Convinced the two continents must meet at some point, Peter sent Vitus Bering, a Danish captain in the Russian Navy, to find out where. More than two and half centuries after Bering brought back news of sea not land (the strait that would bear his name), Russian and American engineers are lobbying for a tunnel to create the link Peter believed was there all along.
Set up for the task is the Interhemispheric Bering Strait Tunnel and Railroad Group, which links Russian, American and Canadian companies. According to Viktor Razbegin, director of the Russian partner, a tunnel would be about 60 miles long, 23 of this underwater, and the rest burrowed through two islands. (The distance is far less than Captain Bering thought. He sailed the strait in fog and believed North America still hundreds of miles away). 'Investigations have already begun and will go on for two or three years,' said Mr Razbegin yesterday.
A fixed link with Alaska would recreate the Bering land bridge over which Asians crossed to North America 12,000 years ago. The last attempt to do this was in 1905. A US-led group, fired by the idea of a train from New York to Paris, raised dollars 5m ( pounds 3.3m) for the Trans Alaska Siberian Railroad, but the scheme got buried by World War I and the Bolshevik Revolution.
Mr Razbegin says a tunnel is only part of the latest venture, which would include transcontinental railways and united energy systems. The closest existing railway in Russia to the Bering Strait is more than 3,000 miles away, and on the American side, the nearest line is 550 miles to the east.
To lay so much new track and dig a tunnel would take at least 20 years, says Nikolai Grom, chief of the Design and Capital Construction Department of the Railway Ministry.
Even this seems optimistic, although a New York to Paris railway is technically feasible. The biggest obstacle is cost. Russian railways estimate the Bering tunnel price at over pounds 5bn, but this looks suspiciously like the original, and far too optimistic, price tag for Eurotunnel. George Koumal, the American representive of the Interhemispheric consortium has been quoted as putting the cost closer to pounds 25bn.
Chances of getting such a mammoth investment back quickly are nil. More than 75 million passengers crossed the English channel last year by ferry or air along with tens of millions of tonnes of freight, yet there are still doubts about whether Eurotunnel can prosper. Traffic across the Bering Strait is miniscule, and without massive state funding the project will go nowhere.
The most enthusiastic backers, aside from excited engineers, are the governors of Alaska and Chukotka, the Russian and American regions that would benefit most from the influx of cash and an eventual redrawing of global trade routes promised by weather- proof crossing.
'The Russians are excellent at big projects,' governor Walter Hickel told the Anchorage Chamber of Commerce recently. 'They just can't get their potatoes across town.'
But Russia shares some of the same anxieties felt in Britain about the channel tunnel. With Nato creeping up from the west, any hint of greater vulnerability from the east does not please Russia's generals. Some, though, see it the other way round - a first step towards getting Alaska back. The tsar's decision in 1867 to sell Alaska to the United States for dollars 7m is still a sore point, not only with the kooky fringe of Russian nationalism.
Mr Grom warned last week: 'Russia's interests must be securely protected. Unless, that is, we want another Alaska story.'
Channel Tunnel, pages 13-16