When I went to the British Museum recently as part of my holiday plans, I saw a really interesting (some might say weird) clock there. And a ball that was counting minutes by running back and forth on a special desk.

There was information about the length of the ball's journey each year, which was 2,500 miles. That's pretty impressive! And even more impressive is – how did they calculate that length?

Well, that's pretty simple, actually, but still – it's impressive how we can get interesting facts by using maths.

So, the ball runs 2,500 miles each year on that funny desk. Using a simple physics formula (I know, that's even worse than maths!), which states that distance is a product of speed and time, we can calculate this impressive 2,500 miles easily: when knowing the time – that was 30 seconds according to the information written next to the clock – and the length of the corridor for the ball... That would give us the speed (length per time), and we choose a year as the time for our formula.

But are we not missing something? Oh yes, the actual length of the corridor where the ball runs like crazy all the time (pun intended)...

Let's have a look:

s = v * t

distance = speed * time
(Yeah, yeah, I should say displacement and velocity when I'm using s and v... sometimes, I like being a rebel.)

2,500 miles – let's pretend we don't know this yet ? = (unknown length of the corridor / 30s) * year

So we have two unknowns and only one equation... Apparently, they didn't give us the rest of the information needed to check their calculation (and the clock was behind glass, so I couldn't just measure the corridor myself!).

Well, I just thought I could calculate at least the length of the corridor backwards and, by eye, check if the result fits my estimation of how long the ball corridor could roughly be...

Let's go back then:

s = v * t

2,500 miles = (x / 30s) * year

Converting units (metres, seconds, therefore m/s as a speed unit):

1 mile = 1.609344 kilometres => * 1000 => 1,609.344 metres

2,500 miles = 1 mile * 2,500 = 1,609.344 metres * 2,500 = 4,023,360 m

1 year = 365.25 days = 365.25 * 24 hours = 365.25 * 24 * 60 minutes = 365.25 * 24 * 60 * 60 seconds = 31,557,600 seconds in an average year.

(I took it astronomically and made a mean for every year, because yes, that's why we have 1 additional day every 4 years => every year 1/4 – or 0.25 – of an extra day. Otherwise, there are 365 * 24 * 60 * 60 s = 31,536,000 s in a non-leap year and 366 * 24 * 60 * 60 s = 31,622,400 s in a leap year if not thinking about the average.)

Again:

2,500 miles = (x / 30s) * year

4,023,360 m = (x / 30s) * 31,557,600 s

After two steps (dividing by 31,557,600 and multiplying by 30 to balance the equation), we'll have:

(4,023,360 / 31,557,600) * 30 = x (x is in metres) = 3.82477755... m ≈ 3.82 m

Hmm, was the length of the corridor for the ball counting minutes (half-minute one way) for that weird clock really over three and a half metres? I'd say it may have been a bit shorter, but thinking again about the size of the clock and the number of curves the ball must do when going from one end to the other – yeah, it could be.

If you want to check it, you could either go to the British Museum or at least Google "Congreve rolling ball clock" and try to estimate it as I did.

So, this is what I think about when on a holiday... I should really go for a proper holiday now! =)