The total number <tex-math>$N_{i}(T)$</tex-math> of ionizations that an incident electron of kinetic energy T generates in a pure gas at low pressure obeys an integral equation known as the Fowler equation. Data show that its solution approximates <tex-math>$N_{i}(T)=(T-U)/W_{a}$</tex-math> for T exceeding many multiples of the first ionization energy I, where U and <tex-math>$W_{a}$</tex-math> are constants having the energy dimension. Attempts are made to derive formulas that express U and <tex-math>$W_{a}$</tex-math> in terms of various cross sections for electron inelastic collisions with a gas molecule. The paper also describes the background of the problem and includes a critique of underlying assumptions that are often left unmentioned.

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