Trekking from South Pole to North, To the Ends of the Earth, by Sir Randulph Fiennes. New York: Arbor House. 547 pp. $17.95.

Why would an English baronet risk his own blue blood to traverse the earth's polar axis? Sir Randulph Fiennes trekked the world from South Pole to North - because no one else had ever done it. It was the last untested polar expedition.

The hazards of the journey - which ended successfully in 1982 - were as chilling as the temperature. Sir Ran remembered ''when fear sits in your stomach and creeps slowly down your back.'' There was the time he lost his footing, nearly ''plunging the height of St. Paul's Cathedral'' down a crevasse, and the mind-numbing occasion when his tent, sledge, and personal gear sank from the ice , 17,000 fathoms into the sea.

''To the End of the Earth'' contains over 500 pages, nine maps, and 30 color photographs of goose-bump adventure, just waiting for the intrepid explorer-by-book.

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