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    Re: Lunar distance accuracy
    From: Henry Halboth
    Date: 2007 Oct 27, 20:46 -0700

    Hi Alex + Frank,
    In my previous postings I stated that I had taken a
    number of Lunars at sea, in the South Atlantic, during
    the late 1940s and early 1950s. Unfortunately, I have
    been unable to find these observations amongst my
    records, however, it is my recollection that results,
    in terms of Longitude, were in the order of within
    15-minutes of arc, as compared with my known positions
    at the time of observation.
    I used Borda's spherical method for clearing distances
    but, as I previously pointed out, had and knew of no
    then published tables of pre-calculated distances
    against GMT - this necessitated that I calculate by
    Great Circle methods the true distances to compare
    with those cleared, all by hand calculation. This and
    the simple fact that I had only 5-place logarithmic
    tables left a greater window for error than I would
    consider acceptable today.
    There has recently been a considerable re-advancement,
    as well as increased interest in the Lunar problem.
    When I first became involved, most of my
    contemporaries considered me a bit loony - no comments
    I appreciate that Alex's interest in Lunars seems to
    be the accuracy of the angular measurement attainable
    with the sextant, a matter of routine to me. I would
    suggest to him that: 1) He equip his sextant with a
    vertical handle, something which I long ago did to
    ease the observation of horizontal angles in
    coast-lining and position finding, and 2) For land
    observations, consider mounting his sextant on a tilt
    table or bracket atop a tripod, which allows
    adjustment to a steady platform in the plane of the
    observed distance.
    --- Alexandre E Eremenko 
    > Frank,
    > > One of these days, clockwk.com is going to
    > disappear,
    > OK.
    > > Considering how carefully he has spelled out other
    > I disagree with this. He even did not care to
    > mention
    > his scope power:-)
    > And I continue to maintain that taking one shot per
    > week
    > with the purpose of investigation of lunars accuracy
    > is ridiculous. All books on the lunars strongly
    > insist
    > on averaging at least 5 shots. And I suppose White
    > read the
    > books he cites.
    > > In a follow-up post, you decided that
    > > this wasn't so ridiculous after all,
    > > and I agree with your logic there.
    > There is a logic in not applying excentricity error.
    > But this makes his results highly suspicious.
    > Especially if we interpret them as single shots.
    > > I propose that his arc error table would have read
    > > something like this:
    > > 30d: 0", 60d: +10", 90d: 0", 120d: -20". It should
    > Highly improbable. Especially on a good sextant.
    > See Simms theoretical formula for the arc error.
    > By the way, one may conclude from the article that
    > this
    > very formula was used to determine his arc
    > excentricity
    > correction:-)
    > > "5. How Frank comes with the "mean error" of 0'.1,
    > I don't know."
    > > Take them in sets of four and average.
    > Averaging observations taken a week or more apart
    > has nothing to do with sea practice. Or even with
    > land travel. It only makes sense when you determine
    > longitude of a fixed observatory.
    > > I found your point "6" amusing.
    > > You seem to be saying that you don't trust
    > > him because he writes plainly and without
    > > pseudo-academic pretense. Oddly
    > > enough, I like him for that.
    > You misunderstood what I said.
    > I did not say anything of the language. I was
    > talking
    > about the whole approach, "philosophy".
    > There is one approach: to find what the truth is.
    > For example, to evaluate the lunar method accuracy.
    > And another approach: to convince people in
    > something
    > which you already know or believe.
    > To promote some agenda.
    > He seems to be using the second approach.
    > I call the first approach "scientific".
    > It has nothing to do with "language".
    > > You know, they do have calm days on the oceans,
    > Alex :-)
    > Yes, they do. Have you seen
    > www.math.purdue.edu/~eremenko/accuracy.html ?
    > where the results of various observers are
    > represented graphically?
    > > That's Henry Halboth.
    > > After getting a longitude accurate to within
    > > 6 miles from a lunar distance
    > I also have one or two lunars taken from sea with
    > this accuracy. I even have a shot with a POCKET
    > sextant
    > from sea with this accuracy! I posted it 2 years
    > ago.
    > So what? I do not conclude from this that one can
    > use a pocket sextant at sea to determine longitude
    > within 6 miles:-)
    > Henry, if by chance you are reading this,
    > could you please tell us, how many times (perhaps in
    > a certain definite period) did you make lunar
    > observations at sea, and how many of those gave you
    > longitude within 6 miles?
    > > ...So that's ONE data point.
    > Yes, exactly.
    > > Finally, I would emphasize that lunars
    > > were widely used in the early
    > > nineteenth century --so they MUST
    > > have been accurate "enough", whatever
    > > "enough" means.
    > For those British officials who made the longitude
    > prize "enough" was 1/2 degree in longitude if I
    > remember correctly.
    > > There is ample evidence
    > > for them in the logbooks.
    > Evidence of WHAT? That lunars were widely practiced?
    > Nobody seems to deny this.
    > Or that "lunars can give you your position reliably
    > to 6 or to 15 miles" ?
    > Alex.
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