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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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