At present there is available no method of soil analysis which provides the information required to estimate with enough precision the quantities of the various nutrients that must be added to a soil to ensure maximum profit to the farmer. Although the results of certain field experiments make possible the estimation of the optimum rate of fertilization required for the commercial production of a crop, it is necessary to wait until the experiment is harvested, and its results are interpreted to carry out this estimation. The information provided by experiments performed with indicator plants prior to the time of fertilization of the commercial crops is as unreliable as that provided by the chemical analysis of the soil. The author has found a mathematical equation that can be used with a high degree of precision to represent the relationship between the content of a nutrient by the plant tissue at a certain stage of its growth cycle and the relative yield of the plant of which the tissue is analyzed. By using this mathematical equation jointly with a relation between the available nutrient content of the soil and the yield of the crop grown in that soil, it is possible to estimate also, with a high degree of precision, the quantities of the different fertilizer elements that should be added to the commercial crop so that the farmer may obtain a maximum profit.

Although much work has been done on the relation between the composition of a plant and its yield, very little specific information exists about the quantitative relationship between plant yields and plant composition. Using data from hegari sorghum grown at various nutrient levels on leading Puerto Rican soils, a general mathematical equation was established relating the sorghum yield to its nutrient composition.

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A new fertilizer-yield equation recently discovered by the author was used to describe the relation between the applications of nitrogen-, phosphorus-, potassium-, calcium-, and magnesium-bearing materials and the yields of sugarcane and corn in 34 experiments carried out in various regions of Puerto Rico near Isabela, Gurabo, Patillas, Lajas, and Río Piedras. The equation under study satisfactorily fitted such fertilizer-yield data, even in cases where the fertilizer-yield equation suggested by other workers do not apply. The general applicability of the new fertilizer-yield equation even in cases of certain abnormal data has been noted. From the data studied, it seems that, as concerns the production of sugarcane in soils similar to those used in the above-mentioned experiments, there is more need to keep the available soil nitrogen and magnesium contents as near as possible to their optimum equilibrium values than is true of phosphorus, potassium, and calcium. In corn production the equilibrium of the available nitrogen, phosphorus, and magnesium seems to be more important than that of the available potassium and calcium.

A new method of performing field experiments with relatively small numbers of treatments is described. The requirement to be fulfilled by the layouts of such field tests is specified and examples of possible designs for a 5-treatment experiment are illustrated. The theory of the procedure of calculation is discussed and a numerical example of said calculations is furnished in connection with the interpretation of a fertilizer experiment performed with cotton.