The Shealian Experiment - The Vertical Hang

The shealian experiment was an eighteenth century experiment designed to test the mean density, or the average density, of the earth. Essentially what they would do is hang a pendulum down on a long string and assess the vertical hang of this pendulum. If the earth was solid, it would have so much more mass than that mountain that there would be no wavering in that pendulum. But you're right, if the earth was hollow, then there's less mass within the earth,. meaning that that mountain near by might actually have a measurable impact on that pendulum  and it woud pull it just a little bit off center.