Studies in crop variation: V. The relation between yield and soil nutrients

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Abstract
The study of the relation of plant-growth to environmental factors has led to much research directed to the elaboration of General Formulae expressing the quantitative response of the experimental plant or crop to the quantity of the nutrients with which it is supplied. For variations of a single nutrient only many different mathematical expressions will serve to describe the facts to the accuracy with which these are usually ascertained by experiment; the practical value of such formulae is, however, much impaired if the parameters or constants which they involve change their value from experiment to experiment. If, on the contrary, we can obtain formulae of a general character which represents satisfactorily not only the response to variation of a single factor, but the response to simultaneous variation of two or more different factors, then we have reason to believe that the parameters of such formulae will not depend upon the casual or non-essential conditions of the experiment, but will be capable of direct interpretation as physical quantities. We have shown that the Resistance Formula does fit the data of several two-factor experiments and the agreement of the three values of an determined from the three potato crops as well as the agreement of the difference in the values of k on a dunged and undunged plot with the potash expected to be available from the ten tons of dung shows that this expectation is so far justified. The parameters of the Resistance Formula are capable of a direct and definite physical interpretation; for each nutrient there are two constants; one represents the importance of the nutrient considered to the crop concerned, and may be expected to vary from crop to crop and from variety to variety, and so to afford a direct comparison between varieties of their manurial needs, while the second represents the amount of nutrient available in the unmanured soil.

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