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    Re: Increments and Corrections
    From: Stan K
    Date: 2013 Jul 16, 16:20 -0400

    A couple of years ago a friend of mine and I were discussing how to implement Increments and Corrections in my Celestial Tools program and his Navigation Calculator Workbook spreadsheet.  Looking at the output of his spreadsheet, we noticed that the Almanac values apparently did not use what we call "standard" rounding, in this case, for instance, 0.00 through 0.04 would round down to 0.0 and 0.05 through 0.09 would round up to 0.1.  He chose to change his spreadsheet to display the values to two decimal places, letting the user decide whether to round up or down.  I did a "study" and was able to tweak my rounding routine so that it almost always gave the Almanac values.  "Almost" because there were seven corrections that would not fit into the tweaked rounding routine, so I hard-coded these into Celestial Tools.

    Yesterday I was testing some changes I'm making to Celestial Tools and noticed a discrepancy between the output of Celestial Tools and a "manual" effort.  By the luck of the draw, it happened to be one of the seven oddballs.  So I looked at the seven in the program, comparing them to the Almanac.  Only two of the seven were wrong, but, even so, how could I make such an error?  On a hunch I grabbed another Almanac from the pile and found that this time the values agreed.  I started going through a bunch of Almanacs and found that these two values changed in 2002 (possibly 2001).  (We were apparently using a later Almanac in our discussions.)

    All the values that were off using standard rounding were the ones where the second decimal place was a 5, and, of course, the values were always off by 0.1'.  (A bizarre thing is that the earlier Almanacs used standard rounding; it was the later Almanacs that did not.)

    But I only looked at seven values.  It is possible that others changed, some that year, perhaps some in other years.  But just having those two is enough to worry me, since the Power Squadrons exams and homework say that any Nautical Almanac can be used for the Increments and Corrections.  If it is only those two values, then the odds are pretty slim that a problem will need one of them, and the problems can be constructed to avoid them.  Nevertheless, I/we (USPS) have been teaching misinformation.

    I'll be sending an email to Catherine Hohenkerk to get her thoughts on this.  She has always been very helpful and responsive.

    BTW, I might have brought the refraction table change to the attention of NavList, but it was not my eagle eye that found it.  I learned of it from a Power Squadrons Educational Department Notice.  However, it was my eagle eye that noticed that although the table changed in 2004, the formula in the back of the Almanac did not change until 2005.


    -----Original Message-----
    From: Frank Reed <FrankReed@HistoricalAtlas.com>
    To: slk1000 <slk1000@aol.com>
    Sent: Tue, Jul 16, 2013 3:04 pm
    Subject: [NavList] Re: Increments and Corrections

    You wrote:
    "After years of having been taught, thinking, and teaching that the Increments and Corrections table at the back of the Nautical Almanac is the same year after year, I have discovered that this is not the case. "
    Fascinating! And bizarre, too. Just to clarify, you have found just those two instances so far, and they only differ by one tenth of a minute of arc. Is that correct? I realize two cases is a small set to judge from, but is there any pattern here at all? Are they 'edge cases' which might be prone to a small round-off difference?
    I would imagine that someone decided to re-calculate the tables at some point because they had not been re-calculated since the adding machine days of the 1950s. Just speculating, perhaps around the year 2000 someone spotted a more substantial typo in that deep sea of numbers, and the folks at the Nautical Almanac Office realized that they might as well just code it up and re-do the whole table (since re-calculating the whole thing in the 21st century is undoubtedly cheaper than a manual check of all the numbers as previously printed). More cynically, the tables may have been re-calculated merely to justify the existence of certain positions at the NA Office.
    And the date of this change is before the minor change in the refraction table which you and your eagle eye brought to the attention of NavList many years ago, right?
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