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    Re: March 22 Lunar Observations
    From: George Huxtable
    Date: 2002 Mar 25, 18:27 +0000

    Bill Noyce said-
    >Thanks, Arthur Pearson, for sharing your data.
    >I haven't yet studied it, but I hope to get a chance to.
    >I'm not yet a sextant user, just playing with the math,
    >so take these comments for what little they may be worth.
    >When adjusting your sextant to measure the distance, do
    >you always make the final turn of the wheel in the same
    >direction?  Do you measure your index error the same way?
    >For altitude measurements, I've seen a suggestion to set
    >the sextant a little ahead of the body's altitude (rising
    >or setting), and then wait until the body's image just
    >touches the horizon, and record the time.  That would seem
    >to give good accuracy, but for lunars it might lead to
    >a long time waiting...
    >For graphically averaging your observations, I don't think
    >you can use the slope of the line from D1 to D2, because
    >of the "parallactic retardation" George Huxtable described.
    >Its effect is to make the slope of apparent distances
    >shallower than the slope of actual distances.  It would
    >probably be appropriate to "un-clear" the D1 and D2
    >distances, using computed altitudes at those times, and
    >applying refraction and parallax with reversed signs.
    >I'm not sure how easy that would be to do with Bruce Stark's
    >tables, though.  But then the un-cleared D1a and D2a
    >should define a slope that ought to match the slope of
    >a line through your observations.
    George Huxtable comments-
    Sextant user or not, every word of Bill's makes good sense.
    Indeed, lunar distances change too slowly for you to wait for a
    limb-contact to happen. You just have to drive the sextant knob, always in
    the same direction, until it does.
    Bill's suggestion, to "unclear" the lunar distances, turning D1 and D2 into
    D1a and D2a, is fair enough, for the limited purpose of finding a rough
    value for that slope or rate-of-change of the apparent lunar distance. And
    indeed, Bruce Stark includes tables for just that purpose, of obtaining
    apparent from true lunar distances, which he labels as "wrong-way" tables.
    At one time I toyed with the idea of calculating out the lunar-distance
    problem in just that way, by interpolating between those values, an hour
    apart, of the apparent lunar distance D1a and D2a (obtained by "unclearing"
    the two true lunar distances D1 and D2, as Bill suggests), comparing them
    with the observed lunar distance. But that particular exercise doesn't
    work, for this reason-
    The true lunar distance varies slowly and smoothly over a month, so linear
    interpolation over an hour (or even over 3 hours) is quite practicable.
    However, when the parallax is included, which varies over a daily cycle,
    these rapid changes cause such short-term non-linearity that linear
    interpolation is no longer possible even over a 1-hour interval. Pity,
    George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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