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    Re: Lunars Tables
    From: George Huxtable
    Date: 2007 Dec 1, 09:41 -0000

    Scott Owen wrote-
    |
    | Bought a copy of Bruce Starks, Tables for Clearing the Lunar Distance a
    | few weeks ago.  From the archives it looks as though Bruce was a regular
    | contributor but I did not see anything of late.  I have two questions:
    |
    | 1)  Are these the tables most members use for reducing Lunar
    | observations or is there some other preferred method/tables?  [I know
    | there are many methods to do this, I'm just trying to get a feel for
    | what method list members are using and what may be considered the most
    | accurate method.]
    
    I've never tried lunars at sea, and these days indulge in such things only
    very occasionally on land. And I would usually use a pocket calculator,
    preloaded with algorithms of my own devising, to do the reduction. In my
    case this would be with an elderly programmable calculator, Casio FX730P or
    FX 795P, and there is no point, then, in using anything other than an exact
    clearing mechanism, just as Alex does.
    
    I've had a copy of Bruce's tables for many years, and have tried them out in
    the past, and found that they work really well, and are reasonably easy to
    use. However, his book is rather bulky for taking to sea. I understand that
    there was talk of republishing it in reduced-size format, but don't know if
    that came to anything. The pleasure of using it is in the cleverness with
    which Bruce has brought everything together to make it all as simple and
    complete, for the user, as it could possibly be.
    
    | 2)  Is anyone familiar with the trig/math that Bruce used to derive his
    | lunar tables?  If so, does anyone know if Bruce is amenable to posting
    | it on the list or has it been posted in the past and I just missed it in
    | the archives?
    
    I did a bit of reverse-engineering myself, years ago, as I was intrigued by
    how the tables did what they did. I remember that Bruce did, later, put out
    a posting to the old Nav-L mailing list which explained it. That ought to be
    in the archives, somewhere. Bruce is still around, very much so, publishing
    a perceptive and detailed series on Lewis and Clark's journey, serialised in
    The Navigator's Newsletter. By now it's at part 4, and the expedition hasn't
    even set off yet! It's giving much detail about their astronomical methods.
    But I've seen no postings from him here, since the change to Navlist.
    
    Some of the tables in the book explain themselves, but others are somewhat
    mysterious. Here are some of my own deductions, for what they are worth.
    Scott may like to check them out, numerically.
    
    From page 71 to 206 is a table for K, which is a function of an angle (call
    it A).
    
    K = -log(hav A) or log (2/ (1-cosA))
    
    from page 207 to 272 is a table for "Gaussians", actually a table of
    
    log ((10^-x) +1)
    
    from page 273 to 279 is a table headed log Dec but actually
    
    - log (cos dec)
    
    from page 291 to 294 is Table 7, which is-
    
    log (240' / A)
    
    from page 295 to 301 is Table 8, which is
    
    log ( 60 / (time in minutes))
    
    ======================
    
    The logs are all (base10), of course.
    
    You will note that all are done in such a way that the logs are all of
    positive quantities greater than 1, so there's no fiddling with negative
    mantissas.
    
    I wouldn't swear to the exactness of those deductions, but they may suffice
    to put Scott on the right road, as he appears to know what he's doing..
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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