With the assumption of two characteristic temperatures, one associated with the transverse momentum distribution, the other with the longitudinal, the differential cross-section, d2 N/dpdΩ, is calculated from the relativistic quantum statistical mechanical number density. Good agreement with experimental data for pions, kaons and antiprotons is obtained by the fitting ofT 0, the transverse temperature,T, the longitudinal temperature, andV 0, the interaction volume. The model is related to a simple physical interpretation.