I discuss a number of additional observations and reports, as well the historical context of the eclipse project, in chaps. 6 and 7 of my Secret science: Spanish cosmography and the New World (Chicago, 2009).
2.
PiñeiroMariano Esteban, “Los cosmógrafos al servicio de Felipe II”, Mare liberum, x (1995), 532–3.
3.
EdwardsClinton R., “Mapping by questionnaire and early Spanish attempts to determine New World geographical positions”, Imago mundi, xxiii (1969), 17–28. Rodríquez-Sala published what were believed to be the sole surviving observations in Rodríguez-SalaMaría Luisa, El eclipse de Luna: Misión científica de Felipe II en Nueva España (Huelva, 1998).
4.
Edwards's opinion is echoed in MundyBarbara M., The mapping of New Spain: Indigenous cartography and the maps of the relaciones geográficas (Chicago, 1996), 55–56. Randles, however, conceded that towards the end of the sixteenth century the Spanish had achieved remarkable accuracy in their longitude calculations, but still asked, “w[ere] such close figure[s] a fluke or the result of a real mastery of the process of measurements?”. RandlesW. G. L., “Portuguese and Spanish attempts to measure longitude in the 16th century”, Vistas in astronomy, xxviii (1985), 1985–41, p. 238.
5.
Edwards, “Mapping by questionnaire” (ref. 3), 17–18. For more on the reforms, see ManzanoJuan Manzano, “La visita de Ovando al Real Consejo de las Indias y el Código Ovandino”, in El Consejo de las Indias en el siglo XVI (Jornadas Americanistas, Valladolid, 1970), 111–23, pp. 119–21, and SchäferErnesto, El Consejo Real y Supremo de las Indias: Su historia, organización y labor administrativa hasta la terminación de la Casa de Austria (2 vols, Madrid, 2003), i, 136–9.
6.
Ordinance 118, in Consejo de Indias, Ordenanzas reales del Consejo de Indias: Gobernación y estado temporal (Madrid, 1585), 21v.
7.
For more on Velasco see chap. 4 of Portuondo, Secret science (ref. 1). For the sake of brevity, I refer to persons with compounded last names by the final name, thus, López de Velasco becomes “Velasco”.
8.
General Archive of the Indies, Seville (AGI), P-184, R. 27 (27).
9.
The sidereal circumstances surrounding the viceroy's report can be reconstructed using positions computed using modern computer algorithms. We know that the beginning of the partial phase of the eclipse took place at 01:05 UT on 17 November 1537 (calculated as the time of maximum eclipse minus the semi-duration of partial umbral phase). Since the time distance from Greenwich (UT) to Mexico City is 6:36 hours, the event would have been visible in Mexico City at 17:28 on the evening of 16 Nov. Sunset on 16 Nov. in Mexico City took place between 17:20 and 17:24. The viceroy noted the start of the event at “half a quarter hour after sunset” (7½ minutes after sunset), thus only minutes from the actual start time. The fact that the eclipse occurred so soon after sunset clearly influenced the accuracy of the reported time. The time-keeping device used, perhaps a sand-clock, would have been started at the moment of sunset. All predictions in this article use historical eclipse data courtesy of Fred Espenak, NASA/Goddard Space Flight Center. See http://Sunearth.gsfc.nasa.gov/eclipse/LEcat/LEcatalog.html.
10.
AGI, P-49, R.12, Bloque 2.
11.
Biblioteca de la Academia de Historia (Madrid) (BAH), Colección Muñoz, xxxiii, f. 249–265. “Relación de Juan Bautista Román, factor de las Islas Filipinas en Macao. Copia de la carta que me envio el P. Matheo Reci Italiano, Religioso de la compañia de Jesús que reside con el P. Miguel Ruggeiro en la ciudad de Junquinn cabeza de esta provincia de los Cantones en los Reinos de China”, 28 September 1584, Macao.
12.
Few texts explain the “longitude problem” in its historical context better than the classic TaylorE. G. R., The haven-finding art (London, 1956). For an explanation of different methods of finding longitude during early modern era, see CotterCharles H., A history of nautical astronomy (London, 1968), 180–208. For a comprehensive survey of the topic, see AndrewesW. J. H. (ed.), The quest for longitude: The proceedings of the longitude symposium, Harvard University, Cambridge, Massachusetts, November 4–6, 1993 (Cambridge, MA, 1993).
13.
KremerRichard L.DobrzyckiJerzy, “Alfonsine meridians: Tradition versus experience in astronomical practice, c. 1500”, Journal for the history of astronomy, xxix (1998), 187–99. Steele cites only seven astronomers known to have systematically observed eclipses during the period 1200–1600. SteeleJohn M., Observations and predictions of eclipse times by early astronomers (Dordrecht and Boston, 2000), 133. For eclipse observations by Muslim astronomers, see SaidS. S.StephensonF. R., “Solar and lunar eclipse measurements by medieval Muslim astronomers, I: Background”, Journal for the history of astronomy, xxvii (1996), 1996–73, p. 262.
14.
The impressive book Velasco used is still in the library of El Escorial: LeovitiusCyprianus, Eclipsium omnium ab anno Domini 1554 usque in annum Domini 1606… (Augsberg, 1556). His notes are in Royal Library of El Escorial, K-III-8, f. 311v–318v: “Copias del Eclipsium omnium ab año Domini 1554 usque in annum 1606 de Cypriani Leovitii”, c. 1581.
15.
Using Peurbach's contact times and adjusting them for Augsburg, Leovitius found the following for the eclipse of 16 (27) September 1577: “relinquuntur hor: 12. minut: 47. Unde principium consequitur hor: 10. minut: 54. Finis hor: 14. minut: 40.” Therefore, he expected the start of the eclipse to take place at 22:54 and the end at 2:40. Modern computations adjusted for Augsburg (48°26′N, 10°56′E) place the start time at 21:33 and the end time at 1:26, for a 1:21 and 1:14 error respectively (eclipse data taken from Table 6).
16.
BennettJ. A., The divided circle (Oxford, 1987), 53–56. For a translation of Werner's method, see AppendixC. in Andrewes (ed.), The quest for longitude (ref. 12), 380, 384–5.
17.
Astronomers throughout the sixteenth century routinely complained about the predictive accuracy of ephemerides, whether these were computed using the Alphonsine or the Prutenic Tables. Tycho expressed his concern in his correspondence. ThorenVictor E., The Lord of Uraniborg (Cambridge, 1990), 16, 326. Thoren cites correspondence in Tychonis Brahe opera omnia, ed. by DreyerJ. L. E. (Copenhagen, 1913–29), v, 106–7. Michael Mastlin and Wilhelm IV, Landgrave of Hesse-Kassel, also questioned the accuracy of the Prutenic Tables. JarrellRichard A., “The contemporaries of Tycho Brahe”, in The general history of astronomy, ii: Planetary astronomy from the Renaissance to the rise of astrophysics, A: Tycho Brahe to Newton, ed. by TatonRenéWilsonCurtis (Cambridge, 1989), 22–32, p. 28.
18.
PohlFrederick J., Amerigo Vespucci, pilot major (New York, 1945), 65–67.
19.
de NavarreteMartín Fernández, Disertación sobre la historia de la náutica y de las ciencias matemáticas que han contribuido a sus progresos entre los españoles, ed. by SerranoCarlos Seco, lxxv—lxxvii: Biblioteca de autores españoles (Madrid, 1954–55), lxxvii, 333–4.
20.
ApianPeter, Cosmographicus liber Petri Apiani mathematici studiose collectus (Landshut, 1524). Regiomontanus preferred to calculate eclipse local contact times from altitude observations made during the eclipse and to determine times using spherical trigonometry. SteeleJohn M.StephensonF. Richard, “Eclipse observations made by Regiomontanus and Walther”, Journal for the history of astronomy, xxix (1998), 1998–44, p. 337.
21.
PogoA., “Gemma Frisius, his method of determining differences of longitude by transporting timepieces (1530), and his treatise on triangulation (1533)”, Isis, xxii (1935), 469–85. Sixteenth-century geared clocks had an expected accuracy of within a quarter-hour a day. Bennett, Divided circle (ref. 16), 60.
22.
FinéOronce, Quadratura circuli…. De invenienda longitudinis locorum differentia … (Paris, 1544), 73–91. In his Protomathesis, Oronce Finé also discussed the mathematics behind the method of using lunar eclipses for determining longitude, but does not discuss instruments. Oronce Finé, Protomathesis … (Paris, 1532), 145v–46.
23.
NuñezPedro, “De erratis Orontii Finoei liber unus”, in Petri Nonii Salaciensis opera (Basel, 1592).
24.
ForbesEric G.WilsonCurtis, “The solar tables of Lacaille and the lunar tables of Mayer”, in The general history of astronomy, ii: Planetary astronomy from the Renaissance to the rise of astrophysics, B: The eighteenth and nineteenth centuries, ed. by TatonRenéWilsonCurtis (Cambridge, 1995), 55–68.
25.
The viceroy of New Spain complained that the instructions arrived on 9 Sept. AGI, Mexico 69, R. 5, N. 83, “Carta del virrey Martín Enríquez al rey”, 19 October 1577.
26.
Biblioteca Nacional de España (BN), MS3035. “Instrucción y advertimiento para observación de los eclipses de la luna, y cantidad de las sombras”, 28 May 1578. This is the earliest known version of the eclipse instructions.
27.
” [A] poco mas o menos, segun el parecer, y arbitrio de los que lo miraren.” BN, MS3035, f. 40v.
28.
de CéspedesAndrés García, Regimiento de navegación e hydrografía (Madrid, 1606), 128–45v.
29.
“Although Juan López de Velasco sent the instructions of what had to be done in the Indies for observing the eclipse, he did not give [in the instructions] order or doctrine on how the start or end time of the eclipse could be known from such observation … nor have I found in all the papers I was given such a doctrine.” García de Céspedes, Regimiento de navegación (ref. 28), 163v–64.
30.
For more on the reform see MarotoM. I. VicentePiñeiroMariano Esteban, Aspectos de la ciencia aplicada en la España del Siglo de Oro, 2nd edn (Valladolid, 2006), 390–414.
31.
I thank the anonymous referee for pointing out the following: “The plane that passes through the gnomon and any given point of the semicircle (the X° value) — Call it the shadow plane — Intersects the plane of the lunar orbit in a line. That is, for a given observation of X°, the Moon could be anywhere along a lengthy arc of its path! The ‘Instrument of the Indies’ works ONLY if you have independent evidence, taken from an ephemerides, for the lunar longitude, a value NOT observed by the instrument”.
32.
“El primero Problema de las tablas de Direccion de Iuan de Monterregio.” He also suggested that an astrolabe could be used to get the declination. In chaps. 15 and 16 he explains how to translate ecliptic longitude into declination using an instrument discussed in the second part of this article. García de Céspedes, Regimiento de navegación (ref. 28), 164–164v, 166–167.
33.
“A esto digo que por las Efemerides, o algunas tablas, se sepa quando sera el principio del Eclipse, y para esta hora se puede hazer la cuenta de la declinacion, que aunque en el lugar de la Luna se errasse medio grado, o uno (lo qual no es possible) en la declinacion aura poca diferencia.” Ibid., 165.
34.
The values computed using modern computer algorithms used in this and other tables rely on estimated values of the parameter ΔT (the difference between Terrestrial Dynamical Time (TD) and Universal Time (UT)). ΔT reflects the change in the Earth's rate of spin due to the effect of the tides. The modern positions used in this article extrapolate values for ΔT of the period 1500–1600 from 3 to 2.33 minutes based on F. R. Stephenson, Historical eclipses and Earth's rotation (Cambridge, 1997). Recently Morrrison and Stephenson have revised their original values of ΔT during the period of 1500–1600 a.d. to between 3.3 and 2 minutes ± 20 sec. MorrisonL. V.StephensonF. R., “Historical values of the Earth's clock error ΔT and the calculation of eclipses”, Journal of the history of astronomy, xxxv (2004), 327–36.
“The altitude ‘alt’ and azimuth ‘az’ of the Moon during any phase of an eclipse depends on the time and the observer's geographic coordinates. Neglecting the effects of atmospheric refraction and lunar parallax, ‘alt’ and ‘az’ are calculated as follows:
37.
h = 15 × (GST0 + t — Ra) + l.
38.
a = arcsin [sin d sin f + cos d cos h cos f].
39.
A = arctan [– (cos d sin h) / (sin d cos f — Cos d cos h sin f)].
40.
where h = hour angle of the Moon (in degrees); a = altitude (in degrees); A = azimuth (in degrees); GST0 = Greenwich Sidereal Time at 00.00 UT; t = Universal Time; ra = right ascension of the Moon (in hours); d = declination of the Moon (in degrees); l = observer's longitude (east +, west –); f = observer's latitude (north +, south –)”.
41.
García de Céspedes, Regimiento de navegación (ref. 28), 164–5.
42.
” [P]or la 30 del libro 4 de los triangulos de Iuan de Monterregio.” García de Céspedes, Regimiento de navegación (ref. 28), 164v. This theorem states that when two sides of a non-right triangle are known together with the angle opposite one of them, the remaining side and two angles may be found. RegiomontanusJoannes, Regiomontanus: On triangles. De triangulis omnimodis, transl. by HughesBarnabas (Madison, 1967).
43.
The following are the spherical trigonometric identities for right-spherical triangles used to solve this problem: Tan B = cot A / cos c; tan a = cos B × tan c, and cos B = tan a / tan c, where A, B, C are the angles at the vertices with C as the right angle, and a, b, c are the arcs on the opposite sides determined by the angles at the centre of the sphere.
44.
To illustrate how Céspedes's equations determine local contact times consider the lunar eclipse of 18 Nov 1584 and the modern values as set out in Tables 1 and 2. The given values are the observer's latitude am = 19°24′N, the Moon's declination mg = 70.90° and the predicted value of X° (from Equ. 3) mat = 63.66°. Using Equ. 4 and 5 we find respectively, ∠amt = 27.70° and mt = 17.32, while Equ. 6 yields ∠tmg = 83.80°. Therefore since ∠amg = ∠amt + ∠tmg and ∠cmg = 180 — ∠amg, we find a value of ∠cmg = 68.50° for a distance of the Sun to the meridian that corresponds to 4.57 hours. Once adjusted by the difference between Greenwich sidereal time (GST0) and right ascension (4.57 + (3.8–3.57) = 4.80), it yields a local end time of 19.20 or 19:12, the same as predicted by modern values.
45.
The instrument's construction appears in de CéspedesGarcía, Regimiento de navegación (ref. 28), 32–33v.
46.
FrisiusGemma, De astrolabo catholico (Antwerp, 1550). The saphea was well-known in Spain. Its construction and use was discussed in a treatise by Ali ibn Khalaf and included in Alphonso X “the Wise”, Libro del saber de astronomía (13th century). The projection was employed in the late sixteenth century in two instruments attributed to Juan de Herrera and discussed in MorenoR.Van CleempoelK.KingD., “A recently discovered sixteenth-century Spanish astrolabe”, Annals of science, lix (2002), 331–61. (Juan de Herrera and Céspedes were well-acquainted; the cosmographer taught at the mathematics academy Herrera instituted at Philip II's court.) The saphea was also known in Northern Europe before Gemma's reintroduction. The fourteenth-century abbot Richard of Wallingford describes in his Albion a very similar instrument to the one Céspedes proposed. NorthJ. D. (ed.), Richard of Wallingford (3 vols, Oxford, 1976), ii, 188–91; iii, 36. For a study of the use of the universal astrolabe for coordinate conversion, see NorthJ. D., “Coordinates and categories: The graphical representation of functions in medieval astronomy”, in his The universal frame (London, 1989), 1–16.
47.
de CéspedesGarcía, Regimiento de navegación (ref. 28), 166–8.
48.
The CAD model of Céspedes's instrument was drawn with the stereographic projection grid at 5° intervals.
49.
AGI, Mapas y Planos, Mexico 34.
50.
AGI, Mapas y Planos, Teóricos-1 & 2. “Observación astronómica de la luna hecha en Puerto Rico demostrada en circulos … 1600?”.
51.
de CéspedesGarcía, Regimiento de navegación (ref. 28), 163.
52.
AGI, I-740, N. 103. Drawings formed part of AGI, P-183, N. 1, R.13, and are currently in Mapas y Planos Mexico-34.
53.
“Magnam enim habet propter varium lunae motum varietatem et non levem errandi suspicionem.” Rodríguez-Sala, El eclipse de Luna (ref. 3), 166.
54.
AGI, Mapas y Planos, Teóricos-1 & 2. “Observación astronómica de eclipse de luna hecha en Puerto Rico demostrada en circulos, c. 1600.” The drawings formed part of AGI, P-175, R. 40.
55.
AGI, Santo Domingo, 155, R. 9, N. 65. de CéspedesJuan, “Carta del gobernador de Puerto Rico al rey”, 20 September 1580. Also, AGI, Santo Domingo, 155, R.10, N. 66. Juan Malgarejo, “Carta del gobernador de Puerto Rico al rey”, 3 February 1582.
56.
AGI, Santo Domingo, 155, R. 11, N. 118. MenéndezDiego, “Carta del gobernador de Puerto Rico al rey”, 7 October 1588.
57.
de CéspedesGarcía, Regimiento de navegación (ref. 28), 165.
58.
AveniA. F., Skywatchers (Austin, 2001), 104.
59.
SteeleJohn M., Observations and predictions of eclipse times by early astronomers (Dordrecht and Boston, 2000), 143, 150, 153–4.
