The transmission characteristics of spherical plate electrostatic analyzers for external sources are studied. Transmission as a function of particle point of incidence, angle of incidence, and kinetic energy, and of analyzer plate geometry (central angle and radii of curvature) and plate potentials, is determined analytically and graphically. Our method (which assumes that the ratio of plate spacing to mean radius is small) uses derived relationships between these parameters and the position of the center of the particle's trajectory, which trajectory is approximated by a circular arc. For a fine incident beam of particles, angular resolution at mean transmitted energy and energy resolution at normal incidence are independent of the point of incidence; the angular resolution is moreover a constant and the energy resolution varies linearly with the mean energy. The area of energy‐angle transmission diagrams is likewise independent of point of incidence. Energy and angle response functions for diffuse beams of particles are derived semi‐empirically. The energy response function (integrated over angle) has the same FWHM as the function for a fine beam incident normally. The angle response function (integrated over energy) has the same FWHM as the function for a fine beam at appropriate fixed energy. Theoretical results for fine beams are compared with experiment and agree well. A practical instrument, specifically for satellite use but suitable for the laboratory, is also described.