The thesis is primarily concerned with the rate of uptake of nutrients by plant roots in relation to the ability of soil to supply nutrients to roots by diffusion and by mass flow. In Chapter One, some current concepts of the chemistry and availability of plant nutrients in soil are briefly discussed. Particular attention is paid to work that stresses the role of the dynamic processes of diffusion, and the mass flow of dissolved nutrients in the transpiration stream, in supplying nutrients to roots. In Chapter Two, diffusion coefficients of nutrients in soil are discussed. In Chapter Three, the mathematical description of nutrient flow to a root system in soil is discussed. An equation is developed which relates the mean nutrient inflow into a root system to the concentration of nutrients initially present in the soil solution, to the mean concentration of nutrients in the soil solution at the surface of the root system,to the mean rate of flow of water to the roots, to the diffusion coefficient of the nutrient in the soil, and to the age of the roots. The mean nutrient inflow into a root system is defined as the mean rate of flow of nutrients into unit length of root. In Chapter Four, an experiment is described in which all the terms in the above mentioned equation were measured apart from the mean root surface concentration of nutrients. In the experiment, the growth and nutrient uptake of leek plants growing outdoors in a moist, fertilised, silty loam soil was followed. The plants were grown in large pots containing an ample reservoir of soil water, so that watering was unnecessary during growth. The growing period was from early May to mid-July. The nutrient uptake rate was followed by harvesting, and analysing for nutrients, samples of ten plants taken at approximately ten day intervals. Root length was measured at each harvest after washing the roots free from the soil. The pots were weighed every few days to determine the water lost by transpiration. At intervals during the growing period soil samples were taken from the pots, and the soil solution was extracted and analysed. From separate experiments, diffusion coefficients for nutrients in the soil were calculated. The data from the experiments yielded all the terms in the above mentioned equation except mean root surface concentration which could be calculated. The nutrients considered were N, P, K, Ca, Na, Mg, S and Cl. It was found that mass flow supplied on average more of all nutrients to the roots than they absorbed apart from K and P, which were supplied mainly by diffusion. For those nutrients that were found to be supplied by mass flow in excess of uptake, calculations indicated that the resultant mean accumulations at the root surface did not give rise to a solution concentration at the root surface greater than 120% of the initial concentration in the soil. In contrast it was calculated that the root surface concentration of K was less than half its initial level in the soil. P had a concentration dependent diffusion coefficient which meant that the quantity of P diffusing to a root had to be calculated numerically using a computer. The results of such a calculation are given in Chapter Five. It was found that even if the roots acted a zero sink for phosphate, the theoretical mean inflow of phosphate was somewhat less than the observed mean inflow. In Chapter Seven an experimental investigation is described into the accumulation of sulphate at the surface of a root in conditions of high mass flow. Autoradiography using S³⁵ was the technique used. In accordance with theory, accumulations became large only when the soil was fairly dry. One of the difficulties in the mathematical analysis of nutrient flow to roots is the uncertainty about the inherent absorbing power of roots of different ages. In Section Three, experiments are described in which the uptake of short segments of leek root of different ages was measured. The leeks for these experiments were grown in solution culture and the mean inflow into the roots was measured by sampling and analysis as described for the pot experiment in soil. Some plants from solution were then selected and short segments of the roots of different ages were sealed into tubes containing two radioactively labelled nutrients, the rest of the root system being grown in unlabelled nutrient solution. P³², and either K⁴² or Sr⁸⁵, Sr⁸⁵ being taken as a label for Ca, were the labelled nutrients used. The plants were harvested after twenty four hours of exposure to labelled nutrients and the quantity of label absorbed was measured. There were no significant differences in the mean absorption of different aged roots, but different root segments varied very widely in their uptake in a way that could not be connected with their age. The possibility of such variation in absorbing power in roots in soil and its consequences in soil are discussed at the end of Chapter Eleven. In Chapter Twelve values for the mean inflow of nutrients into roots from a wide range of published experiments are tabulated. The rates are also given as specific absorption rates, this term meaning the rate of flow of nutrient into unit fresh weight of root. Similar values of mean inflow and specific absorption rate have been measured in widely different conditions, ranging from a few minutes uptake from solution to several weeks uptake from soil. Plant factors which affect mean nutrient inflows are discussed and possible future developments along the lines suggested by the experiment in Chapter Four are considered. In the final Chapter the evidence is stated on which is based current theory of nutrient flow to roots by mass flow and diffusion. In conclusion the insight the theory provides into the concept of nutrient availability in soil, into root competition for nutrients and into ideas about root system efficiency is considered.