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    Re: Contents of Maskelyne's Tables Requisite
    From: Ken Muldrew
    Date: 2003 Jun 8, 00:03 -0600

    > Reply from George Huxtable.
    >
    > Don't believe everything you read in Cotter. Jan Kalivoda and I, with
    > other help, have put together a long list of known (or at least
    > thought-to-be) errors in Cotter's History of Nautical Astronomy. The
    > book contains a lot of careless errors, and some others which I take
    > to be failures of understanding, though its many virtues remain. I
    > will copy a recently-updated error list below.
    
    Thank you (and Jan) for the errata on Cotter. In fact, my error was more
    toward not understanding that there were many methods, both exact and
    approximate, available at that time. Now that arithmetic is absolutely
    trivial, it's sometimes hard to appreciate that two centuries ago it would
    be worthwhile to put effort into cutting out one step in a calculation, and
    that many of the best minds turned their attention to doing so.
    
    > Are you aware of Arthur Pearson's website    www.ld-DEADLINK-com
    > which contains many useful references?
    
    Yes, I've been spending a lot of time reading the articles referred to on
    that page. It's quite a boon to us "lunartics" (if I may be so bold as to
    consider myself one of the fellows, though an untutored one).
    
    > You refer to Jeff Gottfred's papers on Thompson.. This information is
    > valuable and useful, but I have made a number of comments and queries,
    > the first being this-
    >
    > ******Gottfred promises, at the very end of Art. 7, to show "how he
    > uses this time to compute longitude" and again in the heading of Art.8
    > promises to do this using the data from Nov 3, but the vital last step
    > of going from lunar distance and LAT to longitude seems to have got
    > missed.*********
    
    Yes, that seems to be the case. Gottfred calculates the cleared distance
    (and finds that his value is within 4" of Thompson's) and then states how
    one would look this up in the nautical almanac to find Greenwich time
    and so calculate longitude. Earlier he gives Thompson's value for the
    longitude so calculated as 117? 36' 34" but he neglects to give us the
    data from the nautical almanac for that day and perform the interpolation
    within the 3 hour gap.
    
    > This matter is relevant to your statement "where a longitude
    > calculation is fully worked". Trouble is, although that's promised, it
    > doesn't happen.
    
    Well, the final step would be pretty simple if one had the nautical
    almanac for that year; perhaps Gottfred didn't have it.
    
    > Do you know of the interesting paper by the late
    > Richard.S.Preston,"the accuracy of the Astronomical Observations of
    > Lewis and Clark",
    
    Yes, I've read that and the notebook by Patterson (though I need to
    spend some more time with the notebook). I was quite surprised to learn
    that Lewis and Clark were not able (or willing) to actually calculate their
    longitude in the field when this had been a daily routine for many of the
    fur traders for so many years prior to L&C's journey.
    
    > I have in photocopy Maskelyne's Tables Requisite of 1767 and also his
    > British Mariner's guide of 1763.. Neither contains the log trig tables
    > that I think you are asking for. Those are required to be obtained
    > separately. In the Tables requisite there are "proportional logs", a
    > special trick for easing interpolation within the three hours between
    > times for tabulated lunar distances, but those are not what you are
    > asking about, I think.
    
    Actually, I was after all the tables that would have been used by anyone
    navigating ca. 1800. I think I have found out quite a bit about these
    tables now, especially after having seen Moore's textbook (though I will
    need to go back and look more carefully now that I know the libary's
    hours).
    
    > In the British Mariner's Guide Maskelyne says on pages 47 "In making
    > these calculations seven places of figures must be used, besides the
    > index, and proportion must be made for seconds, except Gardiner's
    > logarithms be used, out of which the logarithms may be taken at sight,
    > to the nearest ten seconds", In the following table he shows log sin
    > 25deg 53' 24" as being 9.6401282., and so on.
    >
    > (In my own opinion 6 figures are probably adequate in most nautical
    > applications.)
    
    Moore's logarithms are only given to 5 figures (and by the way, thank you
    for your timely article on logarithm tables; the extra "10" in the index of
    the log-trig tables in Moore would have been rather mystifying if I hadn't
    read your article first). If the quote about 7 figure accuracy is from 1763, I
    wonder if this might have been due to not having good enough
    predictions for the position of the moon and falsely concluding that the
    errors were in the calculation.
    
    Thanks again for your list of errors in Cotter [snipped from this reply].
    
    
    

       
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