Sôbre uma fórmula para o cálculo da dose mais econômica de adubo

Gomes, F. Pimentel; Abreu, Clovis Pompílio de

doi:10.1590/S0071-12761959000100013

Resumo

The authors discuss a formula for the determination of the most profitable level of fertilization (x*). This formula, presented by CAREY and ROBINSON (1953), can be written as: x*= (1/c) log cx u L10 + (1/c) log wu _______ ___ 1-10 x u t being c the growth factor in Mitscherlich's equation, x u a standard dressing of the nutrient, L 10 the Naeperian logarithm of 10, u the response to the standard dressing, w the unit price of the crop product, and i the unit price of the nutrient. This formula is a modification of one of the formulas of PIMENTEL GOMES (1953). One of its advantages is that is does not depend on A, the theoretical maximum harvest, which is not directly given by experimental data. But another advantage, proved in this. paper, is that the first term on the right hand side K= 1(/c) log cx u L 10 ____________ 1 - 10-cx u is practically independent of c, and approximately equivalent to (1/2) x u. So, we have approximately x* = (1/2) x u + (1/c) log wu . ____ x u t With experimental data we compute z = wu ____ x u t then using tables 1, 2 and 3, we may obtain Y - (1/c) log z and finally x* = (1/2) x u + Y. This is an easy way to determine the most profitable level of fertilization when experimental data on the response u to a dressing x u are available. Tables for the calculation of Y are included, for nitrogen, phosphorus, potash, and manure.

E. S. A. "Luiz de Queiroz"

SUMMARY

The authors discuss a formula for the determination of the most profitable level of fertilization (x*). This formula, presented by CAREY and ROBINSON (1953), can be written as:

x*= (1/c) log cx_u L10 + (1/c) log wu

^__________

1-10 x_ut

being c the growth factor in Mitscherlich's equation, x_u a standard dressing of the nutrient, L 10 the Naeperian logarithm of 10, u the response to the standard dressing, w the unit price of the crop product, and i the unit price of the nutrient. This formula is a modification of one of the formulas of PIMENTEL GOMES (1953).

One of its advantages is that is does not depend on A, the theoretical maximum harvest, which is not directly given by experimental data. But another advantage, proved in this. paper, is that the first term on the right hand side

K= 1(/c) log cx_u L 10

^____________

1 - 10^-cx_u

is practically independent of c, and approximately equivalent to (1/2) x_u. So, we have approximately

x* = (1/2) x_u + (1/c) log wu .

^____

x_u t

With experimental data we compute

z = wu

^____

x_u t

then using tables 1, 2 and 3, we may obtain

Y - (1/c) log z

and finally

x* = (1/2) x_u + Y.

This is an easy way to determine the most profitable level of fertilization when experimental data on the response u to a dressing x_u are available. Tables for the calculation of Y are included, for nitrogen, phosphorus, potash, and manure.

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BIBLIOGRAFIA

CAREY, T. M. & ROBINSON, 1953 - The Manuring of Sugar Cane. Empire Jour. Exper. Agric. 21: 99-115.
CROWTHER, E. M. & F. YATES, 1941 - Fertilizer Policy in War-Time. Empire Jour. Exper. Agric. 9: 77-97.
HODNETT, G. R., 1956 - The Response of Sugar Cane to Fertilizers. Empire Jour. Asper. Agric. 24: 1-19.
PIMENTEL GOMES, F. & E. MALAVOLTA, 1949 - Aspectos Matemáticos e Estatísticos da Lei de Mitscherlich. Anais da E. S. A. "Luis de, Queiroz" 6: 193-229.
PIMENTEL GOMES, F., 1953 - The Use of Mitscherlich's Regression Law in the Analysis of Experiments with Fertilizers. Biometrics 9: 498-516.
PIMENTEL GOMES, F., 1957 - Análise Conjunta de 38 Experimentos de Adubação de Cana-de-Açúcar. Rev. Agricultura 32: 113-126.