[en] Taylor's theory of the relaxation of toroidal plasma discharges has accounted remarkably well for the experimentally observed behavior of toroidal z-pinches. His analysis also leads to particularly stable magnetic configurations which have served as the starting point for work on the speromak. We present here a corrected version of Taylor's analysis, including a term improperly left out of his expression for the energy of a force-free state. We also present force-free equilibrium solutions in cusp and higher order multipole external fields. These are to serve as the starting point for a study of modified spheromak configurations having improved magnetic field line curvature