On the concept of equal exchange

A system is said to be in equilibrium when no changes are per ceived in it by gross observation. Yet there may be vigorous activity within such a system which is hidden from gross obser vation, because the inner processes “cancel” each other. Thus, a number of cities can maintain constant populations even though the birth, death, and migration rates are high. A system will be obviously in equilibrium if there is “equal exchange” between every pair of its subsystems, but not all systems in equilibrium are such systems of “strict exchange.” It is a question of some theo retical importance whether a system is a system of strict exchange. Mathematical conditions for such systems are given here. In particular it is shown that a “perfectly mobile society,” i.e., one where the probability of a person's position is independent of that of his father, is a strict exchange system.