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Dear George,

On Tue, 17 Apr 2007, George Huxtable wrote:

> Cook had metal sextants, with large radius, and Vernier scales, so their
> scales could be read rather precisely. But they were divided by hand,
> machine division being a decade or two into the future, so systematic errors
> in the scale calibration were the big problem. I suppose they could have
> been corrected by a programme of measuring star-to-star distances, but I
> have no idea whether that was ever done.

These statements raise several interesting issues.

Let me share my own experience (and I will appreciate if
other list members add to this).

1. Reading a vernier scale to 0.1' is a tricky business,
especially at night. This can be very annoying and time consuming
but this cannot be a serious additional source of errors
I mean no more than 10"-15" if you read with maximal care,
even on a 7 inch arc.

2. That sextants were divided by hand. It would be very interesting
to know how accurately were they divided. I do not see a priori reasons,
why machine division should be more precise. Were not the dividing
machines themselves divided by hand?
More serious matter is that at that time they were not apparently
"certified". (The Kew observatory certificates begin
somewhere in XIX century). And it is not clear to me
how those early sextant were really
tested. And whether they were tested.

3. Concerning the star-distance method of testing,
I remember your own question, George, on the old list
several years ago: "Has anyone succeded in finding the arc error
of a modern sextant with star distances?" (I cite from memory).
Nobody ever replied that s/he succeeded:-)
I failed, despite my serious efforts to so this over 3 or 4 years.
I very seriously doubt that star distances permit you
to test your arc to 0.1' or 0.2' accuracy. I could never do this.
Same applies to IC from stars btw. It is only the constancy of my SNO
index error that permits me to determine it reliably by very many
observations.
My Lunars are better than star distances.

4. When speaking of high precision Lunars
(I am talking of 0.2' accuracy
or so) I see two main difficultiues:
a) How to achieve a precise touch of the two objects in
your field of view. This seems to require years of continuous practice.
It took me 3 years of frequent observations to achieve the results I
recently posted. (My sight is considered normal by doctors and I am 50+
years old). The errors here are NOT random, and cannot be eliminated
by averaging. The observer just has to feel how the picture should look
then the objects really touch. And feel this under very different
conditions of brightness, sextant position and the loo
of the objects themselves. This is what I find hardest.
One needs reasonably good optics. (I find the optics on my old
sextants just terrible
in comparison with the SNO inverting scope).
b) Sextant rigidity. This (together with the optics)
was probably a major
problem
of old sextants. Again, I find my modern SNO far superior to the
old vernier C. Plath in this respect. There is a lot of discussion of
rigidity in XVIII century literature, and one of Cook's associates
complains that his sextant has unpredictably changing instrumental
error which he cannot explain.
Same problem I experienced for several
years, and I still don't know whether this was an instrumental error
or a personal error, but it looks that by now most of it is
eliminated. Though if one looks at the distribution of my
errors produced in a previous message by George, you see that it is
asymmetric, it is not a normal distribution, and it is slightly
biased to the positive side.

U suppose that the main reason why they eventually switched to smaller
frames (6 and 1/2 to 7 and 1/2 inches) was rigidity problems.
It is probably impossible to make a brass frame of 9 inches radius
rigid enough, and so that you could still lift your sextant without
an assistant. I also suspect that modern lightweight alloys
(duralumin) permitted to make much more rigid frames.

Anyway, the conclusions from my limited experience are
that
a) achieving 0.2 accuracy of a measurement is VERY hard
b) averaging does not always help (because systematic personal
and instrumental errors dominate the overall error).
Of course, averaging helps to some extent (as seen from my statistics,
for example)
c) on the question whether the best XVIII sextants were better
or not than those which are available nowadays I still have no
definite answer. Here by "better" I mean "better ultimate accuracy".
There is no doubt that modern sextants are much more convenient
in use. I used to think that the old ones were better
but now I don't think this anymore.

Alex.


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