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The untuned cavity is used to measure dielectric loss in small samples of arbitrary shape. As long as certain constraints on loss and sample size are met, then results do not depend on reflections and interference effects, making the measurement quick and easy to interpret. The authors consider one situation in which more complicated analysis is requiredÂ¿that of thin discs of high refractive index, where internal reflections and interference effects make the measured loss a function of sample thickness. We present an elementary analysis of this case, showing that by an extended set of measurements (over a range of thickness or frequency) both the real part of the dielectric constant Â¿ and the true dielectric loss Â¿ can be found. The theoretical predictions in the paper are supported by a series of measurements with thin ceramic discs.