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    Re: Lunars using Bennett
    From: Frank Reed
    Date: 2008 Jul 04, 04:34 -0400

    Ken, you wrote:
    "Two altitudes were needed, but there was no need for them to be of the
    bodies used for the lunar distance."
    Yes, exactly. From a "blackbox" perspective, this is true --almost any two
    altitudes will do. At some time before or after, you take one sight, of any
    object preferably near the prime vertical, to get local apparent time (the
    famous "time sight") and you take another sight of any other object for
    latitude (probably by a meridian altitude, but there were alternatives).
    These are then carried forward (or regressed) to the time when the lunar
    distance is measured. The time sight is carried forward by setting a decent
    pocket watch to the local time and then adding or subtracting at the usual
    rate of four seconds per minute of longitude for any distance you've
    travelled in between (by DR). The latitude sight is carried forward simply
    by adding or subtracting any change in latitude (again, as estimated by DR).
    This was workaday stuff in the 19th century. Today we would recognize it as
    the ordinary process of keeping a running fix. Then from the advanced local
    time and the adjusted latitude, when you observe a lunar distance, you can
    skip the process of measuring the altitudes of the bodies as long as you're
    willing to put up with the extra work involved in calculating their current
    altitudes. The altitudes taken with a lunar distance are really only
    required to clear the distance of the effects of refraction and parallax.
    Using them for anything else is optional. Calculating them is optional.
    Incidentally, it's not hard to find 19th century navigation authorities who
    will swear that it is "much more accurate" to calculate the altitudes. They
    were mistaken. I suspect they confused the ability to carry the calculation
    of the altitudes out to the last arc second with additional accuracy. Of
    course since calculated altitudes were actually based on data derived from
    earlier observed altitudes which were then carried forward, the calculated
    altitudes would necessarily be less accurate, but generally not by much.
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