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When you think of 
Archimedes' "Eureka!" moment,

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you probably think of this.

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As it turns out, it may 
have been more like this.

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In the third century BC, Hieron,
king of the Sicilian city of Syracuse,

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chose Archimedes to supervise

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an engineering project 
of unprecedented scale.

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Hieron commissioned a sailing vessel

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50 times bigger than a standard
ancient warship,

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named the Syracusia after his city.

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Hieron wanted to construct
the largest ship ever,

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which was destined 
to be given as a present

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for Egypt's ruler, Ptolemy.

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But could a boat the size
of a palace possibly float?

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In Archimedes's day, 
no one had attempted anything like this.

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It was like asking, "Can a mountain fly?"

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King Hieron had a lot 
riding on that question.

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Hundreds of workmen were to labor
for years on constructing the Syracusia

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out of beams of pine 
and fir from Mount Etna,

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ropes from hemp grown in Spain,

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and pitch from France.

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The top deck, on which 
eight watchtowers were to stand,

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was to be supported not by columns,

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but by vast wooden images of Atlas
holding the world on his shoulders.

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On the ship's bow,

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a massive catapult would be able 
to fire 180 pound stone missiles.

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For the enjoyment of its passengers,

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the ship was to feature 
a flower-lined promenade,

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a sheltered swimming pool,

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and bathhouse with heated water,

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a library filled with books and statues,

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a temple to the goddess Aphrodite,

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and a gymnasium.

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And just to make things 
more difficult for Archimedes,

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Hieron intended to pack 
the vessel full of cargo:

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400 tons of grain,

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10,000 jars of pickled fish,

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74 tons of drinking water,

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and 600 tons of wool.

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It would have carried well over
a thousand people on board,

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including 600 soldiers.

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And it housed 20 horses 
in separate stalls.

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To build something of this scale,

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only for that to sink 
on its maiden voyage?

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Well, let's just say that failure

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wouldn't have been a pleasant 
option for Archimedes.

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So he took on the problem: will it sink?

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Perhaps he was sitting 
in the bathhouse one day,

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wondering how a heavy bathtub can float,

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when inspiration came to him.

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An object partially immersed in a fluid
is buoyed up by a force

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equal to the weight of the fluid
displaced by the object.

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In other words, if a 2,000 ton Syracusia
displaced exactly 2,000 tons of water,

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it would just barely float.

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If it displaced 4,000 tons of water,
it would float with no problem.

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Of course, if it only displaced 
1,000 tons of water,

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well, Hieron wouldn't be too happy.

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This is the law of buoyancy,

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and engineers still 
call it Archimedes' Principle.

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It explains why a steel supertanker
can float as easily as a wooden rowboat

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or a bathtub.

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If the weight of water displaced
by the vessel below the keel

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is equivalent to the vessel's weight,

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whatever is above the keel
will remain afloat above the waterline.

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This sounds a lot like another story
involving Archimedes and a bathtub,

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and it's possible that's because
they're actually the same story,

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twisted by the vagaries of history.

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The classical story of Archimedes' Eureka!
and subsequent streak through the streets

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centers around a crown, 
or corona in Latin.

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At the core of the Syracusia story
is a keel, or korone in Greek.

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Could one have been 
mixed up for the other?

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We may never know.

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On the day the Syracusia arrived in Egypt
on its first and only voyage,

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we can only imagine how residents
of Alexandria thronged the harbor

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to marvel at the arrival 
of this majestic, floating castle.

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This extraordinary vessel was the Titanic
of the ancient world,

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except without the sinking,
thanks to our pal, Archimedes.