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I think I can see where Chuck Taylor's discrepancy may have come from.

As Henry Halboth has pointed out, the different methods of calculation
should give indistinguishable results. He put his finger near it when he
expressed suspicion about the conversion of the Sun dec into decimal
degrees.

What seems to have happened is this. The Sun dec. at the time of
observation, which Chuck stated to be 1deg 17.6' S, should actually be 1deg
16.7' S. At least, that's what my pocket-calculator program makes it to be;
I haven't checked it against an almanac. Chuck seems to have made a
transcription error.

However, in Chuck's "Method 1" he has written-

Dec = d = -1.27833

This is the decimal equivalent of 1deg 16.7' S, so there's no error here.

Then, in "Method 2" (and presumably, therefore, method 3) he has written-

First compute polar distance:
p = 90d + 1d 17.6' = 91d 17.6'

So in this case he has used his incorrectly-transcribed value for Sun dec.

I suggest (though I haven't taken the calculation further) that if Chuck
corrects his transcription error and uses 1deg 16.7' S for Sun dec in each
example, he will get good agreement between them.

Such errors are easy to make; I expect that navigators in pre-calculator
days were more fluent in numbers than we are today, and got things right a
bit more often. I keep finding silly errors in my own numberings,
particularly when working in sexagesimals.

George.

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