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Breakdown field strengths have been measured in air and hydrogen at pressures of the order of 1 micron Hg and frequencies from 25 to 90 Mc/sec between flat metal electrodes at separations from 1 to 4 cm. By suddenly applying a high voltage and then lowering it slowly an upper breakdown curve has been observed. This new curve can be combined with the lower breakdown curve and cut‐off frequency such as reported previously by the Guttons, and by Gill and von Engel to form the boundaries of a breakdown region in the frequency‐field strength domain. The simple secondary electron resonance theories developed by Danielsson and Gill and von Engel have been extended by the semi‐empirical determination of minimum and maximum limiting values of the electron‐emission phase angle, a minimum limiting value of electron arrival energy, and a ratio between electron arrival and emission velocities.