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I will lay out my problem, and then ask two questions.  This relates to my
post yesterday where I quote Bowditch's section 2010 method for predicting
meridian transit.

Since the daily pages of the Almanac only give Meridian Passage to the
nearest minute, then I calculated the precise time of meridian passage at
Greenwich to the nearest second using the GHA and EqT methods, and then used
those more precise times to predict the sun's transit time at my meridian
(63o 08.0'W) using the method described in Bowditch section 2010.

The answer for my meridian should be ZT 12h 08m 09s, according to the
calculations described at
http://jimthompson.net/boating/CelestialNav/NoonSunSight.htm

If I use Method 1 (GHA method) to calculate transit time at Greenwich on
September 14, 2003 to the nearest second, then this is what I get:
1. GHA = 000o 00.0' .
2. GHA next lower on that date = 346o 04.6' at whole hour GMT of 11h
3. DLo = 13o 55.4' => 55m 42s .
4. => Transit time at Greenwich = 11h 55m 42s, which agrees with the
Almanac's 11h 56m.

But even if I use that more precise time of meridian passage to estimate
transit at my Lo of 63o 08.0'W, ignoring DST, then I still get a different
answer using Method 2 (Bowditch section 2010), albeit much closer than
before:

5. Transit time at Greenwich = 11h 55m 42s = Transit time at my zone's
central meridian (60o 00.0'W).
6. Add that to DLo 03o 08.0' or 00h 12m 32s.
7. => Transit time at my meridian =  12h 08m 14s, so something is still
wrong here, because the answer I got for my meridian using the GHA method
was 09 seconds, not 14 seconds.

8. Alternatively, using the EqT method, since EqT = 4m 19s at 1200 (Almanac)
then I would have expected transit to occur at Greenwich at a mean time of
 12h 00m 00s
-00h 04m 19s
--------------
=11h 55m 41s, which also rounds to 11h 56m, and so also agrees with the
Almanac's 11h 56m.  Note this time is 1 second different from that estimated
by the GHA method.

9. And if I use that time (11h 55m 41s ) for meridian passage, then of
course I get
 11h 55m 41s
+00h 12m 32s
--------------
=12h 08m 13s for meridian transit at my longitude.  But that's wrong too,
because the answer should be 09 seconds, not 13 seconds.

The two methods predict sun transit time at Greenwich 1 second different
from each other, which I presume must be due to rounding.  Or perhaps it has
to do with interpolating EqT.  By interpolation EqT is 0.8 seconds smaller
at GMT 1100 than GMT 1200, but because the result is closer to 1200 I used
EqT 04m 19s rather than EqT 04m 18s, which would have given a transit time
of 11h 55m 42s in agreement with the GHA method, but I cannot see the logic
in using EqT for 1100 rather than 1200.

I posted a time diagram of the situation as I understand it at
http://jimthompson.net/boating/CelestialNav/NoonSunSight.htm
about halfway down the page, where all the above text is highlighted in
yellow.

My questions:

1. Why are these estimates of transit time at my meridian different by 4-5
seconds from the answers I got by the other methods posted at that webpage?
2. Why do the daily pages of the Almanac give time of Meridian Passage to
the nearest minute, rather than the nearest second?  Because it assumes that
the navigator only needs an estimate of transit time to an accuracy of +/- 1
minute?

Jim Thompson
jim2@jimthompson.net
www.jimthompson.net
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