The treatment of the positive ions in an electropositive gas discharge as though they had a Maxwellian velocity distribution giving a current to a negative probe equal to the random-ion current, is not consistent with most probe measurements, which on this theory would lead to the untenable conclusion that the positive ions had a temperature about equal to that of the electrons. Theoretical reasons are given for the view that the energy distribution of the positive ions at a sheath edge must comply with a certain criterion, and unless this criterion is fulfilled the probe will not be screened by a sheath but the field of the probe will penetrate into the plasma. The penetration of this field modifies the energy distribution and concentration of the positive ions in the probe neighbourhood until, if the probe voltage is sufficient, the criterion is satisfied and a sheath forms. The probe potential necessary to bring this about has been calculated for idealized high- and low-pressure cases. (It varies between 1 and 4 V). The effect of the penetrating field on the saturation positive-ion current as predicted by the conventional theory has been calculated. At pressures of the order of 1 mm. Hg and above, the saturation current to a negative probe is approximately equal to the random current of positive ions in the gas. At pressures below 0.1 mm. Hg it is considerably greater, being very nearly equal to the value the conventional theory would give if the positive ions had a temperature equal to that of the electrons. Experiments with a small probe in the form of a grid with a collector behind it made it possible to obtain. Langmuir probe characteristics in argon with the electron, ion and secondary emission components separated from one another. Although the smallness of the probe (necessary in order not to disturb the discharge) prevents the rigorous application of the theory because of edge effects, yet the general predictions of the theory are confirmed. In particular, the positive-ion current saturation is seen not to occur until the probe is several volts negative to the space, and the value of this current is low at high pressures and high at low pressures. The retardation part of the positive-ion curve enables the determination of a 'temperature' corresponding to the transverse component of the ion velocities. At 0.004 mm. Hg it is about 0.3 of the electron temperature, and about a tenth the latter at 0.0009 mm. Hg. Observations have also been made upon the anisotropy of the ion and electron-energy distributions, and the probe has been shown to be especially useful in studying departures of the electron-velocity distribution from truly Maxwellian form at high energies. Secondary emission from the platinum collector by photons and metastable particles amounted to about 10% of the saturation positive-ion current.