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A general integral expression is formulated for the gravitational attraction due to any solid of revolution based on the attraction of vertical, semi-infinite, circular, cylindrical shells. The expression accommodates solids with radial variation of density. For solids with constant density, further generalization to arbitrary orientation is made through coordinate transformation that considers both vertical and radial components of attraction. Special solutions for solids with simple geometry are listed. Practical applications are demonstrated by forward gravity modelling the effects of volcanic islands (cylindrical core bounded by an outer exponentially trending surface) and inclined finite-length cylinders. Corresponding expressions for the magnetic case are discussed in terms of using Poisson''s relation. [Copyright &y& Elsevier]

Integral expressions are derived for the vertical component of gravitational attraction arising from vertical circular cylinders and horizontal circular disks with radial variation of density. The expressions contain a single elliptic integral of either the first or second kind and are evaluated easily by numerical integration. Various closed-form solutions are obtained for special cases. For constant density, the expressions reduce to well-known solutions as well as approximations that are based on the solid angle and line element, thus providing a unified theme for the derivations of those solutions and approximations. Numerical implementation is discussed in terms of practical application. [Copyright &y& Elsevier]