I'm trying to compute the value of G from Cavendish's own observations. I get $G_{Cav}=5.27501×10^{−10}$ which is 8 times bigger than the accepted value of $G_{True}=6.67430×10^{−11}$. Do you see anything wrong with my computations below?
I'm using this formula (from Wikipedia)
$$ G = \frac{2\pi^2 L r^2 \theta}{M T^2} $$
G = Gravitational constant
L = Length of torsion balance (the distance between the centers of balls)
r = The distance of attraction (between weights and balls)
$\theta$ = Deflection of the arm from its rest position due to gravitational attraction
M = Mass of attracting lead weight
T = Natural period of oscillation of the balance
I take $\theta$ and N from the 4th experiment, (Page 520 in Cavendish's paper), the rest are constants,
L = 1.862 m
r = 0.2248 m
$r^2$ = 0.05053 $m^2$
$\theta$ = 0.00806788 radians
M = 158.04 kg
T = 421 s
$T^2$ = 177241 $s^2$
Substituting in the numbers,
$$ G_{Cav} = \frac{2 \times \pi^2 \times 1.836 \times 0.05053504 \times 0.00806788}{158.04 \times 177241} = 5.27501\times 10^{-10} $$
This is eight times bigger than the accepted value,
$$ \frac{G_{Cav}}{G_{Tru}} = 7.90 $$
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