I am trying to write an exercise in which students need to calculate the density of earth following a procedure "inspired" in the Schiehallion experiment. My idea was to have the derive the following equation:
where $\rho_E$ and $\rho_M$ are the densities of Earth and of the mountain, $V_E$ and $V_M$ are the volumes, $R_E$ is the radius of earth, $d$ the distance between the pendulum and the centre of the mountain, $\theta$ the angle of the pendulum.
So far I have been able to find that $\rho_M=2500 kg/m^3$ and $\theta= 11.6''$. I also know that the result obtained was $\rho_E=4500 kg/m^3$. Therefore, I need at least one more datum. Does anyone know what was the value of $V_m$ used?