Asking the really important question of the day

Wired asks: Should Dwarves stand up in floating barrels?

For a barrel that is partially submerged, I can find the center of mass of the submerged part (assuming straight walls). This would just be half way down from the water level to the bottom of the barrel. Since the the water level is at 0.77 meters above the bottom, the center of buoyancy would be at 0.385 meters.
This is bad. If the center of gravity is higher than the center of buoyancy (which is just barely) then the barrel can tip over.
But Thorin is standing in that barrel. Is he really that foolish? I don’t think so. What if Thorin’s barrel has 132 kg of gold instead of water? Since gold has a much higher density, the center of mass for this gold would be very close to the bottom of the barrel. This should be enough to bring the center of gravity lower than the center of buoyancy.
I bet Thorin stole that gold from the wood elves. No wonder they dislike him.

Well, at least Tolkien had the barrels sealed so they would float...

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update: BoingBoing review notes that the coins in Smaug's lair were gold plated aluminum...

but aluminum is lighter than gold, so the Bilbo sliding around parts might or not be correct...