Several samples of the XIX-century Davenport pottery and XX-century structural masonry were reheated at 500 degrees C and then exposed to a humid gas of controlled relative humidity. Changes in the sample masses were recorded in response to both systematic and transient step changes in humidity. In addition, a reheated masonry sample underwent a sequence of soaking and drying and hundreds of hours of interactions with humid air in between these treatments to examine long-term effects of extreme humidity fluctuations. All experimental results indicate that instantaneous humidity and the sample's hygral history have a negligible effect on the long-term kinetics of mass gain. This important finding provides strong experimental support for the newly developed rehydroxylation (RHX) ceramic dating technique by proving that humidity affects physically bonded water in the ceramics, but has a negligible effect on chemically bonded water.