Remarks on the Theoretical Treatment of Eclipses in Antiquity

Cf. ACT, i; for this and other abbreviations see the appended bibliography.

Herodotus 1, 74.

See most recently Hartner [1], in which are presented and discussed all reasonable eclipse periods. The vagueness of Herodotus's report is emphasised in Neugcbauer [1], 142f., and its interpretation as evidence that Thales predicted the solar eclipse is discredited. For a third approach I can refer to v. d. Waerden [1], 86, and [2], 253.

The Saros of 223 synodic months is so excellent because not only is it very nearly a whole number of draconitic months (242), but also almost a whole number of anomalistic months (239) and only some ten days more than 18 years, so that return in both lunar and solar anomaly after a Saros is assured. These properties are, of course, not improved by tripling. The difficulty with the Saros resides in its excess over a whole number of days which is very nearly one-third of a day. Thus, given a lunar eclipse visible, say, in Babylon, we are quite sure of finding a corresponding lunar eclipse 223 months later, but it will occur about 8 hours later in the day and will be invisible in Babylon unless the first eclipse happened during the first third of the night. It is this that the tripling remedies. It is an impressive achievement that the Babylonian astronomers early recognised the excellence of the Saros, despite this awkwardness, and assigned it crucial rôles in their theoretical structures. For one such rôle of the Saros in Babylonian mathematical astronomy see Neugebauer [2] and, most recently, Aaboe [2], which has references to earlier relevant publications. For a history of the modern use of the term Saros see Neugebauer [1], 141f. A remark about terminology: When I use month without any qualifications, it denotes a synodic month, or a lunation, i.e., the time from new moon to new moon, or full moon to full moon. Further, draconitic month is the period of return of the Moon to the same node, or point of intersection between the lunar orbit and the ecliptic. Anomalistic month is the period of return in lunar velocity.

The Seleucid Era began in 312 B.C.

For the computation of the moment of syzygy in System A see, most recently, Aaboe [2].

Texts B, C, and D in Aaboe and Sachs [1].

For a description of this group of texts see Sachs [1].

These texts will be published shortly by Henderson J. , Neugebauer O. , Sachs A. , and myself.

I use here and elsewhere the standard manner of transcribing sexagesimal numbers: Sexagesimal digits are separated by commas, and integers and fractional parts by semicolons. It should be noted that when a semicolon occurs in transcriptions of cuneiform texts, it is always introduced by the transcriber, for it has no Babylonian equivalent.

This is a very natural step for anyone acquainted with the methods of Babylonian arithmetical astronomy.

I had occasion to inspect this tablet when working with cuneiform material in the British Museum in the autumn of 1971. This visit, as well as some of the work here presented, was supported by a grant from the National Science Foundation.

P. Carlsberg 31 is discussed in EAT, iii.1, 241f., and a photograph of it reproduced in EAT, iii, 2, as Plate 79A (it should be noted that in EAT, iii, 2 Plate 79A is identified, in error, as P. Carlsberg 32).

O. Neugebauer kindly checked the original photograph and there is, unfortunately, no doubt about this reading. The papyrus is very fragmentary, but “year” is preserved once completely, and four times partially. Since the structure of the text is so simple and obvious I have not bothered to indicate by brackets what is restored.

Sivin [1], 69. See also previously Eberhard [2], 9f. For Chinese astronomy of this period see Eberhard [1] as well.

BMR, 24; see further Aaboe [1].

The relations (i) and (ii) are called C and L*, respectively, in Hartner [1].

For the canonical relation 1 year = 12;22,8 syn. mo., see ACT, i, 45.

See v. d. Waerden [2], 153 as well as a forthcoming paper on Babylonian lunar latitude theory by Janice Henderson.

Published most recently, in Pinches's copy, as LBAT No. 1428 (see LBAT for references to earlier discussions). There is a difficulty about identification of obverse and reverse. My choice is consistent with the curvature of the text—usually a reliable guide—as well as with the groupings, while Sach's opposite choice in LBAT saves proper alignment of corresponding cohtmns on the two sides.

For a concordance between these Babylonian dates, in regnal years and months, and Julian dates, see PD³. Incidentally, this work has the Saros Canon as the only instance of dating by the reign of Antigonus (the One-Eyed) in the cuneiform literature, though other astronomical texts, still unpublished, also use this reign, among them B.M. 36754 mentioned below.

B.M. 36910 and B.M. 36754 will be included in the publication mentioned above in ref. 9. At present they are unpublished, though cited and described in LBAT, B.M. 36910 as No. *1422 + * 1423 + * 1424, and B.M. 36754 as No. *1430.

The latter text—the Solar Saros Text, as it has been called—and the Saros Canon overlap in time. Many of the months agree, but the five-month intervals are about half a subgroup out of phase in the two texts. Incidentally, the Solar Saros Text has a colophon saying ki-şa-ri śá […] which literally means the knots (i.e., nodes) for […] (A. Sachs).

It is trivial that texts such as these which give dates correctly in several reigns cannot have been written in advance of the events they describe, at least not in their entirety.

See Bernsen [1].

Aaboe [1]: Aaboe Asger , “On the Babylonian Origin of Some Hipparchian Parameters”, Centaurus, iv (1955), 122–5.

Aaboe [2]: Aaboe Asger , “Lunar and Solar Velocities and the Length of Lunation Intervals in Babylonian Astronomy”, Matematisk-fysiske Meddelelser K. Danske Videnskabernes Selskab, xxxviii, no. 6 (1971).

Aaboe & Sachs [1]: Aaboe Asger and Sachs Abraham , “Two Lunar Texts of the Achaemenid Period from Babylon”, Centaurus, xiv (1969), 1–22.

Bernsen [1]: Bernsen Lis , “On the Construction of Column B in System A of the Astronomical Cuneiform Texts”, Centaurus, xiv (1969), 23–28.

BMR: Kugler F. X. , Die Babylonische Mondrechnung (Freiburg im Breisgau, 1900).

ACT: Neugebauer O. , Astronomical cuneiform texts (3 vols, London, 1955).

EAT: Neugebauer O. and Parker R. , Egyptian astronomical texts (3 vols, London, 1960–69).

Eberhard [1]: Eberhard W. und Henseling Robert , “Beiträge zur Astronomie der Han-Zeit, 1”, Stizungsberichte der Preussischen Akademie der Wissenschaften, Philos.-hist. Klasse, xxiii (1933), 209–29.

Eberhard [2]: Eberhard W. (mit Rolf Müller und Robert Henseling), “Beiträge zur Astronomie der Han-Seit, II”, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Philos.-hist. Klasse, xxiii (1933), 937–79.

Hartner [1]: Hartner Willy , “Eclipse Periods and Thales' Prediction of a Solar Eclipse: Historic Truth and Modern Myth”, Centaurus, xiv (1969), 60–71.

LBAT: Late Babylonian astronomical and related texts copied by T. G. Pinches and J. N. Strassmaier. Prepared for publication by A. J. Sachs with the co-operation of J. Schaumberger (Providence, Rhode Island, 1955).

Neugebauer [1]: Neugebauer O. , The exact sciences in Antiquity (2nd ed., Providence, R. I., 1957; Dover reprint, 1969).

Neugebauer [2]: Neugebauer O. , “‘Saros’ and Lunar Velocity in Babylonian Astronomy”, Matematisk-fysiske Meddelelser K. Danske Videnskabernes Selskab, xxxi, no. 4 (1957).

Oppolzer: v. Oppolzer Th. , Canon der Finsternisse (Wien, 1887; Dover reprint, 1962).

PD⁸: Parker Richard A. and Dubberstein Waldo H. , Babylonian chronology 626 B.C.-A.D. 75 (Providence, Rhode Island, 1956).

Sachs [1]: Sachs A. , “A Classification of the Babylonian Astronomical Tablets of the Seleucid Period”, Journal of cuneiform studies, ii (1948), 271–90.

Sivin [1]: Sivin N. , “Cosmos and Computation in Early Chinese Mathematical Astronomy”, T'oung Pao, Iv (1969), 1–73.

v. d. Waerden [1]: van der Waerden B. L. , Science awakening (London and New York, 1961).

v. d. Waerden [2]: van der Waerden B. L. , Anfänge der Astronomie (Groningen, 1966).