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Numerical calculations and measurements of the radiofrequency size effect (RFSE) in the transmission geometry are reported for potassium plates 0.1 mm thick at 1.25 MHz. The agreement between theory and experiment on the line width, line shape, and magnitude of the effect is very good for specimens with unconstrained surfaces, but for specimens with constrained surfaces the observed line shape is qualitatively different from that predicted theoretically. The numerical calculations of the RFSE show that the amplitude of the fundamental and second resonances are proportional to exp(-1.22/1) and exp (-0.92/1), respectively, for 0.25 < 1 < 2, where 1 is the electron mean free path expressed in units of plate thickness. The origin of these dependences and their implications for measurements of the electron mean free path are discussed.