What Keeps Me Up Nights...

Today in my Physical Science class, I was teaching about measurement-- mass, volumes, etc. and the different ways to measure those things. We were talking about measuring the volume of irregularly-shaped objects, and the use of displacement of water to do this, and I talked about Archimedes.

Just to brush up on him-- he was born in Syracuse, Sicily, when that was part of the Greek empire. He was the genius who came up the Archimedes Screw for moving water and supposedly the Archimedes Death Ray-- thousands of polished shields focusing sun on a ship or other object that would set it aflame. What he's probably best-known for, though, is his solution to a king's problem. King Hieron had had a crown shaped like a laurel made. He suspected that a dishonest goldsmith had mixed the gold he had given him to make the crown with silver and pocketed the extra gold.

Archimedes knew the density of gold, and knew that if he could figure out the volume of the crown, and measure the weight, that he could figure out whether the crown was solid gold or not.

He was stumped, until he got into a bathtub and noticed that the water rose when he got in. It hit him that he could figure out the volume of the crown by measuring the volume of water displaced. He jumped out of the bath and ran through the streets naked, shouting "Eureka."

This method is used today to list the weight of ships, which are listed in tons displacement.

My question, though, as I lectured today was this: so was the goldsmith honest or not? Did Archimedes tests reveal that it was solid gold or mixed? Anyone know?