He filled the bowl with water to the brim a final time, taking care to fill it with exactly the same amount of water as before. This time he lowered the crown into the water. He knew that if the crown was pure gold, its volume would be the same as that of the lump of gold (which he had made sure weighed the same as the crown), regardless of shape, and that it would displace the same amount of water as the gold. But, if the goldsmith had replaced some of the gold with silver, then the volume of the gold+silver crown would be greater than the volume of the gold, and so the crown would displace more water than the gold.

Archimedes found that the crown did, in fact displace more water than the lump of gold of equal weight. Thus he came to the conclusion that the crown was not pure gold, and that the goldsmith had indeed mixed some silver (or other, lighter metal) into the gold in an attempt to cheat the king.

This story of Archimedes and the golden crown is found in 'De Architectura', or 'The Ten Books of Architecture', written by the Roman architect Marcus Vitruvius Pollo some time during the first century BC. This story is not found anywhere among the known works of Archimedes, though in his book, 'On Floating Bodies', he gives the principle known as Archimedes' Principle, which states that a body partially or completely immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

  Archimedes and the Golden Crown cont'd... 

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See also:    Who was Archimedes?    |    Who was Galileo?