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A thoughtful contribution fro Henry Halboth states-

" ... you both ignore the fact that one of the observations in the
Lunar set is also intended for the purpose of establishing the Local
Apparent Time, for ultimate comparison with the GAT deduced from the
GMT established by the distance cleared...."

He is right to point out that determining a longitude involves
comparing LAT (Local Apparent Time) with Greenwich time, and both
those quantities are needed. Most of the discussion about lunars
concentrates on the lunar-distance measurement itself, because it's so
difficult to get sufficient accuracy. That is mostly because of the
slow motion of the Moon with respect to the stars, only about half a
degree in an hour, so that a measurement of lunar distance to 1
arc-minute determines GMT to no better than 2 minutes of time, and
therefore longitude to 30 arc-minutes.

In contrast, determining LAT involves measuring the altitudes of
bodies which move across the sky at 15 degrees in an hour, so that
measuring altitude under optimum conditions to an arc-minute can
determine LAT to (roughly speaking) four seconds of time, which will
have an effect on the resulting longitude of only 1 arc-minute.

Because getting LAT to sufficient precision is so easy, then, it's
rather taken for granted when lunars and longitude are being
discussed. That doesn't mean that it can be neglected.

Henry continued-

"An error in the Altitude or Latitude employed for that purpose will
affect whatever accuracy in Longitude or Chronometer Error may be
expected from the observations as a whole. The Latitude induced error,
of course, being dependent on the distance off the Prime Vertical of
the body employed for the purpose of establishing the LAT."

All that is perfectly true, but for the reasons given above, any such
contribution to the overall error will usually be small, compared with
the errors in the lunar-distance part of the process.

and further-

"In response to my previous comments, George has taken issue with my
statement to the effect that computed altitudes were dependent upon
knowledge of "position/time", but seems to go right on to prove my
point by citing a prior knowledge of LAT to assist in the altitude
computation."

I don't recall having taken issue with such a statement at all.
Indeed, I agree with Henry that a measurement of LAT is necessary.

He had written-

"... yes, I know it's possible to calculate the altitudes - however,
does not that require a position/time of reasonable accuracy - some
authorities stating these calculated altitudes should be within four
arc minutes of the truth,..."

and I hadn't disagreed with that, but answered "no" to his follow-up
question-

" ...and does not such accuracy require a position/time accuracy
better than is ultimately determinable by the Lunar Distance. "

The iteration method, as I explained it, requires a precise value of
LAT, which is a time that doesn't depend on lunar distance for its
measurement, combined with a guessed initial value for longitude. That
guess is improved at each iteration, and that process does indeed rely
on the measured lunar distance. That was my only point of disagreement
with Henry's analysis.

If altitudes of the two bodies involved in a lunar are measured,
rather than calculated, it can often be convenient to use one of those
observations as a time-sight also, to obtain LAT. This is handy,
because it's  a measure of LAT or very near the same moment as the
lunar. Especially handy, in the early days when a ship might not have
carried any timepiece at all; not even a hack-watch.

Often, however, LAT is determined from a time-sight taken at some
other moment in that day from the lunar, in which case the elapsed
time between the two must be accounted for, including any known error
in the rate of the timepiece, and an allowance must also be made for
any change in longitude over that period., derived from
dead-reckoning. You can see the circumstances in which this procedure
must apply. If a Moon-star lunar distance is measured in the dark of
night, with no horizon visible, then altitudes of the two bodies can't
be observed, and must be found by calculation. And neither can a
time-sight be taken; that has to await some light on the horizon, and
the difference between the times of the two observations has to be
allowed for.

Henry has described those possibilities well in his last posting,
which ends "but that is probably a subject for later discussion." I
await his words of wisdom with some interest.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.




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