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    Position lines, crossing
    From: George Huxtable
    Date: 2006 Dec 9, 23:00 -0000

    
    An interesting posting from Geoffrey Kolbe, Subject: [NavList 1849] I
    need some help please
    
    I've changed the threadname to make it more relevant.
    
    The relevant diagram is attached to [Navlist 1848]
    
    He wrote-
    
    "First, look at the Moon-Rasalhague position lines. They are almost
    parallel, but about ten minutes apart (in the area of interest) and
    the bodies are opposite each other. This indicates some systematic
    error of about +5 minutes, which might be index error or an error in
    dip due to some atmospheric effects. Anyhow, draw a line right in
    between these position lines to bisect them and to  amalgamate the
    Moon-Rasalhague sightings. This takes out the systematic error in
    these sightings.
    
    Now look at the Altair-Kochab pair. They are roughly opposite each
    other, so you can bisect these two position lines, which will take out
    the systematic error from these sightings.
    
    Now all you have left is the Venus-Alpheratz pair. These bodies are
    both in the same quarter of the sky, so you cannot take out the
    systematic error by combining them - but bisect them anyway, so
    forming a third amalgamated-position-line which runs pretty much
    exactly North-South. However, note that from the Moon-Rasalhague
    position lines, the systematic error seems to be around +5 minutes.
    Your sextant is reading about 5 minutes too high. So, assume this
    systematic error is present for all your sightings and move your
    Venus-Alpheratz amalgamated position line 5 minutes to the West.
    
    Now you have three amalgamation position lines all crossing at the
    same point at around 40N17,153W13. That is where you are - roughly."
    
    =====================
    
    Well, what Geoffrey has done, in effect, is to presume, from
    discrepancies between these position lines, that there is a systematic
    error, which could be corrected by a shift of  5' "away". The logical
    way to correct such an error, if it exists, would be to shift each of
    those 6 observations, each by 5', in the opposite direction to that of
    the object observed, to discover how those 6 lnew ines intersect.
    Indeed, that procedure doesn't differ, that much, from what he has
    described.
    
    But how reliable is that deduction, from those observations, that
    there must be a systematic error, to be corrected by shifting
    everything 5' away? On the face of it, it seems unlikely. How could it
    possibly come about? What sort of carelessness is going to give rise
    to an index error that's wrong by all of 5'? What extreme temperature
    gradients are going to cause an anomalous dip, differing by 5' from
    the expected value? A minute or two is plausible, but 5' is outside
    common experience, though not quite impossible. For sure, if Geoffrey
    or I suspected such a common discrepancy in our own observations, we
    would think it called for some investigation, at least. In this case,
    we are hampered, in being provided with a set of altitudes which may
    well have been contrived for the sake of creating a problem, and may
    not be at all realistic.
    
    So, in real life, what would be a more likely cause of that
    discrepancy, between position lines of Moon and Rasalhague, observed
    in nearly opposite directions? What about the random scatter that you
    get in making any observation, up from the horizon, with all the
    uncertainties that are involved, in other than millpond conditions?
    What about error in chronometer time, which would systematically
    affect computed position lines, but in quite a different pattern.
    
    I don't disagree with Geoffrey, that the observations may perhaps be
    compatible with a common error in altitude. And there's no doubt that
    in applying the adjustments, as he has done, the apparent scatter in
    the plots is significantly reduced, all 6 of the lines being shifted
    closer to a common intersection. But in my view such an improvement
    may be illusory, based on weak foundations. I would prefer to take the
    observations as they stand and analyse them accordingly.
    
    In the end, however, there's no great difference between Geoffrey's
    final conclusion and mine, based on simple eyeball estimation. What he
    hasn't done is to answer Gary's original question, "My fundamential
    question is which sights form the enclosure of my position?". Mind
    you, I didn't really answer it, either. I hope that Geoffrey isn't
    going to claim that it's bounded by his new, much-reduced, triangle.
    
    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.
    
    
    
    
    
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