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Tony Crowkey wrote-

"I ran the London data through Redshift, an astronomy program, and having
adjusted the date accordingly got a 9 minutes difference on Searle?s time of
the moon?s meridian passage: 4h 34m."

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

I'm not familiar with Redshift, but some care needs to be taken when using
times computed from any modern ephemeris, which will normally be in terms of
Greenwich Mean Time rather than Apparent Time. Perhaps Redshift allows the
choice, or perhaps Tony has already made the correction. That correction
can be up to 15 or 16 minutes, at certain times of the year. Around the 19th
July Greenwich mean noon is about 6 minutes earlier than apparent noon, and
it was nearly the same in 1612. This difference is what's commonly referred
to as the equation of time. It is a useful concept to us today when we have
accurate clocks that can keep mean time, but in Baffin's time, only apparent
time, by the Sun, was relevant.

It seems that Tony has indeed made the correction to apparent time, when he
quotes a 9-minute difference on Searle's apparent time (of 4h 33m 42s) for
the Moon to be on the meridian at Greenwich that day .My pocket-calculator
shows apparent time for that event to be 4h 33m 42s, in agreement with Tony,
and for what it's worth, a GMT of that event at 4h 39m 21s.

My predictions of LAT for the Moon's transit at Greenwich are, for the
previous day, 3h 53m 43s, and for the following day 5h 14m 03s. So the Moon
is lagging on the Sun, in hour-angle, by an extra 40 minutes or so each day,
much less than the 48m 49s that Baffin has assumed for the "Moon's motion".
I will check these predictions when I get to look at Sears' ephemeris, but
it would be useful if Tony would check my own predictions using Redshift.

Of course, if we were being precise, we might make allowance for the fact
that Searle was not at Greenwich, but at London, which was about 6' further
West, so Baffin's longitudes were with respect to London. Greenwich
observatory had not even been proposed at that date. Any such correction
would be negligible, compared with the measurement errors.

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

"The only other reference to Searle?s Ephemerides is in a repeat of the
lunar
culmination procedure on 22 June 1615 (Julian). On this occasion, there are
no problems, Baffin has a second almanac to consult, gets the moon?s
relative motion correct, and the final result is fairly accurate.

...Nowe according to Searle?s Ephemerides, the moone came to the meridian at
London at 4 54 30 and after Origamus, the moone came to the meridian at
Wittenburg at 4 52 05 the same day........74 degrees 5 minutes which is the
latitude of this place west of London
because the moone was later on the meridian at this place by 0 10 22......."

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

Presumably he meant that 74 degrees 5 minutes was the LONGITUDE, not the
latitude.

I've never heard of Origamus (nor had I heard of Searle). It's not at the
Bod. Does anyone know of, or have access to, a library holding that work?

The quoted time difference of 2m 25s between the Moon passages at those two
places does not seem to fit the longitude difference between them, which is
somewhere near 12 degrees. It depends somewhat on the Moon's speed, in
hour-angle. I presume that the Wittenburg quoted is halfway between Hamburg
and Berlin, but there is another town with similar spelling (but not very
different longitude). Does anyone know anything about Origamus, and about
Wittenburg?

Has Tony been reading "The voyages of William Baffin, 1612 - 1622", by
Clements R Markham, published by the Hakluyt Society in 1880 or 81? To my
frustration, and surprise, that volume isn't on the shelves of the Bod.
Cotter tells us of Baffin's account of observations for finding refraction,
off Spitzbergen in 1614, in "Purchas, his Pilgrims". Or has there been a
more recent publication of Baffin? Whichever, if Tony can find a way to scan
or copy those pages, relevant to Baffin's astronomical observations, I for
one would be delighted.

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

It's interesting to reflect on the problems a navigator would have to
overcome in using the Moon to determine his longitude, even if it was
ever-so-crudely, as early as 1612. There were no usable watches, worthy of
the name, in those days. There was a gadget called the "Nuremberg egg" (see
Gould, "Marine Chronometer", 1923), which was good to perhaps a quarter-hour
in a day, with luck. The pendulum hadn't been invented, yet, as a timing
mechanism, so even on land, clocks weren't much better. This hampered
astronomy, because precise timing is one of the astronomer's essential
tools.

Baffin (or perhaps someone else for him) had devised a way to measure
longitude, using the hour angle of the Moon, which differed from the hour
angle of the Sun by about half a degree in an hour, or about 48 minutes of
time in a day. If you could observe the exact moment of Moon culmination
(when it crossed the North-South Meridian) you could determine the local
apparent time of that event by observing  the altitude of the Sun at that
same moment, if you knew the declination and latitude precisely to allow
that calculation to be made.

There were two special problems. It was impossible to determine the
North-South direction with enough precision when at sea, but there were ways
of setting up sighting posts if you were on land. A later generation of
surveyors would have a transit instrument for that purpose, which could be
set up precisely to swing about an East-West axis. Baffin had to use posts
and plumb-bobs. That could tell you the moment the Moon's centre crossed the
meridian. There were no corrections to make for the Moon, no "clearing"
process at all. That was simple.

At that exact moment, you had to observe the Sun's altitude as precisely as
possible. 1612 was more than a century before octants appeared, then
sextants. All he had to measure altitudes was a cross-staff, or perhaps, a
backstaff. Although Baffin quotes altitudes to a minute of arc, there's no
way he could measure to anywhere near that precision. And similar errors
arose when he tried to determine the noon Sun altitude to get his
so-necessary latitude. So his instruments were a big limitation. He needed
to make the usual corrections to altitude.

Nevertheless, in principle if not in practice, it was a simple matter. The
most difficult mathematical step was the spherical trig that was needed to
turn those numbers, altitude, declination, and latitude into Sun LAT (local
apparent time) for that instant.

Then you had to compare that with the LAT of the Sun's transit at Greenwich
(or, before Greenwich existed, at some other base-station). If that had been
pre-calculated in an almanac, and if you trusted that almanac, well and
good. For navigation, that was what you had to depend on. But a geographer
would be content to go back to that base station, after the event, to
discover the LAT of Moon transit that had been recorded there, on that same
day (by a similar method of Sun altitude, perhaps). In that way, the
uncertainties of prediction could be avoided, and the deduced position could
then be marked on a map. It wasn't always possible, though; it might have
been cloudy there at the crucial moment. In the case of Baffin's measurement
of 19 July 1612, when the Moon passed the meridian in London, the Sun there
was only 2 degrees above the horizon, so a precise altitude was unavailable.

Taking the time difference in Moon transit, between the base-point and the
point of observation, as a fraction of the interval between Moon transits
between two successive days, gave the longitude as a fraction of 360
degrees. Simple.

Baffin's longitudes failed, on two counts. First, his instruments weren't
precise enough, in setting North-South alignment, in measuring Sun altitude
or in obtaining his latitude, or some combination. Second, the predictions
weren't anywhere near accurate enough either. But it was a method that, in
principle could have worked (on-shore), if not in practice.

Thanks to Tony for bringing Baffin to our attention.

George.

   

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