PhD Candidate, Institute for the History of Science, University of Tehran
10.22059/jihs.2026.415777.371910
Abstract
This study examines a depth-sounding procedure described by the mathematician Abū Bakr ibn Abī ʿĀbis in the opening section of his treatise fī Akhdh al-abʿād (On the Determination of Distances). Whereas conventional ancient and medieval depth-sounding relied on direct linear measurement, Ibn Abī ʿĀbis proposed an indirect procedure based on a hollow metal ball, a detachable weight, and a pengān . The instrument was first operated at a known depth to establish a reference value from the quantity of water collected during the ball's descent and ascent. The quantity obtained in a subsequent trial at an unknown depth was then compared with this reference value, and the depth was inferred through proportional calculation. This article reconstructs the operation of the instrument and examines its measurement procedure in relation to earlier depth-sounding practices and broader traditions of indirect measurement. It argues that the historical significance of Abī ʿĀbis’s procedure lies not in the invention of his instrument but in the combination within a reference-based method of indirect measurement, in which the duration of a body's motion serves as a proxy for an inaccessible linear distance. No equivalent procedure has been identified in the earlier Greek, Roman, or Arabic sources consulted for this study. Although this does not establish absolute historical priority, the treatise preserves an unusually early description of an indirect determination of water depth.
Kiani Movahed,R . (2026). A Duration-Based Procedure for the Indirect Determination of Water Depth in the Abū Bakr ibn Abī ʿĀbis's treatise. (e108150). Journal for the History of Science, (), e108150 doi: 10.22059/jihs.2026.415777.371910
MLA
Kiani Movahed,R . "A Duration-Based Procedure for the Indirect Determination of Water Depth in the Abū Bakr ibn Abī ʿĀbis's treatise" .e108150 , Journal for the History of Science, , , 2026, e108150. doi: 10.22059/jihs.2026.415777.371910
HARVARD
Kiani Movahed R. (2026). 'A Duration-Based Procedure for the Indirect Determination of Water Depth in the Abū Bakr ibn Abī ʿĀbis's treatise', Journal for the History of Science, (), e108150. doi: 10.22059/jihs.2026.415777.371910
CHICAGO
R Kiani Movahed, "A Duration-Based Procedure for the Indirect Determination of Water Depth in the Abū Bakr ibn Abī ʿĀbis's treatise," Journal for the History of Science, (2026): e108150, doi: 10.22059/jihs.2026.415777.371910
VANCOUVER
Kiani Movahed R. A Duration-Based Procedure for the Indirect Determination of Water Depth in the Abū Bakr ibn Abī ʿĀbis's treatise. JHS. 2026;():e108150 (In Persian). doi: 10.22059/jihs.2026.415777.371910