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According to legend, King Hero of Syracuse commissioned a craftsman to make a crown out of a specific quantity of gold. After the crown was completed, the king heard a rumor that the craftsman had substituted silver for some of the gold he was given, thus devaluing the crown and stealing the rest of the gold for his own gain. Disturbed by the rumor, the king asked Archimedes to determine if the rumors were true.
Archimedes wasn't sure exactly how to determine whether the crown contained the correct amount of gold. Supposedly he was so distracted pondering a solution that he accidentally filled his bath to the rim. When he stepped in, the water overflowed. Suddenly it struck him. The crown would displace water too, in an amount equal in weight to the weight of the crown. A lump of gold the same mass as the one given the craftman should displace the same amount of water as the crown. If it doesn't, the crown is not pure gold. He ran through the streets of Syracuse naked shouting "Eureka!" on his way to test his new theory.
No one knows if Archimedes really ran naked through the streets of Sicily, but we do know that he successfully used this test or something very similar to it to determine that the king was cheated. This principle, called Archimedes' Principle, is formally stated as:
There exists a buoyant force within a fluid pushing on a submerged object equal in magnitude to the weight of that object.
It can be used to determine which materials will float in water. If the material is denser than water, items made from it have more mass than the water they displace and sink when placed in water. If the material is less dense than water, items made from it have less mass than the water they displace and float when placed in water. The ratio of the material's mass to the mass of water determines how much of the floating item is submerged; if the relative density of the material to water is 2/3, two thirds of the item made from it will be submerged.
Archimedes' Principle holds for any fluid, not just water. It can also be used to explain how hot air balloons float.
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