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Sure, there are many cases where 1' accuracy (or even less) is not
relevant, such as open ocean navigation, beginning practice or
instruction, and celestial body identification.  But there are several
cases where it is:  landfall to a low island from a small boat (low
eye level), avoidance of a shallow reef, and an evaluation our CN
skill.

HO 249's tabulation to 1' implies a accuracy of  +or- 0.5'.  But I've
never seen that accuracy claimed.  Now HO 229 is tablulated to 0.1",
but it only claims accuracy to +or- 0.2'.  And when the double second-
difference interpolation is indicated, HO 229 accuracy drops to +or-
0.31', which is not much better than the presumed accuracy of HO 249.
These accuracies are consistent with my own comparisons using 10-digit
computations.

Now consider reducing a sight using HO 249 by working all seven math
operations to only 1' (i.e., + or - 0.5').  The round off error then
ranges from zero to +or- 3.5' from the sight reduction alone.  It
seems to me, that whether navigating in serious situations or just
evaluating our CN skills, we would like to be assured that all the
error is due to sources outside of arithmetic, such as Almanac
(accurate to 0.2' to 0.3', depending on the body), observational,
abnormal refraction, and sextant error.

So, when I want the comfort of eliminating math round off error, I
like to do all math to 0.1' accuracy, neither HO 249 or HO 229 will do
-- only a calculator (or computer) will.  And in other cases, I might
as well use HO 249 for its organizational convenience.  This leaves HO
229 on my bookshelf.

And my confidence in HO 214 is shaken by the corrections that have
appeared since its 1936 publication.  BTW, since John Napier's first
tabulation of logarithms in 1614, how were these hand calculations
checked for errors?  In our age of digital computers, I find the labor
that must have gone into these calculations unimaginable.
(Incidentally, I am old enough to remember when the word "computer"
referred to a person).

....  John Karl


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