The bigger your ship, the more cargo you can pack into it – and, in principle, the more profit you can make with each trip.

The trouble is, if you overload your ship, it could sink. Which tends to make you no money at all, and hence isn’t the best business plan.

But there’s another problem too. Suppose this is your ship – yes, we know it looks like a test tube – with the cargo represented by the ball bearings.

Now, suppose you load your ship up in the icy waters of the North Atlantic, being careful not to fill it so much that it sinks.

Then, you sail your cargo to the warmer waters of the tropics. Perhaps even a river estuary. It’s much warmer, so the water is less dense, and the river water dilutes the salty sea water, so it’s even less dense.

The result is that your ship floats much lower in the water…

…so low that heavy seas could swamp it, sending it to the bottom. Oops.

So what do you do? Well, you could mark your ship with a safe level. When you load your ship, you stop loading when that mark touches the surface of the water.

…like this.

Then, when you sail into warmer waters, you’ve more of a margin, and your ship stays safe.

This is exactly what shipping companies do. If you look on the side of a ship in dock, you’ll see these markings – they’re called Plimsol lines, after the politician who enforced their use after a spate of tragic accidents.

The different marks have different meanings – here, the two to the left of the vertical line are the safe loading levels for the tropics (top) and arctic (bottom).