What Happens When You Squeeze Air?

If it can be squeezed, there are grains

Piece two said matter is grains. So is air. Inside the syringe are billions of tiny grains flying in every direction, knocking against the walls. Push, and they are crowded into a smaller room, knocking more often. That knocking is what your finger feels pushing back.

Let go and it springs back. Not one grain was lost; the room only got smaller and larger.

By how much?

Here one man asked a question the others did not. Everyone knows it shrinks. But by how much? Push twice as hard — half? A third?

In seventeenth-century England he trapped air in a bent glass tube, poured in a heavy liquid to press on it, and after each pour wrote the air's length in a table. A rule appeared: push twice as hard and it is exactly half. Three times as hard, exactly a third.

Same-sized rooms hold the same number of grains

A hundred and fifty years later an Italian said something bolder. At the same temperature and the same push, a room of the same size holds the same number of grains, whatever the gas — hydrogen, oxygen, anything.

It sounds wrong. An oxygen grain is sixteen times heavier than a hydrogen grain, yet the same room holds the same number? But if it is right, something remarkable follows: measure the volume and you know the count. A way to count invisible grains.

Chemists ignored it for fifty years. His other claim — that oxygen and hydrogen grains travel in pairs rather than alone — clashed with the common sense of the day. It was accepted four years after his death.

A little further in

And so they became countable

Put the two together: push and volume tell you the number of grains, and equal volumes mean equal numbers. So with a scale and a ruler you can count grains no eye can see. Every calculation in chemistry today stands on this.

The numbers are enormous. Counting the grains in one spoonful of water at one per second would take longer than the age of the universe. So chemists count grains not singly but by the 'batch', the way eggs are counted by the dozen. The batch bears the Italian's name.

Four pieces about things no eye can see. The next piece turns to something you can hold: how, three thousand years ago, soft copper became a sword.

The question that remainsIf what cannot be seen can be counted with a ruler and a scale — how far apart are 'seeing' and 'knowing'?