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    Re: Easy Lunars
    From: Ken Muldrew
    Date: 2004 May 3, 17:14 -0600

    On 3 May 2004 at 18:16, Frank Reed wrote:
    
    > George also wrote:
    > "I don't know anything about Witchell's method"
    >
    >
    > I bet you do, but you don't recognize it by name. You've got an old
    > copy of Norie, don't you? If not, hit that link on the Mystic Seaport
    > library web site. It's "Method III" in Norie, if I remember correctly.
    > It's also in Moore and Bowditch.
    
    In case anyone is interested, here is Witchell's method from Moore:
    
    Witchell's Approximate Method for Clearing Lunar Distances:
    From Moore - New Practical Navigator, 1798
    
    First add the sun or star's and moon's apparent altitudes together,
    and take half the sum; then subtract the less from the greater, and
    take half the difference; then add together:
       The cotan of half the sum,
       The tan of half the difference, and
       The cotan of half the apparent distance,
    Their sum, rejecting 20 in the index, will be the log tan of an angle
    A.
    
    Second, when the sun or star's altitude is greater than the moon's,
    take the difference between A and half the apparent distance, but if
    less, take their sum, then add together:
       The cotan of this sum or difference,
       The cotan of the sun or star's apparent altitude, and
       The proportional log of the correction of the sun or star's
    altitude;
    Their sum, rejecting 20 in the index, will be the proportional log of
    the 1st correction.
    
    Third, if the sum of A and half the apparent distance was taken in
    the last article, take now their difference; but if their difference,
    take now their sum. Then add together:
       The cotan of their sum or difference,
       The cotan of the moon's apparent altitude, and
       The proportional log of the correction of the moon's apparent
    altitude.
    Their sum, rejecting 20 in the index, will be the proportional log of
    the 2nd correction.
    
    Fourth, when A is less than half the apparent distance, the 1st
    correction must be added to, and the 2nd correction subtracted from
    the apparent distance; but when A is greater, their sum must be added
    to the apparent distance, when the sun or star's altitude is less
    than the moon's; but when the moon's altitude is less, their sum must
    be subtracted to give the corrected distance.
    
    Fifth, in table X, look for this last corrected distance in the top
    column, and the correction of the moon's altitude in the left-hand
    side column; take out the number of seconds that stand under the
    former and opposite to the latter. Look again in the same table for
    the corrected distance in the top column, and the principal effect of
    the moon's parallax in the left hand side column, and take out the
    number of seconds that stand under the former and opposite the
    latter. The difference between these 2 numbers must be added to the
    corrected distance if less than 90?, but subtracted from it if more
    than 90?; the sum or difference will be the true distance.
    
    [From Maskelyne's Tables Requisite:
    Table X. Numbers to be subtracted from the Logarithms in Table IX,
    when the Moon's Distance from the Sun is observed.
    Table XI. Numbers to be subtracted from the Logarithms in Table IX,
    when the Moon's Distance from a Star is observed.]
    
    > And (of Thompson's method) George wrote:
    > "This method adds three correction terms to the observed distance to
    > clear it, just as Frank's method does. But his method appears to
    > differ more from Frank's than he implies. From my limited
    > understanding (it's all rather obscure) it appears that the first two
    > of Thomson's terms relate only to the corrections due to Moon
    > parallax" etc.
    >
    >
    > It's just book-keeping. The differences among the various series
    > methods usually amount to deciding how much of the altitude correction
    > to "fold into" the calculation of the A and B factors.
    
    Jan Kalidova has written about Thomson's method (you should be able
    to find it by searching the NavL website). It appears this method is
    unique in that Thomson cleared thousands of lunars using approximate
    (1st term only, I think) and rigorous methods and created a table to
    find the difference between the two for virtually any condition.
    
    > And just to repeat for anyone who made it to the bottom of this post:
    > Lunars are Easy! Now get out there and shoot some...
    
    As an aside I'd like to thank Frank for his first post in this
    thread. After reading it I stopped trying to get the star onto the
    moon "live" and instead used both hands to steady the sextant while
    rocking. It improved my accuracy by an order of magnitude (down to
    0.1' for three lunars this past weekend). I'm starting to believe
    this technique could work for land navigation (although it still
    seems pretty unlikely on a boat).  ;-)
    
    
    
       \----------------------------+---------------------------------+
    o_,
     O_/ \    Ken Muldrew, PhD      | Voice: (403) 220-5976           |
    <\__/7
     <\__  \  Dept. of Cell Biology | Fax:   (403) 270-0617           |
      | /
      "\ L  | University of Calgary | kmuldrew{at}acs.ucalgary.ca        |
    / /
       <    +-----------------------+---------------------------------+ /
    /
                   Morning coffee recapitulate phylogeny               L/
    
    
    

       
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