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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                                and I x 100/101.8 x 60.2 for pendulum 8: in which expressions the factors of I are sensibly the same. Call
this proportion C. Then the number of vibrations observed
is to be multiplied by <s>[?]</s> 1 + C<sup>2</sup>/64 or
 1 + I<sup>2</sup> x 1/64 . (100/101 x 60.7)<sup>2</sup>. In the first instance therefore
we require the logarithm of 1 + I<sup>2</sup> x 1/64 . (100/101 x 60.7)<sup>2</sup> for
values of I not exceeding 2.5. The following table contains
the numbers required, in units of the last figures
of 8-figure logarithms.

I  Log  I  Log  I  Log  I  Log  I  Log
0.1 2  0.6 65  1.1 218 1.6 462 2.1 796
0.2 7  0.7 88  1.2 260 1.7 522 2.2 874
0.3 17 0.8 116.1.3 305 1.8 585 2.3 955
0.4 29 0.9 146 1.4 353 1.9 652 2.4 1040
0.5 45 1.0 180 1.5 405 2.0 722 2.5 1128

Next, it is necessary to determine experimentally the
law, or rather the numerical succession of values, in
the diminution of the arc of vibration. For this purpose,
observations were made at Greenwich on the extent
of the whole arc in successive half hours. The following
table contains (with sufficient approximation) the
range of arc through each half hour, the middle arc
                            
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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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