Precision of Medieval Islamic Eclipse Measurements

Stephenson F. R. Said S. S. , “Non-tidal changes in the Earth's rate of rotation as deduced from medieval eclipse observations”, Astronomy and astrophysics , ccxv (1989), 181–9.

Ibn Yūnus Abū Al-Ḥasan ‘Alī ibn ’Abd al-Raḥmān (1008), al-Zīj al-Kabīr al-Ḥākimī, ms. Leiden Or. 143. A small part of this Zīj has been published and translated by Caussin C. , Le livre de la grande table Hakemite par Ebn Iounis (Paris, 1804), 16–240. For a biography of Ibn Yūnus and a discussion of his works, see King D. A. , “Ibn Yūnus”, Dictionary of scientific biography , xiv (New York, 1976), 574–80.

al-Battānī, Abū 'Abd Allāh Muḥammad ibn Jābir ibn Sinān (c. 910), al-Zīj al-Sābi, published and translated into Latin by Nallino C. A. , Al-Battānī sive Albatenii Opus astronomicum (Milan, 1899). For a biography of al-Battānī and a discussion of his works, see Hartner W. , “al Battānī”, Dictionary of scientific biography , i (New York, 1970), 507–16.

al-Bīrūnī, Abū-Raiḥān Muḥammad ibn Ahmad (1025), Kitāb Taḥdīd Nihāyāt al-Amākin li-Taṣḥīḥ Masāfāt al-Masākin (Ankara, 1962), 271–2; there is a translation into English entitled The determination of the co-ordinates of positions for the correction of distances between cities by J. 'Alī (Beirut, 1967) and an analysis by Kennedy E. S. : A commentary upon Bīrūnī's Kitāb Taḥdīd al-Amākin (Beirut, 1973). Also al-Bīrūnī (1030), al-Qānūn al-Mas'ūdī (3 vols, Hyderabad, Deccan, 1955), ii, 632 and 740–2. For a biography and discussion of the works of al-Bīrūnī, see Kennedy E. S. , “al-Bīrūnī”, Dictionary of scientific biography , ii (New York, 1970), 147–58.

See Al-Battānī , op. cit. (ref. 3); Al-Bīrūnī , op. cit. (ref. 4, 1955 and 1962).

See Ibn Yūnus , op. cit. (ref. 2).

Several examples of the use of observation to check the accuracy of contemporary eclipse calculations are found in the text of Ibn Yūnus ( ibid. ).

This quotation is from the translation of al-Bīrūnī's Kitāb Taḥdīd by 'Alī J. , op. cit. (ref. 4, 1967), 130. Immediately before this passage, al-Bīrūnī discussed the importance of lunar eclipses compared with solar obscurations in the determination of longitude differences. As he clearly recognized, the course of an eclipse of the Moon is independent of the observer's location whereas the local circumstances of an eclipse of the Sun vary considerably over the Earth's surface. Other allusions to the timing of lunar eclipses for the determination of longitude differences are cited by Al-Battānī , op. cit. (ref. 3) and Al-Bīrūnī , op. cit. (ref. 4, 1955).

The astrolabe was the most widely used astronomical instrument in medieval times. It served two main purposes: (i) as an observational device, in the determination of altitudes of celestial bodies; and (ii) as an analogue computing device, particularly for the determination of local time. For a detailed discussion of the astrolabe, see for example North J. D. , “The astrolabe”, Scientific American , ccxxx (1974), 96–106.

For detailed examples of the use of tables by medieval Muslim astronomers to convert from solar altitude to local time, see King D. A. , “Ibn Yūnus' very useful tables for reckoning time by the Sun”, Archive for history of exact science , x (1973), 342–94, esp. pp. 377–8. This article has been reprinted together with others on the same kind of tables for timekeeping in idem, Islamic mathematical astronomy (London, 1986).

In order to convert eclipse magnitudes from area to diameter or vice versa, the medieval Muslim astronomers may have used tables similar to those of Ptolemy, Almagest VI. See Toomer G. J. , Ptolemy's Almagest (London, 1984), 308.

See Ibn Yūnus , op. cit. (ref. 2), Al-Battānī , op. cit. (ref. 3), and Al-Bīrūnī , op. cit. (ref. 4, 1962).

This quotation is from the translation of al-Bīrūnī's Kitāb Taḥdīd by 'Alī (ref. 4, 1967), 131.

See Stephenson Said , op. cit. (ref. 1).

Newcomb S. , Washington observations for 1875 (Washington, 1878), App. II, 1.

Newton R. R. , Ancient astronomical observations and the accelerations of the Earth and Moon (Baltimore, 1970).

On the quantitative effect of refraction at the horizon as attributed to Ibn Yūnus, see King D. A. , op. cit. (ref. 10), 373–6.

Ptolemy , Optics V. 23–30.

See, for example, Allen C. W. , Astrophysical quantities (London, 1976), 124–5.

A quotation from the translation of al-Bīrūnī's Kitāb Taḥdīd by 'Alī (ref. 4, 1967), 130.

The reference to Johannes de Muris is found on p. 47 of Goldstein B. R. , “Theory and observation in medieval astronomy”, Isis , lxiii (1972), 39–47. This article is reprinted in idem, Theory and observation in ancient and medieval astronomy (London, 1985), article V.

This translation from Ibn Yūnus , op. cit. (ref. 2), is by ourselves.

Newton R. R. , “The Earth's acceleration as deduced from al-Bīrūnī's solar data”, Memoirs of the Royal Astronomical Society , lxxvi (1972), 99–128, pp. 108–9.

An analysis of Late Babylonian eclipse observations is given by Stephenson F. R. Morrison L. V. , “Long-term changes in the rotation of the Earth: 700 b.c. to a.d. 1980”, Philosophical transactions of the Royal Society of London, A, cccxiii (1984), 47–70.

In the fifteenth century, careful European observers such as Toscanelli and Walther began to achieve positional measurements accurate to 0.1°. See, for example, Celoria G. , “Sulle osservazioni di comete fatte da Paolo dal Pozzo Toscanelli e sui lavore astronomici suio in generale”, Publicazione di Reale Osservatorio Astronomico di Brera (Milan, 1921), no. 55; Kremer R. L. , “Bernard Walther's astronomical observations”, Journal for the history of astronomy , xi (1980), 174–91.

During the seventeenth century, European astronomers still preferred to time eclipses by measuring altitudes rather than relying on mechanical clocks. Numerous examples are cited by Pingré A-G. , Annales célestes du dix-septième siècle (Paris, 1783).

Babylonian examples of the use of ‘fingers’ in describing the magnitudes of eclipses are cited by Sachs A. J. Hunger H. , Astronomical diaries and related texts from Babylonia (Vienna, 1988), 24 and 249.

For details regarding the use of digits by the ancient Greeks when estimating eclipse magnitudes, see Ptolemy , Almagest VI, sec. 7–8.

In this (as yet unpublished) analysis of Babylonian eclipse magnitudes, we have used a manuscript translation of Babylonian eclipse records kindly supplied by Prof. P. J. Huber of Massachusetts Institute of Technology.

See Stephenson F. R. , “Some geophysical, astrophysical and chronological deductions from early astronomical records”, Ph.D. thesis, University of Newcastle upon Tyne (1972), 68.

Stephenson Said , op. cit. (ref. 1).