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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                                From these are found the values of the probable error<s>s</s> of <s>[?]</s> a single
comparison<s>s</s>, treating the four Series separately;

     In Series 1, e = ± 420
     In Series 2, e = ± 135
     In Series 3, e = ± 203
     In Series 4, e = ± 173
And hence the probable errors and weight of the mean results are,
<s>[?]</s>
For First Series, probable error = ± 10.4, weight = 93/10000
For Second Series, probable error = ± 3.3, weight = 899/10000
For Third Series, probable error = ± 11.0, weight = 82/10000
For Fourth Series, probable error = ± 9.4, weight = 114/10000

45. Combining the results of the First and Third Series, with the
weights <s>[?]</s> just found, and still adopting as unit, in the
probable error, the unity of the 8<sup>th</sup> decimal of logarithms,
   Log Rate of Pendulum 8 below upon Pendulum 1821 above
     = 9.99928558 ± 3.1 :<s>[?]</s>
And, remarking that log. Gravity below/Gravity above is the sum of these logarithms,
we have finally
log. Gravity below/Gravity above = 0.00002252 ± [?]8.2
or Gravity below/Gravity above = 1.0000518 ± 0.00000019
                            
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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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