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    Re: Lunar distance accuracy
    From: Alexandre Eremenko
    Date: 2007 Oct 24, 14:02 -0400

    My opinion of White's article
    1. George discusses at length the question,
    what is "pillar sextant".
    I think it is reasonable to assume that this was
    a "pillar-frame" sextant, typical for this manufacturer
    (Troughton), rather than a column-mounted sextant.
    White emphasises all the time that his experiments
    are relevant for the sea use. It would be stupid or
    dishonest to use a mounted sextant in such experiments:-)
    2. Several things in White's article look very suspect
    to me. First of all, what his "observations" really mean.
    Are these individual shots or averages of series?
    Notice: he records at most ONE "observation" per day.
    (In fact, one per week, in the average).
    While the normal practice at that time (and in our time!)
    is to take series of several observations.
    Then you can reduce/record each individual observation,
    or the average, but you really DO several shots.
    ALL manuals and authorities on the Lunars I know
    recommend averaging 5-10 shots. All other observers I know
    did this.
    Taking a single lunar shot PER WEEK seems ridiculous to me
    and contrary to the common practice.
    Thus I think that his "observations" are in fact the averages
    of series of shots. Though he never mentions this.
    3. On page 90, White writes that the
    "greatest excentric error
    of his sextant was 20 seconds." Of arc, of course.
    Which is the maximum arc correction
    from the certificate, I suppose.
    And then on page 91, line 1 he says
    "The correction for excentricity have NOT BEEN APPLIED (!!!)"
    and then states a ridiculous reason for this.
    Which means he NEGLECTED a known instrumental correction of
    up to 20"=0.3' for his sextant!
    This correction is LARGER than the supposed typical accuracy
    of his shots, see below:-)
    4. Now about his results, as recorded. He obtains the
    "most probable error" of his "single observation"
    21 seconds of time which is roughly equivalent to 10.5"
    in distance or 0'.2 in distance.
    I confirm this calculation from the data of his table.
    But again as I wrote above, I have very strong doubts
    that his "single observation" recorded in the table
    is indeed a "single shot" rather than the average of
    a series (which would be a normal practice).
    5. How Frank comes with the "mean error" of 0'.1,
    I don't know. But I cannot believe that Frank did what
    George's letter suggests: averaged the errors
    of observations taken in different weeks/months!
    Remembering previous (sad) experience with this list, I don't
    want to begin another discussion of statistics,
    but let me shortly summarize what White and other
    writers on the subject in XIX century do to derive
    a single number characterizing the "typical error"
    of a long array of observations.
    (The procedure is explained in detail in Chauvenet).
    They compute the "most probable error".
    The most probable error is defined (roughly speaking)
    as such number that
    1/2 of all observations have smaller error, and 1/2
    have larger error.
    That is White's results can be interpreted as follows:
    of the 42 "observations" recorded, about 21
    are likely to have the error at most 0'2 and the other
    21 observations more than that.
    Again, I write the word "observations" in quotation marks
    because he never explains what one "observation" really
    stands for, a single shot or an average of 10 shots.
    6. The whole paper makes an impression on me that White's
    approach is not "scientific". (Unlike the approach
    of the german author Bolte who wrote on the same
    subject). By "scientific approach" I mean
    "searching the truth" (whatever this truth can be).
    On the other hand, White's purpose seems to be to
    "convince the seaman in the virtue of the Lunars method",
    which is not exactly the same as unbiased search of
    the truth. But this is only my personal impression from
    reading his paper.
    7. And finally I want to bring the following passage from
    White to your attention:
    "As observations can be taken at sea with nearly
    the same ease as on shore,..."
    Well, I am also mostly an armchair sailor,
    but I would never say such thing:-)
    My very limited sea experience completely contradicts
    this opinion.
    In a future message I will compare White's and other
    observations from shore with observations made in the sea.
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