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    Re: Round-off
    From: John Karl
    Date: 2009 May 18, 20:18 -0700

    Sorry, I messed up my explanation of the expected round off error,
    even though I had the right answer.
    The standard deviation (RMS value) of a uniform random distribution of
    width L (center on zero) is L/sqrt(12).  For calculations carried out
    to 0.1', L= 0.1'.  For calculations carried out to 1.0', L = 1.0'.
    A series of N additions (or subtractions) of these numbers then
    produces a standard deviation sqrt(N) greater.  That is, the standard
    deviation of the result is now L*sqrt(N/12).  Frank gave this result
    also.  This is an interesting result because most of our sight
    reductions (lunar maybe excepted) have N less than 12, so we maintain
    the precision of the original numbers.  I.e., using all values precise
    to 0.1' gives a final result to nearly the same precision of 0.1' --
    But remember, that's only one of many different probability
    estimates.  The max error is still L*N/2.  And as before, I'm just
    talking about round off error here.
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