Ian Lynch wrote:
On Wed, 2008-05-21 at 10:32 +0200, Daniel Carrera wrote:
Daniel Carrera wrote:
Rod Engelsman wrote:
But if, as you say, a second and a metre are related that way it would
have to be an incredible coincidence.
I've tried to double-check, but I can't find a source. I calculated the
period of a 1-metre pendulum and I got 2.0064 seconds. So a single swing
of the pendulum would be 1.0032 seconds. That error, while small, seems
hard to explain by anything other than assuming that the definition of a
second was never a metre and that this is all one big coincidence.
Aha! I have confirmed that this is actually a coincidence. On a page
about the history of the metric system, talking about the metre, it says:
"... there were two favoured approaches to the definition of the
standard unit of length. The suggestion of defining the metre as the
length of a pendulum with a half-period of one second suffered from the
problem of varying gravity, giving a "metre" of 99 cm in Mexico City,
but 99.5 cm in Helsinki. The other approach suggested defining the metre
as one ten-millionth of the length of the Earth's meridian along a
quadrant, that is the distance from the equator to the north pole."
So... the metre is *not* related to the second, but they thought about
it. And we can see why it can't be related because gravity is not
constant around the Earth (btw, Canada also has low gravity, so one way
to lose weight is to move to Canada :D ).
Live on the pole. Not only will you weigh the least, but the cold will
require you to burn more calories (or should I say joules?) to keep
warm.
Actually you would weigh the least at the equator, at least if measured
by a spring or strain guage scale, because the centrifugal force from
the Earth's rotation counters gravity. It is for this reason that space
launches are preferred near the equator.
Second I believe is defined by atomic clocks these days and metre on
wave length of radiation, mass - can't remember. All that really matters
is that there are open standards with specific precision in constancy to
make measurement reliable. Derived units then depend on the number
system and apart from Hex and binary in computers, decimal is the
dominant global number system.
Ian
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