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Alex Eremenko wrote-

>I posted a second series of the Lunars
>made yesterday at Mon Oct 25 2004 - 22:46:20 EDT.

Here they are-

>Oct 26, 0:0:0 GMT
>AP N 40d27.2', W 86d55.8'
>SNO-T, inverting scope, IC=0, T=61F, Pres: 30.04,
>height 12 ft, weather perfect. Frank's calculator.
>
>GMT     0:16:22    0:20:11     0:27:48     0:33:08     0:34:58
>DIST    70d37.4'   70d38.9'    70d41.8'    70d43.2'    70d43.8'
>ERDIST     -0.2'       0.0'        0.3'       -0.1'       -0.1'
>ERLONG     -6.6'      -0.1'        8.4'        3.1'        3.3'
>
>AVERAGE GMT:  0:26:28
>AVERAGE DIST: 70d41.0'
>ERDIST:          -0.1
>ERLONG:          -2.1

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

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'. Good going, indeed! This must be
near to the ultimate precision, determined by the resolution of the human
eye and the division of the sextant.

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've also plotted out Alex's first set, taken 24 Oct, which looks almost as
good, with the exception of that rejected point No 4: which does indeed, I
agree, stick out like a sore thumb. In the light of the consistent
precision Alex shows he can achieve in the second set, I don't disagree
with his decision to reject that point in the first set. Here is a copy of
those observations, including the rejected No 4.

Moon-Altair:

GMT   4:06:49    4:09:58     4:13:10  4:14:58   4:17:12    4:18:57
DIST  51d22.2'   51d23.3'    51d23.8' 51d22.4'  51d24.1'   51d24.3'
ERD       0.0'      +0.5'       +0.3'    -1.5'     -0.2'      -0.4'
ERL      +0.3'     +13.5'       +8.7'   -44.0'     -7.3'     -12.2'

After the rejection of column 4:
AVERAGE GMT: 4:13:13  AVERAGE DIST: 23.54'
ERROR IN DISTANCE: 0.0' ERROR IN LONG: 0.4'

About No 4, Alex states- >On my opinion, one should REJECT such
>an observation in such a series, without any hesitation.
>That looks just evident to me, without any scientific arguments.

Well, a bit of hesitation, in attempting to understand what might have gone
wrong, might be useful, rather than applying blindly a self-imposed rule
which says "if it deviates from a steadily-increasing series, reject it."
Clearly, something did go wrong with that observation, but what?

He tells us-

>the observations are listed in the order I took them.

In which case it can't possibly have been the result of a timing error, as
first supposed, can it?

Could it be the result of misreading or misrecording the Sextant, as 51d
22.4', when it should really have been 51d 23.4'? I repeat my question to
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?.

>There is some difference between Lunar distances observations
>and doing science research.

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

>In my research, I would certainly
>pay great attention to any result that looks unexpected.
>But here we are not in the business of discovery:-)

Well that may be a mathematician's approach. But if you get unexpected
results, due to some error or blunder, then it's important to discover what
the source of the error is, so that it isn't repeated.

>Also: my experience shows that I committ blunders, and I am
>always ready to accept this. But maybe some people don't:-)

We all do, Alex.

After all that, I don't think there's much ground separating us. And Alex
has already shown his mastery of the sextant, far outclassing any puny
efforts of mine. So I have little authority for lecturing him, though
that's unlikely to stop me trying.

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

George.

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