The electromagnetic radiation from an aperture in a plane-conducting screen is identical with that which would exist if screen and aperture were replaced by a double current sheet fitting the aperture. The current density $i$ is equal and opposite in the two layers of the sheet and is determined by the original tangential electric field $E$ over the opening so that $E$ is $\ensuremath{-}\frac{1}{2}j\ensuremath{\omega}\ensuremath{\mu}\ensuremath{\delta}i$. The distance $\ensuremath{\delta}$ between layers is infinitesimal. A rigorous expression for the vector potential of the emergent radiation in terms of $E$ is given. This is the expression used by Bethe in finding the diffraction from small holes. It is shown to provide a simpler method of getting the results of Stratton and Chu for rectangular openings. It is then applied to the calculation of the excitation of a rectangular wave guide by a coaxial line termination in one side. An expression for the output resistance is given.