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Henry H, you wrote:
"In my opinion, for what it may be worth, this statement is not technically 
correct. Arc error [...] does not necessarily change proportionately over the 
full extent of the arc and should be individually determined at any measured 
angle - or at least at far lesser intervals than is normally done."

I agree completely. After the instrument has been tested at sufficiently fine 
intervals, one can then (and only then) provide a table with wide intervals 
(at least for some parts of the arc and interpolate linearly (or 
"proportionately") in between. So for example, one might have an arc error 
table that shows a smooth, linear change from 0 to 30 degrees, then a rapid 
change in one direction to 40 degrees, a change in the opposite direction to 
45 degrees, and then a smooth linear change up to 90 degrees and so on. But 
the common standard of listing the arc error every 30 degrees only gives a 
general idea what's going on.

In the section which I ellipsed out in the quote above, you wrote that arc error:
" necessarily includes centering error, graduation errors, deformation error, 
and the residuals of any other uncorrected errors of mirror parallelism and 
perpendicularity, as well as telescope collimation and mirror prismatic 
errors"

I would only add that the last three can, in principle, be eliminated or 
measured separately though this doesn't make much difference in actual 
practice.

You added:
"This error may also change over the years and old certificates certainly should not be taken as Gospel."

Yes, I agree completely, especially with sextants that have gone through a 
possibly long second-hand market --in other words, ebay purchases. And from 
my perspective at least, this is the main reason that there is continuing 
interest in finding some inexpensive, non-laboratory means of assessing arc 
error.

And you concluded:
"Clarke's little book is great, but there are others out there, including "The 
Sextant and its Applications", Simms 1858, which go into the subject far more 
exhaustively, and may well appeal to the more technically minded. "

Yes, that's a much longer and more mathematical treatment. For those who do 
read Simms re arc error, just bear in mind that the theoretical model of 
"eccentricity" which he applies is too pure. In real sextants, as you've 
noted above, Henry, the arc error is due to multiple sources and it's 
probably not a good idea to constrain it by the theoretical equations in 
Simms. For completeness, this book is also available on Google Books (it's 
been there for a few years). You can find it here:
http://books.google.com/books?id=oDIDAAAAQAAJ

-FER





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