I. On the ellipticity of the earth as deduced from experiments made with the pendulum
James Ivory · The Philosophical Magazine · 1826
T HE experiments made with the pendulum are now very numerous, and the great difficulty is to reconcile them, and to deduce from them the best-founded result with respect to the figure of the earth.Hitherto it has been thought sufficient to proceed on the theory delivered by Clairaut, neffleeting the square and higher powers of the elliptieit).-T~ereason is, that the square of the earth's elliptieity is very small, and at least of the same order with the unavoidable errors of the experimental quantities, and in all probability even of a magnitude much less considerable than those errors.As this remark appears to be well founded, it can hardly be expected that rely practical advantage will be gained by solving the problem to a greater degree of approximation than Clairant has done.But in order to satisfy the present restlessness of inquiry, and to confine, if possible, the attempts of philosophers on this subject within proper bounds, the point is perhaps not undeserving of examination.The equilibrium of a fluid, or of different fluids varying in density,, covering a nucleus is a problem of easier solution than the equilibrium of a homogeneous fluid.In the former case we have in the interior of the fluid a given surface which determines the fi~ure of all tile strata above it.In the latter case there is homing in the interior which can assist us in finding the figure necessary to the equilibrium of the mass.The equilibrium of a mass entirely fluid, but consisting of strata of different densities, comes under the general case of a nucleus.For, however the density varies fi'om stratum Communicated by the Author.