In the last post, we explored the 1925 paper by Vogt that attempted to reverse engineer entries from the presumed Hipparchan star catalog. Assuming that the coordinates derived were actually representative of such, Vogt demonstrated that Ptolemy was unlikely to have based his catalog on that of Hipparchus.
Continuing in the theme of defending Ptolemy, we’ll explore three more texts which come to Ptolemy’s defense: a book by Gundel (1936), a paper by Pannekoek (1955) and a paper by Petersen & Schmidt (1968).
Gundel
In 1936, Wilhelm Gundel published Neue Astrologische Texte des Hermes Trismegistos (New Astrological Text of Hermes Trismegistos). The work Gundel was reviewing was a collection of early Hermetic writings on astrology that he found in the British archives and reviewed. The source text was dated to $1431$ but was a collection of older works. The important chapter for our context was the third one which was “On the Bright Stars & Qualities of Signs”. In it was listed $68$ bright stars, with their ecliptic longitudes given (with one exception) in whole number of degrees.
By reviewing the descriptions and naming conventions of the constellations, Gundel concluded that the list of stars dated to the time of Hipparchus or earlier, matching the descriptions in the Commentary on Aratus.
Gundel then attempted to date the stars in the catalog by another method: Comparison with the Almagest. He found that $22$ of the stars had a longitude between $2;20º – 2;50º$ smaller than the same star in the Almagest. Gundel made the rather lazy assumption that this must place them from the “time of Hipparchus or his students.” However, there are other stars which have an even larger divergence from the Almagest, with a difference in longitude of $3;00º-3;40º$ which Gundel assumes must have been from an even earlier generation of astronomers, perhaps from Timocharis or Arstyllos.
If true, this had two implications. The first was that it would represent a portion of the lost catalog of Hipparchus potentially being discovered, although in a truncated form since it lacked ecliptic latitudes and was rounded to whole degrees. It would also indicate that Hipparchus was not the first astronomer to compile such a catalog.
However, Neugebauer in his The Exact Sciences in Antiquity, reviewed the determination of dates for the stars and found, that $96.5\%$ of the stars could be dated from $130-60$ BCE, making an even stronger case that this was a truncated form of the Hipparchan catalog.
Obviously, since Gundel was already making the simplistic assumption that the dates could be determined by comparison to the Almagest, a deeper comparison was not going to be conducted. However, Grasshoff did explore this later in his History of Ptolemy’s Star Catalog which I will cover later.
Pannekoek
In $1955$ Anton Pannekoek published a short paper entitled Ptolemy’s Precession. This paper has two conclusions.
Firstly, Pannekoek agrees with Delambre that Ptolemy cherry-picked his data to arrive at a desired conclusion and adds a new argument to illustrate the point. He notes that Ptolemy quotes Hipparchus on the position of Spica, stating it had increased by $2º$ between the time of Timocharis and Hipparchus. This provides another potential data point to determine the value of precession – one which would have given the correct value for the rate of precession and Ptolemy ignored.
Pannekoek also conducts an investigation into the distribution of errors in the declination of Vogt’s reconstructed Hipparchan catalog compared with that of Ptolemy’s. He finds that Hipparchus’ values have a notably smaller standard deviation than Ptolemy’s, indicating Ptolemy’s were likely derived independently.
Petersen & Schmidt
The final paper we’ll explore in this post is a $1968$ paper by Petersen and Schmidt on the Determination of the Longitude of the Apogee of the Orbit of the Sun According to Hipparchus and Ptolemy. Ptolemy’s solar model is believed to be no different than that of Hipparchus’. Ptolemy walked us through the calculation of the position (in ecliptic longitude) of the solar apogee in this post. In it, the important parameters were the length of the spring and summer which Ptolemy reports as $94 \frac{1}{2}$ days and $92 \frac{1}{2}$ days respectively.
Petersen and Schmidt compare these values with the true values (calculated using modern astronomy) for the lengths of each season in both Hipparchus’ time and Ptolemy’s and finds they agree better with those of Hipparchus. They then conclude that this, with the addition of the slightly incorrect value used for the length of the year resulted in a significantly incorrect value for Ptolemy’s value for the position of the solar apogee. He found it to be at $65;30º$ ecliptic longitude ($5;30º$ into Gemini) whereas the true value in Ptolemy’s time was $71;09º$1. Continuing this forward through the calculations necessary to determine the mean solar position, Petersen and Schmidt come to the same conclusion as Fotheringham: Ptolemy’s mean solar position was $1;06º$ low, which eliminates the underlying argument linking Ptolemy’s work to Hipparchus’.
Conclusion
There’s still much more to go in this discussion. In the next post, we’ll be discussing R. R. Newton’s book, The Crime of Claudius Ptolemy, which if the title does not make obvious, sides strongly with the notion that Ptolemy’s data was faked, as well as the criticism of this work.
- This had been previously noted by Manitus who had done a German translation of the Almagest, but Petersen and Schmidt do note that this was not Ptolemy’s fault. The inherent uncertainty in the observations necessary for these computations stacks up quickly. When properly analyzed, Ptolemy’s value would have had an error of $\pm14º$ putting his value well within reasonable error.