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A system for continuously monitoring the harmonic coefficients of a superconducting accelerator is described. The method employs a series of magnetoresistance elements placed at specific locations around the circumference of the usable aperture. Difference signals from these probes are used to determine the harmonic coefficients. This method does not require integration of the field measuring signals or rotation of the probes so that the elements can be built into the magnet during construction. Experimental results are given for the simplest configuration and these results are compared to the sextupole signal measured in a more conventional way.