Calculations of the variation of cathode-fall voltage, the cathode-fall distance, and the Aston dark space with current density have been made for the rare gases and a few molecular gases on an electronic computer. The calculations were based upon Townsend's ionization equations, but included the field distortion due to space charge. New analyses of the field variation of Townsend's first ionization coefficient and ion mobilities are presented. The length of the dark space has been obtained from the calculated distribution of light output across the gap and agrees with the cathode-fall distance calculated from the field distribution. Comparisons of the calculated cathode-fall characteristics with published experimental results indicate the probable validity of the model used for the calculations.

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In conjunction with measurements of current-voltage characteristics in hydrogen, a few characteristics have been obtained which include a region with negative slope. The latter characteristics were obtained with plane parallel electrodes at an electrode separation of 2 cm at a pressure of 400 mm Hg and with three values of externally initiated cathode current. The initial currents ranged from about 10~n to 10"^ amp, and the amplified currents reached values as high as 10~4 amp. The characteristics corresponding to the larger initial currents become negative at large currents (~10~6 amp). The voltage at which a characteristic becomes negative, i.e., the maximum attainable voltage across the electrodes, decreases slightly with increasing initial current. The circuit included a series resistor of 20 megohms.These characteristics can be explained quantitatively on the basis of the first and second Townsend coefficients (previously measured with the same apparatus) acting in conjunction with space charge, if a not unreasonable discharge area is assumed. These calculations were carried out on an IBM 704 computer. INTRODUCTIONW HILE measuring static dc breakdown potentials in hydrogen near atmospheric pressure with plane parallel electrodes, Lessin, 1 using apparatus previously described, 2 observed the following effects. With ultraviolet illumination of the cathode, it was noticed that as the generator voltage is gradually raised, the voltage directly across the electrodes initially increases, reaches a maximum value, and then decreases somewhat (by as much as 30 volts), still remaining stable. Further increase in the generator voltage results in the familiar cataclysmic irreversible spark breakdown, with a drastic reduction in the potential across the electrodes. It was also noticed in a rough way that the extent of the above effects depends on the intensity of ultraviolet illumination. The above observations were made with a resistance of 20 megohms in series with the electrodes. This resistance took up the difference between generator and gap voltages. These results imply the existence of a stable negative slope region of the current-voltage characteristics, heretofore unobserved at high pressures.A number of authors have discussed the existence of a negative characteristic theoretically on the basis of space charge along with a concomitant lowering of the breakdown potential by ultraviolet light. One of the earliest attempts to formulate this problem quantitatively was made by von Engel and Steenbeck. 3 More exact calculations subsequently were made by Crowe,