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    Clearing lunars
    From: George Huxtable
    Date: 2010 Aug 25, 01:04 +0100

    I wonder if this might appeal to those who take an interest in lunar
    distances, and in old books and tables on navigation.
    I've recently been looking into the unusual life of Janet Taylor, teacher
    of navigation in London in the mid-19th century, and her book, "Navigation
    Simplified", of which I have the 4th edition of 1840. In my view, this is a
    dreadful book, confusing and confused, and I pity anyone who tried to learn
    navigation from it. The third edition has been Googled.
    In turn, that has led me to an earlier work, her first publication,
    "Luni-solar and horary tables ..." of 1833, which (in my own view, again)
    is even worse, with really serious errors involving the ellipsoidal Earth,
    later dropped.
    This volume, too, is available in full on Google. Looking through some
    examples of her method for clearing lunar distances, she has in some cases
    compared her results with those given, for a similar problem, by John
    Hamilton Moore, in his "Practical Navigator". My eye fell on her "Example
    3" on page 40, about which her words are attached, as "Taylor Luni-solar
    Those words intrigued me. They refer, as stated on another page, to Moore's
    10th ed. I took a look at what Moore said. His "Practical Navigator", too,
    is available on Google, in his 11th ed. of 1795, and I attach the relevant
    passages (using Lyons' and Witchell's methods), from pages 245 and 252.
    And indeed, Janet Taylor has got it absolutely correct. Moore has set
    himself a quite impossible example. With the altitudes that he has given
    for the two bodies, there isn't nearly enough spacing across the sky, in
    any possible geometry, to achieve such a large value of lunar distance.
    It's a contrived example, that can't possibly happen in real life. Yet he
    has gone blindly through the motions of making the corrections to clear
    that absurd value, by two different methods, and indeed, got the same
    result in each case.
    Much of the impact of Taylor's point, made in 1833, is however lost,
    because that mistake occurred  some 38 years earlier. By the time Moore's
    18th edition of 1810 (also on Google) had appeared, that erroneous example
    had been dropped.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.




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