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    Re: Real accuracy of the method of lunar distances
    From: Trevor Kenchington
    Date: 2003 Dec 31, 17:44 +0000

    You wrote:
    > But let us consider that lunars were recommended for checking GROSS errors 
    of D.R. after many days of sailing - they never could be used for verifying 
    the position from one day to another. And facing the real possibility of such 
    gross errors, how the navigator was to recognize a lunar observation to be at 
    the limit of the 99% error and therefore unusable comparing it with his very 
    vaguely known D.R. position?
    Before answering that directly, I should perhaps point out that I
    advanced just one (hopefully plausible) reason why the distribution of
    errors in lunars should be somewhat leptokurtic. I did not intend that
    to be the only reason. Your attempt to estimate how great the error
    might be in two or three cases in every thousand really stretches your
    assumption of Normal errors. Without real-world data (based on many
    thousands of lunars, each separately worked up) to show the probability
    density function of the error term in the outer limits of its tails, I
    would not take such estimates very seriously at all.
    As to gross errors in DR and the navigator's ability to identify
    outliers amongst lunar estimates:
    I think Frank's evidence from whaling log books has already given you
    one answer: In at least some cases, it seems to have been the practice
    to take two lunars a couple of days apart. That way, they would have
    been worked up separately and a careless error in one would not have
    been automatically repeated in the second. If the first one confirmed
    the navigator's DR, then the second lunar might not be needed. If the DR
    was highly suspect, then two lunars that roughly agreed would have given
    grounds to call it a celestial fix and start a new DR reckoning. If the
    DR and the first two lunars were all very different, then do a third
    lunar on another day and see what that indicated.
    We should remember that, before the days of GPS linked to an electronic
    chart, navigation wasn't about knowing exactly where you are. (And
    whatever the textbooks and land-based courses say today, it shouldn't be
    about that now either.) It was (and should still be) more a matter of
    having a general idea of where you are and then conducting your vessel
    so that she would be safe even if you are not where you think you are.
    In the context of lunars: It is entirely possible to navigate your way
    around the ocean with no means of estimating longitude at all, save for
    DR. After all, the Norse operated a regular trade route from Norway to
    Greenland and back (without touching land in between) on that basis
    starting nearly a thousand years ago. The Portuguese opened the way to
    ElMina, then the Cape and ultimately India without being able to
    estimate longitude. And, of course, Columbus and everyone who followed
    him for nearly 300 years managed crossing the Atlantic without lunars or
    Of course accident rates were much higher (and hence the prizes were
    offered for a solution to longitude estimation) but I suspect that the
    real cost was in lost time. Without a firm indication of longitude, a
    navigator had to pick a safe landfall (such as high land rising out of
    deep water), even if that meant sailing a dog-leg course. Then he had to
    stand off the land until he could approach it in clear weather and daylight.
    Lunars allowed a bolder approach to the land and yet a lower risk of
    accident. The combination of one chronometer with occasional lunars gave
    increased confidence in estimates of longitude and hence still bolder
    approaches with still lower risks. Multiple chronometers not only saved
    the work of doing any lunars but also gave sufficient confidence for
    ships to head straight to their ports of destination. [I doubt that it
    was any accident that steamers started the practice of carrying multiple
    chronometers (if, in fact, they did). Time was money for a steamer, in a
    way that it was not for a sailing ship outside of the packet trades.
    Greater navigational certainty paid off in hard cash and so justified
    the cost of the instruments. Of course, it is also true that
    chronometers were a lesser percentage of the higher capital cost of a
    steamer, while the lower accident risk they offered was more important
    with a more valuable ship and typically one carrying more valuable cargoes.]
    Seen in that context, I suspect that a navigator would be very glad of
    the information that a lunar could provide, even though it was imprecise
    and he might have to resort to working up two or three in order to
    identify any outliers. Think of yourself in mid-ocean, unsure of your
    reckoning, though with the ability to determine your latitude and that
    of a safe landfall. Would you rather feel your way towards land,
    shortening sail every night but still worrying through the hours of
    darkness until dawn revealed a clear horizon, lengthening the voyage as
    the water went foul and the food ran out? Or would you welcome a lunar
    that, for all its potential imprecision, told you that you were safe to
    carry a press of sail for the next few days, before feeling your way in
    through the last 100 miles or so to your landfall (by which time you
    might be in soundings or might speak a ship outward bound which could
    give you your longitude? The skilled navigator had many sources of
    positional information and, I suggest, lunars were valuable as part of
    that complex, even though they could not substitute for all of the rest
    -- in the way that too many people suppose that GPS can.
    Trevor Kenchington
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
                         Science Serving the Fisheries

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