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Coralline Algae asked-

| Using sidereal time, meridian transit of a star.
|
| I am going to investigate this method as it intrigues
| me as a solution for a totally non electric culture,
| Although they would have to be able to make
| mechanical clocks.
| With a telescope having crosshairs in the eyepiece, to
| what accuracy can the meridian transit timing be made?
| Assuming accuracy of a few seconds, then I would
| guess that next requirement would be tables converting
| sidereal time to mean solar time for each day of the year?
| After which the primary clock could be adjusted based
| on a timer which started running at the transit.
| If I am missing something here I would appreciate
| clarification.

==============

I'll say a bit about how timing was worked at Greenwich Observatory, some of
which is based on surmise rather than knowledge.

In 1676, only 20 years after Huyghens invented the pendulum clock, the two
Great Clocks were installed in the Octagon Room at Greenwich, by the famous
maker Thomas Tompion, for Flamsteed.

For a precise pendulum clock, it helps to have a long pendulum, a slow beat,
and a small arc of oscillation. The ticks were two seconds apart, half the
speed of a grandfather clock, and the pendulum was 13 feet, so four times
longer than a grandfather.

One clock was set to keep Greenwich Mean Time, and the other to run slightly
faster, to keep Sidereal Time. With a telescope clamped in place to show the
meridian passage of Sirius, in daylight or darkness, then Sirius should pass
the crosswires at the same sidereal time each day, corresponding to its
Right Ascension. There was a small correction to make, of a few seconds over
the year, to adjust for Sirius' known slow change in RA, as a result of
precession. It was a simple matter to note the time of the sidereal clock,
when Sirius crossed the middle wire. For best accuracy, the observer needed
to estimate an interpolated time, between ticks, to a fraction of a second.
I presume that the resolution of the telescope would be good enough that the
star-crossing itself could be observed to a small fraction of a second. In
which case, the main error would be in interpolating between the clock
beats.

I doubt whether the observer at the telescope was in a position to hear the
ticks of the sidereal clock himself, and to be sure which tick came from
which clock. Instead, he would have to call the moment of crossing, for an
assistant to estimate the clock-time. There would be no attempt to reset the
clock or to readjust its rate, just to note its deviation each day. My guess
is that it could be done to a quarter of a second, or so.

Once you have a clock reading sidereal time, with a known error, it becomes
a simple matter to then set the other clock to tick off mean time, knowing
the simple relation between the mean day and the sidereal day. That's just a
matter of arithmetic. There may indeed have existed a table to convert one
to the other, as Coralline suggests, but if so it was very simple. And the
cross-checking didn't call for another timer, as Coralline suggests, but
just of reading one clock against another. Once there's a clock keeping
accurate mean time, that can be used to time Sun meridian passages, at
Greenwich Apparent Noon, to establish the Equation of Time precisely, an
early Greenwich task.

One of Flamsteed's first tasks, once he had his clocks working, was to
establish whether the Earth really turned at a steady speed, so that each
(sidereal) day was the same length as any other. That had been no more than
an assumption before, but Flamsteed was able to establish its truth, within
the accuracy of his clocks. Of course, we know better now, that the Earth's
rotation speed is gradually slowing, to an extent far less than Flamsteed
had any hope of measuring.

Both of Tompion's clocks survive, but the two that a modern visitor can see,
slowly ticking away behind the wainscot in the Octagon Room, are replicas.

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.