Meek's criterion postulates that a streamer will propagate if the positive ion space charge field close to the anode is equal to $K$ times the impressed field, where $K$ should be a constant independent of gap configuration and pressure. Measurements in confocal paraboloid gaps, designed to substantiate this, revealed that $K$ was not constant, but decreased with decreasing pressures. Morton showed that on a negatively charged smaller electrode Townsend's ionization functions do not represent the ionization produced in divergent fields. Consequently it was believed that the calculations of the space charge field of the positive ions produced in such gaps must be inaccurate in view of this erroneous assumption. A series of measurements on the dark current $i$ in the same gap showed that it was not represented by $i=i_0 \exp \left[\int \alpha \mathrm{dx}\right]$ at lower pressures. The trend and the apparent quantitative variation of $K$ with pressure is explained if the apparent $i_0$ versus voltage curves are extrapolated to streamer onset for each pressure. Thus for practical purposes under the conditions studied $K$ is sensibly constant in conformity with Meek's theory. Per contra, the applications of Meek's theory to gaps with very divergent fields where the currents can be expected to deviate markedly from those computed by the relation $i=i_0 \exp \left[\int \alpha \mathrm{dx}\right]$ are not justified, thus placing a practical limitation on the use of Meek's theory to streamer studies. Roughly this phenomenon appears when the change of the field exceeds two percent change over an average electron free path.

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