Eclipse Observations Made by Regiomontanus and Walther

For a recent overview of the development of astronomy during the Renaissance, see Swerdlow N. M. , “Astronomy in the Renaissance”, in Walker C. B. F. (ed.), Astronomy before the telescope (London, 1996), 187–230.

The Toledan Tables were compiled during the eleventh century for use at the meridian of Toledo in Spain. For further discussion see Toomer G. J. , “A survey of the Toledan Tables”, Osiris , xv (1968), 5–174. The Alphonsine Tables were compiled during the first half of the fourteenth century. They are named after King Alfonso X of Castile, who has often been assumed to have been their patron. However, Poulle E. , “The Alphonsine Tables and Alfonso X of Castille”, Journal for the history of astronomy , xix (1988), 97–113, has suggested that they were in fact compiled in Paris, perhaps by Jean de Murs. For a modern edition of the Alphonsine Tables, see Poulle E. , Les Tables Alphonsines avec le canons de Jean de Saxe (Paris, 1984).

For examples of eclipse predictions made with the Alphonsine Tables, see Thorndike L. , “Predictions of eclipses in the fourteenth century”, Isis , xlii (1951), 301–2; “A record of eclipses for the years 1478 to 1506”, Isis , xliii (1952), 252–6; and “Eclipses in the fourteenth and fifteenth centuries”, Isis , xlviii (1957), 51–57.

Newton R. R. , Medieval chronicles and the rotation of the Earth (Baltimore, 1972); Stephenson F. R. , Historical eclipses and Earth's rotation (Cambridge, 1997).

Gushee L. , “New sources for the biography of Johannes de Muris”, Journal of the American Musicological Society , xxii (1969), 3–36; Beaujouan G. , “Observations et calculs astronomiques de Jean de Murs (1321–1344)”, in Actes du XIVe Congrès International d'Histoire des Sciences , ii (Tokyo and Kyoto, 1974), 27–30.

Goldstein B. R. , “Theory and observation in medieval astronomy”, Isis , lxiii (1972), 39–47; Goldstein B. R. , The astronomical tables of Levi ben Gerson (New Haven, Conn., 1974).

Goldstein B. R. , “Medieval observations of lunar and solar eclipses”, Archives internationales d'histoire des sciences , xxix (1979), 101–56.

For a biography of Peurbach, see Hellman C. D. Swerdlow N. M. , “Peurbach”, in Dictionary of scientific biography , xv, 473–9.

Dobrzycki J. Kremer R. L. , “Peurbach and Marāgha astronomy? The ephemerides of Johannes Angelus and their implications”, Journal for the history of astronomy , xxvii (1996), 187–237.

Swerdlow N. M. , “Regiomontanus on the critical problems of astronomy”, in Levere T. H. Shea W. R. (eds), Nature, experiment, and the sciences (Dordrecht, 1990), 165–95.

Schoener J. , Scripta clarissimi mathermatici M. Ioannis Regiomontani (Nuremberg, 1544; reprinted Frankfurt, 1976).

For detailed biographical information, see Rosen E. , “Regiomontanus”, in Dictionary of scientific biography , xi, 348–52; Zinner E. , Regiomontanus: His life and work (Amsterdam, 1990).

Gingerich O. Voelkel J. R. , “Tycho Brahe's Copernican campaign”, Journal for the history of astronomy , xxix (1998), 1–34.

Schaefer B. E. , “Astronomy and the limits of vision”, Vistas in astronomy , xxxvi (1993), 311–61.

Zinner , op. cit. (ref. 12), 51.

Ibid. 141.

It is interesting to note that in Europe purpose-built observatories were not constructed before the sixteenth century. In China, imperial observatories were built and staffed from at least the Han dynasty (c. 200 b.c). This exemplifies one of the main differences between the places of astronomy in Chinese and European society; in China, astronomers were mainly appointed and controlled by the government, whereas in medieval Europe, interest in astronomy was generally the province of wealthy individuals for their own amusement and edification. On the “official” character of astronomy in China, see Needham J. , Science and civilization in China , iii (Cambridge, 1959), 186–94. In the medieval Arab Lands, many observatories, both royal and private, were built. These served not only as places of astronomical research, but also as centres of teaching. For details, see Nasr S. H. , Science and civilization in Islam (Cambridge, Mass., 1968), 80–88; Sayili A. , The observatory in Islam (Ankara, 1960).

Zinner , op. cit. (ref. 12), 151.

Shortly after Regiomontanus's death, rumours spread that he had been the victim of a terrible crime. The sons of Trebizond, whose translation of the Almagest Regiomontanus has criticized, were said to have poisoned him. However, Zinner , op. cit. (ref. 12), 152, notes that there is little evidence in support of this story, and suggests instead that Regiomontanus was probably the victim of a plague that was epidemic in Rome in that year.

Regiomontanus's observations are given in folios 36–43, entitled Ioannis de Monteregio, Georgii Peurbachii, Bernardi Waltheri, ac aliorum, Eclipsium, Comentarum, Planetarum ac Fixarum observationes..

For examples of Arab observations of eclipses during which altitudes were measured, see Said S. S. Stephenson F. R. , “Solar and lunar eclipse measurements by medieval Muslim astronomers, II: Observations”, Journal for the history of astronomy , xxviii (1997), 29–48.

Goldstein B. R. , “A medieval table for reckoning time from solar altitude”, Scripta mathematica , xxvii (1963), 61–66; King D. A. , “Ibn Yūnus' very useful tables for reckoning time by the Sun”, Archive for the history of exact science , x (1973), 342–94.

As noted above, atmospheric refraction is negligible at the precision to which Regiomontanus was observing. However, for completeness, we have made the appropriate correction given by Schaefer, op. cit. (ref. 14), in all calculations. The computed altitudes in the table have also been adjusted to show the ‘apparent’ rather than the ‘true’ value, to enable direct comparison.

In deducing the times of the eclipses, we have used original computer programs based upon the solar ephemeris of Newcomb S. , “Tables of the motion of the Earth on its axis and around the Sun”, Astronomical papers prepared for the use of the American Ephemeris and Nautical Almanac , vi (1895), Part 1, and a corrected version of the lunar ephemeris designated j=2, Transactions of the International Astronomical Union , xiiB (1968), 48. Adopted in all computations was a lunar acceleration of −26’ cy⁻² as given by Morrison L. V. Ward C. G. , “An analysis of the transits of Mercury”, Monthly notices of the Royal Astronomical Society , clxxiii (1975), 183–206, and close to that determined using lunar laser ranging by Dickey J. O. , “Lunar laser ranging: A continuing legacy of the Apollo program”, Science , cclxv (1994), 482–90. Values of the Earth's rotational clock error were taken from the spline fit of Stephenson F. R. Morrison L. V. , “Long-term fluctuations in the Earth's rotation: 700 b.c. to a.d. 1990”, Philosophical transactions of the Royal Society of London , A, ccli (1995), 165–202. Because this clock error is fairly small at this relatively late period, computations of eclipses can be made with very high accuracy.

Newton R. R. , “An analysis of the solar observations of Regiomontanus and Walther”, Quarterly journal of the Royal Astronomical Society , xxiii (1982), 67–93.

Indeed , Walther is not even given his own entry in the Dictionary of scientific biography. For some biographical details see Beaver D. deB. , “Bernard Walther: Innovator in astronomical observation”, Journal for the history of astronomy , i (1970), 39–43. Regarding this article, however, note the cautionary words in ref. 2 of Kremer R. L. , “Bernard Walther's astronomical observations”, Journal for the history of astronomy , xi (1980), 174–91. For a more recent biographical study, see Eirich R. , “Bernhard Walther (1430–1504) und seine Familie”, Mitteilurgen des Vereins für die Geschichte der Stadt Nurnberg , lxxiv (1987), 77–128.

Kremer R. L. , “The use of Bernard Walther's astronomical observations: Theory and observation in early modern astronomy”, Journal for the history of astronomy , xii (1981), 124–32.

Ibid. .

Zinner , op. cit. (ref. 12), 146–7.

In 1503 Walther stated that he could achieve an accuracy of at best 10′ with his armillary sphere. However, Zinner , op. cit. (ref. 12), 145, suggests that this was an underestimate of his ability.

Walther's eclipse observations are given in folios 44–60, entitled Observationes factae per doctissimum virum Bernardum Waltherum Norimbergae..

Kremer R. L. , “Walther's solar observations: A reply to R. R. Newton”, Quarterly journal of the Royal Astronomical Society , xxiv (1983), 36–47.

Newton , op. cit. (ref. 25).

Said Stephenson , op. cit. (ref. 21).

Copernicus N. , De revolutionibus (Nuremberg, 1543).

Tycho's observations may be found in vols x-xiii of Dreyer J. L. E. (ed.), Tychonis Brahe Dani opera omnia (14 vols, Copenhagen, 1913–29).

Tycho's eclipse observations will be discussed in a separate paper.