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A three-dimensional magnetohydtostatic axial system comprises a magnetic field with its gradient set high vertically and low horizontally. The vertical gradient is used for levitation, with its axial rate of change monitored through the horizontal gradient. Useful fields are obtainable with pole faces generating a two-dimensional potential function multiplied by an axial function which obeys the Laplace equation; a tilted two-dimensional profile produces the same apparent effect. Experiment and theory show that the resolving power of the axial system is superior to that of its two-dimensional counterparts.