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On The History of the Ellipse Equation for Soil Drainage

Inst. of Soil Science, Univ. of Hannover, Herrenhaeuser Str. 2, 30419 Hannover, Germany

Don Kirkham

Dep. of Agronomy, Iowa State Univ., Ames, IA 50011-1020

* Corresponding author ( vdploeg{at}mbox.ifbk.uni-hannover.de).

ABSTRACT

Colding from Denmark is considered to be the first who derived (in 1872) a drainage equation based on Dupuit-Darcy theory. Because of the shape of the water table between the drains that is calculated, this equation is frequently called the ellipse equation. It has been believed that Rothe in 1924 in Germany, Kozeny in 1932 in Austria, Hooghoudt in 1937 in the Netherlands, and Aronovici and Donnan in 1946 in the USA independently developed the same equation. Such a coincidence, although possible, appears to be unlikely. Therefore, we decided to study the older European literature that formerly was not always easily accessible. The literature review shows that both Kozeny and Hooghoudt referred to Rothe in previous publications and hence were familiar with Rothe's work. Although less obvious, it appears that also Rothe, as well as Aronovici and Donnan, had knowledge of earlier work on the subject. Hence, it seems that the current view about a multiple, independent derivation of the Colding equation needs a revision. However, since each of the later researchers extended or modified the original Colding equation, all deserve some credit, especially Hooghoudt, who appears to be the first to use Dupuit-Darcy theory to derive a ditch drainage equation.

Received for publication January 8, 1997.