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    Re: Baffled by Baffin
    From: George Huxtable
    Date: 2005 Nov 24, 23:14 -0000

    Tony Crowley wrote-
    
    > Baffin says: Most part of this day I spent about finding of the meridian
    > line; which I did upon an island neere the sea, hanging at the extreames
    > of
    > my meridian line two threads with plummets set them instead of an index
    > and
    > sight.
    >
    > Elsewhere in the journal he mentions his attempts to check compass
    > variation
    > and the use of a very large quadrant (4 feet in semi-diameter).  I assume
    > that on 8th July he used the quadrant and the noon sun to gauge the
    > direction of the meridian, because he finds the compass variation in that
    > place to be 23 degrees and 28minutes West.
    >
    > But I am m still baffled by his data from Searles ephemerides. From my
    > calculations it puts him 60 degrees East of London. Perhaps he misread the
    > tables but didn't spot the error because the final figure of 60 degrees
    > etc
    > was reasonably close to where he thought he was.
    
    ==============================
    
    Response from George.
    
    Tony has now supplied enough information for us to reconstruct Baffin's
    observations, which allowing for the transition from the Julian calendar to
    the Gregorian, put the date at 19 July 1612. And I agree; it's all very
    strange!
    
    And he is quite right; Baffin is recording the time of day as measured
    forward from local midnight, not backwards from noon as I had surmised. So
    the measurement was indeed made at or near 4 17 in the morning, local
    apparent time, which fits in with Baffin's statement that it was "very early
    in the morning". And the Moon was in the third quarter, not the last as I
    had suggested.
    
    In which case Baffin's observation makes little sense to me. The Moon should
    be on the meridian at a later time each day, by about 48 minutes, if it's
    going to get back where it was, with respect to the Sun, after a month of
    about 30 days. So at the longitude of the West of Greenland (around 50 deg
    West) its lag on the Sun should be more each day (or in this case its lead
    on the Sun should be less) by nearly 7 minutes, compared with its London
    value. But Baffin records the local time of the Moon being on the meridian
    as being 7 minute EARLIER than Searle's ephemeris states it for London, not
    7 minutes later! Taking his results at face value, that would put Greenland
    at 60 degrees East, or thereabouts, just as Tony has calculated, not 50 deg
    West. How could Baffin get it so wrong?
    
    Could it be due to some gross error in setting up his North-South line, with
    plumb bobs, to give rise to a 13-minute error in the time of Moon
    culmination? The moon's azimuth will be changing (at a guess, rather than a
    calculation) at somewhere near 15 deg per hour, so that would need an
    alignment error of his plumb-bob transit, off the true North-South line, by
    somewhat more than 3 degrees. To me, that seems the most likely explanation.
    The other possibility is that Searle's predictions of the Moon at London are
    out by all of 30 minutes.
    
    Did that result take him by surprise, I wonder? Did he explain it away, to
    himself and perhaps to posterity, by imagining that the Moon was
    "outstripping the Sun", as Tony puts it, by about 48 min per day, rather
    than vice versa? If so, we have caught him at it, nearly 400 years later.
    
    But how much of that immense discrepancy was due to Baffin's observaional
    errors, and how much due to the predictions of the Moon's position, being on
    the meridian, at London, at 4h 25m 34s that morning, local apparent time.
    Lunar prediction was by no means an exact science in those days. If instead
    the true time of that event had been about 13 minutes earlier than Sears
    predicted, it would have expalained the discrepancy.
    
    Alas, it turns out not to be so. My own pocket calculator gives, for the
    moment that the Moon was on the meridian of London, a local apparent time
    that's about 8 minutes LATER than Sears predicted. However, I wouldn't claim
    great precision at such an early date, which depends on assumptions about
    delta-t (somebody check it, please). So that shifts the prediction the wrong
    way, and requires Baffin's meridian line to be even further misaligned, by
    about 5 degrees altogether.
    
    Tony writes "I would love to see the entry in the ephemerides for 9th July
    1612!". I've checked with the Bodleian library in Oxford, and they have
    copies of "An ephemeris for nine yeares ... from 1609 to 1617", by John
    Searle, master surgeon. I hope I can get to see this in the next few days.
    If I can, and if Tony has other dates and entries he would like to be
    checked, perhaps he will let me know.
    
    George.
    
    
    

       
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