Using the principle of the cross capacitor, a precise system for measuring the dielectric constants of liquids has been developed. The four electrodes of the cross capacitor were formed around fused-silica tubes by plating a gold film. The effect of nonuniformities in the tube wall on the measured permittivity was investigated. It is shown that it should be possible to determine the dielectric constants of liquids with standard uncertainties of the order of 0.02% to 0.05% after allowing for the effects of the dielectric properties of the tube walls.