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Neutralization of space charge around a hot filament by imprisoned positive ions in gas at very low pressures.---(I) Design of tube. If a very small filament, diameter 0.01 cm, is run axially through a cylindrical anode with closed ends, positive ions formed between the electrodes can only rarely escape and will describe orbits around the filament until they lose sufficient energy by collision with gas molecules to enable them to fall into the cathode. The imprisoned ions, during their lives, neutralize a certain amount of the space charge between the electrodes. The effect should increase with the absolute temperature and with the ratio of the cross-section of the anode cylinder to that of the filament. A theoretical calculation indicates that in He at ${10}^{\ensuremath{-}5}$ mm, an ion which misses the filament on its first passage across the tube may circulate around the filament 300 times before discharging to the cathode. (2) Results in $\mathrm{He}$, $H$, $\mathrm{Ne}$, and $\mathrm{Hg}$ at pressures ranging from ${10}^{\ensuremath{-}2}$ to ${10}^{\ensuremath{-}7}$ mm are shown in curves. Comparison of the currents when the cylinder ends were connected (1) to the anode and (2) to the cathode gave the effect of the positive ions, and also their number, and therefore the increase in current per ion, $\ensuremath{\alpha}$. At pressures so low that the 3/2 power space-charge law holds in an ordinary tube, imprisoned ions may still produce large deviations from this law, in favorable cases the current with the ions being 5 or 10 times the current as ordinarily limited by space charge. The relatively much greater effect in Hg vapor than in He is shown to agree well with the theory. If $\ensuremath{\alpha}$ depended only on mean free path, however, it should vary as $\frac{1}{p}$, but the results gave ${(\frac{1}{p})}^{\frac{2}{3}}$. This difference shows the influence of other factors. However, theoretical mean free paths are of the same order of magnitude as those calculated from $\ensuremath{\alpha}$. Moreover, in Hg vapor at 4.2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$ mm, the time required to reach equilibrium after the positive ions began to accumulate was found by oscillograms to be about the same as the calculated life of an ion, 1.4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ sec. The simple theory, then, seems to be pretty well verified.