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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                                end of a Swing were made by different observers,
I compared the logarithms of apparent rates of Earnshaw/Shelton
during that swing, with the logarithms for the preceding
and following swings (in three instances, however, with only the preceding swing), and formed the <s>[?]</s>
<s>[?]</s> excess of the logarithm of the
intermediate swing <s>[?]</s> above the
mean of the preceding and following logarithms. This
numerical <s>[?]</s> excess may be compared with a symbolical
formula, in which the symbols represent, not the actual
error in time committed by each observer, but the
logarithm (in 8-figure units) of the influence of this
error on rates deduced from comparisons at 4-hour intervals.
Twenty-seven equations were thus formed. By the
method of minimum squares, these were reduced to
six, of which (from the nature of the case) one was
unnecessary, their sum being identically equal to zero.
Assuming D (Mr. Dunkin's error) = 0, the others are found
by solution of the equations. Though the equations are not very
favourable, they suffice for giving very good corrections, and they show
in particular that Mr. Simmonds recorded his times too early by
nearly half a second. The following table <s>represents</s> exhibits this work: the
fundamental numbers being obtained from a table which is to follow.
                            
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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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