# The Michell-Cavendish experiment

I added this article to my Cavendish wiki. Like Laurent Hodges Titchmarsh too calls the Cavendish experiment the Michell-Cavendish experiment. This reminds me the Ship of Theseus paradox. Cavendish’s pendulum had three components:

1) the wooden arm
2) the copper wire

Cavendish had a new wooden arm made because what he inherited was warped. Cavendish bought a new copper wire. Cavendish cast his own lead weights because he thought Michell’s was too small. Was the pendulum Cavendish used to weigh the earth still the pendulum he inherited from Michell?

The original apparatus itself did not survive. Baily, a contemparory of Cavendish’s, said that “Cavendish’s apparatus belongs to the Royal Institution, of whom I borrowed it for the purpose of having copies of its several parts made for my experiments.” ((Titchmarsh, p. 321)) Titmarch searched the records of the Royal Institution but could not find any reference to it. But he found a map which shows the shed where Cavendish conducted his experiment.

To compute the density of the earth Cavendish used the formula

N^2/10844 B.

N = mean period of the pendulum
B = number of divisons the arm moved as Cavendish switched the weights from positive to negative or vice versa. (Also from neutral position to other two.)

Probably I am misunderstanding the formula, but I don’t get Cavendish’s results. For instance, his results table ((Titchmarsh, p. 329)) for experiment IV has N = 7 m 1 sec and B = 6.18. Plugging in these values I get

177241 / (10844 * 6.18) =  2.64

Cavendish gives for this experiment 5.29.

Where do I err?