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    Re: Old style lunar
    From: Ken Muldrew
    Date: 2004 Dec 13, 10:00 -0700

    On 12 Dec 2004 at 0:55, Alexandre Eremenko wrote:
    > On Sat, 11 Dec 2004, Fred Hebard wrote:
    > 1. To decide anything on the source of Thompson errors,
    > it is desirable to pull the almanac data for the date of his
    > actual observations. I am a bit confused: who of us has a 1800
    > (and prhaps 1801 almanac? Can we ask this person to post the data?
    Bruce Stark has the old almanacs but they're locked away in storage to
    protect them from further deterioration. If the opportunity arises and
    Bruce is able to photocopy any of the relevant pages then I will post the
    almanac data. The nice thing about this series of lunars at Rocky Mountain
    House is that we know exactly where he was (and now with the help of
    Frank's online almanac we know exactly where the moon was as well). The
    dates for his lunars at Rocky Mountain House are:
    1800  17-Apr, 18-Apr, 22-Dec
    1801  17-Feb, 28-Feb, 28-Feb, 1-Mar, 18-Mar, 17-Feb, 24-Feb, 24-Feb, 25-
    Feb, 25-Feb
    > 2.
    > > Errors for stars east and west of the moon often cancel each
    > > other out.
    > Not the errors in the almanac!
    > It is the measurement errors that cancel, not the errors in almanac.
    I think what Fred meant here is that if Thompson took two lunars on a
    particular night, one on each side of the moon, then his average of the
    two resulting longitudes would tend to be close to the true position but
    the errors of each lunar individually would be unexpectedly large.
    > Let us consider an idealized situation when the stars are
    > exactly on the Moon's path and positions of the stars are known
    > precisely. Consider two stars, Moon in between.
    > Then the error in Moon's position will lead to the errors
    > in distances which are exactly opposite to each other.
    > Now suppose we measured both distances EXACTLY with our sextant
    > and want to deduce longitude (or chronometer corr., does not matter)
    > Averaging the two reduction results will give you nothing.
    > Both will give the same error in time/longitude.
    I don't see how that follows. One error puts you too far West of your true
    position, the other error puts you too far East. Averaging the two cancels
    the systematic error of the moon being in the wrong place.
    > To decide whether the main reason of his errors was the
    > almanac, we
    > need the almanac errors
    > on the specific dates of his observations.
    That would indeed be very helpful. I do have a couple of lunars within the
    October-November time period of 1800 for which I have almanac pages. I'll
    try to post at least one of these soon. Unfortunately I can't tell you his
    true position for these lunars as he is on the trail (though perhaps from
    his DR account and any landmarks that he describes I can get a reasonable
    position from a topo map (I know the terrain that he's travelling over
    pretty well as it's not too far from where I live)).
    Ken Muldrew.

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