[norwaypinesavage]

"But in practice, the tiny difference in volume between a crown made of pure gold and one made of a mixture of gold and silver is too small to be reliably measured."

Leave it to the NYT to get even this wrong. The density of silver is 10.5 grams per cc while the density of gold is 19.3 grams per cc. There is nearly a 2 to one difference. It would be quite easy to determine the difference using Archimedes Principle. Simply weigh the amount of water displaced by immersing the crown in water to determine its volume. Then weigh the crown and divide by the volume. If it is anything less than 19.3 grams per cc, off with his head.

[Sherman Logan]

Too complicated.

Just drop the weight of the crown in gold into a basin filled with water, which overflows. Pull out the gold via a string, and lower the crown in.

If any water overflows, the crown is not pure gold.

Archimedes didn’t have to figure out how much the gold in the crown had been diluted, only that it was.