Borderlines explores the global map, one line at a time.

It’s funny the way close observation can change your perception of things. Heisenberg’s uncertainty principle says something like this about observing quantum particles [1]; maybe borderology needs its own uncertainty principle. Consider: What is the longest straight-line international boundary? Why, that has to be the American-Canadian border between Lake of the Woods (Minnesota/Manitoba) and Boundary Bay (Washington State/British Columbia), which runs for 1,260 miles along the 49th parallel north. Right?

Nope. It may look that way on a world map. But zoom in close enough and it turns out that the straight line running along the 49th parallel north is not really on the 49th parallel north. And it isn’t straight. Like, at all. Marked by a 20-foot strip of clear-cut forest, the border may seem straight as a ruler. But as it zigzags from the first to the last of the 912 boundary monuments erected by the original surveyors, it deviates from the 49th parallel by up to several hundred feet.

Joe Burgess/The New York Times

The border was fixed in different stages during the 19th century by teams of American, Canadian and British surveyors. Back then, the seemingly simple task of drawing a straight line across a continent implied hardship and heroism, as demonstrated in “Arc of the Medicine Line,” the Canadian archivist Tony Rees’s book about the final survey, from 1872 to 1874, which mapped the border between Lake of the Woods and the Continental Divide. As Mr. Rees documents, the men lacked the benefit of roads, electricity or the digital precision allowed by satellite technology; as a result, on average, the markers are three arcseconds (i.e. 295 feet) north or south of the 49th parallel [2].

This page, from the Degree Confluence Project, has an interesting schematic, showing the remarkable variance between the supposed border (49 degrees north) and some of the actual survey markers between 123 degrees west and 96 degrees west (almost the entire length of the “straight line” border). As shown by this map, the markers seem actively to avoid the parallel, straying as much as 575 feet north (monuments 35-37) and 784 feet south (Monument 347) of the line.

So the “49th parallel” is a failure as a straight line; that should not detract from its arbitrariness. In all its imperfection, this border is a monument to the power of mind over topography. The border blithely ignores the lay of the land, slicing through rivers, valleys and mountain ranges with the ruthless precision of a 19th-century laser beam.

In fact, the straight line itself was a compromise. Following the Louisiana Purchase of 1803, the United States and Britain agreed to use the watershed between the Hudson Bay to the north and the Mississippi and Missouri Rivers to the south as the border between their domains. The only problem was that much of the terrain was too flat to measure reliably which way runoff water flowed. Both sides realized the potential for conflict and chose the 49th parallel as the new demarcation, with each side winning and losing some territory.

Joe Burgess/The New York Times

Actually, the straight line was only half a compromise. The Anglo-American Convention of 1818 drew the line from Lake of the Woods to the summit of the Stony Mountains (sic) only. Brits and Yanks agreed to jointly administer the lands to the west, between the Rockies and the West Coast, for an initial period of 10 years. Overlapping claims [3] created a giant territory held in curious limbo, bounded to the north (at 54 degrees 40 minutes north) by the most extreme American claim and to the south (at 42 degrees north) by the farthest British claim. The British called it the Columbia District, the Americans the Oregon Country.

A tug of war ensued. Time was not on the British side; America’s confidence and territorial appetite was growing. This was the era of Manifest Destiny, the conviction that the country should expand from sea to shining sea. James K. Polk won the 1844 presidential elections on an expansionist platform. America’s designs on all of the Oregon Country, and its willingness to use force to obtain it, were condensed in the slogan “Fifty-four Forty or Fight!”

Imagine a maximalist American outcome: North America’s entire Pacific coast in American hands, up to Russian America — and including it, as the Alaska Purchase would certainly follow [4], definitively blocking British access to the Pacific. Or imagine the reverse: The British usurping Oregon Country all the way down to the northern border of California — then still Mexican — locking out America from its bicoastal destiny.

Claims, counterclaims, escalating intransigence: this was how the Balkan wars got started. Fortunately, the wisdom of Solomon eventually prevailed. Proving about 120 years early that only Nixon could go to China, President Polk, the bellicose expansionist, agreed simply to continue the border on the 49th parallel westward.

But Polk’s motive may have been pragmatic rather than pacific. The clean cut dividing Columbia from Oregon allowed America to turn its attention to its southern border. The Mexican-American War of 1846-1848 resulted in a dramatic rollback of Mexico to Baja California and from the Colorado River to the Rio Grande.

After the Oregon Treaty of 1846, the western part of America’s northern border was fixed to run from the top of the Rockies to a point in the sea halfway between the mainland and Vancouver Island (thus avoiding the international border’s slicing off the island’s southern tip). In a curious coincidence, both ends of the almost-straight-line border along the 49th parallel are marked — fastened like a clothesline, you could almost say — by two curious border phenomena.

Joe Burgess/The New York Times

At the border’s western terminus, after it dips into the ocean behind the Peace Arch [5], the line crosses a peninsula before veering south to avoid Vancouver Island — the only place west of Lake of the Woods where Canada extends south of the “49th parallel” border. The last, 2.5-mile-long stretch of land border between the United States and Canada separates Tsawwassen, British Columbia in the north from tiny Point Roberts, an American-administered peninsula (and thus an American exclave [6]) in the south. Residents of Point Roberts are Washingtonians, but have to pass through two international border crossings (or travel by water or air) to reach the rest of their state.

At its eastern terminus, the almost straight line bends northward to include the Northwest Angle in the United States — the only place outside Alaska where the States spills over the 49th parallel. The Angle owes its existence to the mistaken assumption, at the Treaty of Paris (1783), that the Mississippi flowed so far north that the “northwesternmost point” of Lake of the Woods could be connected to it by a westward line to the Mississippi. Quod non. Hence the borderline due south from that “northwesternmost point” when the 49th parallel was agreed upon in 1818 [7].

Joe Burgess/The New York Times

To the east of Lake of the Woods, the American-Canadian border dips south, on a more convoluted course, often following natural features — nowhere again reaching the 49th parallel [8]. On some maps the tip of Maine seems to stick out farther north, but this is mere projection (Mercatorial rather than Freudian): the state’s northernmost point, near Fort Kent, is a mere 47 degrees 27 minutes north. The 49th parallel crosses the Atlantic to touch Paris, Volgograd (formerly Stalingrad) and the island of Sakhalin in Russia’s Far East. Sakhalin, like Vancouver Island stretched north to south and hugging the continental coast close to another major power, intriguingly once suffered the fate that its Canadian doppelgänger was spared. From 1905 to 1945, it was divided in a Soviet north and a Japanese south. Not along the 49th parallel — that would have been too neat — but on the 50th.

Related More From Borderlines Read previous contributions to this series.

Another (ahem) parallel: Both sets of powers divided the territories between each other irrespective of the native peoples present in those areas. In the case of Sakhalin, Japanese/Russian occupation was disastrous for the Ainu, Gilyak and other local tribes.

In the 1870s, Sioux fleeing the might of the United States Army provided the straight part of what is now sometimes known as “the longest undefended border in the world” with its most poetic epithet. Seeing how an invisible force seemed to stop the American cavalry dead in their tracks, they called that imperfectly demarcated boundary the Medicine Line.

Frank Jacobs is a London-based author and blogger. He writes about cartography, but only the interesting bits.

An earlier version of this article misidentified an island off Vancouver. It is Vancouver Island, not Victoria Island. Two of the maps misspelled the name of a body of water. It is Hudson Bay, not Huson Bay.

[1] The more you know about their direction, the less you can know about their speed. And vice versa.

[2] For more background on and the complete data for the Border Monuments on the American-Canadian border, visit the International Boundary Commission.

[3] Initially also by France, Spain and Russia.

[4] The purchase of Alaska, negotiated by Secretary of State William H. Seward in 1867, was a great real estate deal: at $7.2 million for 586,412 square miles, it works out to about 2 cents per acre. The territory was nevertheless seen as a frozen wasteland, and the buy decried as “Seward’s Folly.”

[5] Marking the “mainland terminus” of the 49th-parallel border at the crossing from Surrey, B.C. to Blaine, Wash., the Peace Arch straddles the actual border, and is the centerpiece of the adjacent Peace Arch State Park and Peace Arch Provincial Park, where one can cross freely between the American and Canadian sides (but only after clearing customs on either side).

[6] See this previous Borderlines post for the difference between exclaves and enclaves.

[7] For a discussion of two smaller American exclaves at Lake of the Woods, see Strange Maps No. 516.

[8] Although “49th parallel” is often used as shorthand for the American-Canadian border, estimates based on Statistics Canada’s 2010 population figures are that almost 24 million Canadians (or about 70 percent of the population) live to the south of it.