How the Hydrostatic Balance Works

A hydrostatic balance uses the same physical principle Archimedes is said to have discovered in his bath: an object submerged in water displaces a volume of water equal to its own volume, and the water pushes back against the object with a buoyant force equal to the weight of that displaced water. Weighing an object twice is what makes the principle usable: first the object is weighed normally, in air, giving its true weight, and then it is weighed again while fully submerged in water, hanging from the balance on a fine thread so the water can support none of the balance mechanism itself.

The submerged weight comes out lower than the weight in air, by an amount exactly equal to the buoyant force the displaced water exerts, and that difference between the two readings is directly proportional to the object's volume. Dividing the object's true weight in air by that difference gives its specific gravity, a number that reveals its density relative to water and, crucially, lets an assayer tell a genuine gold or silver object from one debased with a cheaper, less dense metal, without having to melt it down or damage it in any way. Al-Khazini's balance extended this basic method with as many as five pans and multiple graduated scales, letting a single instrument test several substances or compare several density standards at once.