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    Re: The Noon Fix
    From: George Huxtable
    Date: 2009 Apr 8, 17:32 +0100

    Jim Wilson wrote about his new book in an attachment that came with [7875].
    I have no objection at all to Jim Wilson plugging his book on this list. But
    his posting raises a few questions in my mind.
    One problem is that, presumably, he reserves the details of his arguments to
    his book, perhaps in order to encourage us to buy it, but that inhibits
    informed on-list discussion of his points. Here and there, he mentions
    (reference 1), which is presumably that book, but I think most of us can see
    what he's getting at, in that posting, without it.
    As has been discussed at some length on this list in the past, there are two
    major snags about trying to derive longitude from an observation of Sun
    altitude made at noon, and Jim's posting deals with one of those snags, and
    the most tractable one at that. This is the difficulty that the moment of
    maximum altitude differs from the moment of the meridian passage of the Sun
    (or other body) if the observer is moving Northward or Southward, or if the
    declination is changing.
    The simple method of determining the time of maximum altitude of the Sun,
    ignoring that difficulty, is to time the moment before noon when the
    altitude is at a particular value, near maximum, leave the sextant at the
    same setting, and time the moment after noon when it has the same altitude
    once again. Then split the difference between those times.
    Jim proposes to allow for changes in the observer's latitude, or the body's
    declination, by adjusting the altitude of the second observation, by an
    amount that is proportional to the two speeds, and the time interval. And I
    see a practical and logical difficulty here. What the second observation is
    trying to measure is the time of the moment when the body is at the adjusted
    sextant altitude. But you don't know the amount of the adjustment to make to
    the sextant, until you know the time-interval after the first observation,
    which is exactly what you are trying to discover. Each depends on the other.
    Which do you work out first? By the time you've pondered on that, the moment
    may have passed. Am I misunderstanding something, here?
    It's not insoluble, of course. Simply plotting the altitude curve allows you
    to adjust the altitude in retrospect. And adjusting each point on that curve
    according to the Northing that's been logged would even allow for a change
    of tack, around noon, to be allowed for.
    Jim wrote- "Relying on single observations is not recommended, but it does
    illustrate the basic approach." I don't see how a single observation is
    feasible, in this context, and presume that a single pair of observations,
    one before and one after noon, was what he meant.
    All that leaves aside the biggest problem about determining the longitude at
    noon. Whis is this: it can't be done. It's impossible. What is hidden, under
    that catchy title of "The noon fix", or "longitude at noon", is that it's
    actually longitude AROUND noon, comparing observations over a time span that
    extends well before and well after noon. The shorter that time span is, the
    less accurate is the result. Unless that time-span is a well-extended one
    (Bowditch recommended 30 minutes each side of noon), then "longitude around
    noon" becomes impractical, a fact that its proponents often gloss over. I
    hope Jim has come out straight and made reasonable assessments of the
    scatter in the deduced longitude that will result from some plausible
    time-span and a reasonable level of observational scatter in his
    altitudes-at-sea. I suggest we might assume an arc-minute (standard
    deviation), which wouldn't be bad going even in a large vessel, depending on
    sea-conditions. We can allow that one of the more serious
    error-contributors, variation in horizon-dip, doesn't affect us in this
    It would be good to see assessments of how the resulting accuracy is
    affected by higher latitudes and lower declinations; and is not confined to
    climes with a high Sun, when the method becomes more practicable.
    I'm aware that Jim's previous postings show a high level of awareness of
    these problems, so I live in hopes that all this will be addressed.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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