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    Re: Variation and Amplitude
    From: George Huxtable
    Date: 2007 Jan 8, 17:56 -0000

    Guy Schwarz quoted Tom Cunliffe as saying-
    
    "In chapter 11 of Tom Cunliffe's Celestial Navigation book, he talks
    about
    Amplitude tables. He says " Every proprietary nautical almanac should
    have a page devoted to tables know as amplitude tables.
    Checking my 2007 and 2006 Nautical Almanac - Commercial edition, I did
    not see anything about amplitude tables. Am I missing it
    or is it not there?"
    
    I don't have Cunliffe's book, but he is referring to a different sort
    of Almanac that has now disappeared, unfortunately.
    
    The official, UK and US, Nautical Almanac concerns itself only with
    things that vary from day to day, and apply only to the year in
    question. An exception is the refraction table; but in general, things
    that stay constant are omitted, to be found elsewhere. An amplitude
    table comes into that category.
    
    In the past, proprietary almanacs such as the late-lamented Reed's of
    old, before it was subsumed into Macmillan's, would publish a full
    astronomical ephemeris for the year, together with lots of such
    subsidiary, "constant", navigator's tables, including amplitudes. In
    1993, the constant information was split off into a separate volume,
    Reed's Companion. Amplitudes are given in my copy of Norie's tables
    (1963), and in the tables which were part of Norie's Navigation, (mine
    date from 1914); also in Raper's "Practice of navigation", of 1864,
    and probably earlier.
    
    =======================
    
    The amplitude is the azimuthal angle, measured either way (clockwise
    or anticlockwise); either from due East, at which a body rises, or
    from due West ,at which it sets. The only body that is considered, in
    practice, is the Sun, so declinations are given from 0, at 1-degree
    intervals, up to 23 1/2 degrees, seldom more. Latitudes are given in
    degrees up to the limit that the author considers no sensible mariner
    would exceed (usually 66 deg). The resulting amplitude is usually
    given to the nearest 0.1 deg, which is plenty good enough for its
    usual purpose, checking the compass error. Interpolation is possible,
    but seldom worthwhile.
    
    You have to be aware of the special meaning given to "Sunrise" and
    "Sunset" in these tables. It refers to the moment at which the true
    Sun, if there was no refraction, is bisected by the horizon. So,
    because of that refraction, the navigator takes his compass-bearing on
    the Sun at the moment when its whole disc floats well clear of the
    Sun, with a gap between the lower-limb and the horizon, equal to a
    semidiameter. That's easy to estimate by eye, quite well enough for
    the job. A subsidiary table is often offered, to adjust the result if
    you use the apparent Sun, split by the horizon, but it's hardly worth
    the bother of ensuring that you apply it the right way round.
    
    Why bother with tables for amplitude, though, if you have a pocket
    calculator?
    
    The simple expession to use is-
    
    sin amp = sin dec / cos lat, but remember again, that applies at the
    moment when the lower limb is a semidiameter above the horizon.
    
    ===================
    
    Guy continued-
    
    "On to Variation. How was it discovered? My guess is that navigators
    would take a bearing on the setting/rising sun and their almanacs
    had the amplitude tables and determined something was off? Or am I off
    base
    
    Portuguese navigators, setting off deep into the Atlantic around the
    time of Columbus, did their navigation from Polaris, and thought that
    the compass needle was magically drawn toward Polaris. So when it
    started to diverge as they went West, it was a source of great worry
    and confusion.
    
    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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