How a Scottish mountain weighed the earth

An 18th-century quest to weigh the Earth was crucial to better understanding our universe - and a lonely mountain in Scotland helped with the task.

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In the summer of 1774, Nevil Maskelyne, Astronomer Royal, stood on the side of a Scottish mountain and stared at something far deeper than the view. He tried to calculate the weight of the earth.

Schiehallion in Perthshire is what is commonly known as the Whale's Ridge. The mountain runs from east to west - both the north and south slopes are very steep - beginning with a steeper, steeper west slope and ending with a longer, gentler east slope, which most hikes attempt to ascend. .

When I first saw the head of Shehalalion from the north shore of Loch Rannoch, I realized it could almost pass for a volcano, with its steep sides tapering upwards. This was exactly the kind of mountain Maskelyne was looking for when he tasked astronomer Charles Mason in 1772 with finding a suitable volume to measure.

Mason also needs to measure the volume of the mountain and predict its average density based on the type of rock that makes up the mountain. Based on these numbers, Maskelyne will be able to calculate the mass of the mountain. In turn, he could scale up these findings to determine the Earth's mass to acceptable accuracy, use the Earth's radius to calculate its volume, and make the best educated guess at our planet's density at the time. Knowing the mass of the Earth would allow scientists to predict the relative mass of every known object in the known universe, such as the Sun.

Mason traveled extensively and eventually found the 1,083-meter Schiehallion with the expert help of local Gili Outdoor Guides. Although a distinguished surveyor had recently returned to England after settling aristocratic land disputes in America by establishing the Mason-Dixon Line (later chosen as the dividing line in the Civil War), there was no attraction for him in the Scottish Highlands.

Maskelyne therefore chose to personally oversee the work, which ultimately gave Schiehallion something akin to celebrity status in the hiking world, as evidenced by the 20,000 hikers who visit each year. As the walk began, they each passed a memorial stone celebrating the work of Maskelyne and his team at Forthbraith Car Park.

Not long after ascending Schiehallion myself, I saw my first hiker trudging along a less traveled trail, looking a little untidy. Early autumn has renamed the bracken slopes in burnt sienna, while above me there are only clouds and presumably the rest of the mountain. However, with no major mountains nearby, views from the lower slopes have exposed large swathes of central Scotland.

As the hiker approached me, I noticed an urgent weariness about him. "I did it," he said. "My First Munro" refers to the 282 peaks in Scotland whose peaks sit above 3,000 feet. When he saw the parking lot, he couldn't wait to get down the mountain. "I'm glad it's over," he said. His springer spaniel, which looked like a seashell, followed him, barely stopping to smell my boots.

Gravity never seems stronger than when you're going uphill. In just a few minutes, I felt the sweet pull of the mountain. Before long, the ground in front of me was all I had; a morass of rocks and tough grass that guided me forward until whenever I stopped to rest, we dropped like tired heavyweight boxers.

Sir Isaac Newton was the first to establish that everything has its own gravitational pull. He also believed that gravity was too weak to be measured on anything below planetary level. But without a measurement of the Earth's gravity, it's impossible to calculate its weight, because gravity is variable. For example, if I stood on a bathroom scale on Earth, I would be heavier than on the same set of scales on Mercury, a smaller planet than Earth with a lower gravity, even though my mass would remain the same.

Maskelyne and other scientists of his time had realized that a mountain's gravity might actually be strong enough to be measured if you could get close enough to its center of mass. This means finding a hill with a steep slope. But if one mountain has a gravitational pull, so will all the other mountains, which could distort the measurements. For this reason, Schiehallion, located far away from other similarly sized mountains, is the perfect choice.

Maskelyne requested that observatories be constructed on the steep north and south slopes of the Schiehallion at points closest to the mountain's centroid. From here hangs a pendulum, pulled toward the center of the Earth by our planet's own ultra-strong gravity. Crucially, Maskelyne needed to show that the Schiehallion's gravity pulled the pendulum's bob away from its vertical position.

Maskelyne triangulated the so-called "true vertical" (i.e. the angle of the pendulum) by tracking the transits of 43 different stars from each observatory, which would only be the angle if it were suspended over a flat plain. Affected by Earth's gravity and nothing else. He found that from every observation station on either side of the mountain, the pendulum deviated significantly from its true vertical direction, toward the mountain.

The Schiehallion's gravity was thus proven, but the work had only just begun. Next, the entire mountain was measured to calculate its volume, a task that fell to mathematician Charles Hutton's team.

Bad weather is certainly no stranger to Schiehallion. For this reason, it took Hutton's team nearly two years to fully map the mountain. As I reached the top of the ridge, the clouds dropped further, obscuring everything. Soon the well-marked trail disappears into a challenging boulder field. Only strange mist-obscured stone monuments pointed the way.

A spectral couple appeared in the darkness and told me that the summit was not far away. After ten minutes the route I was on seemed to be going downhill. But to make matters worse, the cairns were gone and the trail was heading steeply to the north. I found it hard to tell if the boulder I was standing on was hanging over an abyss or just more rocks, so I stopped and pulled out my map and compass.

When Hutton completed his survey of the mountain, he had a map with thousands of precise longitudinal and elevation readings. In school we learn to calculate the volume of a cube by multiplying its length, width and height. But real life doesn't give us straight lines; it gives us curves, aberrations, humps and cracks. These are exactly what Hutton's measurements show.

It turns out that their calculations were a bit tricky and calculating the volume of the entire mountain was almost impossible. Then Hutton had the ingenious idea of ??dividing mountains by clustering values ??of similar height together. He took a pencil and connected these height points together to form a series of imperfect loops. Unintentionally, he had just invented the contour line, which to this day remains one of the most valuable pieces of information on a map.

As I suspected, I was lost. After a slight descent on the right path from one of Schiehallion's many false peaks, I took a wrong turn. My map showed dense contours where I judged I was standing, which meant it was going to get very steep very quickly. I jerked back, grateful that Hutton and his contours had probably saved me from falling over the edge of the cliff.

In 1775, Mascarene presented his final results to the Royal Society. We now know that Maskelyne and his team's estimate was within 20% of what is now thought to be Earth's mass (5.97 x 10^24kg, in case you were wondering), which was a significant improvement over previous estimates at the time. Maskelyne and Hutton's Measurements were only used in 2007 to obtain a closer estimate of Earth's mass.

Scientific discovery is no different than hiking on a cold, wet, cloudy mountainside. But this 18th-century feat cleared up a lot of fog for future astronomers and physicists, not to mention the many hikers who try to summit Schiehallion every day to pay homage to this geological wonder’s contribution to our understanding of the universe. Thanks to these experiments, those clever contour lines always make us feel the shape of the mountain, even if our eyes can't see it.