Next message: Peter Fogg: "Re: Azimuth and Declination formulae"
Alex wrote:
"I repeat that using a pendulum of fixed length
is not a good standard of time.
Because the period depends on the amplitude.
This was already well-known in XVIII century.
Thus the US proposal (as explained in the following message)
was not scientifically sound."
There's a way around this objection. All you have to do is define the
"pendulum-meter" to be the length that yields a two second period in the limit of
zero swing amplitude. This is relatively easy since the error in the period
depends quadratically on the amplitude. Note that the "pendulum-meter" would
also have to be defined in the limit where the mass of the suspending string is
zero. Neither one of these is achievable in practice, but in both cases we
know how to subtract out exactly the effects of non-zero swing amplitude and
non-zero string mass [non-zero string mass?! drat. I swore I would never get
into string theory...]. As a standard of measurement, the biggest objection to
a "pendulum-meter" is the local variability of the Earth's gravitational
field even along one parallel of latitude. I don't think this was any worse than
the geographic definition which the French originally adopted, and it may
have been better.
-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars
