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This paper examines one basic process causing the d. c. high voltage breakdown of a gas. Specifically, it contains a modified criterion for the transition of a Townsend Avalanche to a Streamer Discharge. Instead of the assumption that the electrons in the avalanche are spread laterally by multiple scattering on gas molecules (thermal diffusion), the assumption used is that the electrons are spread solely by mutual electrostatic repulsion. A criterion is found that yields quantitative results comparable to those obtained using the "multiple scattering" assumption. This modified criterion is probably most useful where "multiple scattering" is improbable - where an electron loses almost all of its energy on colliding with complex gas molecules. In addition, the classical (thermal-diffusion-dominated) breakdown criterion is re-derived in a much simpler form.