The simplest method of determining the volume of the crown would have been to melt it down, shape it into a cube and measure its volume. But Hiero had given strict instructions that the crown was not to be damaged in any way. So how was the volume to be determined? This is where Archimedes' discovery came in useful.

First, Archimedes took a lump of gold and a lump of silver, each weighing exactly the same as the crown, and filled a large vessel with water to the brim, precisely measuring how much water was contained in the vessel.

He then gently lowered the lump of silver into it. This caused as much water to spill out over the sides of the vessel as was equal in volume to the lump of silver. Archimedes took the lump of silver out of the water and carefully measured the amount of water left in the vessel, thus arriving at the amount of water that had been displaced by the silver.

He again filled the vessel with water to brim, taking care to fill it with exactly the same amount of water as before. He then lowered the lump of gold into the water, and let the water displaced by it spill out over the sides. Then, doing as he had done with the lump of silver, Archimedes took out the lump of gold from the water, and arrived at the amount of water that had been displaced by the gold.

He found that a smaller quantity of water had been displaced by the gold than the silver, and the difference was equal to the difference in volume between a lump of gold and a lump of silver of the same weight.

  Archimedes and the Golden Crown cont'd... 

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