[purkka]

Given that the second is an older unit [0] than the redefinition of the metre, and defined based on "nice" subdivisions of the day, it would seem that there's still a bit of a coincidence there.

Since the metre was previously defined by the seconds pendulum, it was entirely defined by the definition of a second and the value of g. From the equations, 1 m = 1 s² × g / π².

While this makes g ≈ π² straightforward, it seems coincidental that the Earth's circumference was close enough to 40 000 km that the redefinition of the metre was a nice power or 10 without too much change to the metre.

[0]: Late 16th century, based on https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day

[marcosdumay]

Well, it's not much of a coincidence. There are all kinds of constants around us, and one of them is prone to be close to a round number.

If the Earth's circumference wasn't a nice number, people would have chosen another one.

[Thorrez]

Was the meter based on the length of the pendulum similar to the length of the meter today? This doesn't necessarily say they were similar:

> In 1675, Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place.

https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian

[petters]

The period is also not independent of the amplitude. That is only the case of you approximate sin x ≈ x in the differential equation

[madcaptenor]

My understanding (which could be wrong) is that actual clocks use a fancier pendulum than just a weight on the end of a string.

[purkka]

The difference in gravity around the Earth is small enough that the pendulums would be within a couple percent. (Wikipedia claims a measured difference of 0.3% from the time.)

Assuming the second was also quite accurate, the seconds pendulum wouldn't be too far from its current definition given that g ≈ π² to within ~1 % in modern units.