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Is the d value listed at the bottom of the sun and planets columns of the daily pages of the Nautical Almanac the average (or mean) hourly change in the sun's declination for the three days listed (as stated in the Nautical Almanac and other references) or the amount the declination changes between 1200 and 1300 on the middle day of the three shown (as stated in Bowditch)?

I heard back from Catherine Hohenkerk, and the answer is neither!  What the Nautical Almanac uses is the absolute value of the difference between the unrounded declinations at 0h UT of the middle day of the page and 0h UT of the bottom day of the page, divided by 24.  I suspect that all three, when rounded to tenths of arc-minutes, will give the same result.

It just goes to show that you can't trust everything you read in Bowditch (Catherine is forwarding this information to the USNO people responsible for Bowditch), and even what is said in the Nautical Almanac is subject to interpretation.

I will be adjusting Celestial Tools to comply with this new information, even though I suspect it won't change anything.

BTW, Catherine will be retiring soon.  She has been a wonderful source of information for me for many years, and will be sorely missed.  You might consider sending her a note of congratulations and appreciation at Catherine.Hohenkerk@UKHO.gov.uk while it still works.