When you think of  Archimedes' "Eureka!" moment, you probably think of this. As it turns out, it may  have been more like this. In the third century BC, Hieron, king of the Sicilian city of Syracuse, chose Archimedes to supervise an engineering project  of unprecedented scale. Hieron commissioned a sailing vessel 50 times bigger than a standard ancient warship, named the Syracusia after his city. Hieron wanted to construct the largest ship ever, which was destined  to be given as a present for Egypt's ruler, Ptolemy. But could a boat the size of a palace possibly float? In Archimedes's day,  no one had attempted anything like this. It was like asking, "Can a mountain fly?" King Hieron had a lot  riding on that question. Hundreds of workmen were to labor for years on constructing the Syracusia out of beams of pine  and fir from Mount Etna, ropes from hemp grown in Spain, and pitch from France. The top deck, on which  eight watchtowers were to stand, was to be supported not by columns, but by vast wooden images of Atlas holding the world on his shoulders. On the ship's bow, a massive catapult would be able  to fire 180 pound stone missiles. For the enjoyment of its passengers, the ship was to feature  a flower-lined promenade, a sheltered swimming pool, and bathhouse with heated water, a library filled with books and statues, a temple to the goddess Aphrodite, and a gymnasium. And just to make things  more difficult for Archimedes, Hieron intended to pack  the vessel full of cargo: 400 tons of grain, 10,000 jars of pickled fish, 74 tons of drinking water, and 600 tons of wool. It would have carried well over a thousand people on board, including 600 soldiers. And it housed 20 horses  in separate stalls. To build something of this scale, only for that to sink  on its maiden voyage? Well, let's just say that failure wouldn't have been a pleasant  option for Archimedes. So he took on the problem: will it sink? Perhaps he was sitting  in the bathhouse one day, wondering how a heavy bathtub can float, when inspiration came to him. An object partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. In other words, if a 2,000 ton Syracusia displaced exactly 2,000 tons of water, it would just barely float. If it displaced 4,000 tons of water, it would float with no problem. Of course, if it only displaced  1,000 tons of water, well, Hieron wouldn't be too happy. This is the law of buoyancy, and engineers still  call it Archimedes' Principle. It explains why a steel supertanker can float as easily as a wooden rowboat or a bathtub. If the weight of water displaced by the vessel below the keel is equivalent to the vessel's weight, whatever is above the keel will remain afloat above the waterline. This sounds a lot like another story involving Archimedes and a bathtub, and it's possible that's because they're actually the same story, twisted by the vagaries of history. The classical story of Archimedes' Eureka! and subsequent streak through the streets centers around a crown,  or corona in Latin. At the core of the Syracusia story is a keel, or korone in Greek. Could one have been  mixed up for the other? We may never know. On the day the Syracusia arrived in Egypt on its first and only voyage, we can only imagine how residents of Alexandria thronged the harbor to marvel at the arrival  of this majestic, floating castle. This extraordinary vessel was the Titanic of the ancient world, except without the sinking, thanks to our pal, Archimedes.