How a Clock Decides How Long a Second Is

A ruler works because you can put it next to the thing you want to know about. Lay it along the table, read off where the edge falls, and you are done.

Now try that with an hour.

You cannot lay anything alongside an hour. It is not in a place. There is nothing to hold a ruler against, nothing to line up with, no edge to read off. And yet clocks work, so they must be doing something other than measuring.

They are. A clock counts.

Find something that repeats, then count the repeats

The whole idea is this. Get hold of something that does the same thing over and over, always taking the same amount of time to do it. Then stop trying to measure at all, and simply keep count.

Heartbeats were used this way for centuries — a doctor with no watch counted a patient's pulse against his own. It works, more or less, and the more-or-less is the problem. Your heart speeds up when you run and slows down when you sleep, so a second measured in heartbeats is a different length depending on what you have been doing.

That is what a clock is really for. Not measuring time, but holding on to something that repeats so evenly you can trust the count.

Everything difficult about clockmaking is that one search.

Why a swinging weight was the first good answer

Tie something heavy to a string, hang it up, pull it aside and let go. It swings across and back, across and back, for a long while.

Two things about that swing are odd, and both of them are what made clocks possible.

The first: the weight does not matter. Hang a heavy nut on the string and time it. Swap it for a light one and time it again. Same. A heavier weight is pulled down harder, but it is also harder to get moving, and the two cancel out exactly.

The second is stranger, and Galileo is said to have noticed it as a boy watching a lamp swing on its chain in a cathedral. How far it swings does not much matter either. Pull the weight a long way out and it has much further to travel — but it also travels faster, and once again those very nearly cancel.

Be careful with the second one, because it is not perfect. Swing the weight really wide — right up towards horizontal — and it does begin to lag behind. But keep it modest, no wider than the slider allows here, and the swing time stays the same to within a whisker. That is close enough to build a clock on, and for nearly three hundred years it was the best timekeeping anyone had.

The one thing that does matter

So if not the weight, and not the distance, what decides how long the swing takes?

The length of the string. That is all.

A string about 25 centimetres long takes very close to one second to go across and come back. To make each swing take twice as long, you do not double the string — you make it four times as long. One metre of string gives you two seconds, there and back.

That relationship is why a grandfather clock is the height it is. It was not designed tall and then filled with a pendulum. It has a pendulum about a metre long, because a metre is what a two-second swing costs, and the case was built around it.

The number inside every quartz watch

A swinging weight has to hang still and stay upright, which rules it out for anything you carry. So watches count something else.

Quartz is a crystal with a useful habit: squeeze it and it produces a tiny electrical push, and give it a tiny electrical push and it bends. So a very small circuit can keep a sliver of quartz shivering back and forth — push, bend, push, bend — and the rate it shivers at is set by its shape, which does not change.

In a wristwatch, that sliver is cut so that it shivers 32,768 times every second.

That is an odd-looking number to choose, and it is not odd at all once you see where it comes from.

Make one and time it

You need a shoelace or a length of string, something small and heavy to tie on the end, and a way of counting seconds.

Tie the weight on and hang the string so it swings freely — off the edge of a table, or from a finger. Pull the weight out a little way and let go without pushing it.

Now do not time one swing. Time twenty, and divide by twenty. One swing is too short to catch accurately by hand, and this way your reaction time gets divided up as well and stops mattering much.

Then change one thing at a time and time twenty again.

Swap the weight for something heavier. The answer will not move.

Now make the string four times longer. The answer should roughly double.

That second result is the one worth sitting with. You have just found the thing that every pendulum clock in the world is built around, and you found it with a shoelace.