Pumping apparatus of the invention using thermal transpiration micropumps comprises a plurality of individual thermal transpiration micropumps distributed over a substrate (5) as a plurality of rows (A, B, C, . . . , D) each made up of a plurality of micropumps (1, 6, . . . , 7, 8, 9), thereby building up a plurality of columns (a, b, . . . , c, d). Respective heater elements (4) in each of the thermal transpiration micropumps are controlled by suitably controlling a row control conductor (10A) and a column control conductor (11a). This greatly simplifies multiplexed control of a large number of individual micropumps, thus enabling pumping capacity to be adapted.