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Smoothed values for the viscosities of water and mercury, as reported in the literature, show surprisingly large percentage deviations from the experimental data. Because water is frequently used as the calibrating fluid in viscometry, it was of interest to apply expressions, suggested by the theory of Eyring, for smoothing experimental data. It was of further interest to apply the Arrhenius expression for the variation of viscosity with temperature to the data for both water and mercury and to compare the closeness of fit with that obtained by the use of the aforementioned expressions. As judged by the Gaussian criterion of fit, an expression suggested by the Eyring theory provides smoothed values for the viscosities of both water and mercury which are believed to be more reliable than those in common use. This is especially true for the viscosity of water, for which relative viscosity data were first smoothed and then pinned to the recent value of 10.019±0.003 millipoises at 20°C as reported by Swindells and Coe. From other empirical equations relating densities and energies of vaporization to temperature, equations are derived for expressing the activation energies for viscous flow as a function of temperature.