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A condensed version of a paper presented to the Centre Beige de Navigation, Brussels, 9 January 1950.
The fact that the most expeditious route between two points on the Earth's surface is not necessarily a great circle is no new discovery. In the days of sailing ships courses were set to take maximum advantage of the wind; the trade winds were so called because they made the voyages of the trading ships possible. To a large extent they dictated the sea lanes and it was not until the arrival of the steamship that more direct routes across the oceans could be followed.