Background
A pendulum hangs straight downwards in a symmetrical gravitational field. However, if a sufficiently large mass such as a mountain is nearby, its gravitational attraction should pull the pendulum's plumb-bob slightly out of true. The change in plumb-line angle against a known object—such as a star—could be carefully measured on opposite sides of the mountain. If the mass of the mountain could be independently established from a determination of its volume and an estimate of the mean density of its rocks, then these values could be extrapolated to provide the mean density of the Earth, and by extension, its mass.
Isaac Newton had considered the effect in the Principia, but pessimistically thought that any real mountain would produce too small a deflection to measure. Gravitational effects, he wrote, were only discernible on the planetary scale. 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 mountain), this angle, though very slight, was within the theoretical capability of instruments of his day.
An experiment to test Newton's idea would both provide supporting evidence for his law of universal gravitation, and estimates of the mass and density of the Earth. Since the masses of astronomical objects were known only in terms of relative ratios, the mass of the Earth would provide reasonable values to the other planets, their moons, and the Sun. The data were also capable of determining the value of Newton's gravitational constant G, though this was not a goal of the experimenters; references to a value for G would not appear in the scientific literature until almost a hundred years later.
Read more about this topic: Schiehallion Experiment
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