I just posted a chart showing the extreme points of the arm observed by Henry Cavendish 210 years ago today :)

Cavendish measured these excursions and computed the period. The average period ((This would be called half period today. It is the motion of the arm from one extreme point to the other.)) is about 7 minutes.

As I was looking at the data I thought that if the weights remained in neutral position and the system was set in motion “by moving the index” ((See experiment V, Aug. 20, 1797)) as Cavendish usually did the pendulum would oscillate with its natural motion. ((Experiments with a replica of Cavendish experiment proves that indeed the natural excursion is about 0.0154 degrees, very close to Cavendish’s pendulum.)) Since the period is independent of excursions we would still measure a period of 7 minutes plus or minus the error of observation.

This means that if we let the Cavendish pendulum oscillate on its own without any attracting weight, we would obtain Cavendish’s value of 5.5 for the mean density of the Earth. We could then easily convert the mean density to G. This way we have measured the value of G between the attracting mass M and attracted mass m even though mass M was in neutral position and was unable to exert its occult Newtonian virtues to mess with the pendulum arm. Nevertheless Cavendish pendulum happily yielded the correct value of G even in the absence of an attracting weight. ((Since mass m is not represented in the equation, we could have a Cavendish pendulum oscillating with no weights attached to it and still obtain the value of G.))

Cavendish built a pendulum with given measurements that could only give 5.5 for the mean density of the Earth. The tradition continues today. Physicists build given pendulums and measure the given period and obtain the given G. When you know the result of your experiment and your pendulum could not but give what you already know ((after all a pendulum cannot oscillate with any other period but its natural period.)) what you do is not an experiment it is a prayer to the authority of Newton.

Cavendish experiment discussion forum.