The pat answer to the everyday puzzle of why things float invariably goes like this: “According to Archimedes’ principle, a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced. And that’s why things float.”

Perfectly correct, of course, but just about as illuminating as a firefly wearing an overcoat. Obviously the water underneath a ship has no information as to whether the object pressing upon its surface is a solid lump or is a sea-going Swiss cheese (except for holes in the hull, which we’ll get to).

Nevertheless, most of our experience with floating things, from dugout canoes to plastic foam, makes us believe that hollowness, air spaces in the interior of an object, is somehow necessary. It is not; hollowing things out is just a way of making them lighter. Light things float and heavy things sink. Which is just what you would have expected if that old Greek Archimedes hadn’t muddied the waters, so to speak.

The question is, just how light does an object have to be in order to float? And the answer is, lighter than an equal bulk or volume of water. The weight of a given volume of a substance is called its density.

Density is usually expressed as the number of pounds per cubic foot of the substance or the number of grams per cubic centimeter. If an entire ship, considered as a huge, complex conglomeration of metal, wood, plastic, air spaces, and so on, weighs less than an equal volume of water, that is, if the ship’s density is less than the density of water, then it will float. A block of wood floats because its density is only about six-tenths as much as the density of water, so no hollowing out is needed.

If we want to float a hundred thousand tons of aircraft carrier, then, we’d better do some serious hollowing out to get its overall density down. That’s no problem, of course, because it gives us quite a few convenient places to stow such necessities as airplanes and sailors.

To find out why a floating object has to be less dense than water, let’s do a little experiment. Let’s lower the one-hundred-thousand-ton aircraft carrier Admiral Nimitz (the world’s largest) very gently into a rather large bathtub of water big enough to float the ship. Gravity does the lowering job for us by pulling the ship downward into the water with a force equal to its weight. (That’s what weight is.)

But as it enters the water, the ship makes a hole in the water. That is, it must push some water aside and upward against water’s natural gravitational preference for settling down. So as gravity pulls the ship down, some water is forced up against gravity. Notice the level rising in the bathtub?

How much water can eventually be lifted upward against gravity? Only as much weight as the downward pull of gravity on the ship. In other words, the weight of the water that is lifted or displaced will be equal to the weight of the ship. When that limit is reached, one hundred thousand tons of displaced water in the case of the Nimitz, the ship stops settling down. By God, it’s floating!

But notice that each cubic foot of displaced water must have been displaced by exactly one cubic foot of the ship’s volume. That means that the volume of ship below the water line is the same as the volume of one hundred thousand tons of water. But because the water is more dense than the ship, one hundred thousand tons of water take up less space than one hundred thousand tons of ship, less than the entire ship’s worth.

So the amount of ship that is below the water line is less than the whole ship. Which is fortunate, because that means that the water line is only part way up the hull, where sailors invariably prefer it to be. All because the ship’s overall density has been made to be less than that of water.