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    Bubble Horizon Follow Up
    From: Bill B
    Date: 2004 Jul 5, 17:16 -0500

    Thank you for sharing your knowledge.  Some of it was a bit advanced for a
    would-be practitioner that is still working his way towards beginner. 
    Thanks to your collective help, I think I have the Sun bubble-horizon
    observation under control and the suggestions given pass my common sense
    The moon is still a bit of a puzzle to me, despite your collective efforts.
    Following up on the Nautical Almanac's instructions (below) and George
    Huxtable's advise, "The Moon has an immense parallax of up to a degree,
    which can't possibly be neglected!" my question is:
    If using the almanac's method, should the Moon Altitude Correction be
    factored in for a Moon-center bubble-horizon observation as well as the
    average of the HP value?  The second paragraph below is not clear (in my
    mind) about that.
    The correction is in two parts; the first correction is taken from the upper
    part of the table with argument apparent altitude, and the second from the
    lower part, with argument HP, in the same column as that from which the
    first correction was taken. Separate corrections are given in the lower part
    for lower (L) and upper(U) limbs.  All 30' degrees is to be subtracted from
    the altitude of the upper limb.
    For bubble sextant observations ignore dip, take the mean of upper and lower
    limb corrections and subtract 15'from the altitude.
    It appears to me that the tables favor LL Sun/Moon observations and then
    adjust to give the center of the body.  I note the -30' (approx. 2X SD)
    correction for UL Moon observations.  So the almanac's -15' for a center
    observation makes sense in that light.  Howell's suggestion that you have
    already observed the center so no corrections are need except for parallax
    (HP average) and refraction also make sense.  Guess it all depends on the
    table's reference point. While updated many times the Howell original was
    published in 1979 and uses 1976 tables.
    Another puzzle to me are the Moon's Altitude and HP (parallax?)correction
    tables.  For the planets, Sun and stars refraction correction gets lower as
    the body approaches the observer's zenith, ranging from 38' to 0'. Howell
    states parallax also declines as the Moon moves towards the observers
    zenith. She states the change in semidiameter of the Moon is only 0.3' from
    horizon to zenith, and the range of possible semidiameters is 14.7' to
    16.8'.  That above makes sense to me.  But in the moon altitude correction
    tables we start with a 34.5' correction on the horizon, climb to maximum of
    62.8' at approx. 15 degrees, and then move down to 10.9' at 90 degrees.
    What is lumped into this correction that causes it to be so large and behave
    as it does?
    I apologize if the level of my questions on celestial navigation are an
    order or two of magnitude below the rather amazing level of knowledge the
    members of this forum demonstrate.  However, I assume you all had to start
    somewhere and a kind soul or two helped you to make sense out of what
    appeared to be magic at the time.
    Believe I am developing a feel for the lack of precision with the bubble
    horizon, both academically and experientially.  I am able to cheat a bit
    here with photo gear.  Level up a tripod head, mount the sextant to the head
    with an articulated arm and clamp, and mount a small LED to light the bubble
    on another articulated arm.  I can also ensure the sextant is perpendicular
    to the horizon. (Swinging the sextant to arc the body on the horizon line
    while handholding AND keeping the bubble level is an art form I have yet to
    master.)  A Rube Goldberg transit if you will. By selecting a star or planet
    in the 30 to 60 degree range and noting its Hc for my time and position from
    Omar's site, and then working backwards from Ho to Hs, I can preset the
    sextant and make adjustments to the bubble level. By adjusting the level so
    the bubble end aligns with one of the limiting lines I can get very good
    repeatability.  Testing it without the bubble by measuring angles of distant
    objects with known heights at known distances and doing the trig, I find its
    accuracy to be *much* better than the designer's claim of a possible 8'.
    Closer to 3' with IC accounted for.  Best to date: within 5 ft of the stated
    height of a 10-story building.  (Better lucky than good!) So I have a pretty
    good feel for the slop this bubble introduces.
    Once I have the instrument calibrated it gives me feedback on various
    stances and positions that I am experimenting with for handholding.  Even
    though the cardboard model is no match for the real deal, it is teaching me
    a great deal about stable shooting positions, and turning a mental exercise
    (Let me think.  The mirror image is too high so I need to move the index arm
    forward to increase the angle the sextant sees therefore lowering the
    image...) into a reflex action.  If I had to stop and think about which way
    to turn the focusing ring on a camera lens to follow focus as subjects move
    toward or away from me, I doubt I would have many shots in focus.
    I understand that some of the minor corrections are superfluous under my
    conditions, given the accuracy of the sextant and the lack of precision of
    my bubble horizon, but will be good to know in the long run.  With a large
    band of sailing buddies, it is not out of the realm of the possible that one
    day a sextant with a $900 adjustable/lighted bubble horizon will find its
    way into my sweaty little palms.

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