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A posting from Trevor ended-

>None of which goes anywhere towards explaining why an educated
>mathematician and astronomer, with the smarts to understand what was
>under his nose, was navigating a ship off the Smalls on the morning of
>17 December 1837. And that is the real question at hand.

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I wonder if a point is being missed in all this discussion about Sumner.

What surprises me, is that it took until 1837 for navigators to realise
that a useful position line could be drawn from a single observation of the
altitude of a body, even if it wasn't at meridian passage.

Indeed, in an earlier era, before Mercator charts were in common use, and
when navigators measured off a globe with dividers, that would seem to be
an obvious conclusion. If you plot the geographical positiuon of a body on
a globe, then draw a circle round it at a radius corresponding to the
measured zenith angle, then that circle is a locus of your position. You
must be somewhere on it. On a globe, it's visual, indeed obvious.

If you could measure the altitude of another body, that would give another
circle. And one of the two crossings of those circles must be the
observer's position. It's hardly rocket-science. Why did it take until
Sumner's time for that deduction to be made?

The world's finest mathematicians had been intimately concerned with
solving a much more complex problem, that of longitude by lunar distances.
Some (Halley, LaCaille, Maskelyne, Wales) had been to sea to test their
ideas. How had that simple position-line concept evaded those great minds?

Or had it? What Sumner had done was to provide a simple way of drawing a
position line on a Mercator chart, by presuming two different latitudes.
Was that position-line concept around, before Sumner showed how to
calculate it?

Then St Hilare showed another, more rational way to compute a position
line, from the azimuth of the observed body. But that didn't happen until
1873, 36 years after Sumner. Things moved slowly in those days.

I recommend the book by Michael Vanvaerenbergh and list member Peter
Ifland, "Line of position navigation" (2003), for the original papers about
those discoveries.

But it still surprises me: why, oh why, did it take so long for intelligent
men to discover such a simple matter?

George.

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