Bernard Walther's Astronomical Observations

See Kennedy E. S. , “A survey of Islamic astronomical tables”, Transactions of the American Philosophical Society, n. s., xlvi (1956), 169; Sayili A. , The observatory in Islam (Ankara, 1960), passim; Thorndike L. , “Dates in intellectual history: The fourteenth century”, Journal of the history of ideas , Supplement no. 1 (1945), passim; Thorndike L. , “Pre-Copernican astronomical activity”, Proceedings of the American Philosophical Society, xciv (1950), 321–36; Thorndike L. , “Astronomical observations at Paris from 1312 to 1315”, Isis, xxxviii (1948), 200–5; Poulle E. , “Les instruments astronomiques de l'Occident latin aux XI^e et XII^e siècles”, Cahiers de civilisation médiévale, xv (1972), 27–40; Newton R. R. , Medieval chronicles and the rotation of the Earth (Baltimore, 1972), passim.

Doppelmayr J. G. , Historische Nachricht von den Nürnbergischen Mathematicis und Kunstlern (Nuremberg, 1730), 23–27, provided the earliest biographical sketch of Walther. For the most detailed and well-documented information, see Pilz K. , “Bernhard Walther und seine astronomischen Beobachtungsstände”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg, lvii (1970), 176–88, and Pilz K. , 600 Jahre Astronomie in Nürnberg (Nuremberg, 1977), 93–100. Another recent study, Beaver D. deB. , “Bernard Walther: Innovator in astronomical observation”, Journal for the history of astronomy, i (1970), 39–43, praises Walther for originating many important observational techniques. Yet many of the innovations Beaver attributed to Walther had been employed by earlier observers. For example, Beaver and most historians cite Walther as the first observer to employ a mechanical clock (which Walther did mention on two occasions). Yet nearly a century earlier, John Abramius had used a clock and an astrolabe to confirm the Persian precessional constant. See Pingree D. , “The astrological school of John Abramius”, Dumbarton Oaks papers, xxv (1971), 201, 213.

Pilz , “Bernhard Walther” (ref. 2), 178, 184. Erasmus Reinhold apparently originated the rumour of Walther's patronage in an oration on Regiomontanus he presented in 1549, printed in Melanchthon P. , Selectarum declamationum (Strassburg, 1559–60), iii, 264.

Celtis C. , “Ad Bernhardum Valerum Barbatum, mathematicum, astronomum, et philosophum”, in Celtis's Libri odarum quattuor, cum epodo, et saeculari carmine (Strassburg, 1513), sig. L4r-v.

Schöner J. (ed.), Scripta clarissimi mathematici M. Ioannis Regiomontani (Nuremberg, 1544); republished in facsimile in Regiomontanus J. , Opera collectanea, ed. by Schmeidler F. (Osnabrück, 1972), 567–752. Walther's observations were also printed in Snel W. , Coeli et siderum in eo errantium Hassiacae (Leiden, 1618), and in L. Barettus [ Curtz A. ], Historia coelestis (Augsburg, 1666). About a third of the observations were included in Riccioli G. B. , Astronomiae reformatae (Bologna, 1665), vol. ii.

The copy of the Scripta annotated by Mästlin is in Houghton Library, Harvard University, GC.R2636.544s (A). See Gingerich O. , “Science in the Age of Copernicus”, Harvard Library bulletin, xxvi (1978), 403. The practical nature of Mästlin's marginalia is immediately obvious. He converted all Walther's solar altitudes, recorded from a Ptolemaic ruler in parts per 10,000, to degrees of altitude; he labelled all planetary and stellar observations in the margin for easier reference; he underlined Walther's comments about an observation's quality; he conscientiously corrected the text as advised by the “errata” sheet bound at the end of the Scripta; and occasionally he converted Walther's sidereal times to mean solar times.

Petz H. , “Urkundliche Nachrichten über den literarischen Nachlass Regiomontans und B. Walters 1478–1522”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg, vii (1888), 247–62; Zinner E. , Leben und Wirken des Johannes Müller von Königsberg, genannt Regiomontanus, 2d ed. (Osnabrück, 1968), 245–65, 293–371.

“Obscurationes sumptae per regulas Ptolomei de motu solis, inde ab a. 1475–1500”, Clm 24103, ff. 46r–54r, Bayerische Staatsbibliothek, Munich.

Thoren V. E. , “New light on Tycho's instruments”, Journal for the history of astronomy, iv (1973), 25–45.

See Schöner (ed.), Scripta (ref. 5), ff. 21r–22v; Zinner E. , Deutsche und niederländische astronomische Instrumente des 11.–18. Jahrhunderts (Munich, 1956), 202–3; Zinner , Leben und Wirken (ref. 7), 219; Sayili , The observatory in Islam (ref. 1), passim; Thorndike L. , “Introduction and canon by Dalmatius to tables of Barcelona for the years 1361–1433 a.d.”, Isis, xxvi (1937), 310–11; Alfonso X, Libros del saber de astronomia, ed. by Rico y Sinobas M. (Madrid, 1863–67), ii, 1–79; Thorndike , “Astronomical observations at Paris” (ref. 1), 200–5; Nolte F. , Die Armillarsphäre (Abhandlungen zur Geschichte der Naturwissenschaften und der Medizin, ii) (Erlangen, 1922). For Nuremberg's instrument-making tradition, see Hartmann J. , “Die ältesten deutschen astronomischen Instrumente”, Zeitschrift für Instrumentenkunde, xl (1920), 227; de Solla Price D. J. , “Precision instruments: To 1500”, in Singer C. (eds), A history of technology (London, 1954–58), iii, 585.

Analysis of variance of errors for each day's observations indicates that the differences between the successive days' mean errors are significant at the 0.01 level. In other words, the variance of errors is significantly greater between days than within a given day of observation. A day's sample is defined as the first three sequential observations that day. Days with fewer than three sequential observations have been dropped, leaving a total of forty-two days. It seems likely, therefore, that Walther repositioned his armillary for each observing session.

Weidler J. F. , Historia astronomiae (Wittenberg, 1741), 323.

Pilz , “Bernhard Walther” (ref. 2), 187. For a photograph of the gable and the observing stand, see Pilz , 600 Jahre Astronomie (ref. 2), plate 7.

Raeder H. (eds), Tycho Brahe's description of his instruments and scientific work (Copenhagen, 1946), 55.

For planetary positions, I have used computer subroutines prepared by Prof. O. Gingerich and Prof. P. Huber which follow the procedures of Tuckerman B. , Planetary, lunar, and solar positions, A.D. 2 to A.D. 1649 (Memoirs of the American Philosophical Society, lix) (Philadelphia, 1964), but include more terms in the series expansions for greater accuracy. For the stars, I have precessed positions given for 1500 by Neugebauer P. V. , Sterntafeln von 4000 vor Chr. bis zur Gegenwart (Leipzig, 1912), ignoring proper motions because of the short time interval involved (four years), and using a mean precessional constant of 1.393819°/100 years, following Allen C. W. , Astrophysical quantities, 3d ed. (New York, 1973), 20.

For Walther's instructions, see Schöner (ed.), Scripta (ref. 5), ff. 56r, 59r.

For less extensive examinations of the errors in thirty of Walther's Mars, and seven of his Jupiter observations, respectively, see Free J. , untitled and unpublished seminar paper in the possession of Prof. Gingerich, 1974, and Bialas V. , Jovialia: Die Berechnung der Jupiterbahn nach Kepler (Abhandlungen der Bayerische Akademie der Wissenschaften, Math.-Naturwiss. Klasse, n.f., cxlviii) (Munich, 1971), 88–101.

Schöner (ed.), Scripta (ref. 5), observations of 7 March 1489, 12 December 1490, 9 September 1490, 12 December 1503, and 20 February 1504.

Because the data points plotted in Figs 3 to 6 (marked with a cross) contain considerable scatter, I have employed various smoothing techniques to draw curves through these points. The circles marked on the figures represent the smoothed values through which the curves are drawn. For Figs 3 and 5, the x-values are sliced at the letter values and the median x-values for each slice are hann-smoothed to give the horizontal values of the circles. The vertical values of the circles are the y-medians for each x-slice, smoothed by running medians of three with end-values copied on, then by splitting the peaks and valleys, then by hanning, and finally by another running median of three with end-value smoothing (3R'SSH3R). The x-values of the circles in Figs 4 and 6 are the hann-smoothed medians of equal-width bins (because of the small number of points in the samples). The vertical values of the circles are the y-medians for each slice, with a 3R'H3R smooth. In Figs 5 and 6, the smooth is broken where indicated. This procedure follows Tukey J. W. , Exploratory data analysis (Reading, Mass., 1977), 205–308.

For zenith distances < 70°, I have computed refraction according to Allen , Astrophysical quantities (ref. 15), 124: R = 58”.3 tan (z_a)-0”.067 tan³ (z_a), where z_a = apparent (i.e., refracted) zenith distance. However, since I choose to correct my computed positions rather than Walther's observed positions in the above equation, I set z_a = true (i.e., unrefracted) zenith distances. Because R changes much more slowly than does zenith distance, this replacement only minimally affects the accuracy of my computed refractions. For zenith distances > 70° (56 out of 212 cases!), I have taken values of refraction from Mueller I. I. , Spherical and practial astronomy (New York, 1969), 107, a table that was computed according to the Willis method for zenith distances < 85°, and was taken from the Pulkovo Tables for distances > 85°. I assumed standard pressure conditions, and set the temperature at observation equal to the average daily low for the given month, plus one-third the average daily temperature differential. The monthly average temperatures for Nuremberg I took from Ruffner J. A. and Bair F. E. (eds), The weather almanac (Detroit, 1974), 175, and the National Geographic atlas of the world, 4th ed. (Washington, 1975), 192–3.

Schöner (ed.), Scripta (ref. 5), f. 57v. By comparison, Tycho's equatorial armillary at Hven could repeatly measure a stellar right ascension to within 3′. See Kepler J. , Gesammelte Werke (Munich, 1937), iii, 120.

Zinner , Leben und Wirken (ref. 7), 202, says Walther's armillary was constructed of brass; Pilz , “Bernhard Walther” (ref. 2), 179, says it was made of wood. Neither identifies the source of his information. The rings of Tycho's armillaries were composed of wood (to decrease their weight) and covered with brass. See Raeder (eds), Tycho Brahe's description (ref. 14), 52–63.

95 per cent confidence levels.

Because the populations here might not be distributed normally, a test of the significance of difference between sample means cannot be used. Instead, for this and the following comparisons of pairs of samples, I have employed a Mann-Whitney U test, which is nonparametric, with a level of significance of 0.01.

Gingerich O. , “Early Copernican ephemerides”, in Science and history: Studies in honor of Edward Rosen (Studia Copernicana, xvi) (Wroclaw, 1978), 410; Wesley W. G. , “The accuracy of Tycho Brahe's instruments”, Journal for the history of astronomy, ix (1978), 42–53, p. 47.

Raeder (eds), Tycho Brahe's description (ref. 14), 56–63.

Pilz , 600 Jahre Astronomie (ref. 2), 96–97.

Schöner (ed.), Scripta (ref. 5), ff. 42v–43r. This was not Regiomontanus's only criticism of Thäbit's theory of trepidation, which the Alfonsine tables employed. The prospectus he printed in c. 1475 of works he planned to publish included De motu octave sphere contra Tebith suos que sectatores. See Regiomontanus , Opera collectanea (ref. 5), 533. And for his star catalogue, containing longitudes taken from Ptolemy and precessed to 1500, Regiomontanus used a precessional constant of about 1°/70 years (19°40′ total precession) rather than the precession plus trepidation (17°41′). See “Tabula stellarum fixarum per Joannem de Monteregio ad annum Christi 1500 supputata”, Vindob. Pal. 5208, ff. 47r–56r, Österreichische Nationalbibliothek, Vienna. I thank for Hill Monastic Manuscript Library, St John's University, for providing me with a copy of this MSS. The Alfonsine trepidation and precession I extracted from Alfonso x, Tabulae astronomicae (Venice, 1483).

I have compared Regiomontanus's Ephemerides with a set of positions generated by computer following Alfonsine parameters, prepared by Professor Gingerich, and kindly loaned by him to me.

Schöner (ed.), Scripta (ref. 5), observations of 20 September 1475, 25 March 1476, 15 October 1477, 30 November 1481, 21 November 1484, 16 March 1485, 16 February 1491, 9 September 1491, 15 February 1497, and 1 March 1504.

Observed conjunctions conveniently allow the predicted positions of tables to be tested, but do not reveal which parameters underlying the tables are faulty. Correcting parameters requires observations primarily of solar oppositions for the outer planets, and of maximal elongations for the inner planets. Only once did Walther record an outer planet's position near opposition prior to 1503. He did measure the inner planets more frequently at maximal elongations, six times before 1503, and twice during his 1503–1504 activity. Yet these few results do not confirm an interest in gathering systematically the strategic positions needed for setting planetary parameters.

See Poulle E. , Astronomie théoretique et astronomie practique au moyen âge (Conference au Palais de la Découverte, D119) (Paris, 1967); Sayili , The observatory in Islam (ref. 1), 43–44, 386; Pingree , “John Abramius” (ref. 2), 197–9; White L. Jr , “Medieval astrologers and Late Medieval technology”, in White's Medieval religion and technology: Collected essays (Berkeley, 1978), 299–302. Bert Hansen kindly pointed out White's article to me. See also Westman R. S. Jr , “The astronomer's rôle in the sixteenth century: A preliminary survey”, History of science, xviii (1980), 105–47.

Kepler J. , Opera omnia, ed. by Frisch C. (Frankfurt-Erlangen, 1858–71), vi, 729; Lichtenberger J. , Prognosticatio in Latino (Heidelberg, 1488), sig. A5v; Kurze D. , Johannes Lichtenberger: Eine Studie zur Geschichte der Prophetie und Astrologie (Lübeck, 1960).

I thank Prof. Gingerich for suggesting this topic of research and for guiding my work, Prof. Peter Huber for instructing me in the statistical methods employed here, and Ms Barbara Welther for assisting me in the computer programming.

The Appendix presents the observational dates in modified Julian days, which begin (like the civil day) at midnight, twelve hours before the same Julian day begins. Those observations marked D, Walther labelled “dubious”; those marked E contain errors greater than four standard deviations from the mean error of the entire sample. Both types have been dropped from my sample. For the observation marked EE, I have excluded only the measured latitude. The designations for observed objects refer to the five planets known since Antiquity, and to Regulus, Spica, Sirius, Procyon, and Betelgeuse. λ_obs and β_obs are presented in degrees and minutes, as Walther recorded them. To those longitudes marked T must be added 10′, as per Walther's instructions. λ_com and β_com are given in degrees, and have not been corrected for refraction. Δλ_rel and Δβ_abs however, have been corrected for refraction and for the erroneous longitudes Walther assumed for his reference stars. The conclusions of the above article rest on these corrected values.