The positive column of a gas discharge in a ternary mixture of mercury with neon and argon is studied at low pressures and at relatively low discharge currents taking into account the deviation of the real electron energy distribution from Maxwellian. The basic equations for the plasma are written and solved, and expressions are obtained for the internal parameters of the positive column (longitudinal electric field intensity, density and average energy of the electrons) in terms of the external ones (discharge current, tube radius, and gas pressure) in which the discharge is produced. Comparison of theory with experiment shows good agreement.