Weighing water to compare materials

For each instrument, say what is weighed, what it is compared with, and what could make the result wrong. Where does the word density fit?

How do you find the volume of a small, uneven stone? The Balance of Wisdom transmits a conical vessel attributed to Abu Rayhan al-Biruni. It directs displaced water through a side tube into a balance pan ². Weighing that water enables a comparison of sample volume and weight, but the tube introduces a problem: drops can remain inside it ². The transmitted text itself reports water remaining in the tube and dripping slowly, followed by a drainage refinement ².

The records do not say why al-Biruni designed the vessel. They show what the measurement was used for. Ansari relates mineral and gem identification and valuation to properties including density, brilliance and hardness, rather than colour alone ³.

"Specific gravity" is not a force. Here it means a ratio to reference water, not gravitational force or a universal constant ⁴. In the same way, specific gravity concerns comparative material density, not the weight of an individual lump ⁵. And old units are not modern ones: Ansari explicitly declines a gram conversion for the mithqal because reference values vary ⁶.

The picture is a print, not the vessel. Our image is printed page 54 of Khanikoff's publication: it is neither an original surviving object nor an autograph drawing ². The 2023 reconstruction of the apparatus witnesses modern construction, not survival from the eleventh century ⁷.

Suppose some of the displaced water stays in the side tube and never reaches the pan. Would the density worked out from the pan's water come out too high or too low, and why, using the words weight, volume and water?

• Al-Biruni's displacement vessel: the conical vessel, its side tube and its problem.
• The balance of wisdom: a balance that compares weight in air and in liquid.
• Al-Biruni: the scholar to whom the vessel is attributed.