We report: measurements of the capillary absorption (imbibition) of water, n-heptane, n-decane, n-dodecane, methanol, ethanol, propan-2-ol, and ethanol-water mixtures into a number of dry calcitic limestones. The data are analyzed on the basis of unsaturated flow theory to give values of sorptivity S for water and for each organic liquid at different temperatures. The results show that for the organic liquids S varies as (surface tension/viscosity)(1/2) but that for the water S is anomalously low, indicating partial wetting. The wettability of these limestones is discussed in relation to natural contamination of the pore surface.