Two-dimensionality on spherical earth — A problem in gravity reductions

Summary A mass distribution which remains constant perpendicular to a diameter, within the walls of a vertical cylinder, is defined as a bounded two-dimensional mass distribution. Assumption of such a distribution may be more realistic than the assumption of an unbounded two-dimensional distribution in many situations. The gravity effect of such a distribution is comparable with the effect calculated by conventional three-dimensional methods of reduction. The effect of sphericity of the earth may be allowed as an additional correction. For the calculation of the gravitational effect of this distribution, a formula for the attraction of a cylindrical strip, at a point on the axis, is derived. The effect is compared with that of a two-dimensional distribution. To calculate the effect of sphericity, a formula for the attraction of a spherical cap is derived and this attraction is compared with that of a flat disc. The proposed distribution and the correction for sphericity are particularly applicable in marine gravity reductions.