A fundamental problem of cardiac electrophysiology is that of relating quantitatively the electrical activity within the heart to the complete timevarying potential distribution at the body surface. A new numerical method is described for the calculation of the surface potential on an irregularly shaped closed external surface due to an arbitrary source distribution in a medium containing regions of different conductivity, subject to the appropriate boundary conditions. The method is intended to provide an exact theoretical analysis of the experimental data acquired by A. M. Scher and others who have been mapping the pathways of ventricular depolarization in dogs and other animals. In anticipation of the above research program, a number of exploratory computations are reported. For example, the surface potential distribution has been calculated for a cylinder of human torso cross-section with a hemispherical dipole layer current source in approximate heart position and orientation and containing "lungs" of conductivity different from that of the surrounding medium. Under certain conditions, when lung-like inhomogeneities are introduced, a simple dipole source can generate a potential distribution having the multiple maxima and minima characteristic of higher multipole sources.