According to legend, King Syracuse had craftsmen make him a pure gold crown. But after the completion, the king suspected that the gold crowns made by craftsmen were not all gold, but as heavy as the pure gold given to the goldsmith at the beginning. Did the craftsman steal gold? The problem of trying to test the authenticity without destroying the crown not only stumped the king, but also made the ministers look at each other. At the suggestion of a minister, the king invited Archimedes to test it. At first, Archimedes thought hard, but he could do nothing. One day, he was taking a bath at home. When he was sitting in the bathtub, he saw the water overflowing and felt his body being gently lifted. He suddenly realized that the proportion of gold crowns can be determined by measuring the displacement of solids in water. He jumped out of the bathtub excitedly and ran out naked, shouting "Eureka! Eureka! " . (Eureka, meaning "I saw it". Greek: ε? ρηκα)。

After further experiments, he came to the palace. He put the crown and pure gold with the same weight in two jars filled with water, and compared the water overflowing from the two jars, and found that the jar with the crown overflowed more water than the other jar. This shows that the crown is larger in volume and different in density than pure gold with the same weight, so it proves that other metals are mixed in the crown.

The significance of this experiment is far greater than finding out that the goldsmith cheated the king. Archimedes discovered the law of buoyancy (Archimedes principle): the buoyancy of an object in a liquid is equal to the weight of the liquid it discharges. Until modern times, people are still using this principle to calculate the specific gravity of objects and determine the load capacity of ships.