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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 george@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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