## Eureka — what’s the truth about Archimedes’ cry?

- June 16, 2021
- Armand D'Angour

Was it a crown or a ship that inspired the ancient inventor’s discovery?

When talking about the history of classical antiquity I sometimes use the image of an iceberg. What we know of the ancient world from surviving evidence is just the tip. While some historians concentrate on exploring that tip, others try to use it to extrapolate the contours of the mass lying beneath the surface, and from time to time a new outline of the hidden contour suggests itself.

A few years ago I came across a fascinating description by an ancient Greek author called Athenaeus (second century AD) of the construction by Archimedes of a huge ship on the orders of the king of Syracuse (Sicily), Hieron II. After reading it, it struck me that historians needed to re-evaluate the basis of Archimedes’ famous ‘eureka-moment.’ The story associated with the third-century BC inventor and engineer Archimedes of Syracuse is that Hieron had commissioned a finely-wrought golden crown to dedicate to the goddess Victory. He provided a craftsman with the gold to have it fabricated, but when the crown was made the king suspected the craftsman might have purloined some of the gold and replaced it with cheaper silver. According to the single ancient source for the story, the Roman author Vitruvius (first century BC), Hieron turned to Archimedes to find a way of ascertaining whether this was the case:

*While he was pondering the matter, Archimedes happened to go and take a bath. On getting into a tub he observed how as his body sank into it the water ran out over the tub. Realising that this was how he could solve the problem, he jumped out of the bath and rushed home naked, shouting that he had found the answer, yelling in Greek repeatedly as he ran ‘eureka, eureka!’ (‘I’ve got it, I’ve got it’). *

What Archimedes had allegedly discovered was that one can measure the mass of an object by observing the quantity of water it displaces. According to Vitruvius, he proceeded to apply this principle using weights of gold and silver equivalent to that of the crown and dropping them into a bowl filled to the brim with water. By discovering that more water spilled over the edge when the equivalent weight in silver was submerged than by the original crown, he proved the crown had been adulterated.

Elements of this story have long been considered implausible. Would Hieron have commissioned such an object as a dedication? Would a craftsman have dared to steal gold from the tyrant? Why would the king ever suspect such a thing? And if so, would he use such an indirect method as a scientific analysis to discover the truth? The notion that water in a bowl might be displaced by dropping objects in it was in fact long known from a fable by Aesop (sixth century BC) about the thirsty crow encountering a pitcher with water at the bottom, and dropping pebbles in until the water rose to the top. However, using the procedure described it would have been near impossible in practice, given the degree of precision required, for Archimedes to prove that any adulteration of gold with silver had taken place.

It has thus seemed more likely that what Archimedes may have discovered was the mathematical formula that allows for the relative density of an object to be ascertained by measuring its mass and volume (i.e. density=m/V). But while this is an important principle in physics, it would not have been new to Archimedes nor likely to cause him particular excitement; and it is not clear to what use the practically-minded inventor might have put it. So might there be a different truth behind the story?

When I read the passage in Athenaeus’ *Learned Diners* Book 5, I had my own ‘eureka’ moment. Athenaeus says nothing of a crown, but reports the detailed description given in a book of how Hieron once commissioned the construction of the largest sailing vessel the world had yet seen. It was built as a gift to Egypt’s ruler Ptolemy, since Alexandria had the only port deep enough to receive it. In addition to carrying massive artillery weapons, the vessel was big enough for 1,400 passengers and 1,800 tons of cargo; it also contained a flower-lined promenade, a library, a gymnasium, a bathhouse, and a temple to the goddess Aphrodite. The architect and construction supervisor was none other than Archimedes.

Before embarking on such a project, Archimedes would have had to prove to himself, if not to Hieron, that such a gigantic ship would actually float. What will have proved it to him was his formulation of the principle not of density, but of buoyancy: a partially immersed object will float if the upward force of the water displaced by the object is greater than the downward force exerted on the water by that object. This is a formula of great theoretical and practical importance, and it is still called ‘the Archimedes principle.’ It may be that Archimedes came up with his formulation while pondering the question in the bath, or while relaxing in the bathhouse. If so, one can understand how the idea of immersing an object in a water tub might have become attached to the story.

What about the crown? The Latin word for crown, *corona*, may have been a misunderstanding created or perhaps inherited by Vitruvius as a result of the use of the Greek word *koronê* in the account transmitted to him. That word may be translated as ‘crown,’ but it was also used for the keel of a ship, so by metonymy for the ship itself. If the story was that ‘Hieron commissioned an exceptionally heavy *koronê* and asked Archimedes to prove that it would not sink when placed on water,’ there is obvious scope for confusion with the notion of an exceptionally valuable, heavy, crown.

However, it might be pointed out that *koronê* is also the Greek for ‘crow,’ which is bound to make one recall the fable of the crow and the pitcher. The hidden outline of the iceberg is there to be traced, but how one traces it always remains a matter for further revision and consideration.