One method for solving boundary value problems involving imperfectly conducting media is to assume, for a first approximation, that the surface currents are the same as if the media were perfectly conducting. Using this type of approximation, the problem of a line source of current situated over a plane surface, with a simple type of mixed boundary condition, is solved. For purposes of comparison the situation of an imperfectly conducting or "lossy" strip on au otherwise perfectly conducting plane surface is treated by an exact method employing elliptic wave functions. The calculations of the scattered fields of the strip by the two methods indicate the extent of the validity of the initial assumption in the approximate procedure.