Diffusion theory and transport theory approaches to the problem of a nuclear reactor with a transverse air gap are compared. It is suggested that the differences in results for thin gaps is due to the fact that diffusion theory does not adequately represent the flux distribution in the immediate vicinity of the gap. For mathematical conveniences previous treatments of the gap problem have made use of fictitious image piles which exaggerate the neutron losses. The extent of the error is estimated by direct neutron leakage calculations.