The method that Vitruvius says was used by Archimedes, though correct in theory, has been criticised by scientists as too difficult to implement with the amount of accuracy that would be needed to detect a component of silver or other lighter metal in the crown. This is because that the amounts of gold and silver in the case of a crown would be so small that the difference in their volumes, and the consequent difference in the amount of water displaced, would be too small to measure with precision with the measurement methods available to Archimedes.

More than eighteen hundred years after Archimedes is said to have helped King Hiero detect the goldsmith's fraud, another young man, also twenty-two years old at the time, pondered the same problem. This young man was Galileo Galilei, the Italian mathematician, physicist and astronomer. In 1586, Galileo wrote a short treatise called La Bilancetta - 'The Little Balance' - in which he expressed his scepticism of Vitruvius' story and presented his own theory of how Archimedes might actually have detected the goldsmith's dishonesty. He based his theory on the Archimedes Principle, and on Archimedes' work on levers.

Galileo's method is simple, yet precise and detailed, even determining the exact quantity of gold and silver (or a lighter metal) in the alloy. It is very likely that Archimedes detected the goldsmith's fraud by a method similar to that described by Galileo. While not detailing Galileo's treatise here, let me give a method, based on what Galileo says, that Archimedes might have used:

Instead of immersing the crown and an equal weight of gold in a vessel filled with water, Archimedes could have suspended the crown from one end of a pair of scales, balancing it with an equal amount of gold on the other end. Once equally balanced, he would have immersed the suspended crown and lump of gold into a vessel of water. Now, since a body immersed in water is buoyed up by a force equal to the weight of the water displayed by the body, the denser body, which has a smaller volume for the same weight, would sink lower in the water than the less dense one.

So, if the crown was pure gold, the scales would continue to balance even when immersed in the water. If the crown was not pure gold, and silver or a lighter metal had been mixed with the gold thus increasing its volume, then the scales would tilt towards the denser gold. And thus it would have been possible for Archimedes to find out quickly and simply, without damaging Hiero's golden wreath in any way, whether the goldsmith had cheated the king or not.

  Archimedes and the Golden Crown

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