Schiehallion experiment data

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:

$$\rho_E=\rho_M\frac{V_M}{V_E}\left(\frac{R_E}{d}\right)^2\frac{1}{\tan\theta}$$

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?