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Transmission line equations in air in the presence of corona are derived. The analysis shows that the corona caused by a voltage or a current pulse propagating along a transmission line can be represented by a series of corona current sources distributed along the line. Corona has two effects on the voltage or current pulses propagating along a transmission line. First, it will clamp down the pulse amplitude at the front of the pulse to the corona threshold. Second, it will cause the portion of the pulse whose amplitude is larger than the corona threshold to travel with a speed less than the speed of light. The effects of corona on the voltage or current pulses propagating along a transmission line can also be evaluated by introducing a time varying capacitance and a conductance into the transmission line. If the time varying capacitance is assumed to be proportional to the ratio between the corona charge and the applied voltage then one requires both this and the time varying conductance to represent the corona effects more accurately. Analysis of the return stroke as a current pulse propagating along a transmission line undergoing corona shows that the corona effects may explain the reason why the measured return stroke speeds are considerably less than the speed of light. Moreover, based on the effects of corona, a physical justification for the concepts used in the current generation type return stroke models is provided.