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    Re: Latitude by Lunar Distance
    From: Victor Garand
    Date: 2006 Nov 12, 09:29 -0700
    Frank, I am doing a bit of catching up here so excuse my interruption ... 
    In 1379, the last paragraph was: "A picture (or two) is worth a few hundred words. I'm going to post some 3d graphics of these cones of position in a follow-up message. I'll leave this message "text-only"...

    Could you tell me in which posting I can find these pictures (3d graphics)?
    ----- Original Message -----
    Sent: Saturday, November 11, 2006 10:21 PM
    Subject: [NavList 1678] Re: Latitude by Lunar Distance

    Wolfgang, of Jaeger's article, you wrote:
    "In our latitudes the error may amount to as much as 40 nm - due to the fact that the moon is not as high in the sky"
    Only for certain observations. This can all be understood most clearly in terms of the relevant "cones of position". If I measure a lunar distance with a star roughly at the same altitude as the Moon, then the resulting cone of position intersects the Earth's surface more or less vertically, and the result is just as accurate as if the Moon were high overhead.
    And you wrote:
    "on the condition that sextant reading is accurate to 10 arc seconds (which is the smallest division of the scale of the Plath Navistar Professional for instance - and Plath only guarantees an accuracy of +/- 20 arc seconds)."
    Is that a formal, legal guarantee from Plath? In other words, does it say on paper somewhere "guaranteed to +/- 20 arc seconds"? If so, then should we not presume considerably better accuracy in practice? Otherwise, they would be dealing with a high number of returned sextants. Guarantees are usually given by companies confident that the majority of their product falls within the limits of that guarantee, wouldn't you say? I suppose in practice, many of the instruments might be worse than that and no one ever bothers to check! As for your comment that the smallest division of the scale is 10 arc seconds, that's not relevant. It tells us nothing about accuracy of observations. Many sextant micrometers have no vernier at all --the "smallest division of the scale" in such cases is 1 minute of arc. But you can still read them to tenths of a minute of arc. The Russian SNO-T is a good example of this.
    And you wrote (referring to Jaeger's article):
    "Best results can be obtained when the moon is near culmination and when the star observed is above or almost above it."
    Does he really say that? If so, then it's clear that he only made it half-way to understanding why this method of navigation works (and this would make sense, given the era). Each lunar distance observation yields a line of position where the full "cone of position" intersects the Earth's surface. Finding the star directly above the Moon is not critical. I should add that I considered this significant, and would have agreed with Jaeger, when I first started pondering this topic back in June. He's coming from the perspective of traditional lunar distance calculations (again, very understandable, given the era).
    And you wrote:
    "When taking the distance to a second star the second star  distance should form a right angle with the first (which is self explanatory) and this may be a rare condition. "
    Rare? No. It is not critical at all that this be a right angle. Anywhere from 60 to 120 degrees will not introduce much error and it can be on either side of the Moon. At night, this condition should be easily satisfied at almost any time by at least pair among the navigational stars. If you want to apply this method in daylight, you would have to wait for the Moon and Sun to move some distance across the sky or use another independent line of position to cross with the available lunar distance LOP.
    And you wrote:
    "There was no reaction or discussion of the method in the "Annalen" afterwards; it obviously sank like a "lead duck" as we say in this country - only to be discovered by Frank almost a century later." "
    I'm not surprised. Any discussion of lunar distances in any way was considered a sort of 19th century hang-over in 1912. It's a bit like discussing celestial navigation, of any flavor, in 2006. Of course, today we have the luxury of cheap calculation, and celestial is no longer a primary means of navigation. If it floats your boat, you can try all sorts of things that were difficult a hundred years ago.
    42.0N 87.7W, or 41.4N 72.1W.

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