The structure of mid-latitude sporadic E layers has been investigated in a series of observations at the Arecibo Observatory. The basic experiment uses phase-coded pulses to measure the electron density profiles with a range resolution of 600 m while scanning the radar beam. The data from incoherent scatter are compared with simultaneous ionosonde observations to determine the source of the partial transparency of sporadic E layers to radio waves at frequencies between fbEs and ftes. It is concluded that sporadic E layers contain electron density irregularities of sufficient intensity to account for the partially transparent echoes observed by the ionosonde. A feature that becomes immediately obvious in examining the data taken with the incoherent scatter radar is that sporadic E layers are as variable in structure as they are unpredictable in occurrence. Some have simple vertical profiles and are uniform in the horizontal plane, consistent with rocket observations; others have complex vertical and horizontal structure, as has been implied by the radio experiments. Wavelike structure in the electron density is present in many of the layers observed. Evidence is shown of the limiting of peak ionization density in a layer by turbulence generated in a Kelvin-Helmholtz instability. The possible proximity of a sporadic E layer to a critical level of a dominant gravity wave mode is discussed as a source of intense ionization irregularities. A possible irregular source of ionization from ablating meteors is also considered. It is shown that under specific conditions an ionized meteor trail can be converged by the action of the neutral wind into an irregularity of relatively small dimensions. It is concluded that the observations support the wind shear mechanism of formation of sporadic E layers when the combined effects of gravity waves, tides, and the irregular deposition of metallic ions are included.