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A Theory on the Soil Atmosphere in and around a Hemisphere in Which Soil Gases Are Used or Released¹

ABSTRACT

If the root system of a plant is taken as approximately hemispherical it is of interest to compute the distribution of partial pressures of soil gases. This can be done by assuming that these gases are taken up, or released, at a constant rate throughout the hemisphere and also that the physical condition of the soil with regard to diffusion is uniform.

Inside the hemisphere the solution is a simple algebraic expression and outside it is an infinite series containing Legendre's polynomials. In addition to the exact formulas the solution is given in the form of a computed graph, which may be used to calculate actual values of partial pressure at any point in the soil, if the necessary constants are known. It appears that the extreme values of partial pressure are closely centered around the apex of the hemisphere.

¹ Contribution from the Department of Agronomy, North Carolina Agricultural Experiment Station, Raleigh, N. C. Published with the approval of the Director of Research as Paper No. 388 of the Journal Series. Presented before Section I, Soil Science Society of America, State College, Pa., August 29, 1951.

² Research Assistant Professor of Soils. The assistance given by Dr. J. W. Cell, of the Department of Mathematics, North Carolina State College, in developing certain parts of this paper, is gratefully acknowledged.