[kaapipo]

If the length of a meter were defined as the length of a seconds pendulum [1], then g would equal exactly π². From the pendulum equation:

`T = 2π√(L/g)`

substitute T = 2 s and L = 1 m:

`2 s = 2π√(1 m / g)`

solve for g:

`g = π² m/s²`.

This holds up in any strength of gravity, but the length of a meter would be different depending on it.

[1]. This actually was proposed by Talleyrand in 1790. Imagine the world if this were true!

[n4r9]

The article explains that Huygens proposed this in the 17th C, and gives the same derivation :)