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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                                small error, we may treat those irregularities of result as if
they were entirely due to irregularities of comparison:
and we have now to investigate the rule to <s>[?]</s> be
followed in combining the special results, supposed
to be erroneous from that cause only, in order to obtain
a final result whose probable error shall be the
smallest possible. It is evident that we are not to
give equal weight to the different results: for we should
thus neglect all comparisons except the first and the
last.

<s>42</s>40. Let the comparisons be numbered
     0, 1, 2, 3, 4, .......(n-1), n,
and let the swings be numbered
     1, 2, 3, 4, ....... n.
Let the actual errors of comparison, <s>(</s> estimated by their effect on
a four-hours rate, in units of the last figure of 8-figure logarithms<s>)</s>, be
     E<sub>0</sub>, E<sub>1</sub>, E<sub>2</sub>, E<sub>3</sub>, E<sub>4</sub>, .......E<sub>n-1</sub>, E<sub>n</sub>,
(where E<sub>16</sub> is supposed to be taken as if the comparison, which was really omitted, agreed with that produced
by interpolating between the two neighbouring comparisons)
and let the probable errors of comparison be
e<sub>0</sub>, e<sub>1</sub>, e<sub>2</sub>, e<sub>3</sub>, e<sub>4</sub>, ........e<sub>n-1</sub>, e<sub>n</sub>.
and let the weight for the results of the separate Swings be
n<sub>1</sub>, n<sub>2</sub>, n<sub>3</sub>, n<sub>4</sub>,...... n<sub>n</sub>     
                            
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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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