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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Lunar trouble, need help
From: Frank Reed
Date: 2008 Jul 01, 16:16 -0400

```Kent, you wrote:
"The factor 60,35� has been provided to me from the Observatory in Stockholm
to be used with the true zenith altitudes for altitudes above approx. 10
degrees. The factor is taken from modern English litterature."

What color light? It's not often mentioned explicitly that this factor
applies only for one specific frequency in the visible spectrum. That's one
reason why two people can quote factors differing by an arcsecond and still
be technically correct. It's also why we shouldn't worry too much about the
tenths and hundredths of an arcsecond. And it's a big reason why we
shouldn't shoot lunars when the objects are below about ten degrees: the
stars and the limbs of the Sun and Moon are stretched out into colorful
bands at very low altitudes. Incidentally, I use 58" usually.

And:
"Yes, this is correct. For altitudes below 20 degrees I use the formula
defined by Smart."

Since you're modeling historical methods, you could just input the whole
refraction table as printed. Then the software would interpolate between
values much as a 19th century navigator would have done on paper. This
approach bypasses all this chatter about various formulae for different
altitudes. It's also a reasonable approach for a modern analysis. Sometimes
people doing these calculations obsess over the "Bennett" formula. This is
because we carry around "baggage" from the calculator era and the early
years of programming small computers. There's no real advantage to a short
formula today (except saving a few keystrokes).

And you wrote:
"So again, what I have tried to achieve is a re-construction of how the LD�s
were measured and reduced in the old days (by Swedish navigators) and not
necessarily what will be achieved with todays know-how."

May I ask, what is your source material? Are you looking at old navigation
manuals and textbooks or old logbooks (or similar)? The textbooks tend to
focus on minor issues (like second-differences, and finding local time from
star altitudes, and correcting for the oblateness of the Earth) which were
almost entirely irrelevant in practical navigation.

And:
"The first way is what I outlined and this way can be used for any celestial
body, incl. the sun and provides the local time (MT). The other method was
to use the sun for generating the local time by finding the sun�s apparent
time and correct it with the TE. This later method required (requires) less
calculations and was therefore probably preferred by navigators."

The general method (which you outlined previously) was also preferred by one
other group: sadistic navigation instructors! Seriously, by the second half
of the 19th century, very few navigators ever used lunars at sea, but many
studied them in schools and instructors used the arcane aspects of lunars as
a means of "spreading the curve" (as we would say today in education) or
more informally "separating the men from the boys." So an instructor might
teach this very involved method of getting local time and then put that on
an exam, just to see who was paying attention. Meanwhile, everyone knew that
local time was determined, almost without exception, by observations of the
Sun.

Yet another reason some instructors and theoreticians emphasized the
possibility of getting local time from the stars is because it seemed "pure"
in a mathematical sense. If you take a lunar distance observation with a
star or planet, then surely you should get local time from that same body.
That sounds good "in theory." In fact, lunars with stars and planets were
nowhere near as common as Sun-Moon lunars. From my experience with logbooks,
I roughly estimate that around 80% of lunars were Sun-Moon observations. So
once again, the common method of finding local time was to measure the Sun's
altitude. In effect, it turns the sextant into a sundial. It's a simple
sight and a simple calculation. These sights were almost as common as Noon
Sun for latitude throughout the period from the late 18th century and into
the middle of the 20th century.

And you wrote:
"Also keeping the local time with a watch was used but after what I have
gathered this was not a common method likely because watches were not good
enough. But this method, when working, was certainly much easier for the
navigator than the first method outlined by me."

Watches were not the issue. Plenty of good watches were widely available in
the period. The real problem with carrying local time on a watch is that you
have to correct it for the change in longitude since the last time sight. In
modern terms, it's a running fix problem. It's hard to guess how much time
since the last sight was considered acceptable historically, but a few hours
was certainly no problem and even twelve hours does not appear to have
caused much concern.

-FER

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