On the Origin of the Ptolemaic Star Catalogue: Part 1

Ptolemy , Syntaxis mathematica [the “Almagest”]. Greek text edited by Heiberg J.L. , Claudii Ptolemaei Opera quae exstant omnia, i (2 parts, Leipzig, 1898, 1903). English translation by Toomer G. J. , Ptolemy's Almagest (London, 1984). Ptolemy describes his method of observing the positions of the stars in Almagest VII, 4.

Delambre J. B. J. , Histoire de l'astronomie ancienne (2 vols, Paris, 1817), ii, 261–4.

Peters C. H. F. and Knobel E. B. , Ptolemy's catalogue of stars: A revision of the Almagest, Carnegie Institution of Washington Publication no. 86 (Washington, 1915), 15.

This point was made forcefully by Dreyer J. L. E. , “On the origin of Ptolemy's catalogue of stars”, Monthly notices of the Royal Astronomical Society, lxxvii (1917), 528–39. Dreyer's discussion continues in “On the origin of Ptolemy's catalogue of stars: Second paper”, ibid., lxxviii (1918), 343–9.

Maass Ernst , Aratea (Philologische Untersuchungen, xii (Berlin, 1892)), 377; reprinted in Maass, Commentariorum in Aratum reliquiae (Berlin, 1898), 134–9. The texts as published by Maass do not contain the star counts. For these, see the paper by Boll, cited in ref. 6.

Boll Franz , “Die Sternkataloge des Hipparch und des Ptolemaios”, Bibliotheca mathematica, Folge 3, ii (1901), 185–95.

Dreyer , “On the origin” (ref. 4), 529–31.

Hipparchi in Arati et Eudoxi Phaenomena commentariorum libri tres, Greek text edited and German translation by Manitius C. (Leipzig, 1894).

Vogt H. , “Versuch einer Wiederherstellung von Hipparchs Fixsternverzeichnis”, Astronomische Nachrichten, ccxxiv (1925), Nr. 5354–5. The most searching (and critical) recent examination of Vogt's conclusions is that of Gerd Graßhoff, Die Geschichte des Ptolemäischen Sternenkatalogs (doctoral dissertation, Universität Hamburg, 1986), pp. 110–37. Graßhoff argues that, while Ptolemy's catalogue is not a direct re-working of Hipparchus's Commentary on Aratus, nevertheless the two works are statistically correlated. Unfortunately, I obtained a copy of Dr Graßhoff's work too late to include a discussion of it here.

Neugebauer O. , A history of ancient mathematical astronomy (Berlin, 1975), Part 1, 280–4. In the succeeding pages (284–92), Neugebauer provides a thorough discussion of the fragmentary documentary evidence on the nature of the Greek star lists and star catalogues before Ptolemy.

Pedersen Olaf , A survey of the Almagest, Acta Historica Scientiarum Naturalium et Medicinalium, xxx (Odense, 1974), 255–7.

Neugebauer , A history of ancient mathematical astronomy (ref. 10), Part 1, 280.

Newton Robert R. , The crime of Claudius Ptolemy (Baltimore, 1977), 245–54.

Newton Robert R. , “On the fractions of degrees in an ancient star catalogue”, Quarterly journal of the Royal Astronomical Society, xx (1979), 383–94. The publication of this paper was followed by a lively exchange between Newton and Owen Gingerich in suceeding numbers of the same journal: See vol. xxi (1980), 253–66; vol. xxi (1980), 388–99; vol. xxii (1981), 40–44. This interesting exchange between one of Ptolemy's severest critics and one of his ablest defenders touches on many issues other than the origin of the star catalogue.

Newton Robert R. , The origins of Ptolemy's planetary parameters (n.p.: Center for Archaeoastronomy of U. of Maryland and Applied Physics Laboratory of Johns Hopkins U., 1982), 86–90.

Rawlins Dennis , “An investigation of the ancient star catalog”, Publications of the Astronomical Society of the Pacific, xciv (1982), 359–73.

See, for example, Curtis Wilson's very useful review of Newton's book, The origins of Ptolemy's astronomical parameters, in Journal for the history of astronomy, xv (1984), 37–47, remarks on pp. 38–39. See also Maeyama Y. , “Ancient stellar observations: Timocharis, Aristyllus, Hipparchus, Ptolemy—; the dates and accuracies”, Centaurus, xxvii (1984), 280–310, p. 307.

Newton , The crime of Claudius Ptolemy (ref. 13), 245. A recount based on Toomer's text of the catalogue (which became available several years after the publication of Newton's book) would give slightly different totals. Small changes in the numbers would not, of course, affect Newton's argument.

E.g., Peters and Knobel , Ptolemy's catalogue of stars (ref. 3), 14–15.

Dreyer went so far as to propose that the 142 stars whose latitudes have the fractions ¼ or 3/4 (plus a certain number of stars with fractions 0 or 1/2) might be the 175 or so stars that Boll has argued were contributed by Ptolemy. The remainder of the stars would then be borrowed from Hipparchus's catalogue. (Dreyer, “On the origin” (ref. 4), 531–3.) While this hypothesis cannot be refuted, I believe it is unlikely to be true, for the reasons set forth in Appendix II.

Newton , The crime of Claudius Ptolemy, 245–8.

Gingerich and Welther have recently discussed the two-instrument hypothesis, pointing out that a distribution very like that of Table 1(a) can be obtained by assuming that “726 stars were observed with an instrument whose latitude scale was calibrated in sixths of a degree whereas 300 other stars were observed with a scale calibrated in quarters of a degree”. Gingerich Owen and Welther Barbara L. , “Astronomical scrapbook: Some puzzles of Ptolemy's star catalogue”, Sky & Telescope, lxvii (1984), 421–3. Perhaps it would be better to postulate two circles divided to thirds and halves of a degree, for it is unlikely that the smallest intervals recorded were of the same size as the smallest divisions on the instrument.

There are in the catalogue four stars with longitudes in 1°/4 that appear to have escaped the common fate. These might be considered to be errors in the manuscript tradition, except for the fact that Ptolemy mentions the longitude of one of these stars (star 11 of Gemini) in a passage in Almagest X, 1 (Toomer, 469), where his subsequent computations confirm the 1°/4 fraction.

There is a modern edition of the Arabic text, accompanied by a few introductory remarks in English: Abu'l-Husayn ‘Abdu'r-Rahmān As-Sūfī, Suwaru'l-Kawākib, or Uranometry, Edited by Nizāmu'd-Din M. (Hyderabad-Deccan, India, A.H. 1373/A.D. 1954). There is also a French translation by Schjellerup: Description des étoiles fixes … par Abd-al-Rahman al-Sûfi … avec des notes par H.C.F.C. Schjellerup (St Petersburg, 1874).

The count was made directly from the latitude columns of the 1954 printed edition. Some 31 stars, the fractional parts of whose latitudes did not fall into any of the principal categories, have been ignored. Many of these 31 should no doubt be attributed to faults of the copyists.

A few stars, whose longitudes did not fall into the principal categories, have been ignored.

The star catalogue of Ulugh Beg has been published in a critical edition: Knobel Edward Ball , Ulugh Beg's catalogue of stars, Carnegie Institution of Washington Publication no. 250 (Washington, 1917). The canons accompanying the tables have received a French translation and commentary: Sédillot L.P. , Prolégomènes des tables astronomiques d'Oloug-Beg (Paris, 1853). As far as I know, the tables themselves have never been published.

Ulugh Beg, or whoever it was that actually composed the Zīj, says that the astronomers reobserved all of the stars of Ptolemy with the exception of 27 that were too far south to be seen at Samarkand. (These included stars in Ara, Argo Navis, Centaurus, and Lupus.) These 27 stars were therefore taken from the catalogue of al-Sūfī, the longitudes being corrected for precession. (In addition, Ulugh Beg omitted 8 stars of Ptolemy that he could not identify in the sky.) Many of the 27 stars borrowed from al-Sūfī, who took their positions from Ptolemy, have fractional degrees in the latitudes that reflect their Ptolemaic origin: 10′, 20′, 40′, 50′, etc. All 27 have been omitted from the count in Table 3(a). In addition, Knobel identified some 151 stars whose latitudes he suspected of being borrowed from al-Sūfī (Ptolemy). This includes stars whose latitudes are the same as those given by Ptolemy and pairs of stars for which the latitudinal difference is the same as in Ptolemy. For safety's sake, these 151 stars have been omitted from the count of Table 3(a). It may be doubted, however, whether there was any necessity for doing so. The distribution of the fractional degrees for these 151 stars is virtually the same as the distribution for the remainder of Ulugh Beg's catalogue: A major peak at 0′, with smaller peaks at 15′, 30′, and 45′. In the distribution of the latitudes of Ptolemy and al-Sūfī, there are valleys at 15′ and 45′. Thus it appears that many, perhaps most, of Knobel's 151 suspect cases must really be due to Ulugh Beg himself, and not borrowings from Ptolemy. If these 151 were added to the count, the shape of the distribution would not be greatly altered. Finally, there are 11 other stars whose fractional degrees did not fall into the categories of Table 3(a). Some of these may be scribal errors. In any case, they have been omitted from the count.

Knobel , Ulugh Beg's catalogue (ref. 27), 11.

Sayili Aydin , Ghiyâth al Dîn al Kâshî's letter on Ulugh Bey and the scientific activity in Samarqand (Ankara, 1960), 102.

Again, we have excluded from the count those stars explicitly said by Ulugh Beg to have been borrowed from al-Sūfī, as well as some 152 stars that Knobel identified as probably or possibly borrowed. In addition there are 5 stars whose longitudes do not fall into any of the principal categories.

Knobel , Ulugh Beg's catalogue (ref. 27), 11.

Sédillot , Prolégomènes des tables astronomiques d'Oloug Beg (ref. 27), 199.

See Sayili Aydin , The observatory in Islam (Ankara, 1960), 260–89.

Sédillot , Prolégomènes des tables astronomiques d'Oloug-Beg, 200. Knobel , Ulugh Beg's catalogue, 8–9.

Sayili , The observatory in Islam, 270–2.

There is some uncertainty about the precession rate actually used by Ulugh Beg. The canons to the tables give one degree in seventy solar years (see Sédillot , Prolégomènes, 200, with correction on p. 289). However, the precession rate used in reducing the longitudes of al-Sūfī to A.H. 841 (for those stars that were too far south to be observed at Samarkand) is not consistent with this figure. (See Knobel , Ulugh Beg's catalogue, 12–13).

Delambre , Histoire de l'astronomie ancienne (ref. 2), ii, 284.

Rawlins , “An investigation” (ref. 16), 362–6.

ε Car, q Car, p Car, θ Car, λ Cen, β Tra, α Ind, α Gru, β Gru, α Phe, γ Phe. These eleven stars account for virtually all of the difference between the values of Rawlins's improbability function evaluated for Ptolemy and for Hipparchus.

Rawlins has somewhat overestimated the apparent brightness of these stars. He adopts, without explanation, a value for the atmospheric extinction coefficient of 0.15 magnitude per unit air mass—a value far more appropriate to a mountain-top observatory than to a sea-level city like Alexandria. A mean visual extinction coefficient of about 0.15 has been reported, for example, for the Cerro Tololo Observatory in Chile, which is located at an elevation of 2195 m. (See the paper by N. S. Laulainen cited in ref. 83.) If a more plausible extinction coefficient is used (say 0.20 mag./unit air mass), Rawlins's eleven critical stars come out about half a magnitude dimmer at Alexandria, with apparent magnitudes ranging between 4.0 and 5.5. This modification would affect Rawlins's numerical results, but not the shape of his argument or the nature of his conclusion. If the more realistic extinction coefficient is used in Rawlins's procedure, the odds against Ptolemy's having compiled the catalogue are reduced by several orders of magnitude. But when one begins with odds of 10¹³ to 1, one has a few orders of magnitude to spare!.

Rawlins has a fourth star, v Carinae, visible from Alexandria but not from Rhodes, that the ancient observer missed. But it was so dim (post-extinction magnitude 5.8 at Alexandria) that it contributes negligible weight to the case against Ptolemy. Of course, one could add as many stars as one pleased, missed by the cataloguer, that were visible from Alexandria but not Rhodes, if one considered the multitude of very dim stars. Rawlins quite reasonably confines himself to stars with pre-extinction magnitudes less than 3.55. Additional dim stars would not, moreoever, contribute significantly to the numerical value of Rawlins's improbability function.

Tycho's appears to be the earliest catalogue to which this test can be applied. In particular, one cannot safely use the catalogue of Ulugh Beg, because some of his stars were not observed, but were borrowed from Ptolemy by way of al-Sūfī. See ref. 28. See also the general remark by Knobel , Ulugh Beg's catalogue (ref. 27), 10, and the remark, for example, on star 957, p. 84.

This sketch of the history of Tycho's star catalogue is from Dreyer J. L. E. , Tycho Brahe: A picture of scientific life and work in the sixteenth century (London, 1890; reprinted, Gloucester, Mass., 1977), 227, 265–6.

Dreyer J. L. E. (ed.), Tychonis Brahe Dani Opera omnia (15 vols, Copenhagen, 1913–29). The 777-star catalogue is found in vol. ii, 258–80. The 1000-star catalogue is in vol. iii, 344–73.

Declinations for these stars were computed for 1591.0 by reducing the positions for 1900 for precession and proper motion. The positions and proper motions for 1900 were taken from Hoffleit Dorrit , The bright star catalogue, 4th edn (New Haven, 1982). Corrections for refraction at 10°C and 760mm atmospheric pressure have been applied.

It should be noted that Tycho was not prevented from extending the earlier (777-star) catalogue to more southerly stars by want of a theory of a refraction. Tycho's investigation of the effect of refraction on the apparent places of the stars was concentrated in the year 1589 ( Dreyer , Tycho Brahe, 335–6). The position measurements for the 777-star catalogue were not completed until 1592. Moreoever, the printed version of the 777-star catalogue was accompanied by a table of refractions. ( Tycho , Progymnasmata, 280 = Opera omnia, ii, 287).