# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Star-star distances for arc error
From: Frank Reed
Date: 2009 Jun 26, 19:16 -0700

```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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