Weeping is a phenomenon characterising the operation of perforated distillation plates and refers to liquid which passes through the perforations rather than down the downcomer. For a single hole it refers to the quantity of liquid which passes through the hole, between the release of one bubble and the formation of the next.This work catagorises bubble formation at a submerged orifice into six regimes: 1. Single bubbling with delayed release 2. Double bubbling with delayed release 3. Single bubbling 4. Double bubbling 5. Pairing 6. Double pairingFor the single bubbling and pairing regimes, a theory of bubble formation and weeping is presented. Potential flow analysis is used to describe the flow of gas from the chamber beneath a "one-holed" perforated plate into an expanding, rising, spherical bubble forming at the orifice. Bubble size and frequency are determined as functions of hole gas velocity, chamber volume, and system physical properties, and weeping rates and weep points are quantitatively predicted.For the other regimes, the mechanisms of bubble formation are qualitatively described and the conditions for each bubbling regime defined. An attempt is made to quantitatively predict bubble formation under delayed release conditions and a comparison is made between pairing and double bubbling, since these regimes can easily be confused although they occur under widely different conditions.Three orifices (3/16 in, 1/4in, 3/8 in) are studied over a range of chamber volumes from 170cc to 28,830cc, up to a mean hole gas velocity of 65 ft/sec, for the air - water system only. Agreement between experimental and predicted results for single bubbling and pairing is considered satisfactory.Finally, a preliminary investigation is made into bubbling from multi-holes. A row of five %in orifices on 1in spacing is investigated over chamber volumes from 170cc to 4,250cc. Some of the difficulties encountered in applying single bubble theory to multi-holes are enumerated and the effect of surface waves on perforated plates are discussed.