Hydrostatic Balance

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.

The physical principle behind the hydrostatic balance, that a submerged object displaces its own volume of water and is buoyed up by the weight of that displacement, is credited to Archimedes in the third century BCE, but building an instrument sensitive enough to put that principle to reliable, repeatable use took much longer. Al-Khazini's Book of the Balance of Wisdom, completed in 1121, is the fullest early treatise on the subject, an encyclopedic work of eight books and fifty chapters covering the theory of statics and hydrostatics behind the hydrostatic balance and describing his own instrument, a five-pan balance spanning roughly two meters, alongside the instruments of his predecessors, including al-Biruni's pycnometer flask.

Al-Biruni and al-Khazini are recognized by historians of science as among the first to bring genuinely experimental precision to the study of specific weights, synthesizing earlier Greek and Islamic theory into a working, repeatable measurement method. That method needed no further reinvention to remain useful into the modern era: determining an object's specific gravity by weighing it in air and then in water is still exactly how density measurements are made in chemistry, mineralogy and materials science laboratories today, using more precise instruments but the identical two-weighing principle al-Khazini set out in the twelfth century.