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I think Jan Kalivoda is a new name to the Nav-L list, and (if I decode his
email address correctly) perhaps our first contributor from the land-locked
Czech Republic.

He has done his homework well, thoroughly understood our discussions, and
asked interesting and pertinent questions. He has no need to apologise for
raising lunar-distances again, from a new perspective. I would like to
welcome him on-board and hope to see more from his pen.

Now to deal with his questions. First, I have to agree that he is factually
correct. Longitudes from lunar-distances were (and still are) just about as
inaccurate as Jan claims.

For example, on Cook's first circumnavigation (with no chronometer on that
voyage) he recorded in 1770 the longitude of the island of Savu, in the
Arafura Sea, to be E 122� 29'. In 1811 James Horsbrugh noted, in
"Directions for sailing to and from the East Indies", part 2, page 444,
that more recent chronometer measurements indicated a long of 122� 00',
adding- "Captain Cook ... made it 30 miles more to the Eastward, but after
his arrival... the lunar tables were found to require a correction of 2
minutes [of time, or 1 minute of arc] or 30 miles Westerly, at the time the
observations were taken at Savu.". This is quoted from a footnote in JC
Beaglehole's Voyages of Captain James Cook, vol 1, page cclxxv.

Cook himself (on page 392 of that same volume) refers to lunar distances as
"a method that we have generally found may be depended on to within half a
degree, which is a degree of accuracy more than sufficient for all Nautical
Purposes".

That quotation gives one answer to Jan's question. Cook had made several
transatlantic voyages, with nothing more than dead reckoning to inform him
of his longitude. Anything was better than that! Cook couldn't conceive of
any navigator requiring a longitude accuracy of better then 30 arc-minutes.
Nowadays we complain if GPS is out by a few metres.

Cook's comments above presumably referred to his errors of measurement
only: he may not have been aware of inaccuracies in the Almanac itself,
which quoted lunar distances to the arc-second, though achieving accuracies
of 1 arc-minute.

Even though his astronomer, Green, was proficient in lunars from the start,
and so was Cook by the time he reached Tahiti, and even though he had both
lat. and long. for Tahiti from Dolphin's previous voyage, he still searched
for that island by running down the latitude in the old familiar way.
Partly this was because he knew his latitude measurements were much more
trustworthy and precise than his longitudes, and partly because he was
riding the Easterly trade winds anyway.

I use Cook as an example because his voyages were so well-documented, and
because he was one of the first to use the lunar distances, that were first
tabulated by Maskelyne in the Nautical Almanac for 1767.

Jan goes on to say-

"I can imagine only two modes of using lunars for navigation in the past -
firstly, the check of D.R. position before a landfall when finishing a long
deep-see passage. But even then, owing to inaccuracy of lunars, so called
"easting/westing" from the target and the final latitude sailing would be
necessary, only the initial amount of this deliberate longitude deflection
could be smaller."

Here I disagree. There were many ocean passages which required a
turning-point to round a cape or avoid a danger in mid-voyage, and where
passing close enough to get a visual fix would only add to the danger. Let
me suggest a few examples-

European navigators have long known that the best sailing-vessel route to
the China seas took them well South of the Cape of Good Hope into the
Westerly trades at S40� until reaching the rocky islands of Amsterdam or St
Pauls, from which they could head Northeast toward Sunda Strait, between
Sumatra and Java. They would try to pass close enough to sight one of those
unlit islands as a turning-point, without striking them. This wasn't easy
if the visibility was poor, as they rose out of deep water, so soundings
didn't help. If neither island had been sighted, at some point the
navigator had to take his chance and steer Northeast anyway, with the risk
that one of the islands might still lie in his path. Those islands became
graveyards for ships. Even a rough figure for longitude would give the
navigator confidence that he had left those rocks behind and could safely
steer for the Sunda Strait.

A navigator heading from the Atlantic around Cape Horn would first have to
pass the Falklands and then head Southward for Le Maire Strait, inside
Staten Island, off the end of a long peninsula jutting Eastward. Until he
could see that land and identify that strait he had no knowlege of whether
he was heading in the right direction. Only longitude, from a lunar
distance (or later, a chronometer) could help. Another graveyard of ships.
Later in that passage round the Horn he would want to know if he was clear
West of Diego Ramirez, another dangerous unmarked rock right in the middle
of the Passage, after which he could safely make some Northing. If he got a
glimpse of clear sky at the right time, a lunar could inform his decision.

Nearer home, sailing vessels from ports in Western Norway, heading South
into the Atlantic, would choose the passage between Orkney and Shetland,
North or South about Fair Isle, to avoid the constricted and congested
waters of the English Channel. Having passed through that gap by latitude
sailing, it was then necessary to delay turning South until the navigator
could be certain of clearing the Outer Isles (Rona, St Kilda). If landmarks
had been sighted, no real problem. But otherwise a lunar distance could
establish the safe longitude to make his left-hand turn.

When a lunar distance was used near the end of an East-West passage, simply
to indicate the distance-to-go, that information could be vital, if the
approaching coast was low (so invisible at a distance), or was being
approached at night, or was strewn with offshore underwater hazards.
Latitude sailing, in ignorance of the longitude, was of little help in
those circumstances.

What I've been listing above was the uses a navigator could give to a lunar
distance, once he had an accurate sextant and a set of lunar distance
tables, but not yet a chronometer. There were ways of improving accuracy. A
"circle", rather than a sextant, could be used to accumulate the results of
several lunar observations, without accumulating instrumental errors. These
were employed by Continental navigators but not much by the British, who
had taken an early lead in accurate scale-division by machine. Lunar
distances of stars, both East and West of the Moon, could be measured in
the same set of observations, which would help to cancel certain errors.
Cook improved accuracy by taking many sets of Sun-lunars, by several
observers, closely spaced, and averaging.

When chronometers became available, and affordable, things got better.
Jan asks-
"What could a sailor achieve on the basis of this piece of information? He
could not rate his chronometer by lunars regularly, as the rate acquired
would be too irregular (if intervals had been short) or not reliable (if
intervals had been long, according to the varying temperature influence on
the chronometer rate) or both (between)."

This is quite correct. There was no hope of RATING (establishing the rate
of gaining or losing) a chronometer, except if its rate became grossly in
error due to a speck of dust in the wrong place, in which case a lunar
distance should show that up. To establish the rate of a chronometer with
any precision, this needs to done on land, with two posts in the ground to
provide a North-South line, and the interval between passages of the same
star across that line compared with a sidereal day. What a lunar could
provide, to some extent, is the integrated error that had built up in the
elapsed time since the ship's departure, or since a previous lunar or
landfall. That is, how much the chronometer was actually fast or slow on
Greenwich Time, but not at what rate it was gaining or losing on Greenwich
Time.

However, the lunar couldn't measure that error to a high accuracy, only to
a couple of minutes of time or thereabouts. If lunar and chronometer agree
within a minute or so, the navigator can relax. His check on the
chronometer has found no fault, and he can continue to use chronometer-time
with some confidence.

If a check on the chronometer by a lunar showed up a discrepancy of a
couple of minutes or slightly more, what should the navigator do about it?
Very little, I suggest. Note it down, certainly. Readjust the chronometer,
never! Keep on using the chronometer as the time reference, but bear in
mind that discrepancy. And measure another lunar as soon as possible.

However, if a series of such time-checks by lunar shows an error
significantly greater than 2 minutes, and more important, a divergence that
grows with time, then chronometer error is strongly indicated. In such a
case, a prudent navigator will establish two different reckonings, one
based on each of his diverging time-scales, and presume (in the lack of any
other information) that the one that puts him closest to danger is the
truer. At this point, he should be adopting latitude-sailing techniques to
minimise reliance on his longitude.

Finally, Jan asks-
"Even so, I wonder if many captains in the merchant sailing fleet used the
lunars regularly."

Well, I can't offer any statistics. The numbers must have dwindled rapidly
from the 1850s, as accurate chronometers became affordable. Remember that
ocean passages were frequently being made by small trading vessels,
schooners of 100 tons or less, which dominated ocean trading in terms of
vessel numbers, if not in cargoes carried. There were far more trading
vessels at sea than there are today. The cost of a chronometer (or more
than one) must have been a great deterrent for masters of such vessels.

In terms of the many textbooks written and sold in the mid-1800s, one gets
the impression that lunars were still, then, an important part of the
navigator's toolbox. However, that may reflect what skills a navigator
needed to pass examinations in that era, rather than the skills he would
actually use. Joshua Slocum, who sailed around the world single-handed at
the very end of the 1800s, used lunars to do so (with much
latitude-sailing), and his familiarity with lunar-distances techniques
stemmed from recent experience as master in the merchant service, when he
regularly kept a check on his chronometers by lunars.


George Huxtable.

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george@huxtable.u-net.com
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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