The stable corona discharge has found use in a large number of electrostatic applications and one of their important properties is the inception voltage which can be easily and accurately measured. The empirical Peek's law which yields the corona inception field is previously made in standard air for wire-to-cylinder geometry and used for many years. However, the generalisation of this law, which at present derives from Hartmann's physical-mathematical model, requires new measurements with varying air physical parameters. This classical law expresses the inception field at the anode surface in function of the anode diameter, the related air density and the humidity. New measurement method of the positive DC corona-current voltage characteristics have been introduced in a wire-to-cylinder and wire-to-plane systems. Remarkable similarities between these basically different systems are shown in this paper and the steady corona-current voltage characteristics are described by the Townsend's square law in a large range of related air density. The normalization factor at air density equals unity and the humidity function suggested by the model are also determined from the measurements. The model values of the inception field at the wire surface agree with measured values in both wire-to-cylinder and wire-to-plane systems.