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I've changed the threadname as this discussion is no longer related to
Wikipedia.

Henry Halboth's contributions are always of interest, and his observations
in the past have shown that he still retains a remarkably keen eye, and a
steady hand.

He wrote-

"Regarding the time necessary to calculate the Lunar Distance problem:
I recently had the opportunity, with a sea horizon available, to observe a
Moon-Jupiter near limb distance, as well as the requisite altitudes for
clearing the distance and calculating the Longitude.
I used Borda's method, which is pure spheical trigonometry, to clear the
distance, and the Longitude Time Sight to subsequently calculate the
Longitude. All was done as it would have been done in the early 1800's,
employing six place logarithmic tables and all corrections applicable per
Norie's Tables. The True Distance at Greenwich was taken from currently
published 3-hour interval tables and interpolated by proportional
logarithms.
The calculation time to complete this work, exclusive of observation time,
but including the Longitude work-up was 22-minutes - and I'm a bit rusty.
Claims that this problem required hours to solve are simply myths."

Response from George-

Yes. As Frank has pointed out, it was true that it took hours, before the
Nautical Almanac was published, but the precalculation of Lunar distances,
from 1767 onwards, bypassed most of that work. For doing the job using
precomputed lunar distances, with logs, 22 minutes is pretty good going, and
shows that Henry's brain, as well as eye and hand, is as good as ever. But I
wonder, did that answer come out right,and within 22 minutes, at his first
attempt? Or did he have to make a few tries at it, with some false-starts,
as I usually have to do, and correcting arithmetic errors, before eventually
getting things right? For mariners of the lunar era, repeating the same
calculations day after day, it would all become a matter of routine,
involving little thought; but for us today , it's rather different.

Before 1767, lunars were indeed taken, and worked out, using the published
motion tables of the Moon (by Mayer, and others). But that was a really
involved and longwinded matter, and usually called, not for a mariner,  but
a seagoing astronomer, such as LaCaille, or Maskelyne (see his British
Mariners Guide, 1763).

Henry continued-

 When I get the opportunity, it is my intent to publish these observations
on the List. However, as the accuracy of Longitude obtained is really
astounding, I am double checking everything before giving George and Frank a
go at it.

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

Well, we know already how good Henry's observations can be. But I wish to
sound a note of caution here, without wishing to detract in any way from any
claim that Henry may make. What follows is pretty self-evident.

Whenever you observe some quantity, in which random errors are involved,
even after all systematic errors have been corrected out, there will always
be some scatter. And the scatter will then centre on the true value of the
result. Indeed, the exact true value is the most likely answer. If, just by
chance, you happen to hit a result which you know, by other means, to be the
exactly correct one, that doesn't tell you much about the errors involved.
You can only tell that from a number of different measurements, and from the
scatter in those measurements.

Perhaps Henry has taken several observations, and found that they average
out to the exact longitude he expects. That's creditable, and worthwhile,
but it's the scatter in the individual values that tells us more about the
precision of the method.

Contrarily, however, if instead of an agreement, there's a discrepancy with
the known value, that tells us more; it tells us that the inherent errors in
the method are likely to be at least of the same order as that discrepancy.

I look forward to Henry's account of his astounding accuracy with great
interest.

By the way, observing lunars with Jupiter is a bit different to observing
stars, in that Jupiter has an observable disc when seen through the
telescope, with a semidiameter of around 20 arc-seconds. I've never tried a
lunar using Jupiter. Presumably, the way to do it is to put the centre of
Jupiter's disc against the edge of the Moon, not align them edge-to-edge. In
that way, no allowance needs to be made for Jupiter's semidiameter. Is that
the way Henry did it, and is that what the lunar distance tables that he
used presume? What were those tables, by the way?

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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