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During the reign of al-Ma'mun, and together with Khālid ibn ʿAbd al‐Malik al‐Marwarrūdhī, he participated in an expedition to the Plain of Sinjar to measure the length of a degree, or the circumference of the Earth.
Based on the measurements of the size of the Earth conducted by Riccioli of Bologna (at 321,815 Bologna feet to the degree), Mouton proposed a decimal system of measurement based on the circumference of the Earth, explaining the advantages of a system based on nature.
Following a proposition of Liu Zhuo from 604 AD, 10 of these were aligned along the meridian 114° east of Greenwich from Central Asia down to Vietnam in order to determine the circumference of the Earth and derivations from a perfect sphere.