Schiehallion Experiment - Measurements - Surveying

Surveying

The work of the surveying team was greatly hampered by the inclemency of the weather, and it took until 1776 to complete the task. To find the volume of the mountain, it was necessary to divide it into a set of vertical prisms and compute the volume of each. The triangulation task falling to Charles Hutton was considerable: the surveyors had obtained thousands of bearings to more than a thousand points around the mountain. Moreover, the vertices of his prisms did not always conveniently coincide with the surveyed heights. To make sense of all his data, he hit upon the idea of interpolating a series of lines at set intervals between his measure values, marking points of equal height. In doing so, not only could he easily determine the heights of his prisms, but from the swirl of the lines one could get an instant impression of the form of the terrain. Hutton had invented contour lines, in common use since for depicting cartographic relief.

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. He found that the attraction of the plumb-bob to the Earth would be 9,933 times that of the sum of its attractions to the mountain at the north and south stations, if the density of the Earth and Schiehallion had been the same. Since the actual deflection of 11.6″ implied a ratio of 17,804:1 after accounting for the effect of latitude on gravity, he was able to state that the Earth had a mean density of, or about that of the mountain. The lengthy process of surveying the mountain had not therefore greatly affected the outcome of Maskelyne's calculations. Hutton took a density of 2,500 kg·m−3 for Schiehallion, and announced that the density of the Earth was of this, or 4,500 kg·m−3. In comparison with the modern accepted figure of 5,515 kg·m−3, the density of the Earth had been computed with an error of less than 20%.

That the mean density of the Earth should so greatly exceed that of its surface rocks naturally meant that there must be more dense material lying deeper. Hutton correctly surmised that the core material was likely metallic, and might have a density of 10,000 kg·m−3. 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.