A study is made of the physics of radiation into the guide between the earth and the ionosphere from a center-fed antenna consisting of a long horizontal wire grounded at its two ends. The length of the wire and the height h of the ionosphere are short compared with the free-space wavelength λ0. The antenna wire, together with its return path through the ground, constitutes the primary circuit of a transformer of which the ionosphere above the antenna to a distance of the order of λ0/2π is a part of the secondary circuit. This portion of the ionosphere, together with the corresponding portion of the ground, constitutes the secondary circuit of the transformer. This circuit applies voltage between the rest of the ionosphere and the rest of the ground, thereby launching a wave that propagates between the earth and the ionosphere towards the antipode. The coefficients of mutual and self-impedance for the transformer are calculated and are used to relate the voltage at the terminals of the antenna to the wave that leaves the transformer for the antipode. The transformer action increases the radiated power by a factor of λ0/4h above that for the same antenna in the absence of the ionosphere.