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Trevor wrote:  "Jim, Explaining the difference between your Methods 1 & 2 is
easy. For Method 2, you started from the time of meridian passage quoted in
the almanac to the nearest minute. You cannot expect calculations based on
that to be accurate to anything better than the nearest minute. Since both
of your calculations round to a time of 1308, they are in full agreement to
this level of accuracy. If you want the time of meridian passage to the
nearest second, you can't use your Method 2."

When I ignored the seconds in Method 2, everything fell into line nicely.
But I have two problems with this neat solution to my problem.

Transit time occured at 13h 08m 09s (Method 1).
http://jimthompson.net/boating/CelestialNav/NoonSunSight.htm

1. My DLo converts to 12m 32s.  So rounding up to the nearest minute should
have brought the DLo to 13m, which would produce a predicted transit time of
1156 + 13 min = 1309, not 1308.  If I simply ignore the 32s, then I get
1308, which is in agreement with all the other methods.

2. However Bowditch Section 2010 instructs us to add 11h 56 m and 12m 32s
for a total of 12h 08m 32s, shown as if accurate to the nearest second.  Why
is that?

Here is the relevant section from the 2002 version of Bowditch: "2010.
Latitude at Meridian Passage.  First, determine the time of meridian passage
from the daily pages of the Nautical Almanac. In this case, the meridian
passage for May 16, 1995, is 1156. That is, the Sun crosses the central
meridian of the time zone at 1156 ZT and the observer?s local meridian at
1156 local time. Next, determine the vessel?s DR longitude for the time of
meridian passage. In this case, the vessel?s 1156 DR longitude is 157? 23.0'
W. Determine the time zone in which this DR longitude falls and record the
longitude of that time zone?s central meridian. In this case, the central
meridian is 150? W. Enter the Conversion of Arc to Time table in the
Nautical Almanac with the difference between the DR longitude and the
central meridian longitude. The conversion for 7? of arc is 28 m of time,
and the conversion for 23' of arc is 1 m 32 s of time. Sum these two times.
If the DR position is west of the central meridian (as it is in this case),
add this time to the time of tabulated meridian passage. If the longitude
difference is to the east of the central meridian, subtract this time from
the tabulated meridian passage. In this case, the DR position is west of the
central meridian. Therefore, add 29 minutes and 32 seconds to 1156, the
tabulated time of meridian passage. The estimated time of LAN is 12-25-32
ZT."

My answer is that the time of LAN so determined in Bowditch should be
written this way:
12-26 ZT, not 12-25-32 ZT.

Is that most correct, and the way that Bowditch should have shown the
estimate?

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