5 ms·

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 s

by purkka 3y ago

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 https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day

marcosdumay 3y ago
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.
- deleted 3y ago
  [deleted]
Thorrez 3y ago
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 https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian
- petters 3y ago
  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 3y ago
    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 3y ago
  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.

by purkka 3y ago

marcosdumay 3y ago

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.

deleted 3y ago
[deleted]

Thorrez 3y ago

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

petters 3y ago
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 3y ago
  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 3y ago
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.