I have calculated an upper limit to the rate of diffusion of sodium and potassium out of Mercury and the Moon and have compared the resulting flux to that required to maintain the known exospheres. I find that diffusion rates are inadequate by 12 orders of magnitude on the Moon and 9 orders of magnitude on Mercury for diffusion out of orthoclase minerals. Diffusion will be more rapid out of pure glass by 5 to 6 orders of magnitude and out of shocked basalt by an amount depending on the microstructure of the mineral. The observed abundance and distribution of volatiles in small glass spherules on the Moon indicates that diffusion is very inefficient after solidification and cooling. At Mercury, the limitation on sodium flux to the atmosphere is shown to be the rate at which new regolith is created. The discrepancy between the observed column abundance of sodium in the Mercurean atmosphere and the known sources may indicate that either Mercury's crust has a larger volatile content than the Moon or that a recycling mechanism exists in the Mercurean atmosphere ¿ American Geophysical Union 1989