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Bill M., of the sextant certificates, you wrote:
"It isn't really all that safe to interpolate, as the sources 
of error are complex and the errors do not usually vary predicatably over the 
measurement range of the sextant."

Yes, I agree, and this is yet another reason why folks have been looking for 
the opportunity to do their own arc error tests. With a flexible method, you 
could zero right in on any areas where there are rapid changes in the error. 
And it may be worth mentioning that 19th century sources on arc error 
sometimes are based on specific theoretical models of this error which are 
simpler than the "complex" sources of error that you mention here. 

I've talked before about a tabletop method for calibrating a sextant without 
giving details while I was considering some options. I do expect to be able 
to describe that on NavList very soon.

And you wrote:
"Ideally, makers should perhaps also calibrate the worm and its centring 
errors through a whole rotation."

Yes, I agree. From talking with Ken Gebhart, I understand that their prefered 
approach is to count micrometer error as unacceptable. That is, it should be 
eliminated in the quality-control at production. Unfortunately, there's no 
guarantee with older instruments, so we have to test it. There's a simple 
method for doing this that we've talked about in NavList posts a few years 
ago. Basically, you create a grid of vertical lines (on a laptop screen, 
e.g., which generally will have a very uniform spacing of pixels). Then you 
view that grid with a sextant sitting on its side on a table from a distance 
such that the individual lines are separated by some convenient angular 
interval like six minutes of arc. You make the first line longer than the 
others or you make another line that is offset from them below some 
horizontal line. Then you just work down the lines carefully lining them up 
and recording the micrometer reading at each line. This alignment process is 
a case of the "vernier acuity" which Douglas mentioned in one post so it's 
something that the human visual system can do really well --up to ten times 
better than normal visual resolution. When you're done, you compare the 
expected angle with the angle on the micrometer. The difference should be a 
straight line, nearly flat, but if there's micrometer error, you would see 
something like a sine curve. I have a sextant with a curve like this whose 
amplitude is 0.7'. Without this information, the sextant was strangely 
inaccurate. With it, it's almost perfect.

After your interesting list of results, you wrote:
"One might wonder then that some people achieve superb results, and this is 
probably because averaging evens out the drum and worm errors, which must sum 
to zero over a whole rotation."

That's quite possible. It would only increase the standard deviation in 
measurements by 0.1-0.2' in most cases. Also, there's a chance that this is 
just luck of the draw in your case. You may have a group of sextants that 
just by chance have appreciable micrometer errors. In the six sextants I've 
tested this way, I only found one (see above) where I could confidently state 
that the micrometer error was larger than 0.1' at any point. May I ask, have 
all of those instruments you tested been disassembled down to the micrometer 
drum?

And you wrote:
"I take it for granted that they must also have great observational skills."

I don't think I have excellent observational skills, and I've seen people 
who've never used a sextant before (but do have familiarity with cameras or 
other optical equipment) get results accurate to 0.1' in lunars on the first 
or second try. The key of course, indeed the absolute pre-requisite, is that 
the sextant has to have been properly adjusted to eliminate adjustable errors 
like telescope collimation, and tested for non-removable (but correctable) 
arc error if any, micrometer drum error if any, and the all-important index 
error. If someone with skill in adjusting and testing the instrument hands 
one that has been properly tested to a group of beginners, I find that many 
beginners can get excellent results.

You wrote:
"it occurs to me that star-star observations might be at least as good a way 
of calibrating a sextant as a laboratory method that looks only at whole 
degrees. One short cut when calibrating an engineer's micrometer is to check 
it at, say, 2.5, 5.1, 7.7, 10.3, 12.9....  and so on, rather than every 2.5 
mm as well as a full turn at each end."

Aha. That's a good trick. I like it.

-FER




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