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In the measurement of environmental levels of radioactivity, the primary problem is the accumulation of a statistically meaningful number of counts within a reasonable period of time. In the case of measurements of airborne 222Rn-daughter concentrations, the problem is further complicated by the particularly short half-life, 3.05 minutes, of RaA (po218). Since three Rndaughters -RaA, RaB (Pb214) and RaC (Bi214) - are of interest, the equations interrelating these Rn-daughter concentrations were derived from the laws of radioactive-series decay. These equations, although straightforward, are cumbersome to solve. To facilitate the efficient use of these equations, a computer program has been written which permits the calculation of Rn-daughter concentrations or expected counts for a given set of measurement parameters (flow rate and detector efficiencies). A subroutine then calculates the optimum pumping and counting times required to provide the number of counts necessary for acceptable statistics at environmental levels of 222Rn-daughter concentrations. This subroutine contains a set of parameters, flow rate and efficiencies, that are fixed using realistic restrictions. The use of these optimized pumping and counting times results in maximum measurement sensitivity under realistic constraints.