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It has been established experimentally that the equilibrium of the plane surface of transformer oil under a corona electrode (needle) becomes unstable when the critical voltage, which increases with the oil layer thickness, is attained at the corona point. When the voltage at the needle exceeds the critical value, regular static cells are formed on the oil surface with characteristic sizes decreasing upon an increase in voltage. The theoretically estimated parameters of the experiment are found to be close to the experimental data. Comparison of the parameters corresponding to the occurrence of instability in the equilibrium of the oil surface in the field of the corona discharge with the parameters of instability in the equilibrium of the charged surface of liquid helium in a uniform electric field [7] demonstrates the similarity of the effects. [ABSTRACT FROM AUTHOR]