Repeat Experiments
A more direct, and more accurate, measurement of the mean density of the Earth was made 24 years after Schiehallion, when in 1798 Henry Cavendish used an exquisitely sensitive torsion balance to measure the attraction between large masses of lead. Cavendish's figure of 5,448 ± 0.033 kg·m−3 was only 1.2% from the currently accepted value of 5,515 kg·m−3, and his result would not be significantly improved upon until 1895 by Charles Boys. The care with which Cavendish conducted the experiment and the accuracy of his result has led his name to since be associated with it.
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, though the then elderly Hutton vigorously defended the original value in an 1821 paper to the Society. 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. With the resources of the Ordnance Survey at his disposal, James extended his topographical survey to a 21-kilometre radius, taking him as far as the borders of Midlothian. He obtained a density of about 5,300 kg·m−3.
An experiment in 2005 undertook a variation of the 1774 work: instead of computing local differences in the zenith, the experiment made a very accurate comparison of the period of a pendulum at the top and bottom of Schiehallion. The period of a pendulum is a function of g, the local gravitational acceleration. The pendulum is expected to run more slowly at altitude, but the mass of the mountain will act to reduce this difference. 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. This experiment yielded a value of the mass of the Earth of 8.1 ± 2.4 × 1024 kg, corresponding to a mean density of 7,500 ± 1,900 kg·m−3.
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 in particular a computer, a 2007 report produced a mean Earth density of 5,480 ± 250 kg·m−3. When compared to the modern figure of 5,515 kg·m−3, it stood as a testament to the accuracy of Maskelyne's astronomical observations.
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