Using a Mountain to Weigh the World
The story of how Schiehallion was chosen for Maskelyne’s famous experiment
Current and future experiments, such as those I have described in my previous posts, would not be possible without the work of scientists throughout history. In 1772, Nevil Maskelyne, the Astronomer Royal, proposed a repeat of a certain experiment to the Royal Society. If successful, the experiment would provide evidence for Newton’s law of gravitation, which says that all objects attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The experiment would also provide estimates for the mass and density of the Earth, which would in turn produce values for the masses of the other planets, their moons and the Sun, as these were only known relative to the Earth’s mass.
In this experiment, the bob of a pendulum is pulled away from its central position due to the gravitational attraction of a nearby mountain. The change in the plumb-line angle on opposite sides of the mountain can be used, together with the volume and density of the mountain, to calculate the mass of the Earth. Newton had considered this experiment, but had dismissed it, thinking that the effects would be too small to measure.
This experiment was first attempted by the French astronomers Pierre Bouguer and Charles Marie de La Condamine on the Chimborazo volcano in Ecuador. This experiment was not the purpose of their expedition, and the difficulties caused by the terrain and climate at an altitude of about 15,000 ft meant that Bouguer was reluctant to attach significance to the small deflection they observed. He instead suggested that a mountain in France or England would be a more suitable location for the experiment.
The Royal Society created the Committee of Attraction, which assigned astronomer and surveyor Charles Mason the job of selecting the most suitable mountain for the experiment. After spending the summer of 1773 searching, he selected Schiehallion, a 3,547 ft mountain in the centre of the Scottish Highlands. The reasons for his choice were the symmetry of the mountain, which would allow its volume to be more easily measured, and the steep slopes to the north and south, which meant that the experiment could be situated near the mountain’s centre of mass. Schiehallion was also not located near other hills, which would have their own gravitational influence on the experiment.
The unspent money from a series of observations of the transit of Venus was provided to the Royal Society by King George III, giving them access to high-quality equipment. Maskelyne journeyed to Schiehallion by sailing from near London to Perth, due to the poor road network at the time. Observatories were constructed by local workmen on opposite sides of the mountain, as well as a basic shelter known as a bothy to protect the scientists and equipment from the weather. Meanwhile, most of the workforce slept in canvas tents. In 1772, outside of its cities, much of Scotland was still poverty-stricken with few natural resources and poor weather, with Maskelyne even being told that the name of the mountain translated to “constant storm”.
Despite frequent mist and rain, and after about 16 and a half weeks on the mountain in total, Maskelyne managed to calculate the apparent difference in latitude between the north and south sides of Schiehallion by observing the stars to find the difference between the measurements of true vertical. He then subtracted from this the “true” difference in latitude of the two observatories provided by surveyors. This gave a total deflection of the pendulums of 11.6 arc seconds (about 0.003º) due to the gravitational pull of the mountain.
It was now the task of Charles Hutton to calculate the volume of the mountain. His method was to first survey the entire mountain, which took several years due to adverse weather conditions, and to then divide it into a set of prisms. Hutton discovered that drawing lines between marker points at equal heights gave an immediate impression of the three-dimensional shape. He had invented contour lines, which are still used in mapping today.
Using the values calculated by Maskelyne and Hutton, together with an estimate of the mean density of the rocks that made up the mountain, the density of the Earth was found to be 4,500 kg m⁻³. This is within 20% of the current accepted value of 5,515 kg m⁻³. The results showed that the Earth’s core must consist of material much denser than the rocks on the surface, and Hutton deduced that it was likely metallic.
In 1798, Henry Cavendish measured the attraction between suspended masses of lead, and used his results to calculate a much more accurate value for the density of the Earth. The mountain experiment was repeated in 1856 using Arthur’s Seat in Edinburgh. This time the survey was extended out to a radius of 15 to 20 miles, and showed that masses at this distance still contributed to the deflection of the pendulum, implying that the survey of Schiehallion was not extensive enough.
With the use of a digital elevation model and improved knowledge of the geology of Schiehallion and the surrounding area, the density of the Earth was recalculated in 2007 using Maskelyne’s astronomical observations. The calculations produced the modern accepted value (within the expected uncertainty), providing evidence for the accuracy of Maskelyne’s observations.
Despite the weather, Maskelyne returned to England with a positive impression of the area, writing “all the gentlemen of the neighbourhood often paid me visits on the hill and gave me the fullest conviction that their country is with justice celebrated for its hospitality and attention to strangers”. Upon completion of his experiment, Maskelyne hosted a party for his assistants and people from the nearby town of Pitlochry. The celebrations became so rambunctious that the observatory caught fire and burned to the ground.
