Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy
<s>44</s>43. For <s>[?]</s> ascertaining the probable error <u>e</u> I have used the following process. Let E<sub0</sub>, E<sub>1</sub>, E<sub>2</sub>, &c, as before, be the actual errors of comparison, estimated by the effect which they produce on a 4hours' rate, in the 8<sup>th</sup> decimal place of logarithms: Let R<sub>1</sub>, R<sub>2</sub>, &c, be the successive individual results for the rate of the lower pendulum on the upper pendulum: and let A be the adopted value of that rate. Now if A <s>[?]</s> were rigorously correct, we should have the following equations: E<sub>0</sub> = E<sub>0</sub> E<sub>1</sub> = E<sub>0</sub> + R<sub>1</sub>  A = E<sub>0</sub> + R<sub>1</sub>  A E<sub>2</sub> = E<sub>1</sub> + R<sub>2</sub>  A = E<sub>0</sub> + (R<sub>1</sub> + R<sub>2</sub>)  2A E<sub>3</sub> = E<sub>2</sub> + R<sub>3</sub>  A = E<sub>0</sub> + (R<sub>1</sub> + R<sub>2</sub> + R<sub>3</sub>)  3A &c and, adding all for the First Series, which terminates with R<sub>26</sub> and E<sub>26</sub>, E<sub>0</sub> + E<sub>1</sub> + &c + E<sub>26</sub> = 27E<sub>0</sub> +26R<sub>1</sub> + 25R<sub>2</sub> + &c + R<sub>26</sub>  [26.25/2]A E<sub>0</sub> is yet undetermined. Now the Theory of Probabilities which we have used requires that the chances of positive and negative errors be equal, and therefore that (subject to the irregularities of chance) E<sub>0</sub> + E<sub>1</sub> + &c + E<sub>26</sub> = 0 This gives E<sub>0</sub> = [26.25/2.27]A  1/27 (26R<sub>1</sub> + 25R<sub>2</sub> + &c + R<sub>26</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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