Archimedes made two masses of the same weight as the
crown, one of gold and the other of silver.
He filled a large vessel with water to
the very brim,
and dropped the mass of silver into it.
The amount of water that overflowed was equal in volume to that of the silver mass sunk in the vessel.
Archimedes refilled the vessel and dropped the mass of gold into the full vessel.
Not as much water overflowed because gold is more dense than silver, so the same weight takes up less volume.
Finally, Archimedes filled the vessel again and dropped the crown itself into the water.
He found that more water overflowed for the crown than for the mass of gold of the same weight.
Hence, reasoning from the fact that more water was lost in the case of the crown than in that of the gold mass, he detected the mixing of silver with the gold, and made the theft of the contractor perfectly clear.
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