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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
longitude.

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
regularly.

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.


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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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