This report is concerned with the theory and confirmation of a stratospheric-tropospheric exchange which accompanies a folding of the tropopause. Air from the lower part of the cyclonic stratosphere is extruded to form a thin inclined layer in the troposphere. The Springfield data prove that the extruded tropospheric layers contain radioactivity concentrations typical of the stratosphere. Concentrations exceeding the tropospheric by one or two orders of magnitude were measured aboard WB-50 and RB-57 aircraft on specially vectored flight paths. The sharp change in concentrations at the boundaries also confirms that the folding process is predominantly laminar, so it is appropriate to refer to the exchange as a transport rather than a diffusion process. The agreement between the radioactivity and meteorological measurements is remarkable. Of particular value to the radiochemist and meteorologist is the high correlation between the concentrations of radioactivity and the potential vorticity. Since the latter can be determined from conventional radiosonde data, the three dimensional distribution of the former can be approximated. Physical processes capable of mixing the radioactivity from the layers to the ground are also discussed, including their probable distribution with respect to the extruded layers.