The mechanisms of cesium transport through a cylindrical tungsten tube are now understood to consist of surface diffusion, molecular flow and ionic flow under the influence of electric fields which exist in the tube. In this paper an exact transport equation is developed for the idealized case of pure molecular flow coupled with surface diffusion. This takes the intractable form of a nonlinear integrodifferential equation of second degree. This is analytically reduced to a nonlinear form of Fredholm's integral equation suitable for solution by numerical iteration.The Langmuir adsorption and diffusion data for cesium on tungsten are introduced and the approximate domain of convergence for the integral equation is found by the use of an appropriate existence theorem. Sample solutions are shown including one which satisfies required boundary conditions at the orifices.