A measuring resonator in the form of a dielectric sphere is proposed for the measurement of low dielectric losses in the millimetre-wave range in liquids. The dielectric sphere resonator (DSR) was made from sapphire crystal with extremely low dielectric losses in the millimetre-wave range. Owing to this super-high-quality oscillations of 'whispering gallery' type are excited in a DSR. The spatial distributions of the electric and magnetic field strengths of E -and H -type oscillations both inside the sphere and in the surrounding liquid are considered. The expression connecting the measured quality of the DSR and the dielectric loss angle of the liquid is found. The condition for the choice of optimal parameters of the resonator for the measurement of the dielectric losses in various liquids is obtained also. The DSR method for the measurement of low dielectric losses in the millimetre-wave range in liquids is described.

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