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    Re: Sun semidiameter
    From: Alexandre Eremenko
    Date: 2007 Apr 15, 08:51 -0400

    
    Bill,
    Yes, they may use some different algorithm.
    I only tried to make 3 points:
    a) that their accuracy seems to be as they claim,
    the error is less than 0.1'
    b) they do not care that the decimal minute digit is
    correct.
    c) that this is OK for all purposes except for the
    "Russian 0.4 test".
    Which implies that this is indeed not a reasonable
    test, at least with US almanac:-)
    
    Alex.
    
    On Sat, 14 Apr 2007, Bill wrote:
    
    >
    >
    > Alex
    >
    > I see your point, that the N.A. lives up to it's accuracy claim.
    >
    > Past that it gets fuzzy for me.  For the 23, 24, 25, August, 2007 pages N.A.
    > SD is 15!8.  For the 26, 27, 28 August, 2007 pages N.A. SD is 15!9.  So it
    > is safe to assume that mean SD will be 15!85 somewhere between the 25th and
    > 28th.
    >
    > Yet we see SD's from other sources of:
    >
    > 23 Aug, 2007   15.82
    > 24 Aug, 2007   15.83
    > 25 Aug, 2007   15.83
    > 26 Aug, 2007   15.83
    > 27 Aug, 2007   15.84
    > 28 Aug, 2007   15.84
    >
    > If we take the average of the 23,24.25 page, 15.83
    > If we take the average of the 26, 27, 28 page, 15.84
    >
    > No way either rounds up to 18.9.
    >
    > --My $10 pocket calculator claims to display 10 digits but works to 11
    > digits and rounds the last up at 5.
    >
    > --My version of Excel claims to work to 13 figures and drops the last
    > digit with no attempt to round up or down.
    >
    > --Even if, as you surmise, the N.A. may drop the last digit the result is
    > still 15.8, not 15.9 based on Frank's numbers, and surveying numbers down to
    > tenths of a second.
    >
    > I suspect something else is at work here, perhaps the N.A. algorithm?
    >
    > Bill
    >
    >
    >
    > Bill wrote
    >
    > > for 14 May 2007 I find agreement in the semidiameter of the sun; 15!83
    > > (Frank) and  15' 49.6" = 15!83 (Cadastral).  Yet the nautical almanac lists
    > > SD as 15.9.  I see this happening on other dates as well.  I would expect it
    > > could happen near a rounding, point, say 15!9 one page and 16!0 the next,
    > > but that thought does check out.
    > >
    > > Why the difference in SD?
    >
    > Alex Replied:
    >
    > The date May 14 is actually close to the date
    > May 15/16 where the almanac data changes to 15.8
    > The explanation in the Almanac (p. 254) says
    > that the almanac data are accurate to 0.1'
    > which means that the difference between the tabulated
    > value and the true value is less than 0.1'.
    > In your example, asuming that the value given by Frank
    > is exact, the difference is 0.07' which is
    > consistent with the Almanac statement of accuracy.
    > But this statement does not imply that the last digit
    > is actually correct. So there is no contradiction.
    >
    > The reason of these errors is probably the rounding
    > subroutine. To get the last digit really true,
    > yoiu have to do all computations with one more digit,
    > and then apply an exact rounding algorithm, while
    > in most cases they just cut off the last digit
    > instead. Because nobody really cares about the exactness
    > of the
    > decimal minute digit.
    >
    >
    >
    >
    > >
    
    
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