Maxwell is credited as the first to invoke the assumption that an impinging gas beam scatters from a surface with a direct contribution exhibiting little change in state and a trapping-desorption fraction that desorbs in equilibrium [J. C. Maxwell, Phil. Trans. R. Soc. London 170, 231 (1879)]. Here a classical mechanical scattering theory is developed to describe direct scattering, trapping, and subsequent desorption of the incident beam. This theory allows a rigorous test of the Maxwell assumption and determines the conditions under which it is valid. The theory also gives quantitative explanations of important new experimental measurements [K. D. Gibson, N. Isa, and S. J. Sibener, J. Chem. Phys. 119, 13 083 (2003)] for direct and trapping-desorption scattering of Ar atoms by a self-assembled layer of 1-decanethiol on Au(111).