The Eureka Moment

Around 250 BCE, King Hiero II suspected his goldsmith had cheated him — mixing silver into a supposedly pure gold crown. He asked Archimedes to investigate without damaging the crown. The solution came in the bath.

Since gold is denser than silver, a gold crown displaces less water than a gold-and-silver one of equal weight. The bath-overflow story is popular legend; the more workable test is hydrostatic weighing, comparing the crown's weight in air with its apparent weight underwater. That buoyancy principle still governs how engineers design every vessel that floats.