In studies of the mechanisms responsible for the formation of the ionized regions of the atmos phere, one of the problems encountered is the solution of the set of differential equations describing the time dependence of the number density of the chemical species present. For simple cases where only one or two species are involved, there is no particular problem. When all the important constituents are included, however, the solution of these equations becomes very complex. A computer technique is pre sented that will solve any size set of these differential equations involving any number of chemical reactions. (Author).

One way to acquire a better understanding of the formation and destruction of ionization in the atmosphere is through the solution of the system of time-dependent reaction rate equations. These ordinary differential equations form a simultaneous set each question of which describes the time rate of change of a particular atmospheric constituent. In the general problem, all the molecules and atoms whether neutral, charged, or excited, as well as the free electrons would be included. A computer program is presented for developing the numerical solution to this problem. The method of solution of the set of equations uses a fourth order Runge Kutta integration with a variable mesh. When a species enters its quasi-equilibrium state, its differential equation is removed from the set and its equilibrium equation is inserted into the simultaneous algebraic set. The algebraic set is solved by the method of successive substitutions. The over-all solution is obtained by iteration between the differential and the algebraic sets. The ability of the computer program to develop extensive solutions is demonstrated by several examples taken under different conditions.