The Schiehallion experiment was an elegant physics experiment done in the 18th century to calculate the density of the Earth. The basic idea is to stand with a pendulum near a mountain of known dimensions and composition. Due to the gravitational attraction of the mountain, the pendulum will swing towards it by a tiny amount. Using this displacement, Newton's law of gravitation, the known density of the mountain, and the known dimensions of both the Earth and the mountain, one can solve for the density of the Earth.
Read the full paper over at Fermat's Library.