Eureka (Greek heureka) means ‘I have found it’. Today we use it as an exclamation of delight at having made a discovery. Archimedes, the Greek mathematician and inventor, originally uttered it when he discovered how to test the purity of Hiero’s crown.

The story is that Hiero, the king of Syracuse, gave some gold to a smith to be made into a crown. On receiving it back, he felt its weight and his suspicions were aroused. Had the smith fraudulently alloyed it with an inferior metal? But he couldn’t prove anything. So he asked Archimedes to devise a test for its purity.

The philosopher did not know how to proceed. He gave the matter a great deal of thought, but still a solution eluded him. Then one morning he got into his bath, which was full to the brim. He noticed at once that some of the water spilled over. Immediately the principle came to him that as a body is immersed it must displace its own bulk of water.

Silver is lighter than gold, he reasoned. Therefore a pound weight of silver is bulkier than a pound weight of gold and would consequently displace more water. Thus he found a simple method to establish if the crown was deficient in gold. As an early writer records:

When the idea flashed upon his mind, the philosopher jumped out of the bath exclaiming ‘Heureka! Heureka!’ and, without waiting to dress himself, ran home to try the experiment.