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Brad wrote-


"For the same lunar distance at 155 degrees 13.1 minutes, I used Frank's
online calculator and a time of 15-48-12.  I injected the altitudes exactly
as given in the log into the LL (lower limb) fields of the calculator.
Frank's calculator states that the error in the lunar is now Zero minutes!
The error in longitude is a mere 1.3 minutes.

Therefore, if you know precisely what Frank means by his altitude fields,
you can determine more about the data presented in the log.  The solution
that Frank provides states "Cleared using observed altitude".

Finally the calculator states an error of 3.8 minutes in Moon altitude and
3.4 minutes in the Sun's altitude. In attempting to use 3.6 minutes as an
index correction, it is shown that the error in alitudes are in opposite
directions."

=======================

Brad needs to be careful here. Frank's online lunar calculator is intended
for a rather different purpose.

It needs to know the observer's position (latitude and longitude), and GMT,
and then it will predict a lunar distance, which an observer can compare
with his observation.

Brad has taken a stated position, and an observed lunar distance, and using
the program backwards, has adjusted the GMT until it gives the right value
for lunar distance. He has found a suitable time, at which the calculated
lunar distance corresponds to Bayly's observation, providing an error on
longitude of just 1.3 arc-minutes. Indeed, another 5 seconds-worth of
adjustment to GMT would have reduced that error to zero.

That is a perfectly valid thing to do, IF the observer's position is known.
But to Bayley, his position wasn't known. His latitude was known (or at
least assumed, well enough). But his longitude wasn't known. It depended on
the result of the lunar observation, the value of GMT. And ALSO depended
(and this is the crucial matter) on his measurement of local time, which
presumably was obtained, at that same moment as the lunar, from the
altitude of the Sun, though there's nothing on that page to tell us so.

If Brad had started from a different position, in longitude, he would have
got a different value for GMT. So, without that crucial observation for
Local Apparent Time, he has, as yet, ascertained nothing. I think (and no
doubt he will correct me here if I have it wrong) that Brad has not yet
deduced the LAT obtained from that Sun altitude. When he has done this, and
differenced GMT and LAT (allowing for equation of time), Adventure's
longitude will be the result. That is unlikely to be very different from
the initial assumption of longitude that Brad has started from, but only
because that assumption was based on Bayly's competent observations, for
both Greenwich Time and Local Time. Both are needed. If the resulting
longitude does differ greatly from the presumed value, then a reiteration
is called for, because position changes affect the clearing process (a
bit).

If we do take Bayly's position, it's interesting that the value for
Greenwich Time that it produces is about two-and-a half hours ahead of the
reading of his chronometer. I had warned, in a previous postin, that times
on that chronometer should not be taken at face value, because of its poor,
and worsening, slow running since the voyage started the year before. And I
reckoned, from the graph that Howes produced, that it was likely to be
running something like 2.5 hours slow, by that stage in the voyage. Which
is just what it's turned out to be. No doubt, Howes deduced that graph from
just the sort of observations, aboard Adventure, that we are looking at
now, which just goes to show that we are all self-consistent.

And also shows that without lunars to correct it, that chronometer would
have become a useless tool by that stage of the voyage. No doubt there will
be a table of corrections to their chronometers, at various dates, to be
found in Wales and Bayly.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

.

   

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