An approximate method is proposed to integrate the ordinary differential equations governing the terms in Philip's (1957) series formulation of the water content profile. The method is related to the weighting solution used earlier (Brutsaert, 1976) for the sorption problem, and it is intermediate between the quasi-steady state method and the sharp front method. In a comparison with an available exact solution (Brutsaert, 1968b) it is shown that the derived solution is usually accurate to within less than 1%. The water content profile and the infiltration rate can be expressed concisely in terms of soil physical parameters by making use of suitable expressions for the soil water diffusivity and the capillary conductivity. As an illustration, the infiltration rate is calculated for the Averjanov-Irmay capillary conductivity and the author's three-parameter power function diffusivity. Inspection of two extreme cases in this calculation finally leads to a new infiltration equation in closed form which is valid not only for short but also for large time of infiltration.
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