Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy

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                                The sum of all the factors for the effects of inequalities is - .044799.
   As the attraction of the shell is 12.566368 x d,
and as the effects of inequality amount to - .044799 x d,
the complete effect of the ground above the lower station
is 12.521569 x d.

60. We are now in a position to obtain a result
requiring only for its complete numerical exhibition a
knowledge of the specific gravities of the mine-rocks. The
formula for gravity at the lower station has been found
to be 69625 x D
and that at the upper station
    (69625 - 8.3776) x D + 12.5216 x d
Hence Gravity below/Gravity above = 1 + 0.00012032<s>4</s> - 0.00017984 x d/D
But the experiments gave (see article 45)
Gravity below/Gravity above = 1.00005185 ± -00000019
Hence 0.00006847 ± .00000019 = 0.00017984 x d/D:
Or D/d = 2.6266 ± .0073
where (as has been explained in article 45) the last term ought
probably to be doubled, to give the uncertainty depending on the
pendulum-experiment only.
                            
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Manuscript details

Author
George Biddell Airy
Reference
PT/54/5
Series
PT
Date
1855
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Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy, 1855. From The Royal Society, PT/54/5

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