Precision of Medieval Islamic Measurements of Solar Altitudes and Equinox Times

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. Also idem, Ancient planetary observations and the validity of Ephemeris Time (Baltimore and London, 1976).

Bretagnon P. , “Théorie de mouvement de l'ensemble des planètes: Solution VSOP 82”, Astronomy and astrophysics , cxiv (1982), 278–88.

ibn Qurra, Thābit al-Ṣābi'al-Ḥarrānī. The Arabic treatise “On the solar year” by ibn Qurra has been edited and translated into French (together with other astronomical works of ibn Qurra) by Régis Morelon, Thābit ibn Qurra oeuvres d'astronomie (Paris, 1987). We have taken all the observations from this text. In addition, we have consulted the Latin translation in Carmody F. J. , The astronomical works of Thābit B. Qurra (Los Angeles, 1960), and an English rendering from the Latin by Neugebauer O. : “Thābit Ben Qurra on the solar year and on the motion of the eighth sphere”, Proceedings of the American Philosophical Society , cvi (1962), 264–99. For a biography and discussion of the work of Ibn Qurra, see Rosenfeld B. A. Grigorian A. T. , “Thābit ibn Qurra”, Dictionary of scientific biography , xiii, 288–95.

al-Battānī, Abū ‘Abd Allāh Muḥammad ibn Jābir ibn Sinān, al-Zīj al-Ṣābi’ (c. 910), published and transl. into Latin by Nallino C. A. , Al-Battānī sive Albateniii opus astronomicum , iii (Milan, 1899). For a biography of al-Battānī and a discussion of his works, see Hartner W. , “al-Battānī”, Dictionary of scientific biography , i, 507–16.

Ibn Yūnus, Abū al-Ḥasan ‘Alī ibn ’Abd al-Raḥmān, al-Zīj al-Kabīr al-Ḥākimī (c. 1008), ms. Leiden, Or. 143. A small part of the zīj has been published and transl. into French 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, 574–80.

al-Bīrūnī, Abū-Raiḥīn Muḥammad ibn Aḥmad, Kitāb Taḥdid Nihāyāt al-Amākin li-Taṣḥīḥ Masāfāt al-Masākin (1025), ed. by Al-Tanjī M. T. (Ankara, 1962); also edited by Bulgakov P. G. (Cairo, 1962); this work has been referred to as ‘6a’ in the various tables. 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, al-Qānūn al-Mas'ūdī (1030), edited by Nizamu M. 'd-Dīn (3 vols, Hyderabad-Deccan, 1955); this work has been referred to as ‘6b’ in the various tables. We are not aware of any translation of this work. For a biography of al-Bīrūnī and a discussion of his works, see Kennedy E. S. , “al-Bīrūnī”, Dictionary of scientific biography , ii, 147–58.

Newton , “The Earth's acceleration” (ref. 1).

Freeman-Grenville G. S. P. , The Muslim and Christian calendars (Oxford, 1977).

1:1,000,000 maps in the Map Library at the University of Newcastle upon Tyne.

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The Times atlas of the world , 6th edn (London, 1980).

Newton , “The Earth's acceleration” (ref. 1).

Kennedy , A commentary (ref. 6), 7 and 29.

On the quantitative effect of refraction at the horizon attributed to ibn Yūnus, see King D. A. , “Ibn Yūnus' very useful tables for reckoning time by the Sun”, Archive for history of exact science , x (1973), 373–6. This article has been reprinted together with others on the same kind of tables for timekeeping in idem, Islamic mathematical astronomy (London, 1986).

Newton , “The Earth's acceleration” (ref. 1).

Ibid. .

Allan C. W. , Astrophysical quantities (London, 1976), 124–5.

Bretagnon , op. cit. (ref. 2).

Stephenson F. R. Morrison L. V. , “Long-term fluctuations in the Earth's rotation: 700 B.C. to A.D. 1990”, Philosophical transactions of the Royal Society , ser. A (in press).

al-Battānī, al-Zīj al-Ṣābi' (ref. 4), 18, 215–17.

A full description of al-Khujandī's sextant is given by al-Bīrūnī in his short treatise entitled “Ḥikāyat al-ālat al-musammāt al-suds al-fakhrī”, edited by Louis Cheikho in al-Mashriq , xi (Beirut, 1908), 68–69. This treatise has been copied, with minor changes, by the later astronomer Abū'l-Ḥasan' Alī al-Marrākushī. For the text of this work, along with a French translation, see Sedillot L. A. , “Les instruments astronomiques des Arabes” in Memoires presentés a l'Académic Royale des Inscriptions et Belles-lettres , première sér., i (Paris, 1844), 202–6.

al-Khujandī, Abū Maḥūd Ḥāmid ibn al-Khiḍr, “Risāla fī taṣḥīḥ al-mayl wa ‘arḍ al-balad”, edited by Louis Cheikho, in al-Mashriq , xi (Beirut, 1908), 60–68.

al-Bīrūnī, Kitab Tahdid (rcf. 6).

Ibn ‘Iṣmat (al-Samarqandī) of Balkh made corrections to two measurements of meridian altitude that he made around the winter solstice in A.D. 888 and the summer solstice in 889. His original measurements, made on 888 Dec 14 and 889 Jun 17, were respectively 29;46° and 76;54°. Firstly he interpolated each of his measurements to obtain the extreme meridian altitude at the solstice itself. He adjusted his winter value by −0;1,16° and his summer measurement by +0;0,4° — leading to results of 29;44,44° and 76;54,4° respectively. Our calculations show that the winter measurement was made roughly 2 days, 5 hours early (presumably unfavourable weather prevented observation in the next few days) so that the true correction should have been −0;1,8°. The summer measurement was made only about 6.5 hours early so that here the amendment should have been 0;0,1°. Hence both corrections are remarkably accurate.

al-Samarqandī made an additional correction for solar parallax to each of his revised results in order to obtain a supposedly improved value for the obliquity of the ecliptic. These corrections are presumably made on the Ptolemaic assumption that the geocentric parallax of the Sun was 3 arcmin. For the revised winter solstice meridian altitude, al-Samarqandī made an adjustment of +0;2,33,6° (to 29;47,17,6°). For the following summer solstice measurement he used the much smaller amendment of 0;0,37,23°. The principle is sound, but of course the true solar parallax (0;0,8,48° arcsec) is negligible.

In our subsequent investigation we have adopted only the two measured meridian altitudes by al-Samarqandī: 29;46° on 888 Dec 15 and 76;54° on 889 Jun 17. None of the solar altitudes measured by other medieval astronomers which we investigate here contains any parallax correction.

al-Bīrūnī, Kitāb Taḥdīd (ref. 6).

Ibn Yūnus, op. cit. (ref. 5).

Stephenson F. R. Said S. S. , “Precision of medieval Islamic eclipse measurements”, Journal for the history of astronomy , xxii (1991), 195–207, pp. 199, 202–3. In this paper were also cited preliminary values for the errors in meridian altitudes — ranging from about 0°.01 to 0°.05.

Newton , “The Earth's acceleration” (ref. 1).

Caussin , Le livre de la grande table Hakemite (ref. 5).

For a biography of Yaḥyā and a discussion of his works, see Vernet J. , “Yaḥyā ibn Abī Manṣūr”, Dictionary of scientific biography , xiv, 537–8. Yaḥyā was appointed director of a group of scholars making observations at Baghdād and Dimashq observatories.

al-Khujandī, “Risāla” (ref. 22).

al-Bīrūnī, Kitāb Taḥdīd (ref 6).