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    Chauvenet on his lunar method
    From: Paul Hirose
    Date: 2019 Aug 2, 20:37 -0700

    While browsing the 1851 Astronomical Journal at the ADSABS site, I ran
    across William Chauvenet's introduction of his lunar distance method.
    "In the year 1832, Bessel gave, in the Astronomische Nachrichten, a new
    solution of the problem of finding the longitude by lunar distances...
    He proposed formulas by which, with a particular disposition of the
    ephemeris, a perfectly accurate result could be obtained. An ephemeris
    arranged upon his plan was immediately prepared and published by
    Schumacher, together with tables and practical directions for
    facilitating its use at sea; and in the hope of reaching British and
    American navigators, all the rules were given in the English language.
    The experiment, however, was unsuccessful, and after the ephemeris had
    reached its third year, it was abandoned. This failure is ascribed
    chiefly to the nature of Bessel's computation... As delivered by its
    author, the method seemed simple enough to the mathematician accustomed
    to considering the varying signs of his functions; but when it was
    reduced to a set of practical rules, dispensing with a consideration of
    those signs, it became embarrassing by the multiplicity of its cases..."
    "In the mean time I have found that something could be done towards
    perfecting the common methods without changing the form of the
    ephemeris, and without introducing any processes of a kind not familiar
    to practical men. The method I have proposed is hardly more laborious
    than the simplest of those in common use, while it attains to that
    extreme precision which is required when we wish to get from our
    observations all that they are capable of giving."
    I have never attempted a solution with Chauvenet's method and have no
    opinion one way or the other on its usefulness.

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