Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy
formed of the measure of depression (including the effect of the attraction of the water) considered as uniform. The line of cliff may be considered as straight. Let a be the distance from the pendulum station to the straight line of cliff, measured perpendicularly to that line: b the depth of the depression: let x <s>and y</s> be parallel to a, and y parallel to the line of the cliff. The matter d x δx x δy x b is at the distance (x<sup>2</sup> + y<sup>2</sup>)<sup>1/2</sup> from the upper <s>and</s> station, and therefore its vertical attraction on the lower station is d.b.c.δx.δy/(x<sup>2</sup> + y<sup>2</sup> + c<sup>2</sup>)<sup>3/2</sup> or d.b.c.δx.δy/(x<sup>2</sup> + y<sup>2</sup>)<sup>3/2</sup> nearly. Integrating first with respect to y, from ꝏ to +ꝏ, we have 2d.b.c.δx/x<sup>2</sup>. Integrating then with respect to x, from a to ꝏ, we have 2d.b.c/a. These formulae will suffice for our purpose. It is only necessary further to remark that, as the unit of measure is absolutely arbitrary, and as the numerical and graphical operators are a little facilitated by using for unit the "depth of the mine",
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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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