Al-Biruni Measures the Earth
The Islamic Golden AgeThe Number That Needed Legs
Around 830 the caliph al-Ma'mun wanted the size of the Earth, and ran into a translation problem. Ptolemy had given a figure in stades; asked how long a stade was, his scholars disagreed, so the number was useless. He sent surveyors into the flat plain of Sinjar, west of Mosul, instead — Khalid ibn Abd al-Malik al-Marwarrudhi with one party, Ali ibn Isa al-Asturlabi and Ahmad ibn al-Buhturi with another — walking north and south with carpenters and brass-workers along to keep the instruments true. They stopped where the noon Sun had shifted by one degree, planted arrows, and measured back. The surviving reports of their answer differ: 56, 56¼, 56⅔ and 57 Arabic miles to the degree. The one that became standard in later Arabic geography, 56⅔, works out close to the truth.
A Man Who Did Not Want to Walk
Two centuries later Abu Rayhan al-Biruni set out to check that figure. Born at Kath in Khwarazm in 973, he was carried off to Ghazna after Mahmud of Ghazni swallowed his homeland in 1017 — honoured guest or something closer to a hostage is still argued over, and he never said plainly. He tried walking first, on ground near Dahistan by the Turkish frontier, and gave it up: the work needed command over huge tracts of desert, he wrote, and then his backers lost interest. Then, at the fort of Nandana in the Punjab's Salt Range, at the southern end of a pass down onto the Indian plain, he found a peak looking south over ground so level that its flatness, in his phrase, served him as the smooth surface of the sea.
One Hill, Two Angles
He fixed the peak's height the ordinary way, by sighting the summit from two points a measured distance apart, and made it a little over 652 cubits — something like 320 metres above the plain. He then climbed it and measured how far the line to the horizon sagged below level: 34 minutes of arc, a little over half a degree. Those two numbers are enough. The Earth's centre, the summit and the far horizon form one enormous right triangle, and the sine law squeezes the radius out of it. He set the result down at Ghazna around 1025, in a book whose real subject was finding the direction of Mecca. Which peak he climbed is still argued over.
How Close, Honestly
His answer came to roughly 12.8 million cubits — and whether that is a triumph depends entirely on the cubit. Convert with the 493-millimetre 'black cubit' and you land near 6,340 km against a modern mean radius of 6,371; use an 18-inch or a 22-inch cubit and the figure swings by hundreds of kilometres. Two more problems sit under the celebrated accuracy. The sine value in his own tables was slightly off, and cleaning up the arithmetic moves his result away from the truth rather than towards it. And the horizon dip is bent by refraction — known as a phenomenon, but not yet correctable — while a single arcminute of dip shifts the answer by hundreds of kilometres. Al-Biruni did not treat his hill trick as an improvement on the survey. When he came to write his great astronomical encyclopedia years later, the figure he carried forward was the Sinjar one, not his own.
The Book That Marks Its Own Gaps
About 1030 he finished the other work of these years, Tahqiq ma li'l-Hind — a verification of what is said about India, whether rationally acceptable or not. He learned Sanskrit in middle age, worked through Aryabhata, Varahamihira and Brahmagupta, and put Patanjali's yoga aphorisms into Arabic; the traffic ran both ways, and he says he rendered Euclid's Elements, Ptolemy's Almagest and his own book on the astrolabe into Sanskrit. Where he disagreed he named the man: he went after Brahmagupta not for getting eclipses wrong but for knowing better and deferring to the tale of a demon swallowing the Sun. Where he was lost he said so — and he blamed his own side, writing that Mahmud had ruined the country and driven Indian learning beyond his reach.
Key Dates to Remember
- c. 830 — Al-Ma'mun's surveyors measure one degree of latitude on foot in the plain of Sinjar, west of Mosul.
- 1017 — Mahmud of Ghazni annexes Khwarazm; al-Biruni leaves for Ghazna, which stays his base for the rest of his life.
- c. 1025 — He completes his book on fixing the coordinates of places, which records the horizon-dip measurement made at Nandana.
- c. 1030 — Tahqiq ma li'l-Hind is finished, the same year Mahmud of Ghazni dies and his son Mas'ud takes the throne.
- 1048 — Al-Biruni dies at Ghazna, aged about 75; a few sources place his death two years later.