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List Members,
I posted the email below to the list but it never stuck.  I was
primarily addressed to George's comments on the recent thread regarding
"Variation of compass", so I forwarded it to him directly. As other
members of the list may be interested, I am posting it again. My
original email is immediately below, and George's very thorough response
follows it.
Arthur

ORIGINAL NOTE:
George, et. al.,

This question pertains to the calculation of Azimuth and Local Time from
a sun sight, and the use of this technique in conjunction with lunars.
Without developing the formulas, I can see that if we have Latitude,
Altitude and Declination, we have all sides of the triangle. We can then
compute Azimuth and LHA, and by converting LHA arc to time, we can get
the difference between observation time and the time of Local Apparent
Noon and thus Local Time (please correct any inaccuracy or imprecision).

Having made these calculations, I can now take a lunar distance and
derive GMT (so much more easily said than done!). Was the determination
of longitude then simply a matter of taking the difference between Local
Time and GMT and converting time to arc to get Longitude?  I had
presumed the purpose of getting GMT from a lunar was to correct your
chronometer such that star sights and running sun fixes could be
accurately reduced to get a fix that revealed both latitude and
longitude. Getting latitude via LAN sight, then local time by afternoon
sun, then GMT by lunar, and then calculating longitude seems a
reasonably efficient alternative.  I am curious what Lecky's indicates
was general practice during the time that lunars were in common use.

One final question: I am not sure why Local Time would be used to set
the ship's clock as Local Time changes with Longitude.  When I have
crewed on ships, the Chronometer was set to GMT and the error and rate
documented at least daily, but this was in the age of radio time checks.

Thanks for any light you can shed.

Regards,
Arthur

GEORGE'S RESPONSE:
Dear Arthur,

You ask some sensible and relevant questions, so it would be worthwhile
to
post it to the list if you possibly can, so anyone else can have a crack
at
replying, not just me.

However, I am happy to have a go.

I will be thinking of the period from say 1750 to about 1870, when
lunars
were an important source of longitude information for mariners, though
being displaced by the chronometer

When you look at early navigational techniques, you have to be aware of
the
mindset of those navigators of the past, the way they thought, and the
tools and information they had available.

>One final question: I am not sure why Local Time would be used to set
the
>ship's clock as Local Time changes with Longitude.  When I have crewed
on
>ships, the Chronometer was set to GMT and the error and rate documented
at
>least daily, but this was in the age of radio time checks.

Let's start with your last question, about the ship's clock. That's not
the
same thing as the chronometer. As you say, on a modern vessel you would
always have a chronometer set to Greenwich. But even on a modern vessel,
wouldn't you always find another clock on the bridge indicating at least
ZONE time, to regulate the ship's business? Zone time, however, is a
rather
modern concept.

In the 18th century, THE TIME meant local time-by-the Sun. On land, the
village church clock would be readjusted according to the sundial in the
churchyard, or by an amateur astronomer with a couple of posts in the
ground to establish a South transit. We know (and even the Greeks knew)
that time measured that way was non-uniform: no accurate clock could be
made to run at that variable rate, and the laws of physics could not be
applied if time was measured that way. Each village kept its own time.
Any
concepts of time-at-other-places such as Greenwich, or of mean time,
were
quite alien notions, familiar only to the astronomers with their
accurate
clocks.

On all ships, including those making long passages in longitude, it was
necessary to keep a clock registering local time-by-the-Sun, if only to
time the routine calling-of-the-watch. For example the dog-watches were
always in the afternoon, and it would never do to have the dog-watches
slide into the morning as the longitude altered when an ocean was
crossed.
At sea, it wasn't possible to time the Sun's crossing of the Southerly
meridian, but it was straightforward to establish the local Sun-based
time
from morning and/or evening Sun altitudes, to allow the ship's clock to
be
reset. Because the ship's clock was never very precise anyway, tweaking
the
clock to adjust for longitude changes was not a very different matter
from
tweaking it to compensate for its own unpredictable gains and losses. It
was usually done at a morning Sun sight, if the Sun obliged by
appearing:
otherwise, some guesswork was used.

Of all our different methods of measuring time, we name that measure
"Ship's Apparent Time", but to a navigator prior to the days of the
chronometer, he would simply think of it as "The Time". That, and the
latitude, were the two quantities he would always know well, provided
his
skies were clear, and without needing recourse to lunars or a
chronometer.

>This question pertains to the calculation of Azimuth and Local Time
from a
>sun sight, and the use of this technique in conjunction with lunars.
Without
>developing the formulas, I can see that if we have Latitude, Altitude
and
>Declination, we have all sides of the triangle. We can then compute
Azimuth
>and LHA, and by converting LHA arc to time, we can get the difference
>between observation time and the time of Local Apparent Noon and thus
Local
>Time (please correct any inaccuracy or imprecision).

Well, nowadays you might calculate the azimuth, but not in those days.
Otherwise, I agree. And as you say, this would be Local Apparent Time
(and
not Mean Time, which has the Sun's timing inconsistencies averaged out).

>Having made these calculations, I can now take a lunar distance and
derive
>GMT (so much more easily said than done!) Was the determination of
>longitude then simply a matter of taking the difference between Local
Time
>and GMT and converting time to arc to get Longitude?

Yes, but there's a complication. It depends somewhat on the year. Let me
explain. The longitude is the difference between the Local Apparent Time
and the Greenwich Apparent Time. Or, which is just the same thing, the
difference between the Local Mean Time and the Greenwich Mean Time. The
important thing being that the two measurements have to be made on the
same
time-scale. Prior to 1834, all times in the Nautical Almanac were in
terms
of Greenwich Apparent Time (which was, in the old sense of the word, the
"argument" of the almanac). So prior to 1834, interpolating in the table
of
lunar distances would provide the Greenwich Apparent Time of the
observation, to compare with the Local Apparent Time from the Sun, so
that's easy. From 1834 the increasing importance of the chronometer
(which
by its nature must measure Mean Time) led to the time-argument of the
almanac changing to Mean Time throughout. The difference between these
two
time scales can be up to about 15 minutes either way, and is tabulated
in
the almanac so it's easy to convert one to the other (though it's often
easy to get the sign wrong!)

>I had presumed the
>purpose of getting GMT from a lunar was to correct your chronometer
such
>that star sights and running sun fixes could be accurately reduced to
get a
>fix that revealed both latitude and longitude.

No. That is the way it would be done after the days of Sumner and St
Hilaire in the mid 1800s, and how we would do it today. Before then,
however, what appears to us as a simple concept of taking an altitude of
any body, whatever azimuth it happeed to be at, and finding a
position-line
at right-angles to that azimuth, just hadn't occurred to navigators. An
extraordinary lapse, it seems to me, that this concept didn't appear
until
so late, when all the mathematical tools existed. Instead, navigators
thought of latitude and longitude as quite separate quantities:
longitude
being determined in a separate observation after the latitude had been
obtained from a noon Sun.

>Getting latitude via LAN
>sight, then local time by afternoon sun, then GMT by lunar, and then
>calculating longitude seems a reasonably efficient alternative.

Here you summarise the position well. The GMT could also be taken from a
chronometer (adjusting for Equation of Time where necessary) and perhaps
the chronometer may have been checked against a lunar observation if the
navigator was a belt-and-braces man.

> I am
>curious what Lecky indicates was general practice during the time that
>lunars were in common use.

Lecky came right at the end of lunars and dismisses them with some
contempt. Definitely a chronometer man.

>Thanks for any light you can shed.

Hope it helps. If anything is unclear, or seems wrong, do come back. I
find
that trying to explain such matters to someone else helps to clarify
one's
own thoughts.

If you find a way to post up your question to the list, you are welcome
to
include this response (or not: whichever you prefer).

Yours, George.

------------------------------

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