When simulating a periodic molecular system, lattice sum methods may be used to evaluate the electrostatic interactions without resorting to an unphysical truncation of the potential. In a previous publication, we compared the computational efficiency of the Ewald and Particle-Particle Particle-Mesh (PPPM) lattice-sum methods. Because the PPPM method discretizes the field equations and utilizes the highly efficient fast Fourier transform algorithm, it requires significantly less computational effort than the Ewald method and scales almost linearly with system size. In this paper, we take a more detailed look into the theory behind the lattice-sum methods to clarify the underlying similarities between the Ewald method and the PPPM method. We also investigate the errors introduced by different approximation used in the discretization of the field equations in the PPPM method.