The first recorded methods I know of were done in the middle of the 18th
century.
One involved measuring the period of a pendulum on solid ground at sea
level and on a plain very far above sea level. This can provide a ratio
of the Earth's average density and the density of the ground that is
above sea level.
A second involved deflection of a pendulum near a mountain. Using a
star as a reference, deflection of a pendulum on top of a mountain and
near the same mountain could provide a ratio of Earth mass to mountain
mass.
Both are recorded in an 1893 essay by J. H. Poynting: The Mean Density
of the Earth. A digitized copy of the text can be accessed currently
through Google at
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