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Peter Fogg asked:

> Any chance of a little more explanation about what this (eg 'flagpole
> paradigm')  is all about?

Many texts on the Marcq St.-Hilaire method  "explain" the intercept with the
help of the following analogy: The vertical angle at which you see a flagpole
increases as you approach it and decreases as you gain distance from it.
Similarly, the observed altitude of a celestial body increases when you approach
its GP and decreases when you move away from it.

The books I mentioned in my previous message fail to make clear that these are
two entirely different problems: The first one is one of plane trigonometry;
indeed it applies to a flat earth only. The second one is a trivial consequence
of the fact that the altitude is the complement of the zenith distance and
therefore grows when the latter shrinks, and vice versa. I will never understand
the didactic purpose of "explaining" a triviality by means of a slightly more
complex and unrelated situation.

I remember once seeing an article in a popular sailing magazine about obtaining
a position line from a sunset. The author got himself all confused over the
question whether his intercept was towards or away as Hc and Ho were both
negative. The analogy with the flagpole collapses in this case.

Herbert Prinz

   

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