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Response from George-

Aren't we doing well! Five heads are better than one. I now agree with what
Dan, Aubrey,Rodney, and Bill are saying. My own suggestion for finding the
shortest distance was too simplistic. I had indeed missed something, by
ignoring the possibility that under some (but by no means all)
circumstances the great-circle path between X and the end-points could take
the vessel nearer the pole than X is. Thanks to the others for pointing it
out.

I think Bill Noyce's suggestion of solving the problem by using a gnomonic
chart is the best approach. It is clear that the direct great-circle course
beteen start and destination is quite irrelevant if it crosses the latitude
limit, and in that case there's no point in following that great-circle
anywhere at all.

For this second shot at it, I addressed the problem by using an analogue
computer, being a piece of string and a globe of the Earth. The globe is in
the form of a blow-up beach-ball, 18 inches in diameter. Made in China,
it's somewhat geographically challenged. For example, the passage between
the Faeroes and Iceland has, for some reason, been labelled "Damascus", and
the outlines of continents and islands don't give confidence in any great
accuracy. It's only a beachball, after all.

However, if I went in for ocean sailing (which I have no great yen to) I
would pack that beach-ball (deflated), and the piece of string, in the
navigator's toolkit, to provide a rough solution to such navigational
questions. From the 15th century, right up to the 18th, the "use of the
Globes" was something that mariners were taught, and distances and
altitudes were derived by measuring across the globe's surface with
dividers, to some low precision. The other globe was of course the Star
Globe.

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george@huxtable.u-net.com
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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