Al-Biruni: Coordinates of Cities

In the book by David A King and Mary Helen Kennedy (eds.), Studies in the Islamic exact sciences. Reprints of papers by E S Kennedy, colleagues and former students (American University of Beirut, 1983) there is an account of survey taken from Coordinates of Cities by al-Biruni.


We know that the Hellenistic stade is approximately 600 feet but this was not known to the caliph al-Mamun. As al-Biruni says in his Coordinates of Cities, al-Mamun:-

... read in some Greek books that one degree of the meridian is equivalent to 500 stadia ... However, he found that its actual length [i.e. the stade's] was not sufficiently known to the translators to enable them to identify it with local standards of length.

Thus al-Mamun ordered a new survey to be made on the large, level plain of Sinjar some 70 miles west of Mosul, and two surveying parties participated. Starting from a common location one party travelled due north and the other due south. In the words of al-Biruni:-

Each party observed the meridian altitude of the sun until they found that the change in its meridian altitude had amounted to one degree, apart from the change due to variation in the declination. While proceeding on their paths, they measured the distances they had traversed, and planted arrows at different stages of their paths (to mark their courses). While on their way back, they verified, by a second survey, their former estimates of the lengths of the courses they had followed, until both parties met at the place whence they had departed. They found that one degree of a terrestrial meridian is equivalent to fifty-six miles. He (Habash) claimed that he had heard Khalid dictating that number to Judge Yahya b. Aktham. So he heard of that achievement from Khalid himself.

Again one sees an Islamic side to this project in the involvement of a jurist, for the law was the Islamic religious law and in this case the jurist was the chief justice of Basra, Yahya b. Aktham. Al-Biruni goes on to say that a second result was also obtained by the survey, namely 56 2/3 miles/degree, and in fact al-Biruni uses this value in his own computations later on.


JOC/EFR March 2006

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