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On Mon, 6 Dec 2004, Ken Muldrew wrote:

> On 5 Dec 2004 at 16:29, Alexandre Eremenko wrote:

> Professional astronomers and surveyors had no difficulties with reducing
> their own sights. The problems with the L&C data were not due to any
> inherent problem with lunars per se.

As I understand the story, L&C were specially taught by
the best available teachers how to do lunars.
Still they:
a) did not understand that it is desirable to take altitudes
(even for the simple reason that taking altitudes reduces
the amount of calculations). I do not accept the argument that
"they had other more important things to do". Look how many
sights they took!
b) tried and were unable to reduce their own sights.
Then, they brought the results of their observations to the
same highly qualified teachers to reduce... and we know
what was the result.

From my point of view this story demontrates that the method was
too complicated for an average XIX century mariner.

> I've done quite a few lunars using only an almanac, log tables, and pencil
> & paper (using old methods such as Witchell's and Maskelyne's for clearing
> the distance). It usually takes me 45-60 minutes from start to finish
> (including the lunar sights, but not a time sight).

This does not disprove my opinion stated above:-)
My undergraduates can solve some problems that puzzled Euler
or Archimedes:-)

> tables were in common use and arithmetic calculation was heavily drilled
> at school,

Norie's 1828 book begins with a special chapter on "decimal
arithmetic".
I doubt this would be necessary if "arithmetic calculation was heavily
drilled at school at that time":-)

> Confidence in the result would come from comparing the lunar
> longitude with the ded reckoning.

I suppose you could check your lunars against GPS or some other
modern tool. I am very curious to know what was the average error?
(I mean, the error in the measurement of the distance).

Alex.

P.S. 1828 Norie is especially interesting to me, not only because of
navigation, but also from the point of view of my main profession:
mathematical education. It tells me a lot about the general state
of mathematical education in England in the beginning of XIX century...
The XX century books in navigation do not explain decimal arithmetic,
and they use formulas instead of "word recipes". Just try to forget
all you know, and follow one of the Norie recipes for reducing lunars:-)

   

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