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The New Zealander and his team arrived safely after travelling 70 miles (113km) through mist and poor weather conditions.
They described seeing the round tower of the South Pole for the first time as a "black blob" on the horizon.
Sir Edmund and his colleagues had only one drum of petrol left when they sighted the Polar base. This would have been enough for the "tractor train" to travel 20 miles (32km).
Earlier, the explorer had said fuel consumption was the party's main worry and that the team were "cutting it fine" because of very soft snow. Members of the team had to use shovels to clear a path for their tractors.
It took the tractor train, which included three tractors, a caboose and two sledges, more than 80 days to complete the 1,200-mile (1,930km) journey.
Sir Edmund was reportedly enthusiastic ahead of his arrival at the South Pole, and had told colleagues of heavy going in snow with a consistency of sugar, although he said good progress had been made.
In the final leg of the journey, the sky was overcast and there was no sun to warm the polar plateau. The party had to travel in "white-out" conditions for most of the time, with Sir Edmund telling Scott Base by radio: "It is tough, but not too tough."
The explorer later thanked his team, which included Ron Balham, Peter Mulgrew, Murray Ellis, Jim Bates and Derek Wright, and everyone involved in the expedition to the South Pole.
A broadcast message congratulating the triumphant group has been sent by New Zealand Prime Minister Walter Nash. All the explorers have spent 16 hours sleeping following their gruelling journey.
Crossing the polar plateau has led to several problems for Sir Edmund and the others in his party, including engine failure and poor weather conditions such as low cloud and strong winds, plus the hidden danger of crevasses.
Meanwhile, Sir Vivian Fuchs - director of the British Antarctic Survey - has reported a significant advance to about 200 miles (322km) from the Pole, and hopes to advance by around 50 miles (80km) per day. The two parties, approaching from opposite directions, had originally intended to link up on the Scott Base side of the South Pole.
Both teams of explorers were able to report progress by radio to the outside world and also made radio contact with each other to discuss future plans. They were also helped by the Beaver aircraft of the Royal New Zealand Air Force.
Sir Edmund Hillary's team is one of two Commonwealth Antarctic Expeditions.There are also 10 other national expeditions currently exploring the vast Antartic continent.
Since October 1956, the Americans have had a station at the geographical pole, with 20 men there at any one time. Russia has five bases - including the biggest in the Antarctic, which is at Mirny.
On 20th January 1958, Sir Edmund welcomed fellow explorer Sir Vivian Fuchs to the South Pole.
Sir Edmund and his team set out from the newly-created Scott camp near the Ross Sea while the British party, led by Dr Fuchs, began their journey at Shackleton camp near the Weddell Sea. Both groups of explorers used motorised vehicles for the trip to the South Pole.
Sir Edmund Hillary and Sherpa Tenzing Norgay became the first men to reach the 29,028ft (8,847m) summit of Everest in 1953, as part of an expedition led by John Hunt. Hunt and Hillary were knighted on their return.
Sir Edmund took part in several expeditions after that including the trip across Antarctica to the South Pole in 1958. He set up a medical and educational trust for the Sherpa people in 1961 and was New Zealand High Commissioner to India in Delhi from 1984 to 1989.
Sir Edmund is remembered primarily for being the first man to climb Everest but today in the region around the mountain he is best known for his charity work - for building schools, hospitals and bridges, through his Himalayan Trust.
Since his ascent in 1953 he has devoted his life to helping the Sherpas of the Khumbu region.
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