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    Re: Latitude by Talcott-Horrebow Method
    From: Paul Hirose
    Date: 2018 Nov 6, 00:37 -0800

    On 2018-11-05 8:45, Brad Morris wrote:
    > Ed described a latitude measurement to 0.1 arc seconds, or about 10
    > feet.  The Chandler Wobble has a magnitude of 0.3 arcseconds but has
    > non predictable variation within.  Yes, the large elements of
    > precession and nutation can be readily corrected for.  However,
    > Chandler Wobble can only be corrected in retrospect, for some past
    > instant in time and not reliably for any future instant in time due to
    > the variation in magnitude.
    That's partly true — back in the Talcott-Horrebow days the correction
    for polar motion was an office job which was not possible until well
    after the observations. To quote Pub. 14, "The reduction to the mean
    position of the pole is derived from the provisional results published
    by the Latitude Service of the International Geodetic Association."
    However, nowadays the polar motion is predicted and published a year in
    advance in IERS Bulletin A to .001″ precision. Bulletin B has more
    accurate values determined after the fact.
    > Which implies that measuring the latitude and claiming significance to
    > 0.1 arcseconds is an empty claim, unless you can know the Chandler
    > Wobble for that instant.
    Talcott-Horrebow was not a navigation technique and so there was no need
    to compute latitude "at that instant." Latitude was computed in the
    field to evaluate the probable error, but the definitive value was
    worked out by the staff at headquarters. In addition to the polar motion
    correction, they used the observations themselves to derive the angle
    corresponding to one turn of the micrometer screw.
    We ought to be clear on the Coast & Geodetic Survey definition of
    "probable error":
    "The probable error of a result is a quantity such that the probability
    that a second determination obtained under the same conditions as the
    first will differ from the first determination by less than the probable
    error is the same as the probability that such difference will be
    greater than the probable error.
    (Hugh C. Mitchell, "Definitions of Terms Used in Geodetic and Other
    Surveys," US Coast and Geodetic Survey Special Publication No. 242, 1948.)
    In the case of a latitude determination, a probable error of .1″ meant
    that if the procedure were repeated on the next night, there was a 50%
    probability the two latitudes would agree within .1″. It was *not* an
    assertion of a 50% probability that a latitude determined thereby was
    within .1″ of the true astronomic latitude.
    To use a firearm analogy, probable error was a measure of how closely
    the latitude "bullet holes" were clustered on the paper target. It said
    nothing about their location relative to the bull's eye. Thus, even if
    the bull's eye was moving around on the target (polar motion), that had
    no effect on probable error.
    On 2018-11-05 7:31, William Porter wrote:
     > If you can pick up a heavy surveying instrument, turn it 180 deg and
    replace it on its mount to an accuracy of 0.1" of arc, you probably need
    to increase your intake of alcohol and/or coffee. But phew no need
    because the telescope of 3" aperture pictured can only resolve 1.5" of
    arc at the theoretical optimum (Dawes' limit). Even that seems
    optiimistic for the mount maneuver.
    The reversing mechanism of the transit instrument is not relied upon to
    keep the telescope at the same inclination with respect to the zenith.
    That's the function of the Talcott-Horrebow level. To prepare for the
    first star, you set the level to the calculated zenith distance and
    center the bubble. Immediately after the star transits, you call out the
    micrometer reading and bubble position to the recorder. (The bubble is
    extremely sensitive and may have drifted a little off center as you
    observed.) Then reverse the instrument and re-center the bubble for the
    second star.
    Once set, the Talcott-Horrebow level remains clamped at a fixed angle
    with respect to the telescope tube until you are finished with that star
    pair. You don't touch it or even breathe on it — literally. The 1917
    manual warns that the observer must not breathe on the vial or shift his
    weight when reading the bubble position.
    As Geoffrey Kolbe has explained, it's not necessary that the telescope
    resolve to a fraction of an arc second. You're not trying to separate
    the components of a close double star. Instead, your job is to
    superimpose the micrometer wire on the center of a single Airy disc. A
    relatively small telescope is sufficient. In fact, the zenith telescopes
    of the international polar motion project that began in the 1890s were
    similar in size and design to those of the US Coast & Geodetic Survey.

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