The Crown Krater

LITVitruvius (De Architectura IX) tells that Archimedes, in the bath, saw how to test Hiero's crown by the water it displaces, and ran out shouting heureka. In 1586 Galileo (La Bilancetta) argued the overflow method was too crude, and that Archimedes would more likely have weighed the crown in water on a balance. Both methods use the same fact: gold (Au, 19.32 g/cm³) is denser than silver (Ag, 10.49 g/cm³).

MODELThe goldsmith has made a 1 kg crown with a secret silver fraction. Measure it again and again, with the noise of a real vessel and a real balance. The estimate emerges from the measurements; watch which method closes on the truth first.

overflow test (Vitruvius)balance in water (Galileo)new crownreveal

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