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Eureka — I have found it. I stepped into the bath and observed the water rise. I had been tasked with determining whether King Hiero's crown was pure gold or alloyed with silver without damaging it. The solution presented itself: a body submerged displaces a volume of water equal to its own volume. Gold and silver have different densities; the same weight of each displaces different volumes. The crown's purity could be measured without touching its substance. I ran home without clothes. The discovery seemed more important than the clothing.