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    Re: Northing correction to Noon longitudes.
    From: George Huxtable
    Date: 2005 Jun 7, 15:09 +0100

    On 4 June, in "Latitude and Longitude by "Noon Sun"", Frank Reed explained
    his method for correcting "around noon" observations for longitude for the
    North-South component of vessel's speed, after explaining how to obtain
    that component, including declination change.
    
    "If you're moving towards the
    Sun,  then for every six minutes away from noon, add 0.1 minutes of arc for
    every knot  of speed to the altitudes before noon and subtract 0.1 minutes
    of arc
    for every  knot of speed to the altitudes after noon."
    
    So, if there were 13 observations plotted, each of these (perhaps only 12
    of them) must be individally adjusted, by taking the time interval in
    minutes between each point and some (arbitrary?) time-zero, dividing by 6,
    and multiplying by 0.1 x the speed in knots, adding or subtracting the
    result from the altitude, and replotting a new point. It doesn't sound like
    a trivial operation to do 12 times over, does it?
    
    Instead, I suggested that the original altitude data points be left
    uncorrected, to provide (using Frank's folding-paper method) the moment of
    maximum altitude, on which-
    
    "The moment of LAN is  delayed by 15.3 (tan lat - tan dec) * v where v is the
    Southerly component of  the speed in knots."
    
    To which Frank responded, on 6 June,
    
    "That adds needless complication to an otherwise  extremely simple procedure."
    
    Well, does it indeed? It appears to be a great simplification, to my mind.
    Perhaps list members will judge for themselves.
    
    This correction doesn't need to be made very precisely because it's only a
    small one, but it certainly must be made. For the purpose, both Sun dec and
    ship's lat will be changing rather slowly. The simple trig expression 15.3
    (tan lat - tan dec) can readily be precalculated (and changes only slowly
    from one day to the next). It just needs multiplying by Northing speed to
    provide a result which is the time-difference in seconds between maximum
    altitude and meridian passage. So: no fiddling with the original graph,
    just one simple multiplication, followed by one time correction. Which is
    simplest?
    
    By the way, I failed to mention, in previous postings, what should be
    rather obvious; that in the above expression both lat and dec should be
    taken as positive North, negative South.
    
    ============================
    
    Then I asked-
    
    "The whole object of the exercise is to discover the  moment of noon. So how
    does the observer know how many minutes each plotted  point is away from
    noon in order to calculate that adjustment?"
    
    I went on to answer my own question, but that part wasn't quoted-
    
    "The answer is, I think, that it just doesn't matter, as far as finding the
    new centre-of-symmetry is concerned. For the purpose of making those
    corrections, any point could arbitrarily be presumed to be the
    moment-of-noon, and then the new centre-of-symmetry would show true noon,
    when the Sun was on the meridian."
    
    Frank's answer was-
    
    >It  makes no difference. Whatever point in time is picked as the "zero"
    >point, where  no adjustment for northing/southing is made, will be the
    >time of the
    >fix. Being  able to label the fix as "noon" is not terribly important but it
    >is nicely  traditional. The real time on it, of course, is a moment of  GMT.
    
    It may be my fault, but I don't understand what Frank is saying here. The
    time that results from the paper-folding operation of the corrected graph
    is the moment of noon, surely, when the Sun crosses the meridian, and what
    we need to know to get the long is the chronometer reading of GMT at that
    moment (after equation of time is chucked in). I don't understand how some
    arbitrarily chosen moment, at which the corrections to altitude are taken
    to be zero, can be the "time of the fix", whatever that means. So I suggest
    that my own answer, above, to my question is the correct one. Nevertheless,
    we seem to agree that choosing a different zero-point for the corrections
    will not shift the timing of the corrected peak, which depends on the slope
    of the corrections, but not their amount.
    
    Then I went on to-
    >"However, it looks to me as if an error in
    >that initial  presumption of noon would give rise to an error in the deduced
    >maximum  altitude, and so in the latitude. Perhaps Frank will comment."
    
    Frank did, as follows-
    
    "Nope. No  error. See above."
    
    However, I urge Frank to rethink his flippant dismissal of the point that I
    have made. What's needed, to calculate latitude simply, is the Sun's
    altitude AT MERIDIAN PASSAGE, and not at any other time. To obtain that,
    Frank tells us to take the altitude from the peak value of the corrected
    Sun-altitude curve, at his "folding" point, which will be at meridian
    passage. But that's not the observed altitude, it's the corrected altitude,
    at meridian passage. The correction that's been made to observed altitude,
    at that moment, depends on how far it is away in time from the zero-point
    of his corrections, and that zero-moment was chosen quite arbitrarily. Only
    if the zero-point of the corrections happened to be at the moment of
    meridian passage, would the peak of the corrected-altitude curve correspond
    to the observed altitude at that moment.
    
    So I suggest that Frank's proposed method should be somewhat modified. Yes,
    certainly, use the corrected-altitude curve to determine, from its
    symmetry, the moment of meridian passage. But then, read off, corresponding
    to that moment of meridian passage, the UNCORRECTED value of altitude,
    which will NOT in general be its peak value.
    
    ====================
    
    Finally, there's a curious comment, as follows-
    
    "By the way, perhaps George could consider addressing people in the second
    person. Thanks in advance."
    
    Can any list member, perhaps Frank himself, kindly explain what he is on
    about here? Otherwise, that request is completely lost on me.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ================================================================
    
    
    

       
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