Archimedes (c. 287–c. 212 B.C.E.) lived in the city of Syracuse on the island of Sicily, then part of Greece. He was charged by the king of Sicily to find out if his crown was made out of pure gold, or an alloy of gold and silver. Archimedes had to do this without destroying the crown. One day, when bathing in the public baths he noticed that when he stepped into the bath the water rose! He had seen this many times before, but this time he recognized that this common occurrence could help him solve his problem. Legend has it that he was so excited that he ran naked through the streets of Syracuse shouting “Eureka!” or “I have found the answer!”

He then did experiments where he hung the crown on one end of a balance and a piece of first gold and then silver from on the other end. When the weight of the crown and that of the metal were equal the balance was horizontal. He then immersed the balance in water. If the crown and the metal had different volumes, the water they displaced would be different and the balance would tip. He found that the balance tipped when both the silver and gold pieces were on the balance. Archimedes had found that the crown was not pure gold, but a mixture of silver and gold. The king had been cheated!

Archimedes had discovered a principle of hydrostatics (liquids at rest) that would one day carry his name: Archimedes’ Principle states that an object immersed in a fluid will experience a buoyant force equal to the weight of the displaced fluid.