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    Re: Baffled by Baffin
    From: George Huxtable
    Date: 2005 Nov 27, 20:19 -0000

    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
    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
    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
    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
    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.

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