This paper is based upon the polytropic Parker model of the solar wind. The critical condition is a regularity requirement for a transonic solution and represents a contraint upon the flow temperature and velocity. This constraint may be imposed at any distance, and this freedom enables us to present the family of all solutions to the flow equations, for each value of the polytrope index &ggr;, in a way that facilitates comparison to experimental solar wind values. The solutions for &ggr;=7/5 are treated analytically, and the results are generalized for other values of the polytrope index. One result is to display the limitations of the polytrope model in satisfying experimental requirements simultaneously at 1 AU and near the sun. The observed dependence of temperature on flow speed at 1 AU is fairly well represented by the model if the one-fluid temperature is taken to be the average of the observed electron and proton temperatures and if &ggr;?1.2.