Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy
ε, the ellipticity. w, the angular velocity. m, the ratio of the centrifugal force to gravity at the equator. Ε, the mass of the Earth. v, the angle between the normal and radius vector at any point of the surface. In the following investigation, small quantities of the second order are neglected, ε and m being regarded as small quantities of the first order. If U = V + w<sup>2</sup>/2 r<sup>2</sup> sin<sup>2</sup>θ, the differential coeficients dU/dr, 1/r . dU/dθ, will give the components of the force along and perpendicular to the radius vector; and, g being the force of gravity, g =  cos v.dU/dr + sin v. 1/r . δU/δθ: which becomes, since v and dU/dθ are small quantities of the first order, g =  dU/dr Let v be measured along the vertical: then dg/dv = cos v. dg/dr  sin v. 1/r . dg/dθ
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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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