82 



April 23, 1849. 



On the Variation of Gravity at the Surface of the Earth. By 

 G. G. Stokes, M.A., Fellow of Pembroke College, Cambridge. 



In the theory of the figure of the earth on the hypothesis of ori- 

 ginal fluidity, a simple expression is obtained for the variation of 

 gravity along the surface, which contains the numerical relation 

 between the ellipticity and the ratio of polar to equatoreal gravity, 

 known as Clairaut's theorem. The demonstration, however, of this 

 expression does not require the hypothesis of original fluidity, if the 

 spheroidal form of the surface and its perpendicularity to the direction 

 of gravity be assumed as results of observation. On the hypothesis 

 merely that the earth consists of nearly spherical strata of equal 

 density, Laplace has established a connexion between the form of 

 the surface, regarded as a surface of equilibrium, and the variation 

 of gravity along it ; and in the particular case in which tbe surface 

 is an oblate spheroid of small ellipticity, having its axis of figure 

 coincident with the axis of rotation, the expression which results for 

 the variation of gravity is identical with that which is obtained on 

 the hypothesis of original fluidity. The object of the author in the 

 first part of this paper is to obtain the general connexion between 

 the form of the surface and the variation of gravity along it, by an 

 application of the doctrine of potentials, without making any hypo- 

 thesis whatsoever respecting the distribution of matter in the interior 

 of the earth. 



The latter part of the paper was devoted to the consideration of 

 the irregularities produced in the variation of gravity by the irregular 

 distribution of land and sea at the surface of the earth. The author 

 has shown why gravity should appear less on continents than on 

 small islands situated at a distance from any continent, which is a 

 circumstance that has long since been observed. The result is ac- 

 counted for by the elevation of the sea-level produced by the attrac- 

 tion of a continent, in consequence of which a station on a continent 

 is further removed from the centre of the earth than it appears to be. 

 It is shown also that the numerical value of the earth's ellipticity, 

 which has been deduced from pendulum experiments, is somewhat 

 too great, in consequence of the undue proportion of oceanic stations 

 in low latitudes, among the group of stations at which the observa- 

 tions were made which have been employed in the discussion. 



The author has given formulas whereby observed gravity may be 

 corrected for the irregularities of the earth's surface. These formulas 

 require a knowledge, or at least an approximate knowledge, of the 

 height of the land and the depth of the sea throughout the earth's 

 surface. The sign and magnitude of the difference between obseiwed 

 gravity, and gravity calculated on the hypothesis of the earth's ori- 

 ginal fluidity, appears on the whole to depend on the insular or con- 

 tinental character of the station at which the observation has been 

 taken. This circumstance renders it probable, that if observed gra- 

 vity were corrected for the irregular attraction due to the irregular 



