Notes on the Compilation of Ptolemy's Catalogue of Stars

Grasshoff Gerd , Die Geschichte des Ptolemaeischen Sternenkatalogs (doctoral dissertation, University of Hamburg, 1986), 147–203.

Evans James , “On the origin of the Ptolemaic star catalogue”, Journal for the history of astronomy, xviii (1987), Part 1, 155–73; Part 2, 233–78.

Shevchenko M. , “An analysis of errors in the star catalogues of Ptolemy and Ulugh Beg”, Journal for the history of astronomy, xxi (1990), 187–201.

Evans formulated this statement after looking at Grasshoff's charts illustrating the patterns of error in constellations ( Evans , op. cit., 276, n. 63). Shevchenko's (op. cit., 188–90) attempt at proving it was indecisive.

See Shevchenko , op. cit., 190. Evans has reached a weaker conclusion, that Spica appeared more likely than Regulus to have been used as a reference star in the observation of zodiacal constellations; cf. Evans , op. cit., 244–5.

Shevchenko , op. cit., 194–5, Figures 3 and 4.

Grasshoff , op. cit., 153–5. He did this by examining the distribution of errors in latitude and longitude according to the order of stars in the catalogue. But as constellations in the Almagest are not listed in the order of observation, the conclusions of Grasshoff are incomplete and problematical.

Shevchenko , op. cit., 190.

Shevchenko (op. cit., 192) also tried to find other groups, although without reaching definite conclusions. Evans argued that only a few fundamental stars were required to produce the whole catalogue (op. cit., 248–9).

I wish to thank Jerzy Dobrzycki for drawing my attention to this point and for making available computer subroutines employed here.

See e.g. Bakulin P. I. , Fundamental catalogues of stars (Moscow, 1980), 26–29 (in Russian).

Cf. Shevchenko , op. cit., Tables 2 and 3.

For a detailed discussion of the problem see Kremer R. , “Bernard Walther's astronomical observations”, Journal for the history of astronomy, xi (1980), 174–91, pp. 182–5; Włodarczyk J. , “Observing with the armillary astrolabe”, ibid., xviii (1987), 173–95, p. 183.

The “group of −89′” is formed by τ, β, α, φ, γ, φ, ζ, ι, and δ Aql; β, α, η, ζ, and θ Del. The rest of stars belong to the “group of —33′”. κ Aql, with the error of +43′, was not taken into account.

Shevchenko , op. cit., Table 3.

Two hours before the setting of Regulus the stars with the mean error of −89′ were 6°–7°, whereas the stars with the error of −33′ were 3°–5°, above the horizon.

Surprisingly, one finds it hard to distinguish a group of constellations referred to Antares (–71′), the most obvious candidate for a reference star subsequent to Spica.

However, the ecliptical latitude of α PsA amounts to −20°20′, whereas the latitude of α Cet is only −12°20′. Thus, the latter rather than the former was one of “stars near the ecliptic”. Cf. Toomer G. J. , Ptolemy's Almagest (London, 1984), VII. 2, 328.

Almagest, ibid.

We may suppose that the mean error of −44′ has arisen from measuring one part of Capricornus in reference to β Cap, and the second using α Cap. Both stars have the same longitude in Ptolemy's catalogue, and were used by him in planetary observations, cf. Almagest, ed. cit., X.2, 471.

As has been shown above, the almost negligible (–4′) error in the longitudes of the stars of Lepus, noted by other authors as a peculiarity of Ptolemy's catalogue (see Grasshoff , op. cit., 165–6), resulted from the dependence of the error in longitude upon the ecliptic latitude.

The estimation of Newton based upon the longitudes of all zodiacal stars gives a standard deviation equal to 22.3′, cf. Newton R. R. , The crime of Claudius Ptolemy (Baltimore, 1977), 216–17.

Kremer , op. cit., 180.

Newton , op. cit., 245–54; Newton R. R. , “On the fractions of degrees in an ancient star catalogue”, The quarterly journal of the Royal Astronomical Society, xx (1979), 383–94. For an explanation of causes of the 40′ shift different from that of Newton, see Evans , op. cit., 239–49.

See ref. 6.

Because of the low size of the samples, the distributions are very sensitive to such anomalies as, e.g., the very large number of longitudes at 0′ in the group of unfigured stars of Taurus: There are nine, out of eleven, stellar longitudes at 0′. They are responsible for the significantly larger number of 0′s than 20′s in B2.

The possibility of such a division of a scale was first considered by Vogt, but in regard to the whole set of longitude data. See Vogt H. , “Versuch einer Wiederherstellung von Hipparchs Fixsternverzeichnis”, Astronomische Nachrichten, ccxxiv (1925), cols 17–54.

For details see Newton , The crime …, 250–2.

This explanation was suggested by Dobrzycki Jerzy .

Cf. Evans , op. cit., 247–9.