Archimedes submerged the crown in a bucket of water until it overflowed, then calculated the volume of the water that was spilled.
Archimedes discovered that the crown really displaced more water than the gold lump of same mass. As a result, he came to the conclusion that the crown was not made of pure gold and that the goldsmith had, in fact, attempted to deceive the king by adding some silver (or other, lighter metal) to the gold.
Then, in order to confirm that the crown is actually composed of pure gold, he used a bar of pure gold of equal mass and compared the volume of spilled water.
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