The equations of Sutton for the atmospheric diffusion of gaseous pollutants are extended to the case of particles of appreciable free falling velocity with the boundary condition that dust fall rate equals ground level concentration times free falling velocity. It is shown that the effect of gravitational settling can be allowed for by (a) substituting the height above ground of the downward deflected plume axis for chimney height and (b) by introducing a factor a(x,z) as a multiplier to the "reflection" term in Sutton's equation.