A cyclical approximation of the evolutionary synthesis of stellar populations has been developed into a general solution for the mass and time-dependence of the 'birth function' of stars. The general solution allows introduction of a function, G(t), which is the ratio of gas injected into a defined region to that which form stars in the same time interval, at time t. On the basis of this direct relation of the output of dying stars with the formation of the next generation, analytical approximations can be made to the macroscopic evolution of stellar populations in a well-defined zone of a galaxy. This is presently demonstrated for the cases of four zones of the dwarf elliptical M32.