Measurements are reported for the rate of mass transfer from the wall to the fluid in packed beds of the kind employed for exothermic reactions in small diameter tubes surrounded by coolant. Correction is made for the varying pressure in the tube from inlet to exit when mercury is vaporised into a nitrogen stream. The transport parameters were then estimated from the experimental axial concentration profiles by a non-linear least squares fitting procedure. The Biot number, Bi, characterizing transfer at the wall was found as a function of the particle Reynolds number: Bi = b Rep-k valid over the range of Rep observed. The Peclet number characterizing radial transfer in the bed was found on the assumption that it was constant over the corresponding range of Rep. Such sets of parameters were found for six different particle sizes.