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    Re: What were the Lunar Distances for?
    From: George Huxtable
    Date: 2002 Dec 27, 16:27 +0000

    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
    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
    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.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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