An approximate theory of the propagation of positive impulse corona is presented based on a model in which electrons are produced by photo-ionization and are multiplied by electron impact ionization in the strong fields near the tip of the corona filament. The filament extends by attracting electrons into itself, leaving behind a positive space charge. Formulae are derived which enable speeds of propagation, electron densities and filament radii to be predicted as a function of applied voltage in terms of fundamental atomic cross-sections, some of which are not accurately known. The theory was compared with the results of one particular experiment and reasonable agreement was obtained. The extension to negative impulse corona and subsequent stages of the breakdown process is briefly discussed.