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    Time Sight Computations
    From: Chuck Taylor
    Date: 2004 Sep 27, 18:09 -0700

    Frank Reed recently described the process of computing
    a time sight in words, but for some people a
    worked-out example is helpful.
    I spent the weekend at anchor and had the opportunity
    to shoot a few sun sights.  The following reductions
    are of one sight taken of the Sun when it bore
    approximately WSW.  I have shown three methods, one
    modern (using a calculator) and two traditional
    methods using log tables. I hope someone finds these
    examples helpful.
    For comparison, this same sight reduced by the method
    of St. Hilaire yielded an intercept of 0.1 nm.
    Chuck Taylor
    North of Seattle
    Time Sight of the Sun
    At anchor, position by GPS:
            Lat   48d 30.1' N
            Lon  122d 49.5' W
    25 September 2004
    Corrected UT (GMT): 23-17-12
    Corrected Ho:       24d 54.3'
    Almanac data:
            GHA Sun:  171d 27.4'
            Dec Sun:    1d 17.6' S
            EqT:   + 8m 38s
            GMT:  23-17-12
            GAT:  23-25-50
    Method 1:  Direct Computation
            Lat = L = 48.50167
            Dec = d = -1.27833
            Ho  = h = 24.90500
    cos t = (sin h - sin L sin d) / (cos L cos d)
    cos t = 0.66093
        t = 48.62894
        t = 48d 37.7'
    For an afternoon sight,
        Lon = GHA - t
            = 171d 24.4' - 48d 37.7'
            = 122d 49.7'
    Method 2:  Using log tables
    First compute polar distance:
    p = 90d + 1d 17.6' = 91d 17.6'
    h    24d 54.3'
    L    48d 30.1'    log sec  9.12462
    p    91d 16.7'    log csc  0.00011
      2)164d 41.1'
    s    82d 20.6'    log cos  9.12462
    s-h  57d 26.3'    log sin  9.92573
    t                 log hav  9.22991
    t    48d 40.1'
    For an afternoon sight, Lon = GHA - t
    Lon = 171d 27.4' - 48d 40.1' = 122d 47.3
    If you don't have haversine tables, you can
    use sin tables as follows:
            sum    2)19.22991
    sin (1/2)t        9.61496
    (1/2)t          24d 20.0'
    t               48d 40.0'
    This was how it was shown in the 1920 Bowditch.
    Later editions used haversines.
    Method 3:  Same as Method 2, except that hour
    angles are expressed in hours, not degrees.  Note
    that nautical almanacs formerly listed the Equation
    of Time for every 2 hours rather than the GHA of
    the Sun for every hour, as is the case now. The
    user was expected to compute GAT from GMT and
    use that instead of GHA Sun.  Older tables allowed
    you to extract the hour angle directly in units of
    The computations are the same up to the point
    t                 log hav  9.22991
    which becomes
    H.A.              log hav  9.22911
    H.A.               3h 14m 40s
    L.A.T.            15h 14m 40s
    G.A.T.            23h 25m 50s
    Lon                8h 11m 10s
    Lon               122d 47.5'
    Notice that using logs and tables instead of
    direct computation yields slightly different
    results for longitude (by about 2'), unless
    I have made an error.
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