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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                                intermediate comparisons have diminished the probable error in the
proportion expressed by the factor √ 6n/(n+1).(n+2). When n =
26, this fraction is <s>[?]</s> √13/63, or the weight of the result is
increased nearly five-fold by the intermediate comparisons.
When n = 15, the fraction is √45/136, or the weight is increased three-fold.
    Second, suppose that the Swings had been discontinuous.
The probable error in <s>the</s> each Swing, found by combining
its first and last comparison, would have been e√2: and,
as the different Swings are strictly independent, the
probable error on the mean of all would have been
e√2/n. Comparing this with our probable error above,
it appears that our system has diminished the probable
error in the proportion √ 6/(n+1).(n+2). When n = 26,
their fraction is √1/126, or the weight of the result is
increased 126-fold by our system. When n = 15,
the fraction is √3/136, or the weight is increased
45-fold.
    These contrasts will suffice to show the great advantage
of a system of continuous Swings with intermediate comparisons
such as has been employed in this experiment. I
cannot quit this subject without <s>stating</s> repeating that my first
impression on the advantage of such a system was derived
                            
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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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