Contour Lines and the Mountain That Weighed the Earth

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Welcome to Origins. In this program we explore the technological and scientific roots of the modern world. Let's begin.

Unfold a hiking map and you'll find hills drawn as sets of wobbly rings, one inside the next, like the growth rings of a cut tree. Where the rings crowd together, the ground is steep. Where they spread apart, the slope is gentle.

Each of those rings follows one simple rule. Walk along it and you never go up or down. It connects every point of the same height.

That rule, a line drawn through equal values, is now one of the most common devices in science. It marks the highs and lows on a weather map, the depths of the seafloor, the spread of an earthquake's shaking. And it had an odd birth. It was invented several times, by people trying to see something they couldn't look at directly.

The first of them were looking at water.

In 1584, a sworn land surveyor in Holland named Pieter Bruinsz drew a map of the Spaarne, the river that runs past Haarlem. Nobody can see the bottom of a brown river. You can only lower a weighted line, read the depth, and write a number down. Bruinsz did something more with his numbers. He drew a line along the places where the depth was the same. His map is usually cited as the oldest known example of what mapmakers now call an isoline.

For more than a century, the idea stayed mostly with river engineers and chart makers. Then it found a much larger subject.

In 1698, the astronomer Edmond Halley took command of a small Royal Navy ship called the Paramore and sailed it into the Atlantic. His quarry was invisible. A compass needle doesn't point to true north. It strays east or west by an amount that changes from place to place, and getting it wrong could wreck a ship. Halley gathered nearly a hundred and fifty measurements, from the North Atlantic down to about fifty degrees south. In 1701 he published a chart of the ocean crossed by long, sweeping curves, each joining places where the needle strayed by the same amount. What was "properly new," he wrote, was "the Curved-Lines drawn over the several seas." For a time, they were known as Halleyan lines.

After a riverbed and the planet's magnetism, the line's next subject was a mountain.

In the summer of 1774, the Astronomer Royal, Nevil Maskelyne, set up camp on Schiehallion, a lonely, steep-sided peak in the Scottish Highlands. He had come to weigh the Earth.

The plan came from Isaac Newton. If every mass pulls on every other mass, a big mountain should tug a hanging plumb line slightly toward itself. Newton thought the effect too small to detect, but instruments had improved since his day. Measure that tiny tug, compare it to the pull of the whole planet, and you could work out how dense the Earth is. First, though, you had to know exactly how much mountain there was.

Maskelyne built small observatories on the north and south slopes and spent more than sixteen weeks there, much of it in mist and rain, sighting stars against his plumb line. The combined deflection came to about eleven and a half seconds of arc. That's roughly the width of a coin seen from a quarter of a mile away.

Then came the long, dull part. Surveyors measured angles and heights to more than a thousand points around the mountain, and someone had to turn all of it into a volume. That job went to Charles Hutton, a mathematician from Newcastle who had worked in the coal pits as a young man and now taught at the Royal Military Academy at Woolwich.

Hutton divided the ground around each observatory into rings and wedges, close to two thousand little columns in all. Each column needed a height. But the survey points were scattered unevenly, and many columns had no measurement inside them at all. The problem, Hutton admitted, gave him "much trouble and dissatisfaction."

Then he found a shortcut. In his words, it was "the connecting together by a faint line all the points which were of the same relative altitude." The faint lines closed into loops, irregular rings nested one inside another. Hutton recognized what they were: level slices through the hill, as if the mountain had been cut into layers like a cake. With those rings drawn, he could read the height of any column from the lines passing through it.

He published in 1778, in a paper more than a hundred pages long. The Earth, he concluded, was about nine-fifths as dense as the mountain's rock, roughly four and a half times as dense as water. The modern figure is about five and a half. He also drew a bold inference. Since surface rock was much lighter than the average, there had to be "great quantities of metals" somewhere toward the center. Seismologists would confirm a dense iron core more than a century later.

Hutton's contour map of Schiehallion was never published, and it hasn't survived. He may not even have been the first to draw lines of equal height on land; an Italian map of Modena from 1746 has a claim. But within a few decades, French engineers were drawing contours on maps of France, and by the mid-1800s national surveys across Europe used them routinely.

The idea kept spreading sideways. In 1817, Alexander von Humboldt drew lines through places with the same average temperature and showed that climate doesn't simply follow latitude. Weather maps soon carried lines of equal air pressure. The same device now traces ocean salt, noise around airports, and maps of Earth's gravity built from satellite data, the force Maskelyne went to Scotland to catch.

The device works because people are poor at reading thousands of numbers and very good at seeing shapes. A contour line turns a field of measurements into an edge the eye can follow.

The Schiehallion story has one more scene. According to local tradition, when the observations were finished, Maskelyne threw a party in his hut on the mountain. During the celebration the hut burned down, taking with it the fiddle of the camp's cook and musician, a local man named Duncan Robertson. The story goes that Maskelyne later sent him a replacement from London: a Stradivarius.

The violin can't be confirmed. Hutton's faint lines are easier to find. Each time a hiker counts the rings to see how steep tomorrow's climb will be, they're using the shortcut a mathematician devised to get through a mountain of arithmetic.

Thanks for listening to Origins.