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A probe has been designed for making point-by-point mapping measurements of contact resistance over large surface areas. The probe, which operates in the low force range of 5 mg to 5 g, permits simultaneous measurement of both contact resistance as a function of load and the integral of contact resistance versus force. To accomplish this a magnetically damped torsion bar mounted pendulum/sample holder is electromagnetically driven against a smooth spherical probe tip mounted directly on a force transducer which, in turn, is mounted on an x-y precision translation stage. The associated instrument package includes a variable sweep rate electromagnetic drive, high-frequency rejecting load and contact voltage amplifiers (the latter being an ultrastable differential amplifier), a voltage-to-frequency converter, a scaler, and an x-y recorder. The probe has been used to explore spatial variations in contact resistance due to a nonuniform fiuoropolymer film on a gold substrate. The data show a large statistical variability, which is simply analyzed by assuming normally distributed surface asperities and applying this assumption to the accepted model for multi-asperity electrical contact. This procedure leads to a prediction that the square of the conductance will follow a Gaussian distribution. Contact resistances that were obtained in the course of this work as a function of force are shown to be consistent with the multi-asperity model, Data are presented which agree well with the statistical model. This insight into the statistical variability of contact resistance data is useful in that it suggests a successful data smoothing technique that presents a reasonable appearing line map of the effective contact resistance due to a nonuniform film. It is demonstrated that data smoothed in this fashion can be favorably compared to the degree of surface contamination as determined with a scanning electron microscope.