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    Re: Time Sight Computations
    From: Henry Halboth
    Date: 2004 Sep 28, 10:40 -0400

    Quite frankly, a 2" difference in longitude, as between the methods,
    should be explainable. It could be as simple as the difference in
    trigonometric functions as developed by your computer and as presented in
    your tables - they may be rounded off differently as respects the number
    of places to which they are carried; also, you will find some slight
    differences as between using five place and six place tables, although
    this may not account for as much as 2 minutes. As previously posted, I
    have never found any significant difference between the various methods
    of solution, if rigorously (yes Frank, I said it) analyzed - but then
    again, I have never used a calculator not specifically programmed for
    astro observations. It also would seem that your conversion of 1-17.6
    (declination) to 1.27833 may be somewhat off, however, I have not
    recalculated to find the effect.
    
    Many thanks otherwise for an interesting posting.
    
    On Mon, 27 Sep 2004 18:09:45 -0700 Chuck Taylor 
    writes:
    > 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
    > time.
    >
    > 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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