One morning he was thinking of this question while he was getting ready for a bath. The great bowl or tub was full to the very edge, and as he stepped into it a quantity of water flowed out upon the stone floor. A similar thing had happened a hundred times before, but this was the first time that Archimedes had thought about it. Anybody can see that I displaced a bulk of water equal to the bulk of my body. Now suppose, instead of putting myself into the tub, I had put Hiero's crown into it, it would have displaced a bulk of water equal to its own bulk.
Gold is much heavier than silver.
Ten pounds of pure gold will not make so great a bulk as say seven pounds of gold mixed with three pounds of silver. If Hiero's crown is pure gold it will displace the same bulk of water as any other ten pound of pure gold. But if it is part gold and part silver it will displace a larger bulk. Forgetful of everything else he leaped from the bath. The crown was tested.