Читать книгу Science: A History in 100 Experiments - John Gribbin - Страница 6

No. 1

THE UPWARD THRUST OF WATER

One of the first, and most famous, scientific experiments was carried out by Archimedes, who lived in the third century BC. Not much is known about Archimedes’ personal life, but it seems that he was a relative of King Hieron II of Syracuse, in Sicily, and, after extensive travels, he settled down as the King’s astronomer and mathematician. According to legend, King Hieron had a new crown, probably in the form of a laurel wreath, made for him from a bar of gold he supplied to the jeweller, to give as an offering to the gods in a temple. He suspected that the jeweller had kept some of the gold and mixed in cheaper silver instead to make up the same weight for the crown. This would be a doubly serious matter; not only would the king be cheated, but the gods might be offended at being given an inferior offering. So Hieron ordered Archimedes to find out if the crown was made of pure gold – without, of course, damaging it in any way. Archimedes had no idea how to do this, and worried about the problem for days. Then, when stepping in to a bath filled to the brim, he noticed how the water slopped over the side as it was displaced by his body. The story has come down to us from Vitruvius, a Roman architect, in a book written two centuries after Archimedes had died. We do not know where he got it from, but this is where we get the image of Archimedes immediately realizing how to test the crown, and becoming so excited that he ran out into the street, naked and wet, shouting ‘Eureka!’ (‘I have found it!’).

© Science Photo Library

An imaginative portrayal of the Greek mathematician and physicist Archimedes (287–212 BC) in his bath. Archimedes showed that an object immersed in a fluid is supported with a force equal to the displaced fluid’s weight (Archimedes’ principle).

What Archimedes had realized was that the volume of water displaced from the bath was equal to the volume of his body immersed in the water. As silver is less dense than gold, if the crown were made of a mixture of silver and gold it would have to be bigger than a crown made of pure gold in order to have the same weight. And he could measure the volume of the crown, without damaging it, by immersing it in water and seeing how much water was displaced.

Nobody knows exactly how Archimedes carried out the experiment. But the most likely method is based on an observation he described in his book, On Floating Bodies. There, Archimedes explained that the upward force (buoyancy) exerted on an object placed in water (or any other fluid) is equal to the weight of fluid that is displaced. This is now known as Archimedes’ Principle. And, of course, the weight of water displaced will be proportional to the volume of water displaced.

The obvious way to use this to test the purity of the crown, as Archimedes must have realized, would be to balance the crown against exactly the same weight of pure gold on a beam balance above a tank of water. Then, the balance is lowered until the crown and the pure gold sample are immersed in the water, while the balance arm stays above it. If both objects are made of pure gold, they will each displace the same volume (and therefore the same weight) of water, experience the same buoyancy force, and stay in balance. But if the crown is less dense than gold it will have a bigger volume, displace more water, and be more buoyant than the pure gold, so the balance will tip down on the side of the gold. The beauty of this experiment is that you don’t actually have to measure the volume of the crown, or the volume of water that it displaces; you just watch to see if the balance tilts.

That, it seems, is exactly what happened. Archimedes did the experiment (or something very similar) and found that the jeweller had indeed cheated the king. About five centuries after Vitruvius, the story was re-told in a Latin poem ‘Carmen de ponderibus et mensuris’ which described the use of such a hydrostatic balance, and in the twelfth century a manuscript called ‘Mappae clavicula’ gave detailed instructions on how to make weighings in this way to calculate the proportion of silver in the adulterated crown.

Archimedes’ Principle also explains why a ship made of steel can float. A solid lump of steel displaces a relatively small amount of water, much less than its own weight, and sinks. But if the same amount of steel is spread out in the shape of a boat, or even a simple bowl (like a coracle), a larger volume of water is displaced, weighing more than the weight of the steel, resulting in a large enough upwards force to make the boat float.