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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



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.


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


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


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


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.




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