The use of a Hankel transform can reduce the solution of Laplace's equation in cylindrical coordinates (p, z) in the region 0 < p < ∞, 0 < z < h when the boundary condition on z = 0 is a ‘mixed’ one and that on z = h is of the usual type to the solution of the dual integral equations where G(μ), g(p) are given functions of the variables indicated and f(μ) is to be found. A formal solution of these equations is given and, as an example, the solution is applied to find the potential due to a circular disk at constant potential placed with its plane parallel to, and equidistant from, two carthed parallel plates.