The problem of the transmission of power over a transmission line from an alternating current generator at one end to a synchronous motor at the other is easily solved when the line is uniform or made up of a small number of uniform line segments. The object of the present note is to apply the theory of integral equations to the general case of the non-uniform line. The solution obtained for the current at any point on the line in the form of a rational function of the frequency of the two alternators is of advantage when resonance effects are being considered; the latter effects are hard to trace in the case of the uniform line by the usual methods. It seems probable that numerical methods and computing devices can be developed for the solution of the integral equations given. The effect of armature inductance on the power limit of the system may then be more easily studied than at present.