Legend has it that Archimedes, a famous scientist of Ancient Greece, was once commanded by the king to determine if a crown he received was pure gold or a gold–silver alloy. He was not allowed, however, to damage the crown (by slicing off a piece, for example). If you were assigned this same task, what would you need to know about both gold and silver, and how would you make a measurement that would tell you if the crown was pure gold?