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Dear George,
Thank you very much for so careful analysis of my data!

On Wed, 27 Oct 2004, George Huxtable wrote:

> I've plotted out that second set of lunars,
> and indeed they show great
> precision. If you strike a straight line through them by eye,
> no points
> diverge from it by more than about 0.25'.

I did not do any analysis of this sort. The numbers looked
plausible to my eye, so I just reduced them and posted on the list.

> near to the ultimate precision, determined by the resolution
> of the human
> eye and the division of the sextant.

This is an interesting question, indeed. How much the natural
abilities of humans eyes vary, and whether one can increase
the resolution by practice.

Examples. Once a famous XVIII century Russian scientist
(Lomonosov)
showed Venus in
a telescope to his mother, a non-educated peasant woman.
Her immediate reaction surprised him. She asked:
"Why does it look up side down?!"
(The telescope was inverting). She saw the phase of the Venus.
According to the usual wisdom (and theories of vision), this is
impossible for a naked eye.

There is a reliable record of a XIX century German shoemaker whose
eye had resolution of 1", which sounds totally incredible.

Or look at the world records of target shooting. The professional
marksmen somehaw have the ability to aim their rifles with
much more than 1' precision (1' resolution is usually
considered
best possible
for a naked human eye.)

All these facts I learned from my mother who was an ophtalmologist.
She said her science had no explanation of these facts.

> One minor puzzle arises, however.
> If I sum the 5 values of ERDIST, and
> divide by 5, the average comes out at -0.02, not -0.1.
> And, more strangely,
> if I sum the 5 values of ERLONG, and divide by 5,
> I get an average of +1.6
> minutes, not -2.1 as stated.
> Not that it matters; all these values are well
> within the error range expected from a lunar.
> But what causes a simple
> averaging to go wrong?

I also noticed this. I think this is a question to Frank Reed:
how his program really works. I introduced the row data and
printed what his program returned. Then I introduced the average
of my row data and printed the program output.

So I am only responsible for computing the
averages of GMT and DIST,
which I computed by hand (and then verified with my calculator:-)

> Alex: if his point-4 had been 51d 23.4',
> would he then have rejected it on
> the grounds that it breaks his monotonic rule?.

I am not sure. Depends on the purpose of the observation.
In any case, I certainly preserve all records.
In this case (of a quite experimentation on my balcony)
I reduced all sights anyway.
So essentially number 4 was rejected only to
a) Compute the average and
b) Report to the list
If my life depended on these observations,
I would certainly take all results into account (as a precaution)
but in computing the average I'd reject 51d22.4'
but probably not 51d23.4 to compute my chronometer correction.

Another example: I am always measuring index error before
every observation. The Sun measurements consistently give -0.25'
but the star measurements give zero. The Sun error could be due
to the filters I use, or to the difference in air the temperature
during the day and night.
For the Lunars I assumed it to be zero,
always measuring it from a star before taking lunars..
But imagine that my Lunars results were systematically skewed
by about .2 or .3. Then I'd have to reconsider my views about
index error:-)

> Not a lot of difference, really. In both cases the aim
> is to squeeze the
> most accurate information out of data which

In science you are exploring the Unknown. And you have a chance
to discover something new. In measuring the Lunar distances with
a sextant you follow a routine established for centuries
and you are not likely to discover anything new:-)
This is the difference.

> One day, we will learn how he gets on with lunars at sea...

I hope this will happen. Thanks.

Alex.

   

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