As the barometer falls, gases are drawn upward out of the permeable Earth into the atmosphere. Conversely, a rising barometer pushes air downward. In a homogeneous permeable medium, these cyclical gas motions are piston-like and nearly reversible, so they contribute only modestly to the net transport of contaminant gases. In a fractured permeable medium, however, the fractures will generally serve as breathing passages for all of the gas-filled porosity, greatly increasing the amplitude and nonuniformity of vertical motions. The resulting transport process may be orders of magnitude more significant than molecular diffusion, according to the theoretical analysis presented here. Analytical solutions are first derived for the sinusoidal pressure response of a medium containing identical vertical fractures equally spaced by slabs of permeable matrix material. These solutions are then used to constrain the relationship between fracture aperture and fracture spacing, based on field comparisons between surface and subsurface pressure variations. The final phase of the analysis addresses the diffusive and advective transport of an inert trace gas which is carried by an oscillatory flow along a fracture having permeable walls. A maximum rate of transport is predicted to occur for an intermediate fracture spacing which is typically a few meters.