A stable positive corona discharge in coaxial electrode system with varying humidity is analysed using a model which separates the corona in two distinct regions. A careful choice of boundary conditions in the drift region, particularly at the cathode surface, is needed. A new method of current and electric field measurements with a linear biased probe, incorporated in the outer cylinder, is used. The corona current, at a given voltage, decreases with humidity but the electric field at the outer cylinder is independent of humidity. The fields at the surfaces of the cathode and the anode vary linearly with the applied voltage between electrodes. The exact value of the average mobility of positive ions in the drift region is deduced from current and field measurements. This mobility increases when the potential difference across the drift region increases and it decreases slightly as the air is made more humid. Other parameters of the positive corona are successively determined by the current and field measurements, in particular, the total field distribution between electrodes.