Previous model calculations of the helium exospheres of Mercury and the moon have been based on a regime in which each helium atom impact with the surface results in the selection of a new particle chosen from a given source distribution. The particular velocity space distribution in the source particles was chose with the implied intent that the resulting atmosphere would be barometric under ideal conditions. In effect, two particle source distributions have been used in the kpublished calculations, which we describe here as Maxwell-Boltzmann (M-B), and Maxwell-Boltzmann flux (M-B-F). In the instances in which the atmospheric distribution has been calculated for regions above the surface, the resulting model atmosphere represents a mixture of the M-B and M-B-F sources. We suggest that none of the published exospheric calculations for the two bodies represent atmospheres produced by a barometric source of particles. Although a barometric source of particles cannot be justified in terms of surface physics, an exosphere produced by such a source is a valuable point of reference for calculations based on more realistic conditions. According to the analysis presented below, the appropriate source distribution should be M-B-F if the particles in the distribution are to be treated as components of flux. Monte Carlo calculations with an M-B-F source are compared with Mariner 10 ultraviolet spectrometer data. The comparison suggests that present models are incapable of fitting the observed Mercury exosphere.