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|" In thinking about Galileo's experiments with pendulums and the
length of the| string, he must have had some standard to decide what
the length of the| string ought to be for accuracy to a second.  Going
to look into this| further as this seems to have set a new standard
for clockmaking in general."

I found it interesting that the period of a pendulum of length one
meter is almost exactly two seconds.

Bill Wells



On May 16, 4:09�am, "George Huxtable" 
wrote:
> Coralline Algae asks some perceptive questions about time, but also seems to
> get a few things wrong.
>
> She wrote-
> | I have asked on navlist in the past about the time unit, a second, and was
> | able to find one of the recommended books �Revolution in Time, by David S.
> | Landes.
>
> Landes' book is beautifully written, and very comprehensive, but is also
> wildly discursive, and goes off into philosophical rambles which, to me,
> obscure the historical line of technical development.
>
> Coralline continues-
> | The author mentions that perhaps before there was even a second
> | hand on the early clocks, Astronomers would count the teeth of the gears
> to
> | measure times of less than a minute. It wasn't expected that the clocks
> | could keep time over any long interval.
>
> I wonder if she is referring here to the account, on page 107, of Berhard
> Walther of Nuremberg (c.1430-1504), who used a clock with not even a minute
> hand, just an hour hand. �To measure a short(ish) interval, he interpolated
> minutes by counting the teeth of the hour wheel.
>
> | The thing I can't quite understand though, is what standard the
> clockmakers
> | used to decide on the length of a second, in building their timepieces.
> | Here is my first guess, the solar day length on the equinoxes along with
> the
> | suns meridian transit set the day length standard.
>
> Until good pendulum clocks appeared, in the late 1600s, one day-by-the Sun,
> measured between noon and noon, at the Sun's meridian transit, was
> indistinguishable in length from another. It didn't matter that the Sun was
> not a perfect timekeeper (which Herbert Prinz has pointed out) because
> clocks were far worse. They were set, when the Sun happened to shine at
> noon, from a sundial, or better, from a vertical wall and a post used as a
> meridian transit. As that necessary adjustment usually amounted to several
> minutes each day, the few seconds in a day caused by Sun-error wasn't
> noticed. So everyone (except 17th century astronomers) happily used apparent
> time, not mean time. It was simply "the time". And the "day" was taken as
> the interval between one noon and another, inconstant though that may have
> been.
>
> That unit of a day was the basic unit of time measurement. It was subdivided
> into 24, then 60, then 60 again, to define the second. If Coralline is
> asking why, and by whom, it was divided in that sexagesimal way, then
> presumably we can blame the Babylonians, in what's now Iraq.
>
> That doesn't mean, however, that the discrepancy between Sun-time and
> mean-time was unknown, or unrecognised, even as far back as Ptolemy, in
> about 150AD. who tabulated what was effectively the Equation of Time, in his
> Handy Tables. At that date, he had only water-clocks to time with, so would
> have been quite unable to measure that time discrepancy directly. But he had
> a pretty good model of how the Sun moves around the sky, and from that he
> could predict what the Sun's timing-error must be, on theoretical grounds.
>
> Coralline then suggests-
> | Then build a gear train dividing the day into 24 by 60 by 60 parts.
>
> Well, building a clock was never quite like that. It's the other way round;
> to make up a daily rotation by dividing a faster ticking action, but it's
> clear what she means.
>
> Once pendulum clocks had got to be better timers than the Sun was, timing
> Noon was no longer a satisfactory way to set or check them, unless you used
> a table of Equation of Time as a correction, and this table was often to be
> found tacked inside the case of early clocks.
>
> But better, because it didn't rely on anyone else's tabulation, was to use
> the passage of a known star across a transit, which was always at the same
> altitude, and at intervals of exactly 1 sidereal day. Of course, because you
> can see a star only at night, you had to switch to different stars as the
> seasons changed. At Greenwich, they got round this by clamping a fixed
> telescope in place at the meridian altitude of Sirius, big enough so that
> Sirius was visible day or night, and checked their two Great Clocks (with
> 13-foot pendulums) by its transit of the crosswires, if the sky happened to
> be clear at the crucial moment..
>
> It was by a variant of that method that Harrison checked his own
> timekeepers, just as Caroline says-
>
> | Recalling that Harrison used sidereal time to calibrate his clocks, it
> must
> | have been well known by his time ( or much earlier ?) The "exact"
> difference
> | in time
> | between the solar day and the sidereal day so the clock needed to run
> slower
> | by about 4 minutes. Wikipedia says 86164.1 seconds. �If the exact
> difference
> | in time was well known and transit times could be measured to tight
> accuracy
> | this would seem to be the best option.
>
> It a later message, Coralline adds- "Perhaps the long history of measuring
> the length of the solar year provided the time difference relative to
> sidereal time.", and that's exactly the case
>
> It was indeed VERY well known. It didn't need to be actually measured, but
> could be deduced from the number of days in a year, which was itself rather
> well known. Back in 280BC, Hipparchus had worked that out to be 365.2467
> days (which Ptolemy didn't improve on), and you can compare that with a
> better modern value of 365.2422.
>
> There is exactly one extra rotation of the Earth, with respect to the stars,
> in a year, so we can now say there are 366.2422. So the length of a sidereal
> day is just 365.2422 / 366.2422 days, or, 86164.0905 seconds. And even
> taking Hipparchus' number, he could have deduced 86164.0394, 2000 years
> earlier!
>
> | In thinking about Galileo's experiments with pendulums and the length of
> the
> | string, he must have had some standard to decide what the length of the
> | string ought to be for accuracy to a second. �Going to look into this
> | further as this seems to have set a new standard for clockmaking in
> general.
>
> and added later-
>
> " read further online about Galileo and apparently he used water clocks to
> time some of his experiments as they were more accurate than using a
> pendulum as he had not worked out all the details. "
>
> Remember, neither Galileo nor his son succeeded in getting a self-sustaining
> pendulum clock to work. That had to wait for Huyghens in 1656, 14 years
> after Galileo's death. What Galileo did was to show that the time of a
> pendulum's swing didn't depend (much) on the size of that swing, and to show
> that it could be the basis of a clock. All that Galileo could do was to
> count a diminishing series of swings of a free pendulum, as its motion
> gradually died away. He could have checked it against an hour-glass, which
> itself could have been checked against the Sun's motion, after many
> reversals. If he wanted a way to measure time continuously, a water-clock
> may have been the best instrument he had to hand. Clocks existed in
> Galileo's time, in monasteries and in palaces and some public places, but
> they worked, not with a pendulum, but with a foliot, a horizontally-swinging
> bar with no natural period of its own. Because of this, they were bad
> timekeepers; they were used for timing prayers and services, often having
> just an hour hand.
>
> George.
>
> contact George Huxtable at geo...@huxtable.u-net.com
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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