Laying out the math (assuming earth is an homogeneous sphere) just in case it's not clear:

F_gravitational = G m1 m2 /r^2

g = G Mass_earth / r_earth^2

Mass_earth = r_earth^2 * g/G

Density_earth = r_earth^2 * g/G / V_earth

Density_earth = 3*g / (4*Pi*G*r_earth)

Prior to Cavendish we already new g and r_earth, just missing G.

Yup, that's exactly it:

- get the gravitational constant with these two known masses

- then can deduct the mass of the unknown Earth by its interaction with other masses (say the "g" gravitational acceleration value)

- then from the mass and the otherwise measured size of Earth the density pops out

More details in good ol' Wikipedia: https://en.wikipedia.org/wiki/Cavendish_experiment#Derivatio...

Oh so the earth density is merely the motivation for the experiment? I read it as the earth mass actually being used somewhere in the formulas within the setup itself which was what confused me.

He uses his experiment to calculate G based only on the test masses and spring and then the _result_ of the calculation was just used as a final step to calculate the mass of the earth, and then from that the density?