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    Re: Longitude via lunar altitudes, simplified
    From: Peter Fogg
    Date: 2007 Mar 12, 10:02 +1100

    Thanks to George Huxtable for a clear description of the ways that
    longitude derived from lunar altitudes is likely to be less accurate
    than longitude derived from lunar distances.
    He sums up his argument with:
    > .. Even at its
    > best, lunar distance was a crude tool, and only viable because
    > mariners had no alternative.
    No small thing, that, of no alternative ...
    And then:
    > We need to ask ourselves whether the price that has to be paid, in
    > using lunar altitudes, is worth the gain. That gain is no more than
    > this; that observers can use their familiar above-the horizon
    > technique, and don't need to make a slant distance observation between
    > two bodies.
    Its a fair question. Lunar distances, I would contend, have NEVER
    really caught on, in the sense of becoming an accepted and widely used
    method of establishing what was so sorely needed by navigators: their
    Yes, dedicated navigators from Cook onwards used them (Cook thought
    they solved the longitude problem). But those who did use them
    successfully on a regular basis tended to be professional navigators
    such as were found on naval vessels and similarly well organised
    ships; typically with multiple observers making the necessary multiple
    observations at much the same time. It was, typically, only those
    master craftsmen at the pinnacle of their profession who could claim
    to be at ease with the technique and to be able to rely on it
    If lunar distances never really caught on its not because chronometers
    appeared at much the same time, as these contraptions had their own
    problems. The main limiting factor here was their great cost, compared
    even to the cost of a ship. It wasn't until the cost came down due to
    (relative) mass production techniques that chronometers became
    widespread and most mariners could move across oceans with a
    reasonably good idea of longitude.
    Well into the nineteenth century many smaller and not particularly
    well-endowed ships (in terms of navigational equipment and/or
    expertise available) crept about the seas much as mariners have always
    done; with little reliable idea of longitude, as though Harrison and
    Maskelyne (and others) had not made their contributions.
    Why? because chronometers were too expensive (and you needed at least
    three of the wretched things to have much confidence in their
    conflicting advice) and the techniques involved in producing a
    longitude from a measurement of lunar distances were widely perceived
    to be way too difficult.
    Too hard on two fronts: of observation and of calculation. According
    to Frank Reed, a little earlier in this discussion:
    "...Ashe mentions [in 1849] that he has seen the chronometers checked
    by lunar distances only once in his twenty years of experience at sea,
    which is good evidence on the era when they had fallen out of use.
    Like far too many commentators, Ashe assumes that this was because
    lunar distance calculations were too difficult (this was definitely
    not the case)."
    This seems to me to miss the point. If so many of those who needed
    longitude were unable to derive it because of their perception of the
    difficulties of calculation, then that was a very real drawback. They
    were not, typically, men of much training in astronomy or mathematics.
    Usually they were thrust into the vagaries of navigation out of
    necessity rather than inclination (like us) and more often that not
    they were the master of the vessel as well, which meant they had other
    responsibilities and demands on their time.
    Specifically; they did not have Bruce Stark's tables or Frank Reed's
    website to help them with the mathematical challenges of clearing
    lunar distances.
    Joshua Slocum WAS a master navigator; a clever and resourceful
    professional ship's captain who, when his ship washed up on a sandbank
    off the coast of Brazil, was quite capable of building a smaller boat
    from the remains and sailing it home to New York. Yet the one time (at
    the end of the nineteenth century) that he reports having made a
    successful lunar distance observation and calculation while sailing
    around the world alone in a yacht he makes such a song and dance about
    it, and congratulates himself so thoroughly on eventually achieving
    what he clearly saw as a difficult feat (including, according to him,
    needing to correct his log tables as part of the process) that we are
    left in little doubt that it was an operation rarely performed.
    Reading Slocum's laconic (and limited) descriptions of his
    navigational techniques, achieved with a cheap tin clock, both before
    and after the minute hand fell off - as a chronometer was judged to be
    an excessively expensive luxury by this thrifty Yankee - leaves no
    doubt that long experience of sailing the seas and intuition composed
    a large part of his expertise.
    Pity the poor navigator then, largely still without longitude.
    This is the context in which an easier alternative; that of deriving
    longitude via measurement of lunar altitudes, should be considered.
    Put most simply, it is a much easier ask. And the price of that, it
    seems, is its relative lack of accuracy (although bear in mind that
    the results of lunar distances are also limited in accuracy).
    As George has pointed out in other words: if you really needed to
    establish an improved idea of longitude/time, that could influence how
    much you might despise the relative inaccuracy of a technique you
    could master, as compared with using an only somewhat more accurate
    technique whose intricacies of observation and calculation were quite
    beyond you.
    However, its all rather a moot point nowadays. As the idea keeps
    getting reinvented I can only conclude that it never became well
    known. Apparently so many navigators, including Francis Chichester,
    independently thought out the concept and imagined he was the first of
    think of it. Each of these inventers imagines what a great boon he can
    contribute to navigation: longitude via a relatively simple technique,
    using well known processes (Chichester certainly did).
    Now it is little needed as a practical tool, due to the easy
    availability of cheap and accurate clocks (and GPS) - but then that
    applies to lunar distances as well.
    I think that longitude via lunar altitudes has its rightful place
    alongside lunar distances as a workable and potentially useful
    technique, and George Bennett has shown us a relatively simple way to
    derive clock correction / corrected longitude through extrapolation.
    While we may find this lunar altitude versus distance stuff
    fascinating, for others it all seems rather like the excerpt from that
    Rolling Stones song "Nineteenth Nervous Breakdown":
    "... Your mother who neglected you owes a million dollars tax
    And your father's still perfecting ways of making sealing wax ..."
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