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, substituting this for E<sub>0</sub> in the different expressions
above, E<sub>1</sub>, E<sub>2</sub>, &c will be formed. Squaring each,
forming 1/27 part of the sum of squares, and multiplying <s>the/s> its square root
by 0.6745, the probable error is obtained.
     The quantity thus obtained is however a little
too great. For S, <s>[?]</s> the number which we have found for E<sub>0</sub> contains
26.25/2.27 .A or 12A nearly: and as the probable error
of A is about 1/40 .e, the probable error of 12A is
about 3/10 .e: and therefore we have on the right side of the
equation an aggregate of terms whose probable error is
√e<sup>2</sup> + 9/100 .e<sup>2</sup> or 
e(1 + 1/22) nearly. The same is true for
E<sub>26</sub> and those near it. Bu for E<sub>43</sub> the factor of A is 0.
Thus it will easily be seen that the quantity which we
obtain is really e(1 + 1/66) nearly. The correction scarcely
deserves notice.
44. In this manner the following (uncorrected) values of
E<sub>0</sub>, E<sub>1</sub>, &c, are found: arranged with reference to the
Swings to which they relate. It will be remembered that
the number 300 represents an error of 0<sup>s</sup>.1 in
absolute time, very nearly.

                            
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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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