Abstract: A method and apparatus for providing in a web of sheet material, particularly a paper web, a predetermined moisture content which is uniform throughout the web. The web which has been dried so as to be within the hygroscopic range is directed through an enclosure which is closed off from the outer atmosphere while lapping in the enclosure a perfusion roll having a foraminous wall through which a treating gas, such as air of a given humidity or steam with predetermind properties, can pass into the interior of the roll after first passing through the web which laps the roll.