Physical Processes in Gaseous Nebulae. II. Theory of the Balmer Decrement

An exact algebraic solution of the equations given in the first paper of this series is carried out for the statistical equffibrium of an assembly of hydrogenic atoms. The ex- citing radiation is assumed to come oniy from beyond the limit of the Lyman series. Hence discrete states are filled only by capture from the continuum and by cascade from higher discrete states. The electrons are assumed to have a Maxweffian velocity dis- tribution. The formula is given in terms of a quantity b~, the ratio between the actual population of state n and the population under conditions of thermodynamic equffibri- urn. An asymptotic expression is given for b~ in the case of large quantum number, from which it is shown that b~ approaches unity as n becomes infinite. Numerical solu- tions are deferred until the next paper