

THE 



PHILOSOPHICAL MAGAZINE 

 AND JOURNAL. 



31 st JULY 1826. 



I. On the Ellipticiiy of the Earth as deduced from Experiments 

 made with the Pendulum. By J. Ivory, Esq. M.A. F.R.S.* 



r 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 suf- 

 ficient to proceed on the theory delivered by Clairaut, neg- 

 lecting the square and higher powers of the ellipticit} 1 . The 

 reason is, that the square of the earth's ellipticity 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 any practical advantage will be gained by solving the 

 problem to a greater degree of approximation than Clairaut 

 has done. But in order to satisfy the present restlessness of 

 inquiry, and to confine, if possible, the attempts of philoso- 

 phers on this subject within proper bounds, the point is per- 

 haps 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 figure of all the strata above it. In the latter 

 case there is nothing 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 from stratum 



* Communicated by the Author. 

 Vol. 68. No. 339. July 1826. A 2 to 



