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Frank wrote:

> This
> is an example of something that mathematicians and other "natural
> philosophers" understood from a very early era (try Ptolemy)

Certainly Ptolemy would understand everything about dip, but he did not
really care. He had more important things to care about (parallax,
refraction), and never used natural horizon. The accuracy of observations
at that time and instruments used is a hotly discussed question,
but I suppose he was happy with 1'.
Unfortunately nothing is known about how they divided the arcs of their
instruments.

Alex.


>
> The dip table from 1599 that Gary posted is easy enough to
> reverse-engineer. You can calculate nearly matching values using the
> simple formula dip=1.10*sqrt(h) with dip in minutes and h in feet (with
> that constant the dip calculated for 90 feet altitude rounds to 10 instead
> of the listed 11 but the difference is only half a minute of arc in any
> case). Since the mathematical details of refraction were unknown, we can
> safely conclude that this was a geometric dip table for a slightly
> over-estimated radius of the Earth.
>
> -FER
>
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