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Bill,
The date May 14 is actually close to the date
May 15/16 where the almanac data changes to 15.8
The explanation in the Almanac (p. 254) says
that the almanac data are accurate to 0.1'
which means that the difference between the tabulated
value and the true value is less than 0.1'.
In your example, asuming that the value given by Frank
is exact, the difference is 0.07' which is
consistent with the Almanac statement of accuracy.
But this statement does not imply that the last digit
is actually correct. So there is no contradiction.

The reason of these errors is probably the rounding
subroutine. To get the last digit really true,
yoiu have to do all computations with one more digit,
and then apply an exact rounding algorithm, while
in most cases they just cut off the last digit
instead. Because nobody really cares about the exactness
of the
decimal minute digit.

But I understand your concern:-)
When you determine your IC from Sun, and then apply
the "Soviet 0.4' test" you may be in trouble just
because of the inaccuracy of the Almanac data.
Indeed, the true 4SD computed from the Almanac can
in principle differ from the true value by up to 0.4.
(In your example it is 0.32' if we assume Frank's value
to be correct to the last digit).

Indeed, this makes the "0.4 test" sometimes somewhat
too rigid. (I don't know to what precision they give
this value in Soviet almanac, though:-)

All this shows that in fact nobody (including the
almanac publishers) is really concerned with higher
accuracy than about 0.5'.
(The days of the Lunars are gone, indeed!)
And they hope that many various
errors of the order of fractions of a minute will
in most cases cancel each other. And they are right.

I can give an example.
Yesterday I measured a Lunar distance
Sun-Moon GMT April 13 2007, 16:15:40,
sextant reading 53d03.1, IC=-0.5.

Then I reduce with Frank's calculator. The measurement
turned out to be precise: Frank's calculator gives:
error in the distance: 0.0', Error in longitude 0.7'.

Then I reduce the same distance by hand, using the almanac
(and Frank-computed altitudes). Using the algorithm
outlined on the Frank web site.
In the process of
reduction
I notice a lot of differences between Frank's numbers
and my numbers (I use the almanac). Namely:
Sun GHA: 63d46.5' (alm) 63d46.4' (Frank)
Moon GHA: 112d27.3' (alm) 112d27.2' (Frank)
Moon Decl: S12d37.6' (alm) S12d37.5' (Frank)
True distance: 53d00.27' (my computation) 53d00.2' (Frank)
Alt Moon corr'n: -49.4' (my) -49.6' (Frank).
This is the largest discrepancy; I used the Moon tables
in the almanac.

The final result of my computation gives
cleared distance 53d00.26' which is just
0.01' off the true value. That is 0.3' in longitude,
while Frank says 0.7' in longitude.

So you see all these plus-minus 0.1 errors usually
cancel each other nicely in the process.
And you can really use the almanac data for the Lunars
and obtain very precise results.

Not speaking of "practical navigation" for which
the Complete on Board Celestial Navigator with its
1' rounding is probably adequate.

Alex.

On Sat, 14 Apr 2007, Bill wrote:

>
>
> Looking at Frank's site
>
> http://www.clockwk.com/lunars/nadata_v5.html
>
> and Sun and Polaris Ephemerii�for Land Surveyors
>
> http://www.cadastral.com/2007ephs.htm
>
> for 14 May 2007 I find agreement in the semidiameter of the sun; 15!83
> (Frank) and  15' 49.6" = 15!83 (Cadastral).  Yet the nautical almanac lists
> SD as 15.9.  I see this happening on other dates as well.  I would expect it
> could happen near a rounding, point, say 15!9 one page and 16!0 the next,
> but that thought does check out.
>
> Why the difference in SD?
>
> Bill
>
>
> >
>


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