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The Application of the Mitscherlich Equation for the Calculation of Plant Composition Due to Fertilizer Increments¹

ABSTRACT

The equation introduced by Mitscherlich has been generally used to express nutrient-yield relationships as follows:

y = A(1—e^-eb-ex)

This paper reports an attempt to apply such a curve to soil nutrient-plant composition relationships, using the wheat plant. For this study soils deficient in phosphorus were selected in four different soil areas. All nutrients were supplied in adequate amounts except phosphorus which was added in five increments as superphosphate (0-45-0).

Wheat grain was analyzed for phosphorus and the constants for the above equation, after Bray's modification, were established. The equation arrived at was

y = 0.5834 (l—e^{-0.03296b-0.002097x})

where y is percent phosphorus in the grain, in the presence of x pounds of P₂O₅ and b pounds of soil phosphorus as determined by the soil test.

The equation, besides expressing quantitatively the soil nutrient-plant composition relationship, may provide a means to differentiate between the amount of the nutrient taken up by the plant from the soil sources and that from the added fertilizer sources. The relative magnitude of the efficiency factors may be considered as a quantitative measure for the net relative availability of the nutrient forms involved. It may serve to predict the soil phosphorus level through the plant composition or vice versa.

¹ Presented before Div. IV, Soil Science Society of America, Davis, Calif., Aug. 18, 1955.

² Graduate student in Agronomy and Professor of Soil Fertility, respectively. The authors wish to express their appreciation to Dr. W. C. Jacob and Dr. H. W. Norton for their cooperation and help in the statistical part of this investigation. This work was submitted by the senior author as part of a thesis in partial fulfillment of the requirements for the Ph.D. degree in the Graduate College.

Received for publication August 8, 1955.