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Dear Antoine,

I think I can propose now a very plausible way out of all difficulties.
You wrote that this Lunar distance was "an average of 10".
Now, how long does it take to make 10 Lunar observations?
From my experience, at least 5 minutes, even if you use an assistant:-)
How many times do you think they measured Sun and Moon altitudes?
Are they also averages of 10??

Unikely. They certainly knew that 1 degree error in altitudes
does not affect the result for a Lunar.
So, most likely they took each altitude ONCE for the series of 10 Lunar
distances.

There could be 3 observers of course: one for the Sun, one for the Moon
and one for the distances. (I even remember a picture in some old book
showing this ritual:-) But even if there were 2 or 3 observers,
they probably took just one altitude of each and 10 Lunars.
Then it is not surprising that the Sun and Moon altitudes are
separated by an interval of few minutes.

In these low latitudes, in the early morning, when observations were
made, the altitudes change very quickly.

I think this can easily explain the mismatch of the altitudes and
the Lunar distance. They were just taken at slightly different times.
Few minutes apart.

Now they say that the local time was derived from the observation of
the Sun. This means that probably the Sun atitude has to be used to
determine the "time of the observation".

On the other hand, the Sun was approximately in the East in
the morning, and the horizon under Sun was obscured by land, as
we see from the map. Which makes it somewhat difficult to understand how
they
used the Sun altitude to determine the local time.

Alex.

   

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