A single-root technique is used to measure the rate of supply of potassium by diffusion to 1-cm portions of cylindrical roots of onion and leek plants growing in soils containing different levels of exchangeable potassium. The relation between uptake and characteristics of the plant and soil is interpreted on the basis of a diffusion supply model. Uptake is accounted for in terms of the geometry of the absorbing root surface, the physiologically controlled absorbing power of the root, and the diffusion through the soil. The different uptakes of potassium by roots of comparable absorbing power from different soils can be predicted with some success from calculations using the root dimensions and either diffusion coefficients of potassium in soil, derived from flux to a cation exchange resin paper, or the form of the potassium scorption isotherm relating the concentration of labile ions to those in the soil solution. It is calculated that diffusion through the soil has reduced potassium uptake by the roots to between 87 and 39 per cent of that expected for roots of the same absorbing power in a stirred culture solution at the same initial soil solution concentration. © 1969 Martinus Nijhoff.