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    Re: No Lunars Era
    From: Frank Reed CT
    Date: 2004 Dec 6, 18:45 EST
    Alex E wrote:
    "Did lunars really qualify for the Longitude Prize"? The condition of the prize, if I remember correctly was to find a reliable method of determining longitude with 30' precision."
    There was a sliding scale of prizes. 60' accuracy would win 5000 pounds, 40' would win 7500, and 30' wins 10,000 pounds.

    "Can one really guarantee this with lunars?"
    Guarantee? No. There are no guarantees in navigation. I can get lunars accurate to 0.2 to 0.3 minutes on a regular basis (and hence 6 to 9 minutes of longitude), and this seems to be the typical expectation for lunars at sea in the 19th century.

    "You have to be able to measure distances (sometimes large) with better than 1' accuracy."
    Yes. Now this business of "sometimes large" angles is perhaps asking too much of the method. People today tend to view lunars as pure theory. But the way they were used in practice is what's relevant to their usefulness historically. When you look through old logbooks and check when lunars were taken, patterns of use emerge that are not apparent in the navigation manuals like Norie and Bowditch. First, the Sun was the second object in the vast majority of lunars shot at sea --something like 80 to 90% of lunars were Sun-Moon lunars. Second, the elongation was typically between 50 and 100 degrees with an average roughly around 80. Lunars were taken typically for two or three days every two weeks. It's a pattern that confused me when I first noticed it in the logbooks; why two days in a row and then nothing for two weeks? But it's rather obvious when you look at the Moon's phase at the time of the observations. First Quarter and Last Quarter were the prefered times for shooting lunars. I should add that these two patterns in the observations are not entirely independent. If you limit yourself to Sun-Moon lunars, a two-week pattern is bound to emerge. The part that is striking though is that lunars were done during a relatively specific period of the lunar month.
    "(With all this irradiation, collimation and other sort of corrections)."
    Ahem. Just because things are discussed on this list ad nauseam does not mean they were serious problems for navigators in practical situations.

    "I measured quite a lot of lunar distances from my balcony, under best possible conditions with a modern sextant, which most rate as very good, using computer reduction."
    That's all well and good, but you're still a rank beginner, right? A navigator might spend ten years at sea.
    And wrote:
    "My conclusion is that I am reasonably confident in 1' accuracy (of the distance) but not much better. Some of my lunars are 0.6 and even 0.7 off."
    But those occur under specific circumstances, right? Large angles, and always positive error, right? This should be telling you something. Either, find the source of that error and fix it. Or, accept it as an error of unknown origin and subtract that amount as an instrument error (it may very well be just that). Or, avoid those angles! As noted above, navigators limited themselves to certain angular ranges in the great majority of cases.
    "Second, as we know from the Lewis and Clark story, even professional astronomers/surveyors had difficulties with reducing the sights."
    They didn't reduce them, and I agree completely with Ken Muldrew that this was the source of their difficulties. They had no "feedback", as he puts it somewhere, from their other navigational information.
    And concluded:
    "Only once I tried to reduce a lunar observation "by hands", but still using a primitive electronic calculator. My experience shows that this is not easy:-)"
    I'm sure you agree that the evidence of "once" is no evidence at all. Lunars were NOT, repeat NOT, difficult from a calculational standpoint. Indeed, the "time sight" which was a daily calculation in the chronometer era involved almost exactly the same mathematical steps and procedures. A lunar calculation was roughly three times the length of a time sight calculation hence more tedious but not more difficult than a time sight. Did you take a look at the lunar calculation that I posted under the thread "A Lunar from the 1840s"?? That is a COMPLETE lunar calculation from observations to GMT (this is in the second period where lunars were being used to check the chronometer rather to find the longitude directly).
    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
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