The Boltzmann equation is solved analytically for a physically reasonable model of dilute neutral gas transport through a prism containing randomly located hard sphere scattering centers. The role of boundary and bulk scattering in establishing local equilibrium is clearly illustrated. Asymptotically exact expressions are given for the particle density, pressure, and temperature distributions in the limits of large and small mean free path. The particle flux and the heat flux are calculated exactly for all values of the mean free path.