In the summer of 1774, a team of British astronomers working under the patronage of the Royal Society established camp at the foot of a lonely mountain in the Scottish Highlands to conduct one of the most ingenious scientific experiments of the 18th century. Armed with telescopes, pendulums, quadrants, barometers, and delicate measuring rods, these men were attempting to weigh the Earth.
The mountain they chose was Schiehallion, an isolated peak in Perthshire whose smooth, symmetrical shape made it ideal for the audacious experiment. The project became known as the Schiehallion experiment, and it represented one of the first serious attempts to determine the planet’s mass using Newtonian physics.
The Schiehallion in Perthshire. Credit: Tim Hayes
In 1687, Newton had published his monumental work, Philosophiæ Naturalis Principia Mathematica, introducing the law of universal gravitation. According to Newton, every object in the universe attracted every other object with a force proportional to its mass.
The question that immediately arose was: if gravity depended on mass, how massive was the Earth itself?
Newton understood that the problem could theoretically be solved by comparing the gravitational pull of a known object with that of the Earth. He even suggested that a mountain might provide enough attraction to slightly deflect a pendulum or alter the direction of a plumb line. Newton calculated that a mountain with a height of 3 miles and a base of 6 miles would cause a plumb line to deviate by less than two minutes of arc. But in Newton’s lifetime, no one possessed the instruments or surveying precision necessary to perform such a delicate measurement.
By the eighteenth century, however, astronomy and geodesy had advanced dramatically. The scientific world was increasingly confident that Newton’s ideas could be tested with real measurements.
The first attempt to carry out the plumb-line deflection experiment was made by a pair of French astronomers, Pierre Bouguer and Charles Marie de La Condamine, in 1738, while they were on a geodesic expedition to Peru. The expedition had departed France in 1735 with the aim of measuring the length of one degree of latitude near the equator, but the two scientists seized the opportunity to attempt the deflection experiment as well.
Chimborazo in the Andes in Ecuador, the subject of the French 1738 experiment. Credit: Mark Horrell
The mountain they chose was the 6,268-metre volcano Chimborazo—the farthest point on Earth from its center. Working under harsh conditions at extreme altitude, Bouguer and La Condamine attempted to detect the tiny gravitational pull exerted by the mountain on a plumb line. In a paper published in 1749, Bouguer reported that they had succeeded in measuring a deflection of about eight seconds of arc.
Bouguer himself attached no quantitative significance to the results, and he concluded his report by expressing the hope that a smaller and denser mountain in France or England might someday be selected for a similar experiment. Such a site, he noted, would allow observations to be conducted under far more favourable conditions and with an improved experimental arrangement employing observation stations on both the north and south sides of the mountain, effectively doubling the deflection effect to be measured.
Some twenty years after the publication of this report, Astronomer Royal for Scotland, Nevil Maskelyne, proposed to the Royal Society in 1772 that another attempt on the experiment should be made in England. The proposal received support from Royal Society, which understood the immense importance of the undertaking. Determining Earth’s density would not merely confirm Newtonian theory, but it would establish a numerical foundation for planetary science itself. A committee was formed and Maskelyne, Joseph Banks and Benjamin Franklin, among many others, were appointed its members.
Nevil Maskelyne
Surveyor Charles Mason was dispatched to find a suitable mountain. After a lengthy search over the summer of 1773, Mason found Schiehallion, a 1,083 meter peak lying between Loch Tay and Loch Rannoch in the central Scottish Highlands, the ideal candidate. Schiehallion had several advantages. It stood relatively isolated from neighbouring mountains, reducing interference from surrounding masses, and its symmetrical east–west ridge would simplify the calculations. Its steep northern and southern slopes would allow the experiment to be sited close to its centre of mass, maximising the deflection effect.
In 1774, Maskelyne and his assistants established observation stations on opposite sides of Schiehallion. The plan was elegant in principle.
Normally, a plumb line hangs straight toward the center of the Earth because Earth’s gravity pulls it downward. But if a massive mountain stood nearby, its own gravity would tug the plumb line slightly sideways. The deviation would be tiny but measurable.
If the mountain’s mass could be estimated through surveying, and the sideways gravitational pull could be measured astronomically, scientists could compare the attraction of the mountain with the attraction of the Earth. From that ratio, the Earth’s density, and eventually its mass, could be calculated.
Credit: John Smallwood
The challenge lay in measuring an almost unimaginably small effect. Maskelyne’s team built stone observatories on the north and south sides of the mountain. Using telescopes and other astronomical instruments, Maskelyne measured the apparent positions of selected stars from both sides of the mountain. If the mountain’s gravity pulled the plumb line slightly northward or southward, then the zenith—the point directly overhead—would appear shifted by a tiny amount.
The difference between the astronomical measurements on the two sides revealed the mountain’s gravitational attraction.
Maskelyne took hundreds of measurements from both sides of the mountain. To accurately determine the deflection due to the mountain, he took into account the curvature of the Earth, as well as observational effects such as precession, aberration of light and nutation. In the end, he measured a deflection of 11.6 arcseconds.
While Maskelyne carried out the astronomical observations, the mountain itself had to be painstakingly surveyed and mathematically dissected. This task fell largely to the Scottish mathematician Charles Hutton, who supervised an elaborate survey of Schiehallion’s shape and volume. To aid the calculations, Hutton invented an innovative technique of drawing lines connecting points of equal elevation, known as contour lines, that’s commonly used in topographic maps today.
A sketch of Schiehallion and the surrounding landmarks, from Charles Hutton's paper on calculating the density of the mountain.
Hutton had to compute the individual attractions due to each of the many prisms that formed his grid, a process which was as laborious as the survey itself. The task occupied his time for a further two years before he could present his results, which he did in a hundred-page paper to the Royal Society in 1778.
Hutton calculated that the average density of Earth is approximately 1.8 times the density of the mountain. Surveying data gave him the density of the mountain to be approximately 2,500 kg per cubic meter, which means that the Earth’s calculated density is 4,500 kg per cubic meter. The modern value is 5,515 kg per cubic meter.
Considering the limitations of 18th-century instruments, the result was astonishingly close. From this density estimate, scientists could infer the Earth’s total mass. For the first time in history, humanity possessed a reasonably scientific estimate of the weight of the planet beneath its feet.
The determination of the Earth’s density opened up other lines of thought. If the mean density of the Earth should so greatly exceed that of its surface rocks, it naturally meant that there must be denser material lying deeper. Hutton correctly surmised that the core material was likely metallic, and might have a density of 10,000 kg/cubic meter. He estimated this metallic portion to occupy some 65% of the diameter of the Earth. With a value for the mean density of the Earth, Hutton was able to set some values to Jérôme Lalande's planetary tables, which had previously only been able to express the densities of the major solar system objects in relative terms.
Hutton's calculations showing the division of the mountain into triangles to calculate its volume.
The Schiehallion experiment inspired later and even more precise attempts to determine Earth’s density. Most famous among them was the Cavendish experiment of 1798, in which Henry Cavendish used a torsion balance to measure the gravitational attraction between lead spheres.
The Schiehallion experiment was repeated in 1856 by Henry James, director-general of the Ordnance Survey, who instead used the hill Arthur's Seat in central Edinburgh. James arrived at a density of about 5,300 kg/ cubic meter.
A modern re-examination of the geophysical data was able to take account of factors the 1774 team could not. With the benefit of a 120-km radius digital elevation model, greatly improved knowledge of the geology of Schiehallion, and the help of a computer, a 2007 report produced a mean Earth density of 5,480 ± 250 kg/cubic meter. When compared to the modern figure of 5,515 kg/cubic meter, it stood as a testament to the accuracy of Maskelyne's astronomical observations
The Schiehallion experiment represented one of the greatest triumphs of 18th-century experimental science. The Scottish mountain experiment also demonstrated that Newtonian gravity worked not merely for planets and moons, but for ordinary terrestrial objects.
Today, Schiehallion remains a celebrated landmark in the history of science. Hikers climb its slopes for panoramic Highland views, often unaware that the mountain once served as one of the world’s greatest scientific instruments. But those who cared would have surely noticed the commemorative plaque mounted on a stone cairn at the beginning of the ascent, celebrating the work of Maskelyne and his team.
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