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.
Kada razmišljate o Arhimedovom trenutku „Eureke”, verovatno pomislite na ovo. Ispostavlja se da je bilo više ovako. U trećem veku pre nove ere, Hijeron, kralj sicilijanskog grada Sirakuze, izabrao je Arhimeda da nadgleda građevinski projekat jedinstvenih razmera. Hijeron je naručio brod 50 puta veći od standardnog drevnog ratnog broda, koji je po gradu nazvan Sirakuzija. Hijeron je želio da sagradi najveći brod ikada, koji je predodređen da bude poklon egipatskom vladaru, Ptolemeju. Ali može li brod veličine jedne palate uopšte ploviti? U Arhimedovo doba, niko nije pokušao ovako nešto. To je kao kada biste pitali, „Može li planina da leti?” Kralj Hijeron je mnogo polagao na to pitanje. Stotine radnika bi godinama radilo na izgradnji Sirakuzije od drveta borova i jela sa planine Etna, užadi od konoplje uzgojene u Španiji, i katrana iz Francuske. Gornja paluba, na kojoj bi se nalazilo osam osmatračnica, ne bi bila oslonjena na stubove, već na ogromne drvene likove Atlasa koji drži svet na ramenima. Na pramcu broda bi se nalazio ogroman katapult koji bi izbacivao kamene rakete teške oko 80 kg. Da bi putnici uživali, na brodu bi se nalazilo šetalište ukrašeno cvećem, zatvoreni bazen, i kupatilo sa vrućom vodom, biblioteka puna knjiga i kipova, hram boginje Afrodite, i teretana. I samo da još više oteža Arhimedu, Hijeron je naumio da napuni brod teretom: 400 tona žita, 10 000 tegli ukiseljene ribe, 74 tone vode za piće, i 600 tona vune. Brod bi poneo preko hiljadu ljudi, uključujući 600 vojnika. I moglo bi se smestiti 20 konja u zasebne štale. Izgraditi nešto ovolikih razmera, samo da bi potonulo na svom prvom putovanju? Pa, recimo samo da takav neuspeh ne bi bio ugodna opcija za Arhimeda. Tako je on uzeo da razmatra problem: hoće li potonuti? Možda je jednog dana sedeo u kupatilu, pitajući se kako jedna teška kada može da pluta, kada mu je došla inspiracija. Predmet koji je do pola zaronjen u tečnost izbacuje sila koja je jednaka težini tečnosti izbačene tim predmetom. Drugim rečima, ako Sirakuzija od 2000 tona izbaci tačno 2000 tona vode, jedva da će plutati. Ako izbaci 4000 tona vode, plutaće bez problema. Naravno, ako izbaci samo 1000 tona vode, pa, Hijeron ne bi bio baš presrećan. Ovo je zakon potiska, i inženjeri ga i dalje zovu Arhimedovo načelo. On objašnjava zašto jedan čelični supertanker može da pluta jednako lako kao i drveni čamac ili kada. Ako je težina vode koju brod potopljen do kobilice izbaci jednaka težini broda, šta god da se nalazi iznad kobilice će ostati da pluta iznad nivoa vode. Ovo dosta zvuči kao jedna druga priča o Arhimedu i kadi, i moguće je jer je to zapravo jedna te ista priča, izobličena ćudljivošću istorije. Klasična priča o Arhimedovoj „Eureki” i jurnjava kroz ulice koja je usledila zasnovana je na kruni, ili koroni na latinskom. U srži priče o Sirakuziji je kobilica, ili na grčkom korone. Da li je jedna priča možda pomešana sa drugom? Možda nikada nećemo saznati. Na dan kad je Sirakuzija stigla u Egipat na svom prvom i jedinom putovanju, možemo samo da zamislimo kako je luka vrvela od stanovnika Aleksandrije koji su došli da se dive dolasku veličanstvenog, plutajućeg dvorca. Ovaj izvanredan brod je bio Titanik drevnog sveta, izuzev potapanja, zahvaljujući našem drugu Arhimedu.