One class of mass-transfer devices consists of assemblies of individual units, or stages, interconnected so that the materials being processed pass through each stage in turn. The two streams move countercurrently through the assembly; in each stage they are brought into contact, mixed, and then separated. Such multistage systems are called cascades. For mass transfer to take place, the streams entering each stage emust not be in with one another, for it is the departure from equilibrium conditions that provides the driving force for transfer. The leaving streams are usu- ally not in equilibrium either but are much closer to being s than the entering streams are. The closeness of the approach to equilibrium depends on the effective- ness of and mass transfer between the phases. To simplify the design of a cade, the streams leaving each stage are often assumed to be in equilibrium which, by definition, makes each stage ideal. A correction factor or efficiency is applied later to account for any actual departures from equilibrium. To illustrate the principle of an equilibrium-stage cascade, two typical counter- current multistage devices are described here, one for distillation or gas absorption, where the stages are arranged one above the other in a vertical column, and one for solid-liquid contacting as in leaching, where the stages are a series of stirred tanks on the same level. Other types of mass-transfer equipment are discussed in later chapters.