How Accurate Is the Mason-Dixon Line?

The resolution of the 18th-century mapping is also a story of 20th-century technology

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Hi, this is Steven Cherry for IEEE Spectrum’s “Techwise Conversations.”

We recently had on the show freelance writer Mark Anderson author of the new book, The Day the World Discovered the Sun, about the various astronomical expeditions in the 1760s. He mentioned that Charles Mason and Jeremiah Dixon, who are famous for their surveying of the border between Pennsylvania and Maryland, first met when they were paired together to sail to the Indian Ocean to measure the 1761 Transit of Venus. As it happens, I did a radio show almost 10 years ago about the Mason-Dixon line, and the surprising use of today’s technology to reassess the line. It was produced for National Public Radio, but it never aired, so I thought it would be worth running in light of the recent show. Here it is.

Steven Cherry: A few years ago, singer Mark Knopfler had a hit song “Sailing to Philadelphia” with the improbable theme of the epic 1760s survey of the Mason-Dixon Line. It was a good choice. Ask a geographer for the most interesting border in the United States, and the odds are one area comes to mind, the northern border of the state of Delaware near where it forms a common point with Pennsylvania and Maryland just a few miles from Philadelphia. The Delaware-Pennsylvania border is a perfectly circular arc, perhaps the only one in the world. And the Maryland-Pennsylvania border is surely one of the most famous. It’s the only one named for its surveyors, Charles Mason and Jeremiah Dixon.

The 1760s was a rough time to be walking around with surveying equipment. Philadelphia, a city of fewer than 25 000 souls, was ravaged by yellow fever and malaria. Further west, the French and their American-Indian allies had defeated a British army led by Lt. Col. George Washington. I’m walking with Robert Mentzer, a retired high school physics teacher and treasurer of the Delaware Astronomical Society.

Robert Mentzer: In their private lives, they were just average men, really. They weren’t famous or wealthy in that sense. So…

Steven Cherry: We’re coming up on mile marker 0, the starting point of the Mason-Dixon Line.

Robert Mentzer: There are no portraits of Mason or Dixon. And obviously no photos, well before photography, so we have no idea what they look like. I retired in ’98 from teaching and, you know, you’re looking for things to do. And my buddy gave me a book called “Walking the Line,” and it was very—very well written, very good book. But I said, gee, I live in Delaware and I really don’t know much about this line that’s right there. So I—I started digging and it just got out of hand.

Steven Cherry: Mentzer has studied the line and the crucial question of its accuracy. With the help of today’s global positioning system technology, Mentzer was able to give it a definitive answer. As we walk the Mason-Dixon Line today, Mentzer and I cross tiny streams and march through tree-filled forests and grassy fields. Sometimes we’re just yards away from drugstores and driveways. Today, to find out where you are, you just buy a map in one of those drugstores. Back then, you first had to locate your position relative to the stars. A sextant was one way to do that back then. But, according to Mentzer, better technology was needed.

Robert Mentzer: A sextant is good to maybe a mile. Well, that works on a ship when you can see 15 miles, but if you ask a farmer where’s your land and he says it’s either here or a mile down the road, that doesn’t work.

Steven Cherry: A landowner wants his perimeter marked more accurately, especially if you’re Thomas Penn and the King of England gives you, say, all of Pennsylvania, or Frederick Calvert, also known as Lord Baltimore, who was given neighboring Maryland. But the king’s grants were just wordy descriptions not lines on a map. After years of arguing and a failed attempt by local colonial surveyors to put those lines on a map, these two aristocratic British families asked the Royal Society for help. The society recommended a surveyor and an astronomer, and arranged for a special astronomical tool. At the time, the most accurate scientific instrument on earth was a 25-foot-tall device at the Royal Observatory known as a zenith sector; essentially, a telescope that points straight up. It was accurate to within one-tenth of one arc second, which is about 3 meters or about 10 feet. So the Royal Society asked the greatest equipment maker of the day, John Bird, to make a six-foot-long version of the Royal Observatory’s zenith sector. The apparatus Bird constructed, just a quarter the size of the observatory’s, was the smallest, most accurate instrument in the world. In 1763, equipped with Bird’s new instrument, the surveyor and the astronomer left Britain and sailed to Philadelphia to help Penn and Calvert settle their border dispute.

[Mark Knopfler, “Sailing to Philadelphia”]

I am Jeremiah Dixon

I am a Geordie boy

A glass of wine with you, sir

And the ladies I’ll enjoy

All Durham and Northumberland

Is measured up by my own hand

It was my fate from birth

To make my mark upon the earth

Steven Cherry: Jeremiah Dixon hailed from England’s northeast. He was, in other words, a Geordie boy, as singer Mark Knopfler says. Born in County Durham in 1733, son of a Quaker coal mine owner, Dixon was a trained surveyor.

He calls me Charlie Mason

A stargazer am I

It seems that I was born

To chart the evening sky

They’d cut me out for a-baking bread

But I had other dreams instead

This baker’s boy from the West Country

Would join the Royal Society

Steven Cherry: Charles Mason, son of a Gloucestershire baker and miller, was an astronomer, a stargazer. In the song’s only historical inaccuracy, Mason was never made a member of the Society, lacking, as he did, a college education.

Sailing to Philadelphia

To draw the line

A Mason-Dixon line

Steven Cherry: Mason and Dixon arrived in Philadelphia in November 1763 with Bird’s zenith sector, with a set of star tables prepared by the Royal Observatory, and with some 200 stone pillars, each weighing at least 400 pounds, to be used as mileage markers. They would add to their technological arsenal a longcase pendulum clock specially made for them in Philadelphia to be used to time their astronomical observations. Their first task was to mark the latitude of the southernmost point of Philadelphia, which took Charlie Mason a hundred and thirty-four observations of five different stars to determine. They then traveled 31 miles west and made observations again to find a point with exactly the same latitude. That’s how it would go for the next five years, astronomy to mark individual points, then surveying to chain straight lines between them. Mason, the astronomer; Dixon, the surveyor. They first had to survey the western boundary of Delaware, which served as their starting point. That line was defined from an agreed-upon point in the south to the arcing border in the north, land which at the time was owned by the Duke of York. Why an arc? Mentzer explains.

Robert Mentzer: When Penn wanted to form a colony, the Duke of York said yeah, you can—[the] Duke of York is going to be the new king, so he’s, he’s got plenty of clout. He said yeah, you can, but you’ve got to stay at least 12 miles away. So that’s the 12-mile radius that forms the northern boundary of what is now Delaware.

Steven Cherry: Throughout 1764, Mason and Dixon surveyed the western border. It’s a hundred and thirty kilometers long and their line is accurate to within one meter, or about three and a half feet. In the spring of 1765, the two finally set out to walk the line between Pennsylvania and Maryland.

Now you’re a good surveyor, Dixon

But I swear you’ll make me mad

The West will kill us both

You gullible Geordie lad

You talk of liberty

How can America be free

A Geordie and a baker’s boy

In the forests of the Iroquois

Steven Cherry: It was a dangerous and difficult time. The British were still quelling tribal rebellions. Once west of Philadelphia, farmhouses were few and far between and settlements were nonexistent. A troop of axmen was needed to clear a 10-meter path through the dense woods. And, in western Pennsylvania, they would be almost completely stymied by a mountain range, the snaking Potomac River, and still more violent uprisings.

Now hold your head up, Mason

See America lies there

The morning tide has raised

The capes of Delaware

Come up and feel the sun

A new morning has begun

Another day will make it clear

Why your stars should guide us here

Steven Cherry: How important was the survey? Not only would it determine a border between two states that has lasted 240 years, it almost cleaved one of them in half. Maryland’s southern border was defined as the Potomac River, which arches north from its end point in Chesapeake Bay. Halfway to the western border, it curves back south. In 1764 no one knew whether it drifted so far north before curving back that it crossed the northern border, the one that Mason and Dixon were marking. If it did, Maryland would lie in two discontiguous parts, a potential political and economic disaster for Lord Baltimore. According to Mentzer, with winter’s chill approaching, Mason was determined to check this vital detail.

Robert Mentzer: So when they get out here, they—they get a Mr. Shelby who lives in that area, who incidentally is one of the heroes of—of the Indian Wars and—and the Revolutionary War. And he takes them up on the top of the mountain and points out the northernmost bend of the Potomac. He said that’s the northernmost point. And it’s off to their left or south, so they know then that Maryland will not be cut in two. But this is only about a mile wide here.

Steven Cherry: They were only half done and the job was to get much more difficult. They had been setting out as milestones the rectangular limestone posts. Every fifth one was special.

Robert Mentzer: They’re called crown stones. Normal stones have a P on one side and an M on the other side, for “Pennsylvania” and “Maryland.” But every fifth stone, they had the crest of the Penns on one side and the crest of the Calverts on the other side, with no P or—P or M.

Steven Cherry: By 1766, they’d reached such mountainous terrain that the milestones could no longer be brought along; they stacked nearby rocks instead. Eventually they made their way to the Alleghany Mountains, defined by a king’s edict to be the western edge of British land. Beyond, in what we now call Ohio, the mighty Shawnees ruled. Half the survey crew and their Iroquois protectors refused to go any further. It was, literally, the end of the line, 231 miles due west from Delaware. According to Mentzer, the pioneering pair sailed back to England, their mission a complete success.

Robert Mentzer: When Mason and Dixon got back to England, they told the Astronomer Royal they thought they—they ran the line within 50 or 60 feet.

Steven Cherry: Jeremiah Dixon returned to his home in County Durham, to the life of a gentleman and expert land surveyor. Mason went back to work for the Royal Astronomer. In 1780 he was given only partial payment for a Longitude Prize, far less than he felt he deserved. Disappointed, he returned to America in 1786, fell ill on the journey, and died. He’s buried in the same Philadelphia church as Benjamin Franklin.

Steven Cherry: For more than two centuries, there was no way of knowing whether Mason and Dixon were right about how accurate the line was. Then, in 1990, a group of amateur historians and astronomers formed the Mason and Dixon Line Preservation Partnership. The group, led by a man named Todd Babcock, walked the line and inventoried the milestones, preserving those they could. The group also made GPS measurements of the stones. As it turns out, Mason and Dixon were wrong.

Robert Mentzer: Now when the data first came back from Todd Babcock’s group that said they’re off by 800 or 900 feet, you felt these guys are idiots; they did a terrible job.

Steven Cherry: Until 2002, it was generally thought that John Bird’s instruments must be to blame. That’s when Mentzer realized that no one with an astronomy background had ever examined the data.

Robert Mentzer: If you look at the star scatter and their tables, it’s in the neighborhood of a few hundred feet, but they’re doing five different stars and they’re averaging them. So you’d expect a hundred-, maybe two-hundred-foot scatter. But yet, when you look at the—the data, they can be off by 900 feet. And so it kind of hints at a hidden error there. At the time they were running this survey, there were men like Cavendish, the great English physicist, working with Newton’s Laws and saying hey, if you got a mountain west of you and you got an ocean east of you, the mass of that mountain is gonna pull a plumb-bob off line a little bit, and that’s gonna mess up your readings. Well, there’s no experimental proof for it. And there was no way of measuring how much it would be pulled off. Cavendish’s results, calculations are too crude to do anything but indicate that there probably is a problem there. So they—there was nothing they could do. They just assumed that there wasn’t a problem.

Steven Cherry: And it’s not just mountains that wreak havoc with the calculations.

Robert Mentzer: There can be masses of dense rock just underground. And since Newton’s Law is an inverse-square law, if something’s close, it has much more effect than something further away. So the U.S. Geological Survey has surveyed the United States for these gravitational variations. And there’s a website that you can go to and punch in a latitude and longitude and it’ll tell you how much a plumb-bob is disturbed at that particular location. So if you go back to the 12 spots where Mason and Dixon set up their zenith sector and you correct their values for the gravitational effect at that particular spot, instead of the—that line being off by 800 or 900 feet, everything is within 200 feet, and all but one or two are within a hundred feet.

Steven Cherry: So how accurate was Mason and Dixon’s line?

Robert Mentzer: And they actually did a superb job consistent with the technology of their day, the zenith sector, and consistent with the science of their day, the gravitational attraction. If you look at the scatter and correct for the difficulty in using the zenith sector, the state of the art they had there, and then you realize that they had to correct for the gravitational effect, which they had no way of correcting for. And if you do now, you find that they ran a beautiful line.

Steven Cherry: Mason and Dixon were never named fellows of the Royal Society. They were, though, elected to the American Philosophical Society, the highest intellectual honor the New World had to offer. They also have the distinction of the only border in the world named for the men who walked the line.

We are sailing to Philadelphia

A world away from the coaly Tyne

Sailing to Philadelphia

To draw the line

A Mason-Dixon line

A Mason-Dixon line

Steven Cherry: For IEEE Spectrum’s “Techwise Conversations,” I’m Steven Cherry.

This show was recorded in May 2005.
Segment producer: Sharon Basco; audio engineers: Paul Ruest,
Dennis Foley, and Francesco Ferorelli
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