In 1577 Philip II ordered a coordinated program to determine longitudes across the Spanish Indies by timing lunar eclipses with a purpose-built dial instrument (the 'Instrument of the Indies'), whose reports were later reduced (converted from raw shadow readings and timings into longitudes) by the cosmographer Andrés García de Céspedes in Seville. Portuondo (2009) reconstructed the method and the handful of surviving observations but showed that the project's actual accuracy cannot be fully assessed: the larger observation dataset is lost, the lunar declination values and tables used in the reduction are unrecorded, the error contributed by the contemporary ephemerides (printed tables of predicted celestial positions, such as Leovitius's or Chaves's) versus modern computation is unquantified, contact-timing and refraction errors cannot be decomposed from the surviving data, and no coordinated Spain–Indies observation pairs survive. Gislén (2025) has now settled the flagship case — the 18 November 1584 Mexico City observation, whose ~12° longitude error traces mainly to a predicted Seville end-time taken from Chaves's 1554 Chronographia — but the error budgets of the remaining observations, the ephemeris/declination facet for the project as a whole, the possible archival recovery of lost reports (e.g., from the Philippines), and an overall bound on the uncertainty of the project's longitudes remain open.

Background

Determining terrestrial longitude before chronometers and lunars required comparing the local time of the same instantaneous astronomical event at two places: since Earth turns 360° in 24 hours, each hour of time difference equals 15° of longitude. A total lunar eclipse is the classical event choice, because the moments the Moon enters and leaves Earth's shadow (the 'contacts') are, to good approximation, simultaneous for all observers who see them; the Moon's passage through the shadow's faint outer part (the penumbra) is only a gradual dimming, which is why penumbral contact times are subjective to fix by eye. The practical difficulty is measuring local time accurately: mechanical clocks of the era drifted minutes per day, so local time had to be obtained astronomically, e.g., from the local time angle of the Sun or Moon (the 'hour angle', the angle between the object and the local meridian, which converts to time at 1 hour per 15°). In 1577 Philip II of Spain decreed such eclipse measurements to fix the geography of his American empire; the program was administered by the cosmógrafo mayor (chief cosmographer) Juan López de Velasco, folded into the Relaciones Geográficas questionnaires sent to colonial officials (Edwards 1969), and its results were later reduced by Andrés García de Céspedes, cosmographer at the Casa de la Contratación (the crown's House of Trade in Seville, which controlled navigation and cartography). The prescribed device — the 'Instrument of the Indies' — was a leveled plank carrying a combined horizontal and vertical dial: gnomons (shadow-casting pins) let observers record the length and direction of the Sun's noon shadow (fixing the meridian and checking the clock) and, on a vertical east–west face, the position of the Moon's shadow at the eclipse contacts; spherical-astronomy relations then convert the shadow reading into the Moon's altitude and hour angle (Morato-Moreno 2016 reconstructed these instruments graphically). Crucially, the instrument could not measure the Moon's declination (angular distance from the celestial equator) directly, so the reduction depended on external lunar tables — taken from contemporary ephemerides such as those of Cyprian Leovitius or the predictions printed in Jerónimo de Chaves's Chronographia o reportorio de los tiempos (Seville, 1554) — which for the Moon were notoriously poor. Times were kept in local apparent solar time (time given by the Sun itself, differing from mean solar time by the equation of time), and Spain used the Gregorian calendar from 1582 while its empire's records mix both calendars. Portuondo (2009) analyzed the few surviving observation reports, reconstructed how Seville derived longitudes from them, and demonstrated encouraging observer skill — but concluded that the full accuracy of the project cannot be assessed because the error sources cannot yet be decomposed or bounded, most of the dataset is lost, and no coordinated Spanish-side reference observations survive.

Problem Statement

Produce a complete, quantified assessment of the accuracy of the longitudes derivable from the 1580s Spanish lunar-eclipse longitude project. Concretely: (i) for each surviving observation report of the program, determine a full error budget that decomposes the discrepancy between the project-derived longitudes (or local times) and modern values into the contributions of (a) contemporary ephemeris error — the lunar declinations and contact times available in the tables actually used on the Spanish side (candidates including Leovitius's ephemerides and the predictions in Chaves's 1554 Chronographia), which remain unidentified for Céspedes's reductions, versus modern computation; (b) instrumental and method error of the Instrument of the Indies procedure (shadow-to-hour-angle conversion, dependence on external declination tables, treatment of lunar parallax — the apparent shift of the Moon's position caused by the observer's location on Earth — and of atmospheric refraction near the horizon); (c) observational error in the subjective timing of penumbral contacts; and (d) reference-station error on the Spanish side; and (ii) combine these into an overall bound on the uncertainty of the longitudes derivable from the project. This includes establishing, by archival search and documentation, whether any of the reported lost observations (e.g., the eclipse reports from the Philippines and other regions mentioned by Céspedes) can be recovered in Spanish and colonial archives, since without them the representativeness of the surviving sample — and hence the project-wide uncertainty — cannot be finally bounded. The 18 November 1584 Mexico City case, whose dominant error Gislén (2025) traced to Chaves's predicted Seville end-time, is settled; the remaining observations and the project-wide assessment are not.

For each component in (i), the assessment is to determine how far the component can be quantified from the surviving records and the cited sources, and to state explicitly what the data do not allow to be separated; where a component cannot be isolated — for instance the specific tables behind Céspedes's reductions, or Spanish-side reference observations for an eclipse with no coordinated pair — it is to be bounded, or reported as currently unquantifiable, rather than decomposed by assumption. For (ii), give the tightest bound on the project-wide uncertainty that the surviving records support, leaving the contribution of the unrecovered observations open.

References

  1. María M. Portuondo (2009), 'Lunar Eclipses, Longitude and the New World', Journal for the History of Astronomy 40(3), 249–276. DOI: 10.1177/002182860904000301. https://doi.org/10.1177/002182860904000301
  2. Lars Gislén (2025), 'The Lunar Eclipse in Mexico City on 18 November 1584: A Missed Opportunity', Journal of Astronomical History and Heritage 28(3), 778–784. DOI: 10.3724/sp.j.1440-2807.2025.03.12. https://doi.org/10.3724/sp.j.1440-2807.2025.03.12
  3. Manuel Morato-Moreno (2016), 'La medición de un imperio: reconstrucción de los instrumentos utilizados en el proyecto de López de Velasco para la determinación de la longitud', Anuario de Estudios Americanos 73(2), 597–621. DOI: 10.3989/aeamer.2016.2.09. https://doi.org/10.3989/aeamer.2016.2.09
  4. Richard de Grijs (2020), 'European Longitude Prizes. 1: Longitude Determination in the Spanish Empire', Journal of Astronomical History and Heritage 23(3), 465–494. DOI: 10.3724/sp.j.1440-2807.2020.03.03. Preprint arXiv:2009.12778. https://arxiv.org/abs/2009.12778
  5. Clinton R. Edwards (1969), 'Mapping by questionnaire: an early Spanish attempt to determine New World geographical positions', Imago Mundi 23(1), 17–28. DOI: 10.1080/03085696908592330. https://doi.org/10.1080/03085696908592330
  6. Ricardo Uribe (2023), 'Indios anónimos en los albores de la sincronía global. Charcas, Tlatelolco y Zhaoqing en 1584', Anos 90 30, e2023204. DOI: 10.22456/1983-201x.129867. https://doi.org/10.22456/1983-201x.129867
  7. Rizoi Bakhromzod (2026), 'Determination of the longitude difference between Baghdad and Khwarezm using a lunar eclipse (the method of Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani)', arXiv:2601.15837. https://arxiv.org/abs/2601.15837