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SummaryMeasurements were made at intervals during the growth of seven different vegetable crops grown on the same soil to find how far root development and crop growth could be described by simply derived equations and to find how far the parameter values varied from crop to crop.For each crop K1 In W + W, (where W is total plant dry weight, t ha-t and K 1 is equal to 1 t ha -1) was linearly related to time from emergence, as in past experiments.The derived equationwhere L is total root length per unit area, t is time from emergence, cj and bj are coefficients that depend on the crop (j) and m is a coefficient having the same value for all crops, removed 89.4% of the total variance in In L. The best fit was obtained with a value of m that implied that about 3% of the root carbon was mineralized each day. Generally the logarithm of root density declined linearly with increasing depth. Most of the variation between the gradients of these relations for the different crops was removed by a single regression against logarithm of total root length.The main discernible differences between species in their rooting patterns were that root length for a given top weight of legumes was about half that of non legumes, that the development of storage roots was associated with a less steep decline in root density with depth than for other crops and that onions were exceptional in that the depth to which their roots penetrated did not change appreciably during much of the growing season.A single linear relationship between root depth and top weight (r 2 = 0.85) covered all nonleguminous crops except onions and another relationship (r 2 = 0.80) covered the legumes.

Mathematical models to describe the density of plant roots in the soil have been developed by analogy from the equations describing diffusion or heat flow. Results from an experiment with isolated plants (lettuces) shows that the equation for diffusion from a point source applies, while results from a row crop (onions) indicate that when allowance is made for the assymetry resulting from a preferred direction of growth, the equation describing diffusion from a line into a semi-infinite medium can be applied. Results reported by other workers for ryegrass are used to demonstrate that for a sward the appropriate equation is that describing diffusion from a plane into a semiinfinite medium.

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In order to investigate the depths in field soils from which plants derive their phosphate nutrition, uptake of s2P from depths of 6, 12, 24 and 36 inches was studied, using a shallow-rooted crop (lettuce) and a deeper-rooted crop (carrot). A soil at two different fertility levels was used, the higher level of fertility having been attained by heavy applications of farmyard manure over a period of twelve years.The exchangeable pool of phosphate in the high-fertility soil, at the depths investigated, was about twice that in the low-fertility soil. Total phosphate uptake by lettuces on the two soils was almost proportional to the size of the exchangeable pool, but the uptake by carrots on the high-fertility soil was much less than twice that on the low-fertility soil.Phosphate uptake, computed as the product of measured radioactive phosphate and the size of the exchangeable phosphate pool at the depths investigated, shows that lettuces derived almost all their requirements of phosphate from the uppermost foot of soil. Carrots obtained most of their phosphate from this layer, but also obtained appreciable amounts from depths of 24 and 36 inches.Some implications of these findings are discussed.