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    Re: Lewis and Clark lunars
    From: Ken Muldrew
    Date: 2004 Apr 23, 11:28 -0600

    On 23 Apr 2004 at 16:30, George Huxtable wrote:
    
    > Ken Muldrew has been very inventive in speculating about different
    > possible errors that might have been made in those Lewis and Clark
    > lunars.
    
    Sometimes too inventive, or at least too hasty in posting my
    speculation. Nevertheless, I do enjoy thinking about these inverse
    problems. I'm having similar difficulties trying to figure out some
    of David Thompson's data, but observation errors of this kind don't
    appear there since he always reduces his measurements. Sometimes
    you'll see an observation without a longitude accompanied by a note
    in his journals that he took the wrong star. He would have discovered
    this while calculating, but since he never shows any of his
    calculations, all we have is the curt notice of failure.
    
    > And even considered a combination of two possible errors. I'm
    > sure this is the right attitude to take. If there was an observational
    > blunder that it was possible to make, you can be pretty sure that at
    > one time or another L&C will have made it. There most be SOME
    > explanation for that strange data-set of Dec 2-3 1803!
    
    Yes, I think so too.
    
    > His first speculation was that he had found the mystery star which had
    > the right coordinates to correspond with the measured distances,
    > supposedly to "Aldebaran". Already, we have established roughly how
    > much out-of-line with the Moon's track (to one side or the other) a
    > star would have to be so that the same star could possibly fit both
    > sets of observations, A and C. And then, we have to search those two
    > segments of sky for a star that's just the right distance from the
    > Moon.
    
    I also searched the sky for a plausible star that was taken from the
    wrong side of the moon (a third blunder!), but found nothing.
    
    > Well, there's such a plethora of stars in the sky, that there must be
    > many that will fill the bill, but the question is: is there a bright
    > and prominent star, that could have been mistaken for Aldebaran?
    > However, the only one Ken has been able to come up with so far is
    > magnitude 4.5, and Frank Reed has pointed out that such a dim star
    > could hardly have been seen in the sextant, let alone mistaken by
    > Aldebaran, not even by L&C. I agree with that view, and now Ken
    > Muldrew has acknowledged it too.
    >
    > Next Ken proposed that the sextant may somehow have been set to an
    > angle exactly 15deg less than was intended. Then, as Frank has
    > suggested, casting around the sky for a bright star at that wrong
    > angle from the Moon, Betelgeuse would become the obvious candidate.
    >
    > But why should the sextant have been set to exactly 15deg in error for
    > observation-set A? And then, set to some new value, for
    > observation-set B, of "Regulus", which so far we have not considered
    > in detail. And then set again exactly 15deg in error for
    > observation-set C. This is not a single accidental error, it's a
    > recurring error. What might cause the 15deg displacement?
    >
    > I thought that the answer might perhaps be found if, in error, the
    > required angle had been set against the wrong end of the vernier
    > scale, if that was just 15deg wide; an easy mistake to make. However,
    > with a sextant divided to quarter-degrees, and a vernier reading to
    > quarter-minutes, as this one seems to be, I presume that the vernier
    > scale would be marked 0 to 15 (minutes), but this would have to span a
    > length on the main scale, not of 0 to 15 (degrees) but 0 to 49 and
    > three-quarters. Or perhaps 15 and a quarter; either should work. Can
    > anyone, such as Henry Halboth, with an instrument calibrated to 15
    > arc-seconds to look at (which I don't have) check that this view is
    > correct, please. If so, setting the degree scale at the wrong end of
    > the vernier would give rise, not to a 15 degree error, but one that
    > differs by from 15 degrees by all of 15 minutes. Quite enough to
    > destroy that otherwise-attractive hypothesis, I'm afraid.
    
    Not quite! I originally cleared the distances based on L&C's actual
    data (i.e. using 60.* degrees) and then subtracted 15? from the error
    to get a perfect fit. If I subtract 15? from the original distances
    and then clear, I'm left with an error of about 15'. When instead I
    first subtract an error of 15? 15' (more on this in a minute), then I
    get near perfect results.
    
    Looking at the vernier in Fig. 8 of page 210 of Norie's Epitome that
    can be found at the Mystic Seaport on-line depository, we can see the
    source of this systematic error. If the 15 mark on the nonius is used
    instead of the 0 to read from the arch, but the vernier addition is
    still counted from right to left, then we can see that the actual
    reading on the arch (under the 0 of the nonius) is 15' greater than
    the misread reading. So given the alignment in the picture, the
    actual reading of 25? 22' 30" is misread as 40? 7' 30". Because
    they're reading the other way, taking the 15' mark on the arch from
    the left side rather than the right side, they actually add 15'
    rather than subtract it.
    
    > So I am still unconvinced about the suggested scenario: that the
    > sextant angle was set 15deg too small, on two separate occasions, and
    > then Betelgeuse was substituted for Aldebaran. I can accept that the
    > second might follow from the first, however. Can anyone offer further
    > persuasion?
    
    The big problem I still have is the Regulus measurement in the
    middle. I can't see them reading from one side of the nonius at one
    series, switching to the other side for the next series, and then
    switching back. The same technique would have to be applied (but with
    correct number on the arch in the case of Regulus, made more
    plausible by being close to zero). I think you found that their
    distances were about 5' too large for Regulus in your original post,
    whereas this hypothesis predicts their measurement of Regulus to be
    out by 15'. The error is in the right direction but it's just not
    large enough to be believable.
    
       \----------------------------+---------------------------------+   o_,
     O_/ \    Ken Muldrew, PhD      | Voice: (403) 220-5976           |   <\__/7
     <\__  \  Dept. of Cell Biology | Fax:   (403) 270-0617           |     | /
      "\ L  | University of Calgary | kmuldrew{at}acs.ucalgary.ca        |   / /
       <    +-----------------------+---------------------------------+ / /
                   Morning coffee recapitulate phylogeny               L/
    
    
    

       
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