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Improvements in the method of determining the magnetic fields of nonlinear dc machines are introduced in part I of the paper. A modified, successive line overrelaxation technique to satisfy boundary conditions is developed. A novel block relaxation technique, the additive acceleration of convergence, is explained. The improved method also takes care of relative position changes between field and armature. In part II  the improved method is applied to a large dc machine. A new computer flux plotting procedure is developed in part III .