sempre certo minuto, e se possam ao juízo do observador orçar os segundos’), MS BNP 511, fl. 43v.
61 Being graduate by Pedro Nunes' method Monteiro da Rocha means the vernier scale that Pedro Nunes had presented in De Crepusculis (1542).
62 In the Biblioteca Central da Marinha (Lisbon) there is a manuscript (n.d.) of this book (Complete Navigation Treaty), being dated from c.1740. In this manuscript, we could find for the first time in Portuguese language a technical description of the octant (only 9 years after Hadley has introduced it).
63 Monteiro da Rocha is referring to William Hughes (d. 1794?), clockmaker in London. He was elected honorary Freeman of the Worshipful Company of Clockmakers in 1781. He was in business until 1794 at the Dial near King Street, High Holborn, and also at Lower Grosvenor Street. In 1763 he took Thomas Earnshaw (1749–1829) as an apprentice, who eventually took over his premises when Hughes died. Later in 1805, Earnshaw would be granted by the Board of Longitude for his improvements to marine timekeepers (see https://biography.wales/article/s-HUGH-WIL-1794). Robert Fleetwood (1763–1794) had his workshop first in Featherstone Buildings, Holborn (1760) and AbchurchLane (1766), he was working between 1760–1790, see ANON, An Encyclopaedia of Famous Clock and Watchmakers - Details of Famous and World Renowned Watch and Clock Makers (Alcester, UK: Read Books, 2011).
64 Letter from Monteiro da Rocha, Queluz, January 20, 1805, Rio de Janeiro, National Archives MS ANRJ Cd. 807, v.23, fl.60. There is a letter from Maskelyne attesting to the skills of this Portuguese pilot in lunar distances, « António de Abreu Marques has showed me his observations of the Longitude by the moon, and his calculations relating to the same, and that they appear to me to be made with care and exactness », MS ANRJ Cd. 807, v.23, fls.65–66.
65 It is very curious to note what Lalande writes in the Magasin encyclopédique: ou Journal des sciences, des lettres et des Arts, janvier 1805, about that Monteiro da Rocha would have made lunar distance observations on his return voyage from Brazil, « dans son retour en 1766, il observoit les distances de la lune» (p. 247) – it is the first printed reference (as far as we know) of Monteiro da Rocha and the longitudes by lunar distance before 1780’s.
66 It was proposed in 1751 by Pierre Charles Lemonnier (1715–1799) as an alternative to the method of lunar distances and published by Alexander Guy Pingré (1711–1796) in the Etat du Ciel, for 1757 (Lalande 1771–81, v.3 p.795): «[Leadbetter] propose de trouver les longitudes par l'observation d'une seule hauteur de Ia Lune en supposant l'inclinaison de l'orbite de la Lune à l'écliptique connue par les Tables. Sa méthode est un peu longue. D'ailleurs les tables ne sont point entre les mains de tous les navigateurs. Je la passerai donc sous silence. […] M. Le Monnier au second livre de ses 'Observations' expose une autre méthode qui ne demande pareillement que l'observation d'une seule hauteur de la Lune. Mais il faut de plus connaître la déclinaison de cet astre, ce que l'on peut faire facilement en observant sa plus grande hauteur […] Cette méthode est fort bonne. Elle a cet avantage, que je n'en connois point qui exige moindre calcul. D'un autre côté, il y a des cas où elle n'est point praticable, comme lorsque la Lune est couverte de nuages à l'heure de son passage au méridien, lorsque l'on ne peut voir pour lors assez distinctement l'horizon […] L'angle horaire de la Lune étant donné par observation, il est facile de conclure la distance au méridien de I'observation à celui de Paris», Alexandre Guy Pingré, Etat du Ciel pour l’an de grâce MDCCLV, (Paris: Durand Pissot, 1755, p. 181.
67 For a full description of the algorithm of the all 5 methods see: José Manuel Malhão Pereira, ‘Um manuscrito de cerca de 1767, do P. José Monteiro da Rocha, S.J. com uma solução matemática para a obtenção da longitude pelas distâncias lunares’, Cuadernos de Estudios Borjanos, 50–51 (2007–2008), 339–394, and Fernando B. Figueiredo, ‘José Monteiro da Rocha e a actividade científica da 'Faculdade de Mathematica' e do 'Real Observatório da Universidade de Coimbra': 1772–1820’, (unpublished PhD thesis, University of Coimbra, 2011), pp. 418–439.
68 In fact, Monteiro da Rocha doesn’t specify what is the Lisbon meridian he was referring to. At that time (c. 1765) there was no astronomical observatory in Lisbon. The Jesuit astronomical observatory of Santo Antão had been shut down in 1759. But being an ex-Jesuit, it is probable that he had used the coordinates of that observatory to establish the meridian.
69 ‘With the work of these men, the perfection of the lunar tables has reached a degree of perfection greater than we ever could wish. The Mayer’s lunar tables calculated under Euler's principles, and the Clairaut's tables built on the principles developed by himself, very rarely give errors above one minute on the moon’s position, where their movement is more irregular, compared with the most precise observations.’ (MS BNP 511, fl. 14).
70 See Boistel 2001: pp. 340–353 (for errors from observations) and part IV, pp. 546–564 (for the Saros and the tables of the Moon’s motion).
71 Boistel 2001, pp. 571–689 for the development and use of Clairaut’s lunar tables made by French astronomers, between 1754 and 1786.
72 Josef Mendonza e Rios, Tables for facilitating the calculations of Nautical Astronomy, useful in Astronomy and Navigation (London, Oriental Press, 1810), p. v. About the history and development of this type of auxiliary and complementary tables see Charles H. Cotter, ‘A History of Nautical Astronomical Tables’ (PhD, University of Wales Institute of Science and Technology, 1974).
73 The title of Marquis of Pombal, as Sebastião José de Carvalho e Melo (1699–1782) will be known in the historiography, was only awarded in 1769. The title of Count of Oeiras was awarded in 1759.
74 ‘From knowledge first derived from translations of Spanish and Portuguese manuals English astronomers and mathematicians quickly improved the theory of navigation and compiled more accurate astronomical tables. A flourishing school of instrument-makers, chartmakers, and teachers grew up and English practice at sea improved, while Spanish and Portuguese methods became stereotyped and outmoded’, Eva Germaine Rimington Taylor and M. W. Richey, The Geometrical Seaman: a book of early nautical instruments (Londres: Hollis & Carter, 1962), pp. 10–11.
75 In fact, that booklet appeared in 1767 in two forms, an English-only publication (London: Richardson and Clark, 1767), and a bi-lingual French/English version, Esprit Pezenas, The principles of Mr Harrison's timekeeper, with plates of the same, published by order of the commissioners of longitude / Principes de la montre de M. Harrison, avec les planches relatives a la meme montre (Avignon: Veuve Girard & Francois Seguin, 176). See Boistel 2010.
76 For example, the International Longitudes Colloquium which held in Greenwich at the Royal National Maritime Museum in July 2014.
77 This classical historiographical vision went through the entire nineteenth century and still marks the historiography of the twentieth century.
78 See Ana Isabel Rosendo, ‘Inácio Monteiro e o ensino da matemática em Portugal no século XVIII’ (unpublished master thesis, University of Coimbra, 1998), and Miguel Correa Monteiro, Inácio Monteiro (1724–1812), um jesuíta português na dispersão (Lisboa: CHUL, 2004).
79 They were calculated in reference to the mean Sun instead of the true Sun (like CDT or NA did). They made use of the 360° measure and not the widely used sign unit; they provide the lunar distances not only for the Sun and the stars but also for Mars, Jupiter and Saturn. Unlike the other foreign ephemerides where the positions of the moon were calculated for both noon and midnight directly from the astronomical tables, at the ‘Ephemerides Astronómicas’ only the noon position was directly calculated from those tables, being the position for midnight calculated using a particular interpolation method proposed by Monteiro da Rocha.
80 On the Bureau des Longitudes ANR Project, see: http://bdl.ahp-numerique.fr/ and its perspectives : https://histbdl.hypotheses.org/a-propos
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Fernando B. Figueiredo
Fernando B. Figueiredo (b. 1970) Ph.D. in Mathematics. Researcher at CITEUC. His research interests are the history of astronomy and mathematics, focusing on the history of the circulation of knowledge in the Enlightenment and Empire (center-periphery exchanges and dichotomies). Recently his interests evolved into the 19th-century observatory sciences (astronomy, geodesy, meteorology, geomagnetism, and seismology). He is PI of the research project, «150 years of the scientific activity of the Geophysical Institute of the University of Coimbra: history and heritage of the Earth and Environment Sciences in Portugal», financed by the Portuguese Foundation of Science and Technology (FCT) for the next three years (2019–2021). https://orcid.org/0000-0003-1769-8241, https://coimbra.academia.edu/fernandobfigueiredo
Guy Boistel
Guy Boistel (b. 1961) Ph.D. in History of Science and Technology (‘Docteur habilité à diriger des recherches’). Associate Researcher at CFV at the University of Nantes and co-host of the Astronomy History Group (GHA). Laureate of the Academy of Marine 2002 (Prix de Fondation André-Jacques Vovard) of the Academy of sciences, letters and arts of Marseille 2004 (Prix Duc de Villars). He is the author of several papers and books’ chapters on the history of astronomy in the 18th and 19th centuries. http://guyboistel.wix.com/histoire-astronomie-sciences | https://univ-nantes.academia.edu/GuyBoistel