The electrokinetic characteristics (the electron energy distribution function, the strength of the longitudinal electric field and the concentration and average energy of electrons) are measured and calculated in a (Hg + Ar)-discharge plasma under a high pressure of argon (up to 30 Torr) and in narrow tubes (the tube radius is less than 1.0 cm). A simple method of treating the second derivative of the probe current with respect to the probe potential is proposed for a straightforward way to obtain the electron energy distribution function under a high pressure of a gas. It is shown that the main assumptions on which modelling of the plasma of mercury luminescent lamps is based are also valid for the plasma in question. This leads to the existence of special similarity laws and gives a new possibility for diagnostics based on the similarity properties of the plasma. The approach proposed in the work can be easily extended to the mixtures of mercury vapour and other rare gases.