The king asks Archimedes (did they actually have kings in ancient Greece?) to test whether his crown is pure gold or a gold-silver alloy. Archimedes uses the following procedure.
- get a balance, which can tell whether two samples have the same or different mass
- put the crown in one pan of the balance, and add pure gold to the other end until the masses are even
- get a thing of water
- put the crown in the water and mark how high the water level is
- take the crown out of the water, put the pure gold in, and see if the water rises to the same level. if it does, the crown is pure gold. if not, the crown is part silver
Unfortunately, Archimedes’ test is not very sensitive. Even if he did not lose or add a single drop of water when switching the crown for the known pure gold, he would still have a hard time telling whether the water level was exactly the same, or a tiny bit different.
Using the same physical ideas, and without any fancy new material, Archimedes can design a far more sensitive test. How?