One method for solving boundary value problenls involving imperfectly conducting ~nedia is to assume, for a first approximation, that the s~~r f a c e currents are the same as if the media were perfectly conducting. IJsing this type of approxin~ation, 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 inlperfectly conducting or "lossy" strip on ail otherwise perfectly conducting plane surface is treated by an esact method employing elliptic wave functions. The calc~~lations 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.libfanuscript