For a thorough understanding of flat earth upward continuation, Poisson's integral equation is transformed from a coordinate system with spherical symmetry to one with planar symmetry. The two separate cases of infinite and finite flat earths are considered. In resulting exact forms a functional factor in the integrands is isolated, a factor which allows the translation of a spherical earth surface potential into an exact flat earth surface potential. In the infinite flat earth case the 'upward continuation' of Heiskanen and Moritz is discussed and is seen to result when the corresponding functional factor is set equal to 1.