A portion of a single plant root is treated as an absorbing cylindrical sink to which nutrients move by diffusion. Assuming that the rate of uptake of nutrient is proportional to its concentration at the root surface, and that the nutrient, though reacting with the solid, moves only through the soil solution, standard diffusion equations are used to calculate the effect of soil and plant characteristics on the rate of uptake. The treatment is applicable to phosphorus and potassium. Among soil properties uptake should increase directly with the soil solution concentration. It should also increase, but only slowly, with increasing buffering power. It increases with increasing soil moisture. Among plant characteristics, uptake should increase with the root absorbing power until diffusion through the soil becomes limiting. Absorption by unit surface area of root increases as the root radius decreases. A root hair is shown to interfere quickly with the uptake of adjacent hairs. The hairs increase absorption by the root because they can exploit rapidly the soil between the hairs, and they have the effect of extending the effective root surface to their tips.