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    Re: Semi-diameter in the Nautical Almanac
    From: Gary LaPook
    Date: 2009 Dec 22, 18:06 -0800

    It can be stated very simply. Add the two micrometer readings,
    subtract 60 then divide by two.
    
    (This assumes an index error in the range normally found, less than
    plus or minus 28 minutes.)
    
    gl
    
    gl(
    
    On Dec 22, 5:44�pm, frankr...{at}HistoricalAtlas.com wrote:
    > 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
    
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