Schiehallion experiment
[2] Newton's pessimism was unfounded: although his calculations had suggested a deviation of less than 2 minutes of arc (for an idealised three-mile high [5 km] mountain), this angle, though very slight, was within the theoretical capability of instruments of his day.
[3] An experiment to test Newton's idea would provide supporting evidence for both his law of universal gravitation and estimates of the mass and density of the Earth.
[4] A pair of French astronomers, Pierre Bouguer and Charles Marie de La Condamine, were the first to attempt the experiment, conducting their measurements on the 6,268-metre (20,564 ft) volcano Chimborazo.
Their expedition had left France for South America in 1735 to try to measure the meridian arc length of one degree of latitude near the equator, but they took advantage of the opportunity to attempt the deflection experiment.
[5] Between 1763 and 1767, during operations to survey the Mason–Dixon line between the states of Pennsylvania and Maryland, British astronomers found many more systematic and non-random errors than might have been expected, extending the work longer than planned.
[7] When this information reached the members of the Royal Society, Henry Cavendish realized that this effect might have been due to the gravitational pull of the nearby Allegheny Mountains, which had probably diverted the plumb lines of the theodolites and the liquids inside spirit levels.
[9] He suggested that the experiment would "do honour to the nation where it was made"[3] and proposed Whernside in Yorkshire, or the Blencathra-Skiddaw massif in Cumberland, as suitable targets.
The Royal Society formed the Committee of Attraction to consider the matter, appointing Maskelyne, Joseph Banks and Benjamin Franklin amongst its members.
[11] Generous funding for the experiment was available due to underspend on the transit of Venus expedition, which had been turned over to the Society by King George III.
It was necessary for him to determine the zenith distances with respect to the plumb line for a set of stars at the precise time that each passed due south (astronomic latitude).
[1] To determine the deflection due to the mountain, it was necessary to account for the curvature of the Earth: an observer moving north or south will see the local zenith shift by the same angle as any change in geodetic latitude.
[6] Once the surveying team had provided a difference of 42.94″ latitude between the two stations, he was able to subtract this, and after rounding to the accuracy of his observations, announce that the sum of the north and south deflections was 11.6″.
[3][6][14] Maskelyne published his initial results in the Philosophical Transactions of the Royal Society in 1775,[14] using preliminary data on the mountain's shape and hence the position of its center of gravity.
To make sense of all his data, he hit upon the idea of interpolating a series of lines at set intervals between his measured values, marking points of equal height.
[21] The Scottish scientist John Playfair carried out a second survey of Schiehallion in 1811; on the basis of a rethink of its rock strata, he suggested a density of 4,560 to 4,870 kg·m−3,[22] though the then elderly Hutton vigorously defended the original value in an 1821 paper to the Society.
[3][23] Playfair's calculations had raised the density closer towards its modern value, but was still too low and significantly poorer than Cavendish's computation of some years earlier.
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.
This experiment has the advantage of being considerably easier to conduct than the 1774 one, but to achieve the desired accuracy, it is necessary to measure the period of the pendulum to within one part in one million.
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·m−3.
