NavList:

Gary, you wrote:
" But you don't need to know the S.D. to do it and it really doesn't provide a "sanity check" all it does is give you a measure of the accuracy of the scale between plus and minus about half a degree."

It really does provide a useful check. The limb-to-limb observation yields two pieces of data:
1) subtract the on and off arc values and you get the observed index correction.
2) add the on and off arc values and you get the observed diameter of the body (2x).

Now, the second calculation can be ignored but if you work it out (hardly any effort to it), you should get 4xSD as listed in the almanac. If the observed value differs by, let's say, 0.5 minutes of arc from the predicted value from the almanac data, then you ALSO know that your observation for the index correction has uncertainty of the same order of magnitude. On the other hand, if your observed value for the semi-diameter exactly matches the published number in the almanac, then you can have good confidence in the observed index correction. This is not an absolute test since it is possible to make the observations in such a way that both on and off arc angles are over-estimated without introducing any error in their difference, but normally observational error will affect both the sum and the difference.

You added:
"This type of check can be done with any far away object such as a building or telephone pole, the actual width of the object makes no difference in finding the index error."

Yep. Anything with clearly defined edges beyond roughly a mile (for minute of arc accuracy) or ten miles distance (for tenth of a minute accuracy). In fact, you can use two distinct objects with well-defined edges. Two masts will do, as long as they're stationary, and as long as they're far enough away. A big advantage with terrestrial objects is that you can lay the sextant on its side on a table, and then the observation can be done much more carefully. You can also remove the sextant's standard telescope and place a higher-power "spotting scope" in line with the normal placement of the telecope. Measuring IC at 20x is certainly better than measuring it at 3x.

And you wrote:
"The method I use is slightly different. I simply treat the off the arc
reading much like the characteristic of a logarithm. In the example, the
below zero reading is 32 with an understood -60 behind it. So I add the
two readings from the micrometer, 36 + 32 = 68 minus the understood 60 =
8 divided by 2 = 4, the same answer but easier to do in your head."

Yes. Your method, I think, has the advantage that it may be easier to teach in writing. I have found that a considerable number of people who learn this method from books (as normally taught) don't really understand what they're supposed to write down for the off-arc reading. It's confusing because the diameter of the Sun (and Moon) just happens to be close to 30 minutes of arc. So if the index on the micrometer is pointing at 34.5 on the arc and 30.5 off the arc, then half the difference of 34.5 and 29.5 (60-30.5) yields an IC of -2.5', but some people instead think that they're supposed to take half the difference of 34.5 and 30.5 which yields an IC of -2.0'. In cases like this where the index error is a minute or 2 "on the arc", the result of the calculation would be nearly the same even if it's done incorrectly and that unfortunately enforces the erroneous method. Now if instead of reading about it, you've seen somebody do this observation and calculation, then you see them read the scale backwards (equivalent to subtracting from 60), but if you've only read about it, it can be confusing. The approach you use strikes me as less likely to be misinterpreted when read.

-FER