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Soil Science Society of America Journal Abstract -

Inefficiency of Fertilizer Use Resulting from Nonuniform Spatial Distribution: I. Theory1


This article in SSSAJ

  1. Vol. 26 No. 2, p. 170-173
    Received: Feb 6, 1961
    Accepted: Apr 5, 1961

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  1. Don Jensen and
  2. John Pesek2



Nonuniform physical distribution of a fertilizer nutrient was expressed as a function of space coordinates and substituted into an equation which characterizes yield response to that nutrient. The resulting differential equation was then integrated over the area fertilized to give a new yield potential function which is valid under any specified nonuniformity restriction. In particular, a periodic cosine function with amplitude “a” was selected to represent the spatial distribution function for a single fertilizer nutrient, while a quadratic equation of the form Y = b0 + b1X + b11X2was used to express the relationship between yield and the nutrient. The new yield potential equation was derived from these particular functional forms. Yield loss associated with the cosine distribution pattern then was obtained as the difference between the ideal and the restricted production equations.


A corresponding derivation was made for the case of n variable factors of production under the assumption of a quadratic response equation and distinct cosine laws for physical distribution of each variable. Yield losses were expressed in the form where bij is the coefficient for interaction of the i'th and j'th factors, and ai and aj are respective amplitudes of the cosine distribution funcations of the i'th and j'th nutrients.

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